en-gb	Draft Curriculum for Wales 2022: 
cy-gb	Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 01
cy-gb	Mathemateg a Rhifedd 01

en-gb	Draft Curriculum for Wales 2022: 
cy-gb	Cwricwlwm Drafft i Gymru 2022: 

en-gb	April 2019
cy-gb	Ebrill 2019

en-gb	DRAFT STATUTORY GUIDANCE AREA OF LEARNING AND EXPERIENCE
cy-gb	CANLLAWIAU STATUDOL DRAFFT MAES DYSGU A PHROFIAD

en-gb	Mathematics and Numeracy
cy-gb	Mathemateg a Rhifedd

en-gb	CONTENTS
cy-gb	CYNNWYS

en-gb	Introduction to the Mathematics and Numeracy Area of Learning and Experience 03
cy-gb	Cyﬂwyniad i Faes Dysgu a Phroﬁad Mathemateg a Rhifedd 03 

en-gb	What Matters in Mathematics and Numeracy
cy-gb	Yr Hyn sy’n Bwysig mewn Mathemateg a Rhifedd

en-gb	The number system is used to represent and compare relationships between numbers and quantities. 
cy-gb	Defnyddir y system rifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau. 

en-gb	18
cy-gb	19

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations. 
cy-gb	Mae algebra yn defnyddio systemau symbolau i fynegi strwythurau’r perthnasau rhwng rhifau, meintiau a chydberthnasau. 

en-gb	28
cy-gb	29

en-gb	Geometry focuses on relationships involving properties of shape, space and position, and measurement focuses on quantifying phenomena in the physical world. 
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud  â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol. 

en-gb	37
cy-gb	38

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions. 
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus. 

en-gb	46
cy-gb	48

en-gb	Glossary 55
cy-gb	Geirfa 58

en-gb	INTRODUCTION TO THE MATHEMATICS AND NUMERACY AREA OF LEARNING AND EXPERIENCE
cy-gb	CYFLWYNIAD I FAES DYSGU A PHROFIAD MATHEMATEG A RHIFEDD

en-gb	Mathematics is an international discipline, and numeracy, the application of mathematics, plays a critical part in our private, social and civic lives, and in the economic health of the nation.
cy-gb	Mae mathemateg yn ddisgyblaeth ryngwladol, ac mae rhifedd, sef y broses o gymhwyso mathemateg, yn chwarae rhan hanfodol yn ein bywydau preifat, cymdeithasol a dinesig, ac yng nghyﬂwr economaidd y genedl.

en-gb	It is imperative that mathematics and numeracy experiences are as engaging, exciting and accessible as possible for learners, and that they ensure learners develop mathematical resilience (the ability to embrace challenge as a positive aspect of learning). 
cy-gb	Mae’n hanfodol bod proﬁadau mathemateg a rhifedd mor ddiddorol, cyffrous a hygyrch â phosibl i ddysgwyr, ond eu bod hefyd yn sicrhau bod dysgwyr yn datblygu gwydnwch mathemategol (sef y gallu i goﬂeidio heriau fel agwedd gadarnhaol ar ddysgu). 

en-gb	Developing mathematical resilience contributes to the development of ambitious and capable learners.
cy-gb	Mae datblygu gwydnwch mathemategol yn helpu i ddatblygu dysgwyr galluog ac uchelgeisiol.

en-gb	In the early years, play forms an important part in the development of mathematics and numeracy, enabling learners to solve problems, explore ideas, establish connections and collaborate with others. 
cy-gb	Yn ystod y blynyddoedd cynnar, mae chwarae yn rhan bwysig o’r broses o ddatblygu mathemateg a rhifedd, gan alluogi dysgwyr i ddatrys problemau, archwilio syniadau, creu cysylltiadau a chydweithredu ag eraill. 

en-gb	In later years, learners need to have opportunities to work both independently and collaboratively to build on the foundations established in the early years.
cy-gb	Yn ystod y blynyddoedd diweddarach, mae angen cynnig cyﬂeoedd i ddysgwyr weithio’n annibynnol ac i gydweithredu er mwyn adeiladu ar y sylfeini a sefydlwyd yn ystod y blynyddoedd cynnar.

en-gb	For learners of all ages, real-life examples drawn from the local, national and international environment help them make connections between the concrete and the abstract. 
cy-gb	Ar gyfer dysgwyr o bob oedran, bydd enghreifftiau go iawn o’r amgylchedd lleol, cenedlaethol a rhyngwladol yn helpu dysgwyr i greu cysylltiadau rhwng y diriaethol a’r haniaethol. 

en-gb	Real-life contexts can be used to introduce and explore mathematical concepts, as well as to consolidate them. 
cy-gb	Gellir defnyddio cyd-destunau go iawn i gyﬂwyno ac i archwilio cysyniadau mathemategol yn ogystal â’u hatgyfnerthu. 

en-gb	Indeed, teaching that introduces a reasoning and problem-solving approach to all mathematics and numeracy experiences supports the development both of positive dispositions and of the four purposes of the curriculum, as well as the development of the mathematical proﬁciencies.
cy-gb	Yn wir, mae addysgu drwy gyﬂwyno dulliau rhesymu a datrys problemau i bob proﬁad mathemateg a rhifedd yn helpu i ddatblygu ar y naill law ymagweddau cadarnhaol ac ar y llall pedwar diben y cwricwlwm, ac yn ategu’r broses o ddatblygu’r hyfedreddau mathemategol.

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 04
cy-gb	Mathemateg a Rhifedd 04

en-gb	A transformational curriculum
cy-gb	Cwricwlwm gweddnewidiol

en-gb	The White Paper Our National Mission: 
cy-gb	Mae’r Papur Gwyn Cenhadaeth ein Cenedl: 

en-gb	A Transformational Curriculum 1 set out the detailed
cy-gb	Cwricwlwm Gweddnewidiol 1 yn nodi’r cynigion

en-gb	legislative proposals for Curriculum for Wales 2022.
cy-gb	deddfwriaethol manwl ar gyfer Cwricwlwm i Gymru 2022.

en-gb	The proposal is that funded non-maintained settings and schools will be required to provide a broad and balanced curriculum that meets the four purposes of the curriculum, and comprises the six areas of learning and experience. 
cy-gb	Y cynnig yw y bydd gofyn i leoliadau a ariennir nas cynhelir ac ysgolion ddarparu cwricwlwm eang a chytbwys sy’n bodloni pedwar diben y cwricwlwm ac sy’n cynnwys y chwe maes dysgu a phroﬁad. 

en-gb	There will be statutory duties to teach Welsh, English, religious education, relationships and sexuality education, and the three cross-curricular responsibilities of literacy, numeracy and digital competence. 
cy-gb	Bydd dysgu Cymraeg, Saesneg, addysg grefyddol, addysg cydberthynas a rhywioldeb, a’r tri chyfrifoldeb trawsgwricwlaidd, sef llythrennedd, rhifedd a chymhwysedd digidol, i gyd yn ddyletswyddau statudol. 

en-gb	Further information on how the Mathematics and Numeracy Area of Learning and Experience can support this is provided in the‘Developing a broad and balanced curriculum’ section of this document.
cy-gb	Mae rhagor o wybodaeth ar sut y gall Maes Dysgu a Phroﬁad Mathemateg a Rhifedd gefnogi hyn yn adran ‘Datblygu cwricwlwm eang a chytbwys’ o’r ddogfen hon.

en-gb	Funded non-maintained settings and schools will have discretion as to how they design their school-level curriculum to meet their curriculum duties. 
cy-gb	Bydd hawl gan leoliadau a ariennir nas cynhelir ac ysgolion i ddewis sut i gynllunio’u cwricwlwm ar lefel ysgol er mwyn cyﬂawni eu dyletswyddau cwricwlaidd. 

en-gb	However, in considering the exercise of that discretion, they must have regard to statutory guidance issued by Welsh Ministers. 
cy-gb	Fodd bynnag, wrth arfer yr hawl honno, bydd rhaid iddynt roi sylw i ganllawiau statudol a gaiff eu cyhoeddi gan Weinidogion Cymru. 

en-gb	In practice, that means they should follow the statutory guidance unless they have good reason not to.
cy-gb	Yn ymarferol, golyga hyn y dylent ddilyn y canllawiau statudol oni bai bod ganddynt reswm da i beidio.

en-gb	This statutory guidance for the Mathematics and Numeracy Area of Learning and Experience, which forms part of the wider Curriculum for Wales 2022 statutory guidance, is intended to provide a national framework that funded non-maintained settings and schools can build on to develop their own curriculum. 
cy-gb	Nod y canllawiau statudol hyn ar gyfer Maes Dysgu a Phroﬁad Mathemateg a Rhifedd, sy’n rhan o’r canllawiau statudol ehangach ar gyfer Cwricwlwm i Gymru 2022, yw rhoi fframwaith cenedlaethol y gall lleoliadau a ariennir nas cynhelir ac ysgolion ei ddefnyddio i ddatblygu eu cwricwlwm eu hunain. 

en-gb	It is not intended to be a comprehensive or exhaustive syllabus, nor a guide for organising timetables. 
cy-gb	Ni fwriedir iddynt fod yn faes llafur hollgynhwysfawr, nac yn ganllaw ar gyfer trefnu amserlenni. 

en-gb	It sets out:
cy-gb	Maent yn nodi:

en-gb	• what funded non-maintained settings and schools should take into account in designing their curriculum and how it could be structured
cy-gb	• yr hyn y dylai lleoliadau a ariennir nas cynhelir ac ysgolion roi ystyriaeth iddo wrth lunio’u cwricwlwm, a sut y gellir ei strwythuro

en-gb	• the broad expectations for learners for the Mathematics and Numeracy Area of Learning and Experience at each progression step.
cy-gb	• y disgwyliadau eang ar gyfer dysgwyr ar bob cam cynnydd ym Maes Dysgu a Phroﬁad Mathemateg a Rhifedd.

en-gb	1 beta.gov.wales/our-national-mission-transformational-curriculum
cy-gb	1 llyw.cymru/cenhadaeth-ein-cenedl-cwricwlwm-gweddnewidiol

en-gb	Introduction D D r r a a f f t t C C u u r r r r i i c c u u l l u u m m f f o o r r W W a a l l e e s s 2 2 0 0 2 2 2 2 : : M M a a t t h h e e m m a a t t i i c c s s a a n n d d N numeracy 05
cy-gb	Cyﬂwyniad Draft C w ur r r i i c c w ul w um m f D or ra W fft a i le G s y 2 m 0 r 2 u 2 2 : 

en-gb	How the area of learning and experience
cy-gb	0 M 2 a 2 t : h M em at a h t e ic m s a a t n e d g n a u R m h e if r e a d c d y 05

en-gb	supports the four purposes of the curriculum
cy-gb	Sut mae’r maes dysgu a phroﬁad yn cefnogi pedwar diben y cwricwlwm

en-gb	The development of mathematics has always gone hand in hand with the development of civilisation itself. 
cy-gb	Mae datblygiad mathemateg wedi mynd law yn llaw â datblygiad gwareiddiad ers y cychwyn cyntaf. 

en-gb	Mathematics surrounds us and underpins so many aspects of our daily lives, such as architecture, art, music, money and engineering. 
cy-gb	Mae mathemateg o’n cwmpas ni ac yn sail i gynifer o agweddau ar ein bywydau bob dydd, megis pensaernïaeth, celf, cerddoriaeth, arian a pheirianneg. 

en-gb	And while it is creative and beautiful, both in its own right and in its applications, it is also essential for progress in other areas of learning and experience, not least in Science and Technology, which would be virtually impossible without it. 
cy-gb	Ac er ei bod hi, ohoni hi ei hun ac o’i chymhwyso, yn greadigol ac yn hardd, mae hefyd yn hanfodol i gynnydd mewn meysydd dysgu a phroﬁad eraill, yn enwedig mewn Gwyddoniaeth a Thechnoleg, a fyddai, i bob pwrpas, yn amhosib hebddi. 

en-gb	What is more, numeracy – the use of mathematics to solve problems in real-world contexts – is required in almost all areas of life.
cy-gb	Ar ben hynny, mae angen rhifedd – y defnydd o fathemateg i ddatrys problemau yng nghyd-destunau’r byd go iawn – ymhob maes o fywyd, fwy neu lai.

en-gb	Formal mathematics is founded on basic truths and develops through rigorous logical reasoning. 
cy-gb	Mae mathemateg ffurﬁol wedi ei seilio ar wirioneddau sylfaenol ac mae’n datblygu drwy resymu rhesymegol trylwyr dros ben. 

en-gb	It involves inventing or discovering abstract objects and establishing the relationships between them. 
cy-gb	Mae’n cynnwys dyfeisio neu ddarganfod gwrthrychau haniaethol, ynghyd â sefydlu perthnasau rhyngddynt. 

en-gb	It also teaches us the difference between conjecture, likelihood and proof.
cy-gb	Mae hefyd yn dysgu’r gwahaniaeth rhwng dyfaliad, tebygrwydd a phrawf i ni. 

en-gb	Mathematical thinking involves applying similarly logical reasoning, this time to the investigation of relations within and between concepts, along with justifying and proving ﬁndings. 
cy-gb	Mae meddwl mewn ffordd fathemategol yn cynnwys rhoi ar waith yr un math o resymu rhesymegol eto, y tro hwn wrth archwilio’r perthnasau sydd o fewn cysyniadau a rhyngddynt, ynghyd â chyﬁawnhau a phroﬁ canfyddiadau. 

en-gb	Indeed, understanding mathematical concepts and being able to apply and reason with the abstract representations of concepts is central to learning mathematics. 
cy-gb	Yn wir, mae deall cysyniadau mathemategol a gallu cymhwyso cynrychioliadau haniaethol y cysyniadau hynny, a gallu rhesymu â nhw, yn greiddiol wrth ddysgu mathemateg. 

en-gb	And essential to this is comprehension of, and proﬁciency with, the symbols and symbol systems used in mathematics.
cy-gb	Ac mae dealltwriaeth o’r symbolau a’r systemau symbolau a ddefnyddir mewn mathemateg, a’r gallu i’w defnyddio, yn hanfodol yn hyn o beth.

en-gb	Applying mathematics requires strategic competence in the use of abstraction and modelling, and learners also develop resilience, as well as a sense of achievement and enjoyment, as they overcome the challenges involved. 
cy-gb	Er mwyn cymhwyso mathemateg, mae angen cymhwysedd strategol o ran defnyddio haniaethu a modelu. Mae dysgwyr hefyd yn datblygu gwydnwch, yn ogystal â phroﬁ ymdeimlad o lwyddiant a mwynhad, wrth iddynt oresgyn yr heriau sy’n codi. 

en-gb	Subsequently, mathematical activities teach learners not to be afraid of unfamiliar or complex problems, as they can be reduced to a succession of simpler problems and, eventually, to basic computations. 
cy-gb	O ganlyniad, mae gweithgareddau mathemategol yn dysgu’r dysgwyr i beidio â bod ofn problemau anghyfarwydd neu gymhleth, oherwydd gellir eu crynhoi i gyfres o broblemau symlach ac, yn y pen draw, i gyfriﬁannau sylfaenol. 

en-gb	And as they reﬂect on the approaches used, and on their own mathematics and numeracy learning, learners develop metacognitive skills which help them know which steps to take to improve performance. 
cy-gb	Ac wrth iddynt fyfyrio ar y dulliau a ddefnyddiwyd, ac ar yr hyn a ddysgwyd ganddynt am fathemateg a rhifedd, mae dysgwyr yn datblygu’r sgiliau metawybyddol sy’n eu helpu nhw i wybod pa gamau sydd angen eu cymryd er mwyn gwella eu perfformiad. 

en-gb	Thus they become ambitious, capable learners, ready to learn throughout their lives . 
cy-gb	Drwy hyn fe ddônt yn ddysgwyr uchelgeisiol, galluog sy’n barod i ddysgu drwy gydol eu hoes . 

en-gb	Mathematics also contributes to developing enterprising, creative contributors, ready to play a full part in life and work . 
cy-gb	Mae mathemateg yn cyfrannu at ddatblygu cyfranwyr mentrus, creadigol sy’n barod i chwarae eu rhan yn llawn yn eu bywyd a’u gwaith . 

en-gb	It encourages learners to be creative because it requires them to play, experiment, take risks and be ﬂexible in tackling mathematical problems. 
cy-gb	Mae’n annog dysgwyr i fod yn greadigol, gan alw arnynt i chwarae, arbroﬁ, cymryd risg a bod yn hyblyg wrth fynd i’r afael â phroblemau mathemategol. 

en-gb	Because mathematics is essentially abstract, it teaches learners to operate with objects that do not physically exist, using and developing their creativity to imagine and discover new realities. 
cy-gb	Gan fod mathemateg yn haniaethol yn y bôn, mae’n dysgu dysgwyr i ymwneud â gwrthrychau nad ydynt yn bodoli’n fﬁsegol, gan ddefnyddio a datblygu eu creadigrwydd er mwyn dychmygu a darganfod realitïau newydd. 

en-gb	It also supports numerical modelling and forecasting to encourage entrepreneurial thinking.
cy-gb	Mae hefyd yn ategu gwaith modelu a rhagfynegi rhifyddol er mwyn annog ffordd o feddwl entrepreneuraidd.

en-gb	Mathematics promotes ethical, informed citizens of Wales and the world by providing learners with tools to analyse data critically, enabling them to develop informed views on social, political, economic and environmental issues. 
cy-gb	Mae mathemateg yn hyrwyddo dinasyddion egwyddorol, gwybodus yng Nghymru a’r byd drwy roi’r gallu i ddysgwyr ddadansoddi data yn feirniadol, gan eu galluogi i ddatblygu safbwyntiau gwybodus ar faterion cymdeithasol, gwleidyddol, economaidd ac amgylcheddol. 

en-gb	It encourages clarity of thinking, allowing learners to understand and make reasoned decisions.
cy-gb	Mae’n annog meddwl clir, gan alluogi dysgwyr i ddeall a gwneud penderfyniadau rhesymedig.

en-gb	In mathematics and numeracy, learners encounter contexts involving health and personal ﬁnance, and develop the skills needed to manage their own ﬁnances, make informed decisions and become critical consumers. 
cy-gb	Mewn mathemateg a rhifedd, daw dysgwyr ar draws cyd-destunau sy’n cynnwys iechyd a chyllid personol, a byddant yn datblygu’r sgiliau i reoli eu cyllid eu hunain, gwneud penderfyniadau gwybodus a dod yn ddefnyddwyr beirniadol. 

en-gb	They learn to interpret information and data to assess risk, and they use their numeracy skills across the curriculum to make effective choices, becoming healthy, conﬁdent individuals, ready to lead fulﬁlling lives as valued members of society .
cy-gb	Maent yn dysgu sut i ddehongli gwybodaeth a data er mwyn asesu risg, ac maent yn defnyddio eu sgiliau rhifedd ar draws y cwricwlwm er mwyn gwneud dewisiadau effeithiol, gan ddod yn unigolion iach, hyderus sy’n barod i fyw bywyd gan wireddu eu dyheadau fel aelodau gwerthfawr o gymdeithas .

en-gb	WHAT MATTERS STATEMENTS FOR MATHEMATICS AND NUMERACY
cy-gb	DATGANIADAU O’R HYN SY’N BWYSIG   MEWN MATHEMATEG A RHIFEDD

en-gb	The number system is used to represent and compare relationships between numbers and quantities.
cy-gb	Defnyddir y system rifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau.

en-gb	Numbers are the symbol system for describing and comparing quantities. 
cy-gb	Rhifau yw’r system o symbolau ar gyfer disgriﬁo a chymharu meintiau. 

en-gb	This is the ﬁrst abstract concept that learners meet in mathematics, and it helps to establish the principles of logical reasoning. 
cy-gb	Dyma’r cysyniad haniaethol cyntaf y bydd dysgwyr yn dod ar ei draws ym mathemateg, ac mae’n fodd i sefydlu egwyddorion rhesymu rhesymegol. 

en-gb	In mathematics the number system provides a basis for algebraic, statistical, probabilistic and geometrical reasoning, as well as for ﬁnancial calculation and decision-making.
cy-gb	Ym mathemateg, mae’r system rifo’n sail i resymu o ran algebra, ystadegau, tebygolrwydd a geometreg, yn ogystal ag o ran cyfrifo ariannol a gwneud penderfyniadau.

en-gb	Knowledge of, and competence in, number and quantities are fundamental to conﬁdent participation in the world, and provide a foundation for further study and for employment. 
cy-gb	Mae gwybodaeth a gallu ym maes rhifau a meintiau yn hanfodol ar gyfer cyfrannu i’r byd, ac yn cynnig sylfaen ar gyfer astudio pellach a chyﬂogaeth. 

en-gb	Computational ﬂuency is essential for problem-solving and progressing in all areas of learning and experience. 
cy-gb	Mae rhuglder o ran cyfriﬁannu yn allweddol i ddatrys problemau a gwneud cynnydd ym mhob maes dysgu a phroﬁad. 

en-gb	Fluency is developed through using the four basic arithmetic operations and acquiring an understanding of the relationship between them. 
cy-gb	Datblygir rhuglder drwy ddefnyddio’r pedwar gweithrediad rhifyddeg sylfaenol a datblygu dealltwriaeth o’r berthynas rhyngddynt. 

en-gb	This leads to preparing the way for using algebraic symbolisation successfully.
cy-gb	Mae hyn yn arwain at baratoi’r ffordd ar gyfer defnyddio symbolau algebra yn llwyddiannus.

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations.
cy-gb	Mae algebra yn defnyddio systemau symbolau i fynegistrwythurau’r perthnasau rhwng rhifau, meintiau a chydberthnasau.

en-gb	Algebra is the study of structures abstracted from computations and relations, and provides a way to make generalisations. 
cy-gb	Mae algebra yn astudio’r strwythurau sydd ymhlyg mewn cyfriﬁannau a chydberthnasau, ac yn cynnig ffordd o gyffredinoli. 

en-gb	Algebraic thinking moves away from context to structure and relationships. 
cy-gb	Mae meddwl algebraidd yn symud o’r cyd-destun i’r strwythur a’r perthnasau. 

en-gb	This powerful approach provides the means to abstract important features and to detect and express mathematical structures of situations in order to solve problems. 
cy-gb	Mae’r dull gweithredu pwerus hwn yn cynnig ffordd o gyrraedd at nodweddion pwysig ac o ganfod a mynegi strwythurau mathemategol sefyllfaoedd,gyda’r nod o ddatrys problemau. 

en-gb	Algebra is a unifying thread running through the fabric of mathematics.
cy-gb	Mae algebra yn rhedeg fel llinyn cyd-gysylltiol drwy frethyn mathemateg i gyd.

en-gb	Algebraic thinking is essential for reasoning, modelling and solving problems in mathematics and in a wide range of real-world contexts, including technology and ﬁnance. 
cy-gb	Mae meddwl algebraidd yn hanfodol er mwyn rhesymu, modelu a datrys problemau mewn mathemateg ac mewn amrywiaeth eang o gyd-destunau go iawn, gan gynnwys technoleg a chyllid. 

en-gb	Making connections between arithmetic and algebra develops skills for abstract reasoning from an early age.
cy-gb	Mae gwneud y cysylltiadau rhwng rhifyddeg ac algebra yn meithrin sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.

en-gb	Geometry focuses on relationships involving properties of shape, space and position, and measurement focuses on quantifying phenomena in the physical world.
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	Geometry involves playing with, manipulating, comparing, naming and classifying shapes and structures. 
cy-gb	Mae geometreg yn ymwneud â chwarae â siapiau a strwythurau, eu trin, eu cymharu, eu henwi a’u dosbarthu. 

en-gb	The study of geometry encourages the development and use of conjecture, deductive reasoning and proof. 
cy-gb	Mae astudio geometreg yn annog dysgwyr i ddatblygu a defnyddio dulliau dyfalu, rhesymu diddwythol a phrawf. 

en-gb	Measurement allows the magnitude of spatial and abstract features to be quantiﬁed, using a variety of standard and non-standard units, and can support the development of numerical reasoning.
cy-gb	Mae mesur yn golygu y gellir meintioli graddau nodweddion gofodol a haniaethol, gan ddefnyddio amrywiaeth o unedau safonol ac ansafonol, a gall ategu’r broses o ddatblygu dulliau rhesymu rhifyddol.

en-gb	Reasoning about the sizes and properties of shapes and their surrounding spaces helps us to make sense of the physical world and the world of mathematical shapes. 
cy-gb	Mae rhesymu ynghylch meintiau a phriodweddau siapiau a’r gofod o’u hamgylch yn cynnig modd i ni wneud synnwyr o’r byd fﬁsegol a byd siapiau mathemategol. 

en-gb	Geometry and measurement have applications in many ﬁelds, including art, construction, science and technology, engineering, and astronomy.
cy-gb	Gellir cymhwyso geometreg a mesur mewn sawl maes, gan gynnwys celf, adeiladu, gwyddoniaeth a thechnoleg, peirianneg, a seryddiaeth.

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions.
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus.

en-gb	Statistics is the practice of collecting, manipulating and analysing data, allowing representation and generalisation of information. 
cy-gb	Ystadegau yw’r arfer o gasglu, trin a dadansoddi data er mwyn gallu cynrychioli a chyffredinoli gwybodaeth. 

en-gb	Probability is the mathematical study of chance, enabling predictions of the likelihood of events occurring. 
cy-gb	Tebygolrwydd yw’r broses fathemategol o astudio siawns, er mwyn gallu rhagfynegi’r tebygrwydd y bydd rhywbeth yn digwydd. 

en-gb	Statistics and probability rely on the application and manipulation of number and algebra.
cy-gb	Mae ystadegau a thebygolrwydd yn dibynnu ar gymhwyso a thrin rhifau ac algebra.

en-gb	Managing data and representing information effectively provides the means to test hypotheses, draw conclusions and make predictions. 
cy-gb	Mae rheoli data a chynrychioli gwybodaeth yn effeithiol yn cynnig ffordd o broﬁ rhagdybiaethau, dod i gasgliadau a gwneud rhagfynegiadau. 

en-gb	Reasoning with statistics and probability, and evaluating their reliability, develops critical thinking and analytical skills that are fundamental to making ethical and informed decisions.
cy-gb	Mae rhesymu gan ddefnyddio ystadegau a thebygolrwydd, a gwerthuso eu dibynadwyedd, yn meithrin y sgiliau dadansoddi a meddwl beirniadol sy’n hollbwysig wrth wneud penderfyniadau egwyddorol a gwybodus.

en-gb	Relationships between what matters statements in Mathematics and Numeracy
cy-gb	Y berthynas rhwng y datganiadau o’r hyn sy’n bwysig mewn Mathemateg a Rhifedd

en-gb	The different areas of mathematics are highly interconnected and dependent on one another, and, as any teacher of mathematics knows, concepts are built up over time, drawing on prior knowledge and learning, often from more than one area of mathematics. 
cy-gb	Mae cysylltiadau agos rhwng y meysydd mathemategol gwahanol ac maent yn ddibynnol iawn ar ei gilydd. Fel y gŵyr unrhyw athro mathemateg, caiff cysyniadau eu hadeiladu dros amser, gan ddefnyddio gwybodaeth a dysgu blaenorol, a hynny, yn aml, yn dod o fwy nag un maes mathemategol. 

en-gb	What is important when planning to teach any speciﬁc topic is to work out the prior knowledge the learners need in order to be able to access and understand the new topic.
cy-gb	Yr hyn sy’n bwysig wrth gynllunio ar gyfer addysgu unrhyw bwnc penodol yw sefydlu pa wybodaeth ﬂaenorol sydd ei hangen ar y dysgwyr er mwyn gallu astudio a deall y pwnc newydd.

en-gb	Algebra, geometry and statistics cannot be understood without a prior understanding of number and consistent reference to numbers, calculations and the number system. 
cy-gb	Ni ellir deall algebra, geometreg nac ystadegau heb ddealltwriaeth ﬂaenorol o rif a chyfeiriadau cyson at rifau, cyfriﬁadau a’r system rhifau. 

en-gb	As learners progress they learn to see numerical expressions as relational rather than computational, e.g. a computation such as 2 + 8 = 10, and that this is the basis for deriving other facts, e.g. 8 + 2 = 10, 8 = 10 – 2, and so on. 
cy-gb	Wrth i’r dysgwyr ddangos cynnydd, byddant yn dysgu i ystyried mynegiadau rhifyddol fel mynegiadau perthynol yn hytrach na mynegiadau cyfriﬁannol, e.e. maent yn gweld bod cyfriﬁant fel 2 + 8 = 10, ac mae hynny yn sail i ddod o hyd i ffeithiau eraill fel 8 + 2 = 10, 8 = 10 – 2, ac yn y blaen. 

en-gb	This lays the foundations for using algebraic symbolisation successfully. 
cy-gb	Mae hyn yn gosod y sylfeini ar gyfer defnyddio dulliau symboleiddio algebraidd yn llwyddiannus. 

en-gb	Making connections between arithmetic and algebra helps to develop tools and skills for abstract reasoning from an early age.
cy-gb	Mae gwneud y cysylltiadau rhwng rhifyddeg ac algebra yn fodd i ddatblygu’r adnoddau a sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.

en-gb	Measure is an aspect of geometrical thinking which is closely connected to number, and much of the development of understanding of number can emerge through increasingly sophisticated measuring. 
cy-gb	Mae mesur yn agwedd ar feddwl geometregol sydd â chysylltiad agos iawn â rhif, a gall cryn dipyn o’r broses o feithrin dealltwriaeth o rif ddod i’r amlwg drwy ddulliau mesur cynyddol sofﬁstigedig. 

en-gb	Geometric thinking involves reasoning with proportion, which connects with development in number work; 
cy-gb	Mae meddwl geometrig yn cynnwys rhesymu â chyfrannedd, sy’n gysylltiedig â datblygiad mewn gwaith rhif; 

en-gb	it also involves transforming shapes, which relates to the use of functions and mapping in algebra.
cy-gb	mae hefyd yn cynnwys trawsffurﬁo siapiau, sy’n ymwneud â defnyddio ffwythiannau a mapio mewn algebra.

en-gb	Probability is expressed through number in various ways, using percentages, fractions and decimals, and an understanding of the different representations, and the connections between them, is necessary for effective expression of probability. 
cy-gb	Caiff tebygolrwydd ei fynegi drwy rif mewn amrywiaeth o ffurﬁau, drwy ddefnyddio canrannau, ffracsiynau a degolion, ac mae angen deall gwahanol gynrychioliadau, a’r cysylltiadau rhyngddynt, er mwyn gallu mynegi tebygolrwydd yn effeithiol. 

en-gb	Statistics involves manipulation, representation and interpretation of data, which in turn require numerical and geometric thinking.
cy-gb	Mae ystadegau yn ymwneud â thrin, cynrychioli a dehongli data, sydd yn eu tro’n galw am feddwl mewn ffordd rifyddol a geometrig.

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 09
cy-gb	Mathemateg a Rhifedd 10

en-gb	Progression within this area of learning and experience
cy-gb	Cynnydd o fewn y maes dysgu a phroﬁad hwn

en-gb	Progression in Mathematics and Numeracy involves the development of the following interconnected and interdependent proﬁciencies 2 .
cy-gb	Mae cynnydd mewn Mathemateg a Rhifedd yn cynnwys datblygu hyfedreddau rhyng-gysylltiedig a rhyngddibynnol 2 .

en-gb	• Conceptual understanding; having the knowledge to understand and explain a mathematical concept.
cy-gb	• Dealltwriaeth gysyniadol; meddu ar yr wybodaeth i ddeall ac egluro cysyniad mathemategol.

en-gb	• Communication with symbols.
cy-gb	• Cyfathrebu â symbolau.

en-gb	• Strategic competence (i.e. formulating problems mathematically in order to solve them).
cy-gb	• Cymhwysedd strategol (h.y. gosod problemau allan mewn ffurf fathemategol er mwyn eu datrys).

en-gb	• Logical reasoning. 
cy-gb	• Rhesymu rhesymegol. 

en-gb	• Fluency.
cy-gb	• Rhuglder.

en-gb	A key point to note in any planning and assessment of Mathematics and Numeracy is that the proﬁciencies are interconnected and interdependent; 
cy-gb	Pwynt allweddol i’w nodi wrth ymgymryd ag unrhyw waith cynllunio ac asesu ar gyfer Mathemateg a Rhifedd yw bod y hyfedreddau yn rhyng-gysylltiedig ac yn rhyngddibynnol; 

en-gb	they cannot be seen as hierarchical (e.g. strategic competence does not come after learning facts and techniques) and they can be developed alongside each other. 
cy-gb	ni ellir eu hystyried mewn modd hierarchaidd (e.e. nid yw cymhwysedd strategol yn ail i ddysgu ffeithiau a thechnegau) a gellir eu datblygu ochr yn ochr â’i gilydd. 

en-gb	However, it may be helpful to target certain proﬁciencies at certain points, if this is appropriate to ensure progression.
cy-gb	Fodd bynnag, gall fod yn ddefnyddiol targedu rhai hyfedreddau penodol ar adegau penodol, os yw hynny’n briodol er mwyn sicrhau cynnydd.

en-gb	Contextual example 1: 
cy-gb	Enghraifft gyd-destunol 1: 

en-gb	Learning about fractions – the case of ½ Conceptual understanding
cy-gb	Dysgu am ffracsiynau – achos ½ Dealltwriaeth gysyniadol

en-gb	Understanding that a half is a result of dividing something into two equal parts. 
cy-gb	Deall bod hanner yn deillio o rannu rhywbeth yn ddwy ran gyfartal. 

en-gb	This could be through connecting their concrete and/or real-life experiences of partitioning objects and numbers into equal parts with images (e.g. pictures and images on the number line) and the abstract representation of a ½ using the symbolic notation. 
cy-gb	Gallai hyn ddigwydd drwy gysylltu eu proﬁadau diriaethol a/neu go iawn o rannu gwrthrychau a rhifau yn rhannau cyfartal â delweddau (e.e. lluniau a delweddau ar y llinell rhif) a chynrychioli ½ mewn ffordd haniaethol gan ddefnyddio’r nodiant symbolaidd. 

en-gb	A learner who understands what a half is might be able to give real-life or visual examples, and would also be able to explain why something might not be a half (e.g. a pizza cut into two parts which are not equal).
cy-gb	Mae’n bosibl y gall dysgwr sy’n deall beth yw hanner roi enghreifftiau go iawn neu enghreifftiau gweledol, ac y byddai hefyd, efallai, yn gallu egluro pam nad yw rhywbeth yn hanner go iawn (e.e. pizza wedi’i dorri’n ddwy ran nad ydynt yn hafal o ran maint).

en-gb	Communicating with symbols
cy-gb	Cyfathrebu â symbolau

en-gb	Understanding the convention of how a half is written and what the symbols mean. 
cy-gb	Deall y confensiwn ar gyfer ysgrifennu hanner ac ystyr y symbolau. 

en-gb	This could also involve linking division and fractions (i.e. ½ = 1 ÷ 2) and using terms such as numerator and denominator.
cy-gb	Gallai hyn hefyd gynnwys cysylltu rhannu a ffracsiynau (h.y. ½ = 1 ÷ 2) a defnyddio termau megis rhiﬁadur ac enwadur.

en-gb	Strategic competence
cy-gb	Cymhwysedd strategol

en-gb	Being able to recognise real-life situations which involve a half; 
cy-gb	Gallu adnabod sefyllfaoedd go iawn sy’n ymwneud â hanner; 

en-gb	being able to represent these mathematically; 
cy-gb	gallu cynrychioli’r sefyllfaoedd hyn ar ffurf fathemategol; 

en-gb	being able to model situations involving halving mathematically; 
cy-gb	gallu modelu sefyllfaoedd sy’n ymwneud â haneru mewn ffordd fathemategol; 

en-gb	using pictures/images and language and symbols.
cy-gb	defnyddio lluniau/delweddau ac iaith a symbolau.

en-gb	2 Based on Adding It Up: 
cy-gb	2 Yn seiliedig ar Adding It Up: 

en-gb	Helping Children Learn Mathematics by Kilpatrick, Swafford and Findel (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics gan Kilpatrick, Swafford a Findel (National Research Council, 2001)

en-gb	and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
cy-gb	ac wedi’i addasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen,2018.

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 10
cy-gb	Mathemateg a Rhifedd 11

en-gb	Logical reasoning
cy-gb	Rhesymu rhesymegol

en-gb	Being able to understand the relationship between a half and a whole; 
cy-gb	Gallu deall y gydberthynas rhwng hanner a chyfan; 

en-gb	being able to justify why ² / ⁴ is also a half. 
cy-gb	gallu cyﬁawnhau pam bod ²/ ⁴ hefyd yn hanner. 

en-gb	Being able to reason that ½ + ½ = 1, ½ x 2 = 1 and 1 ÷ 2 = ½. 
cy-gb	Gallu rhesymu bod ½ + ½ = 1, ½ x 2 = 1 ac 1 ÷ 2 = ½. 

en-gb	Being able to justify why there may be many ways of splitting a shape in half.
cy-gb	Gallu cyﬁawnhau pam y gall fod sawl ffordd o rannu siâp yn hanner.

en-gb	Through connecting these proﬁciencies within a learner’s experience of ½, learners should develop a deep understanding of a half as an example of a fraction. 
cy-gb	Drwy gysylltu’r hyfedreddau hyn o fewn proﬁad dysgwr o ½, dylai dysgwyr feithrin dealltwriaeth ddofn o hanner fel enghraifft o ffracsiwn. 

en-gb	The way in which these foci are introduced could vary, but ultimately, having opportunities to explore and connect these proﬁciencies should ensure learner progression within this idea.
cy-gb	Gallai’r dulliau ar gyfer cyﬂwyno’r ffocysau hyn amrywio ond, yn y pen draw, dylai’r ffaith bod cyﬂeoedd yn cael eu cynnig i archwilio a chysylltu’r hyfedreddau hyn sicrhau bod dysgwyr yn gwneud cynnydd mewn perthynas â’r syniad hwn.

en-gb	Fluency
cy-gb	Rhuglder

en-gb	Being able to count in steps of a half and being able to begin to recall halves of numbers.
cy-gb	Gallu cyfrif fesul hanner a gallu dechrau galw haneri rhifau i gof.

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 11
cy-gb	Mathemateg a Rhifedd 12

en-gb	Developing a broad and balanced curriculum
cy-gb	Datblygu cwricwlwm eang a chytbwys

en-gb	Literacy, numeracy and digital competence
cy-gb	Llythrennedd, rhifedd a chymhwysedd digidol

en-gb	The cross-curricular responsibilities of literacy, numeracy and digital competence support almost all learning and are essential for learners to be able to participate successfully and conﬁdently in the modern world.
cy-gb	Mae cyfrifoldebau trawsgwricwlaidd llythrennedd, rhifedd a chymhwysedd digidol yn cefnogi bron yr holl ddysgu ac maent yn hanfodol er mwyn i ddysgwyr allu cymryd rhan yn llwyddiannus ac yn hyderus yn y byd modern.

en-gb	Literacy
cy-gb	Llythrennedd

en-gb	Literacy can be developed through engaging and accessible experiences where learners are given regular opportunities to describe, explain and justify their understanding of various mathematical concepts, using appropriate mathematical vocabulary. 
cy-gb	Gellir datblygu llythrennedd drwy broﬁadau diddorol a hygyrch, lle y cynigir cyﬂeoedd rheolaidd i ddysgwyr ddisgriﬁo, egluro a chyﬁawnhau eu dealltwriaeth o amrywiol gysyniadau mathemategol, gan ddefnyddio geirfa fathemategol briodol. 

en-gb	The development of these skills can be seen in rhymes and songs through to discussions around abstract concepts. 
cy-gb	Caiff y sgiliau hyn eu datblygu mewn rhigymau a chaneuon yn ogystal â thrafodaethau am gysyniadau haniaethol. 

en-gb	Learners will also use and develop their literacy skills in a written form in order to describe mathematical processes, such as reasoning.
cy-gb	Bydd dysgwyr hefyd yn defnyddio ac yn meithrin eu sgiliau llythrennedd ar ffurf ysgrifenedig er mwyn disgriﬁo prosesau mathemategol, megis rhesymu.

en-gb	Learners will increasingly use literacy skills in order to understand a range of calculation strategies, describing visualisation of shapes, studying and interpreting information in statistics and comparing alternative methods before arriving at a solution to a mathematical problem. 
cy-gb	Bydd dysgwyr yn defnyddio sgiliau llythrennedd yn gynyddol er mwyn deall amrywiaeth o strategaethau cyfrifo, gan ddisgriﬁo’r broses o ddelweddu siapiau, astudio a dehongli gwybodaeth mewn ystadegau a chymharu dulliau amgen, cyn cynnig datrysiad i broblem fathemategol. 

en-gb	They should use these literacy skills as they encounter practical, real-world problems.
cy-gb	Dylent ddefnyddio’r sgiliau llythrennedd hyn wrth iddynt ddod ar draws problemau ymarferol go iawn.

en-gb	Numeracy
cy-gb	Rhifedd

en-gb	Mathematics and Numeracy, by deﬁnition, has numeracy at its heart.
cy-gb	Yn ôl ei ddifﬁniad, mae rhifedd wrth wraidd Mathemateg a Rhifedd.

en-gb	Numeracy involves applying and connecting the ﬁve mathematical proﬁciencies 3 in a range of real-life contexts, within the Mathematics and Numeracy Area of Learning and Experience, and the wider curriculum.
cy-gb	Mae rhifedd yn cynnwys cymhwyso a chysylltu’r pum hyfedredd mathemategol 3 mewn amrywiaeth o gyd-destunau go iawn, o fewn Maes Dysgu a Phroﬁad Mathemateg a Rhifedd, a’r cwricwlwm ehangach. 

en-gb	Real-life contexts can be used to introduce and explore mathematical concepts, as well as to consolidate them. 
cy-gb	Gellir defnyddio cyd-destunau go iawn i gyﬂwyno ac ystyried cysyniadau mathemategol, yn ogystal â’u hatgyfnerthu. 

en-gb	For example, the use of percentages can be applied to annual percentage rates (APRs) to demonstrate their application to ﬁnancial literacy.
cy-gb	Er enghraifft, gellir cymhwyso’r defnydd o ganrannau at gyfraddau canrannol blynyddol (APR) er mwyn dangos bod y defnydd hwnnw yn berthnasol i lythrennedd ariannol.

en-gb	Digital competence
cy-gb	Cymhwysedd digidol

en-gb	Digital approaches will enhance learners’ mathematical and numeracy skills across a range of situations that will naturally occur within the area of learning and experience. 
cy-gb	Bydd dulliau gweithredu digidol yn gwella sgiliau mathemategol a sgiliau rhifedd dysgwyr mewn amrywiaeth o sefyllfaoedd a fydd yn digwydd yn naturiol yn y maes dysgu a phroﬁad. 

en-gb	Digital competence is more than the interaction with technology. 
cy-gb	Mae cymhwysedd digidol yn fwy na dim ond ymwneud â thechnoleg. 

en-gb	For example, collaborating to solve a problem and the development of algorithms to support the understanding of patterns will provide the opportunity to support the development of learner’s digital skills. 
cy-gb	Er enghraifft, bydd cydweithio er mwyn datrys problem a datblygu algorithmau er mwyn ategu dealltwriaeth o batrymau yn cynnig y cyﬂe i ategu’r broses o ddatblygu sgiliau digidol dysgwyr. 

en-gb	Creating a graph by using a spreadsheet, for example, will enhance digital understanding and also strengthen learners’ mathematical and numerical skills.
cy-gb	Bydd creu graff gan ddefnyddio taenlen, er enghraifft, yn gwella dealltwriaeth ddigidol ac yn atgyfnerthu sgiliau mathemategol a rhifyddol dysgwyr.

en-gb	Naturally, as learners develop and progress they will increasingly use more complex digital skills and processes, techniques and systems to create solutions to address speciﬁc problems, opportunities or needs. 
cy-gb	Yn naturiol, wrth i ddysgwyr ddatblygu a gwneud cynnydd, byddant yn defnyddio’n gynyddol sgiliau a phrosesau, technegau a systemau digidol mwy cymhleth, i greu datrysiadau er mwyn ymdrin â phroblemau, cyﬂeoedd neu anghenion penodol. 

en-gb	Aspects of collection, representation and analysis, for example, will become more sophisticated as learners progress.
cy-gb	Bydd agweddau ar gasglu, cynrychioli a dadansoddi, er enghraifft, yn dod yn fwy sofﬁstigedig wrth i ddysgwyr wneud cynnydd.

en-gb	3 See ‘Progression within this area of learning and experience’ section.
cy-gb	3 Gweler yr adran ‘Cynnydd o fewn y maes dysgu a phroﬁad hwn’.

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 12
cy-gb	Mathemateg a Rhifedd 13

en-gb	Welsh language
cy-gb	Y Gymraeg

en-gb	The number system in Welsh (Cymraeg) is an area that highlights the distinctive nature of mathematics in a Welsh context. 
cy-gb	Mae’r system rhifau yn y Gymraeg yn faes sy’n tynnu sylw at natur arbennig mathemateg mewn cyd-destun Cymreig. 

en-gb	In the early years, in particular, it would be helpful if teachers could consider teaching learners the traditional (vigesimal) way of counting in Welsh, as well as the more modern way. 
cy-gb	Yn ystod y blynyddoedd cynnar, yn arbennig, byddai’n ddefnyddiol pe gallai athrawon ystyried addysgu dysgwyr sut i gyfrif yn y Gymraeg gan ddefnyddio’r dull traddodiadol (fesul ugain), yn ogystal â’r ffordd fwy modern. 

en-gb	The decision as to when to introduce it, however, should be left to individual schools, to reﬂect the context of the school. 
cy-gb	Fodd bynnag, dylai ysgolion unigol benderfynu pryd i’w gyﬂwyno, gan adlewyrchu cyd-destun yr ysgol. 

en-gb	Children from homes/communities where Welsh is widely spoken, for example, may already know these from an early age, whereas for English-medium schools and some Welsh-medium schools it could be taught when learning to tell the time or date.
cy-gb	Mae’n bosibl y bydd plant sy’n dod o gartreﬁ/cymunedau lle y caiff y Gymraeg ei siarad yn helaeth, er enghraifft, eisoes yn gyfarwydd â’r dull hwn, o oedran cynnar, ond mae’n bosibl y gellid ei addysgu mewn ysgolion cyfrwng Saesneg a rhai ysgolion cyfrwng Cymraeg wrth ddysgu sut i ddweud yr amser neu’r dyddiad.

en-gb	The Welsh number system, as with other Celtic and some European languages, traditionally used the vigesimal system, using a base of 20 instead of the modern (and common) base of 10. 
cy-gb	Yn draddodiadol, roedd y system rhifau yn Gymraeg, fel gydag ieithoedd Celtaidd eraill a rhai ieithoedd Ewropeaidd, yn defnyddio’r system ugeiniol yn hytrach na’r sail fodern (a chyffredin) sy’n defnyddio sail o 10. 

en-gb	In comparatively recent times a decimal system, in common with other Indo-European languages, was set up to simplify the teaching of number. 
cy-gb	Yn gymharol ddiweddar, sefydlwyd system ddegol, yn gyffredin ag ieithoedd Indo-Ewropeaidd eraill, er mwyn symleiddio’r broses o addysgu rhif. 

en-gb	(For example, in the old system 11 was ‘un ar ddeg’ [1+10] and 14 was pedwar ar ddeg [4+10]. 
cy-gb	(Er enghraifft, yn yr hen system, cyfeiriwyd at 11 fel ‘un ar ddeg’ [1+10] a chyfeiriwyd at 14 fel pedwar ar ddeg [4+10]. 

en-gb	In the ‘new’ system, 11 is ‘un deg un’ [10+1] and 14 is ‘un deg pedwar’ [10+4]).
cy-gb	Yn y system ‘newydd’, cyfeirir at 11 fel ‘un deg un’ [10+1] a chyfeirir at 14 fel ‘un deg pedwar’ [10+4]).

en-gb	Welsh dimension and international perspective
cy-gb	Y dimensiwn Cymreig a phersbectif rhyngwladol

en-gb	The Welsh dimension and international perspective elements will enable learners to understand the connection between mathematics (and numeracy) and authentic real-world contexts that span across both Wales and the world. 
cy-gb	Bydd elfennau’r dimensiwn Cymreig a phersbectif rhyngwladol yn galluogi dysgwyr i ddeall y cysylltiad rhwng mathemateg (a rhifedd) a chyd-destunau dilys yn y byd go iawn sy’n berthnasol i Gymru a’r byd. 

en-gb	Mathematics is a universal language, but in order for learners to make sense of this language, and to understand mathematical concepts, it helps to provide examples rooted in everyday life. 
cy-gb	Mae mathemateg yn iaith i bawb, ond er mwyn i ddysgwyr wneud synnwyr o’r iaith honno, a deall cysyniadau mathemategol, mae’n helpu i ddarparu enghreifftiau sy’n berthnasol i fywyd pob-dydd. 

en-gb	Learners, especially young learners, are often unable to think abstractly and ﬁnd it easier to learn mathematics in more concrete terms.
cy-gb	Yn aml, nid yw dysgwyr, yn enwedig dysgwyr ifanc, yn gallu meddwl mewn ffordd haniaethol ac maent yn ei chael hi’n haws dysgu mathemateg mewn ffordd fwy diriaethol.

en-gb	Each school in Wales will have a unique environment in which they work, and schools should explore local sources and resources that might have a mathematics application. 
cy-gb	Bydd gan bob ysgol yng Nghymru amgylchedd unigryw y bydd yn gweithio ynddo, a dylai ysgolion ystyried ffynonellau ac adnoddau lleol y gellid eu defnyddio mewn perthynas â mathemateg. 

en-gb	The Learned Society of Wales refers to Wales providing ‘practical contexts through which procedure, theories, and/or principles are given concrete form through examples, case study, and illustrations of real-lifeapplications’ (The Learned Society of Wales, 2018). 
cy-gb	Mae Cymdeithas Ddysgedig Cymru yn nodi bod Cymru yn darparu cyd-destunau ymarferol ar gyfer cynnig ffurf ddiriaethol i weithdrefnau, damcaniaethau a/neu egwyddorion drwy enghreifftiau, astudiaethau achos a chyﬂwyniadau o gymwysiadau go iawn (Cymdeithas Ddysgedig Cymru, 2018). 

en-gb	Emeritus Professor Gareth Ffowc Roberts, in his submission to the Learned Society paper, stated that ‘while there may be no such thing as ‘Welsh mathematics/numeracy’ there are very particular Welsh ways of experiencing mathematics/numeracy’. 
cy-gb	Yn ei gyﬂwyniad i bapur y Gymdeithas Ddysgedig, nododd yr Athro Emeritws Gareth Ffowc Roberts er nad oes y fath beth â ‘mathemateg/rhifedd Cymreig’ fod yna ffyrdd Cymreig penodol iawn o broﬁ mathemateg/rhifedd. 

en-gb	The challenge is to teach and learn mathematics and numeracy in Wales so that children gain ownership of them, and perceive them as being a natural part of their culture rather than believing that they are copying another community’s culture. 
cy-gb	Yr her yw addysgu a dysgu mathemateg a rhifedd yng Nghymru mewn ffordd sy’n cynnig perchenogaeth i blant drostynt, ac yn eu hannog i’w hystyried fel rhan naturiol o’u diwylliant yn hytrach na chredu eu bod yn copïo diwylliant cymuned arall. 

en-gb	Various local and national organisations (e.g. the National Museum of Wales and CADW) have already developed mathematics teaching resources. 
cy-gb	Mae amrywiol sefydliadau lleol a chenedlaethol (e.e. Amgueddfa Genedlaethol Cymru a CADW) eisoes wedi datblygu adnoddau addysgu mathemateg. 

en-gb	Since April 2019 the Welsh Government has had responsibility for deciding the rates of Income Tax paid by Welsh taxpayers. 
cy-gb	Ers Ebrill 2019, mae gan Llywodraeth Cymru gyfrifoldeb dros benderfynu y cyfraddau treth incwm sy’n cael eu talu gan drethdalwyr Cymru. 

en-gb	Schools are encouraged to use Welsh examples when teaching ﬁnancial matters, and speciﬁcally about forms of taxation, highlighting the link between Mathematics and Numeracy, the real world and the responsibility Welsh Government has for determining Income Tax levels in Wales.
cy-gb	Mae ysgolion yn cael eu hannog i ddefnyddio enghreifftiau Cymreig wrth addysgu materion ariannol, megis treth, gan bwysleisio y cysylltiad rhwng Mathemateg a Rhifedd, y byd go iawn a chyfrifoldeb Llywodraeth Cymru i bennu cyfraddau treth incwm yng Nghymru.

en-gb	There are particular contributions to the ﬁeld of mathematics from Wales and internationally that could be used to support understanding of mathematical concepts and conventions, and also to support understanding of the development of mathematics as a body of knowledge. 
cy-gb	Ceir cyfraniadau penodol at faes mathemateg o Gymru ac yn rhyngwladol y gellid eu defnyddio i ategu dealltwriaeth o gysyniadau a chonfensiynau mathemategol, yn ogystal ag ategu dealltwriaetho’r broses o ddatblygu mathemateg fel corff gwybodaeth. 

en-gb	Wales has a proud history of producing outstanding mathematicians such as Robert Recorde and William Jones. 
cy-gb	Mae gan Gymru hanes balch o gynhyrchu mathemategwyr eithriadol megis Robert Recorde a William Jones. 

en-gb	Schools should consider every opportunity to highlight their achievements and, hopefully, inspire learners to become mathematicians themselves. 
cy-gb	Dylai ysgolion ystyried pob cyﬂe i dynnu sylw at eu cyﬂawniadau gan ysbrydoli dysgwyr, gobeithio, i ddod yn fathemategwyr eu hunain. 

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 13
cy-gb	Mathemateg a Rhifedd 14

en-gb	Using international examples from a range of cultures could enable learners to understand the history of mathematics and its development into an international and universally applicable language. 
cy-gb	Gallai defnyddio enghreifftiau rhyngwladol o amrywiaeth o ddiwylliannau alluogi dysgwyr i ddeall hanes mathemateg, a’r ffordd y mae wedi datblygu’n iaith ryngwladol y gellir ei defnyddio gan bawb. 

en-gb	This could also promote and support cross-curricular learning. 
cy-gb	Gallai hyn hefyd hyrwyddo a chefnogi dysgu trawsgwricwlaidd.

en-gb	The Mathematics and Numeracy Area of Learning and Experience has developed a set of mathematical proﬁciencies which permeate every aspect of what matters statements and have shaped progression in the area of learning and experience. 
cy-gb	Mae Maes Dysgu a Phroﬁad Mathemateg a Rhifedd wedi datblygu cyfres o hyfedreddau mathemategol sy’n treiddio i bob agwedd ar y datganiadau o’r hyn sy’n bwysig ac sydd wedi llywio cynnydd yn y maes dysgu a phroﬁad. 

en-gb	These proﬁciencies build on the work of Kilpatrick et al. 4 and elsewhere (such as the Australian curriculum), but have been adapted to the Welsh context by the pioneer group following considerable work with experts. 
cy-gb	Mae’r hyfedreddau hyn yn seiliedig ar waith Kilpatrick et al. 4 a gwaith mewn mannau eraill (megis cwricwlwm Awstralia), ond fe’u haddaswyd i gyd-destun Cymru gan y grŵp arloesi, yn dilyn cryn dipyn o waith gydag arbenigwyr. 

en-gb	These proﬁciencies are fundamental to learning within the discipline and will be part of a recognisably Welsh identity of the emerging Mathematics and Numeracy curriculum.
cy-gb	Mae’r hyfedreddau hyn yn hanfodol er mwyn dysgu yn y ddisgyblaeth a byddant yn rhan o hunaniaeth Gymreig amlwg sy’n gysylltiedig â’r cwricwlwm Mathemateg a Rhifedd arfaethedig.

en-gb	Wider skills
cy-gb	Sgiliau ehangach

en-gb	The Mathematics and Numeracy Area of Learning and Experience provides opportunities for learners to develop all four of the following wider skills.
cy-gb	Mae’r Maes Dysgu a Phroﬁad Mathemateg a Rhifedd yn darparu cyﬂeoedd i ddysgwyr ddatblygu pob un o’r pedwar sgil ehangach canlynol.

en-gb	Critical thinking and problem‑solving
cy-gb	Meddwl yn feirniadol a datrys problemau

en-gb	The development of logical and critical thinking underpins learning in mathematics. 
cy-gb	Mae datblygu sgiliau meddwl yn rhesymegol ac yn feirniadol yn sail i ddysgu mewn mathemateg. 

en-gb	Mathematics teaches us problem-solving skills, which transfer to all areas of the curriculum, to life in general and to the world of work. 
cy-gb	Mae mathemateg yn addysgu sgiliau datrys problemau sy’n trosglwyddo i bob maes o’r cwricwlwm, i fywyd yn gyffredinol ac i’r byd gwaith. 

en-gb	The work of mathematics involves solving problems, beginning by analysing requirements, asking questions and evaluating information. 
cy-gb	Mae mathemateg yn ymwneud â datrys problemau, gan ddechrau drwy ddadansoddi yr hyn sydd ei angen, gofyn cwestiynau a gwerthuso gwybodaeth. 

en-gb	In the development of solutions, learners identify potential approaches and develop arguments, justifying their decisions.
cy-gb	Wrth ddatblygu datrysiadau, mae dysgwyr yn adnabod dulliau gweithredu posibl ac yn datblygu dadleuon, gan gyﬁawnhau eu penderfyniadau.

en-gb	Planning and organisation
cy-gb	Cynllunio a threfnu

en-gb	Mathematical thinking requires learners to be organised and, as they progress through school, their organisational skills will develop, particularly as they plan and implement the data-handling cycle. 
cy-gb	Mae meddwl yn fathemategol yn gofyn i ddysgwyr fod yn drefnus ac, wrth iddynt wneud cynnydddrwy’r ysgol, bydd eu sgiliau trefnu yn datblygu, yn enwedig wrth iddynt gynllunio a gweithredu’r cylch trin data. 

en-gb	In their mathematical problem-solving, learners are encouraged to predict and estimate solutions and then to check their answers, reﬂect on their results and evaluate their approaches. 
cy-gb	Wrth ddatrys problemau mathemategol, anogir dysgwyr i ragfynegi ac amcangyfrif datrysiadau ac wedyn i wirio eu hatebion, myfyrio ar eu canlyniadau a gwerthuso eu dulliau gweithredu. 

en-gb	Increasingconﬁdence in decision-making for mathematical problem-solving supports learners to be more aspirational in setting goals and challenges for themselves.
cy-gb	Mae cynyddu eu hyder wrth wneud penderfyniadau er mwyn datrys problemau mathemategol yn helpu dysgwyr i fod yn fwy uchelgeisiol wrth bennu nodau a heriau iddynt eu hunain.

en-gb	Creativity and innovation
cy-gb	Creadigrwydd ac arloesi

en-gb	Mathematical working requires and develops creativity and curiosity which also transfer to other aspects of life. 
cy-gb	Mae gweithio’n fathemategol yn gofyn am greadigrwydd a chwilfrydedd ac yn datblygu’r agweddau hynny y gellir hefyd eu trosglwyddo i agweddau eraill ar fywyd. 

en-gb	Frequently in mathematical problem-solving the learner does not immediately know how to approach the problem; 
cy-gb	Yn aml, wrth ddatrys problemau mathemategol, nid yw’r dysgwr yn gwybod ar unwaith sut i ymdrin â’r broblem; 

en-gb	it takes creativity and courage to explore different approaches before deciding how to proceed. 
cy-gb	mae angen creadigrwydd a beiddgarwch wrth ystyried gwahanol ddulliau gweithredu cyn penderfynu sut i fwrw ymlaen. 

en-gb	Planning and modelling tasks within mathematics develops learners’ ability to turn ideas into action.
cy-gb	Mae cynllunio a modelu tasgau ym maes mathemateg yn datblygu gallu dysgwyr i roi syniadau ar waith.

en-gb	Personal effectiveness
cy-gb	Effeithiolrwydd personol

en-gb	Studying mathematics develops personal effectiveness. 
cy-gb	Mae astudio mathemateg yn datblygu effeithiolrwydd personol. 

en-gb	Everyone encounters challenges in studying mathematics at some point, and overcoming the challenges requires and develops resourcefulness and resilience.
cy-gb	Mae pawb yn wynebu heriau ar ryw adeg wrth astudio mathemateg, ac mae goresgyn y rhain yn gofyn am ﬂaengaredd a gwydnwch ac yn fodd o ddatblygu’r rhinweddau hynny.

en-gb	4 Adding It Up: 
cy-gb	4 Adding It Up: 

en-gb	Helping Children Learn Mathematics (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics (National Research Council, 2001)

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 14
cy-gb	Mathemateg a Rhifedd 15

en-gb	Communicating about mathematical thinking and solving problems is a core aspect of mathematics. 
cy-gb	Mae cyfathrebu am feddwl yn fathemategol a datrys problemau yn agwedd greiddiol ar fathemateg. 

en-gb	Mathematical communication is precise and logical and transfers to other areas of life.
cy-gb	Mae cyfathrebu mathemategol yn broses fanwl gywir a rhesymegol a gellir ei throsglwyddo i feysydd bywyd eraill.

en-gb	Careers and work‑related experiences
cy-gb	Gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith

en-gb	Learning from careers and labour market information
cy-gb	Dysgu o wybodaeth am yrfaoedd a’r farchnad lafur

en-gb	Mathematics and numeracy are an essential part of every aspect of our lives, whether at work or undertaking practical everyday activities. 
cy-gb	Mae mathemateg a rhifedd yn rhan hanfodol o bob agwedd ar ein bywydau, boed yn y gwaith neu wrth ymgymryd â gweithgareddau pob-dydd ymarferol. 

en-gb	We use mathematics when we go shopping, plan holidays, decide on mortgages or evaluate and plan career pathways. 
cy-gb	Rydym yn defnyddio mathemateg wrth siopa, cynllunio gwyliau, penderfynu ar forgeisi neu werthuso a chynllunio llwybrau gyrfa. 

en-gb	Decisions in life are so often based on numerical information that, to make the best choices, we need to be numerate.
cy-gb	Mae penderfyniadau mewn bywyd yn aml iawn yn seiliedig ar wybodaeth rifyddol ac, er mwyn gwneud y dewisiadau gorau, mae angen i ni fod yn rhifog.

en-gb	Mathematics helps to develop skills such as problem-solving, interpreting data and information, attention to detail, and accurate measuring and reasoning – all of which are highly desirable to employers. 
cy-gb	Mae mathemateg yn helpu i feithrin sgiliau megis datrys problemau, dehongli data a gwybodaeth, manylder, a mesur a rhesymu cywir – sydd i gyd yn sgiliau dymunol iawn i gyﬂogwyr. 

en-gb	The ability and knowledge developed through mathematics and numeracy are a fundamental part of most professions. 
cy-gb	Mae’r gallu a’r wybodaeth a gaiff eu meithrin drwy fathemateg a rhifedd yn rhan hanfodol o’r rhan fwyaf o broffesiynau. 

en-gb	As competency increases, a wider range of opportunities can be accessed. 
cy-gb	Wrth i gymhwysedd gynyddu, gellir manteisio ar amrywiaeth ehangach o gyﬂeoedd. 

en-gb	There is substantial evidence that a lack of numeracy skills leads to poorer outcomes. 
cy-gb	Ceir tystiolaeth sylweddol fod diffyg sgiliau rhifedd yn arwain at ddeilliannau gwaeth. 

en-gb	Organisation for Economic Co-operation and Development (OECD) data indicates that those with poor numeracy skills are more than twice as likely to be unemployed. 
cy-gb	Dengys data’r Sefydliad ar gyfer Cydweithrediad a Datblygiad Economaidd (yr OECD) fod y rheini â sgiliau rhifedd gwael ddwywaith mor debygol o fod yn ddi-waith. 

en-gb	It also indicates a direct relationship between wage distribution and numeracy skills 5 .
cy-gb	Noda hefyd fod cydberthynas uniongyrchol rhwng dosbarthiad cyﬂogau a sgiliau rhifedd 5 .

en-gb	Linking the area of learning and experience to careers and work‑related experiences A number of careers speciﬁcally require the use of mathematics, including air trafﬁc controller, surveyor, accountant, psychologist, teacher and carpenter or joiner. 
cy-gb	Cysylltu’r maes dysgu a phroﬁad â gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith Mae angen defnyddio mathemateg yn benodol fel rhan o nifer o yrfaoedd, gan gynnwys rheolydd trafﬁg awyr, tirfesurydd, cyfrifydd, seicolegydd, athro, saer coed neu asiedydd. 

en-gb	It is essential for learners to be aware of the wide range of careers available to them, and to be shown how the experiences, knowledge and skills made available in mathematics and numeracy can be applied in the world of work, whether in employment or as an entrepreneur, where these skills are increasingly crucial.
cy-gb	Mae’n hanfodol i ddysgwyr fod yn ymwybodol o’r amrywiaeth eang o yrfaoedd sydd ar gael iddynt, ac i ddangos iddynt sut y gellir cymhwyso’r proﬁadau, yr wybodaeth a’r sgiliau a gynigir ym maes mathemateg a rhifedd at fyd gwaith, boed mewn cyﬂogaeth neu fel entrepreneur, lle y mae’r sgiliau hyn yn gynyddol hanfodol.

en-gb	Incorporating careers and work-related experiences into mathematics can help contextualise learning and increase engagement. 
cy-gb	Gall cynnwys gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith fel rhan o fathemateg helpu i roi’r dysgu mewn cyd-destun a chynyddu lefelau ymgysylltiad. 

en-gb	For instance, statistical analysis and probability can be used in the evaluation of labour market intelligence and information. 
cy-gb	Er enghraifft, gellir defnyddio gwaith dadansoddi ystadegol a thebygolrwydd i werthuso deallusrwydd a gwybodaeth am y farchnad lafur. 

en-gb	Learners will therefore be able to effectively identify where jobs are, the qualiﬁcations and skills required, and whether this is an area of job increase or decline, thereby applying mathematics in a practical, constructive manner.
cy-gb	Gall dysgwyr, felly, adnabod yn effeithiol ble mae swyddi ar gael, y cymwysterau a’r sgiliau sydd eu hangen a ph’un a yw swyddi yn y maes hwn yn cynyddu neu’n lleihau gan gymhwyso mathemateg mewn ffordd ymarferol ac adeiladol.

en-gb	Careers and work-related experiences can help to raise aspirations and support ﬁnancial planning by adding realism and context. 
cy-gb	Gall gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith helpu i godi dyheadau ac ategu gwaith cynllunio ariannol drwy ychwanegu realaeth a chyd-destun. 

en-gb	Learners can be encouraged to plan for the future and to consider the implications of ﬁnance on career pathway decisions, for example, in considering the pay scale of various jobs. 
cy-gb	Gellir annog dysgwyr i gynllunio ar gyfer y dyfodol ac i ystyried goblygiadau cyllid ar benderfyniadau a wneir fel rhan o’r llwybr gyrfa, er enghraifft, wrth ystyried graddfa cyﬂog amrywiol swyddi. 

en-gb	This engages and motivates learners and can be further enhanced by the incorporation of valuable lifestyle budgeting exercises and money management for independent living.
cy-gb	Mae hyn yn ennyn diddordeb dysgwyr ac yn eu cymell a gellir eu hannog ymhellach drwy gynnwys ymarferion cyllidebu gwerthfawr mewn perthynas â ffordd o fyw ac ymarferion rheoli arian er mwyn byw’n annibynnol.

en-gb	Learner progression relating to careers and work-related experiences is part of a continuum of learning for learners aged 3 to 16. 
cy-gb	Mae cynnydd dysgwyr o ran gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith yn rhan o gontinwwm dysgu ar gyfer dysgwyr rhwng 3 ac 16 oed. 

en-gb	Success for a young primary school learner could include:
cy-gb	Gallai llwyddiant i ddysgwr iau ysgol gynradd gynnwys:

en-gb	5 www.nationalnumeracy.org.uk/why-numeracy-important
cy-gb	5 www.nationalnumeracy.org.uk/why-numeracy-important (Saesneg yn unig)

en-gb	Introduction Draft Curriculum for Wales 2022: 
cy-gb	Cyﬂwyniad Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 15
cy-gb	Mathemateg a Rhifedd 16

en-gb	• acting a variety of different jobs through role play
cy-gb	• chwarae rôl ar gyfer amrywiaeth o wahanol swyddi

en-gb	• belief that they can do any job – tackling gender stereotyping
cy-gb	• y gred y gallant gyﬂawni unrhyw swydd – gan fynd i’r afael â stereoteipiau rhywedd

en-gb	• communicating with people in their community about the different jobs they do and the rewards that a job can bring.
cy-gb	• cyfathrebu â’r bobl yn eu cymuned am y gwahanol swyddi y maent yn eu gwneud a’r boddhad a all ddeillio ohonynt.

en-gb	By progressing learning, success for 16-year-old learners could include:
cy-gb	Drwy wneud cynnydd dysgu, gallai llwyddiant i ddysgwyr 16 oed gynnwys:

en-gb	• demonstrating and applying the skills learned in relation to the world of work
cy-gb	• dangos a chymhwyso’r sgiliau a ddysgwyd mewn perthynas â’r byd gwaith 

en-gb	 • identifying interests, strengths and skills to make informed post-16 choices
cy-gb	• adnabod diddordebau, cryfderau a sgiliau er mwyn gwneud dewisiadau gwybodus ôl-16

en-gb	 • understanding and demonstrating the behaviours an employer looks for in a good employee
cy-gb	• deall ac arddangos y mathau o ymddygiad y mae cyﬂogwr yn dymuno eu gweld mewn cyﬂogai da

en-gb	• evaluating risks when developing a business idea and exploring different methods of setting up and sustaining an enterprise.
cy-gb	• gwerthuso risg wrth ddatblygu syniad busnes ac ystyried gwahanol ffyrdd o sefydlu a chynnal menter.

en-gb	Work‑related experiences
cy-gb	Proﬁadau sy’n gysylltiedig â gwaith  

en-gb	Learners develop interests, strengths, skills and aspirations through experiences as part of the curriculum and in life beyond school. 
cy-gb	Mae dysgwyr yn datblygu diddordebau, cryfderau, sgiliau a dyheadau drwy broﬁadau, fel rhano’r cwricwlwm ac mewn bywyd y tu hwnt i’r ysgol. 

en-gb	Employer engagement, whether by employer talks, visits to workplaces, events or practical activities are essential in adding realism to the world of work and underlining the importance of mathematics and numeracy. 
cy-gb	Mae ymgysylltu â chyﬂogwyr, boed drwy sgyrsiau gan gyﬂogwyr, ymweliadau â gweithleoedd, digwyddiadau neu weithgareddau ymarferol yn hanfodol o ran ychwanegu realaeth i’r byd gwaith a phwysleisio pwysigrwydd mathemateg a rhifedd. 

en-gb	It can further support learner progression to enable an understanding of the labour market and trends locally, pan Wales, nationally and globally. 
cy-gb	Gall ategu cynnydd dysgwyr ymhellach er mwyn galluogi dealltwriaeth o’r farchnad lafur a thueddiadau yn lleol, ledled Cymru, yn genedlaethol ac yn fyd-eang. 

en-gb	Employers raise awareness of roles within the workplace to challenge stereotypes and preconceptions and to raise awareness of all learning and training routes available.
cy-gb	Mae cyﬂogwyr yn codi ymwybyddiaeth o rolau yn y gweithle, er mwyn herio stereoteipiau a rhagdybiaethau ac er mwyn codi ymwybyddiaeth o’r holl lwybrau dysgu a hyfforddi sydd ar gael. 

en-gb	Incorporating careers and work-related experiences within Mathematics and Numeracy allows learners to understand, evaluate and engage with the world of work and enables greater engagement, raised aspirations, and informed, effective decision-making. 
cy-gb	Mae cynnwys gyrfaoedd a phroﬁadau sy’n gysylltiedig â gwaith o fewn Mathemateg a Rhifedd yn galluogi dysgwyr i ddeall, gwerthuso ac ymwneud â’r byd gwaith ac yn galluogi gwell lefelau diddordeb, dyheadau uwch, a’r gallu i wneud penderfyniadau gwybodus ac effeithiol. 

en-gb	In addition, it creates an environment where stereotypes can be challenged and the merits of diversity expressed.
cy-gb	Yn ogystal,mae’n creu amgylchedd lle y gellir herio stereoteipiau a mynegi manteision amrywiaeth.

en-gb	Effective careers guidance is essential in securing the most appropriate route for learners’ aspirations, informing them of the diversity of entry points and pathways into the world of work. 
cy-gb	Mae arweiniad gyrfaoedd effeithiol yn hanfodol er mwyn sicrhau’r llwybr mwyaf priodol ar gyfer dyheadau dysgwyr, gan eu hysbysu am y pwyntiau mynediad a’r llwybrau amrywiol i mewn i’r byd gwaith. 

en-gb	Schools should offer opportunities to foster entrepreneurial skills and learners should be aware of the beneﬁts of setting up enterprises.
cy-gb	Dylai ysgolion gynnig cyﬂeoedd i feithrin sgiliau entrepreneuraidd a dylai dysgwyr fod yn ymwybodol o’r buddiannau sy’n gysylltiedig â sefydlu menter.

en-gb	Understanding post‑16 and higher‑education opportunities
cy-gb	Deall cyﬂeoedd ôl-16 ac addysg uwch

en-gb	It is essential for learners to be aware of all opportunities available to them post-16. 
cy-gb	Mae’n hanfodol bod dysgwyr yn ymwybodol o’r holl gyﬂeoedd sydd ar gael iddynt ôl-16. 

en-gb	Therefore, as well as understanding about employment, training and apprenticeships, learners should be provided with information and the opportunity to engage with a range of learning providers. 
cy-gb	Felly, yn ogystal â deall am gyﬂogaeth, hyfforddiant a phrentisiaethau, dylid rhoi gwybodaeth i ddysgwyr am ddarparwyr dysgu a chynnig y cyﬂe iddynt ymgysylltu ag amrywiaeth o ddarparwyr o’r fath. 

en-gb	Opportunities for engagement should include attending careers and skills fairs, talks from and visits to further and higher education providers, as well as presentations from students in further or higher education. 
cy-gb	Dylai’r cyﬂeoedd ymgysylltu gynnwys mynychu ffeiriau gyrfaoedd a sgiliau, sgyrsiau gan ddarparwyr addysg bellach ac uwch ac ymweliadau gan y darparwyr hynny, yn ogystal â chyﬂwyniadau gan fyfyrwyr mewn addysg bellach neu uwch. 

en-gb	Learners should be directed to online research tools that provide course and progression information to support their understanding of the range of learning opportunities available, to help raise their aspirations and form a basis on which informed decisions can be made.
cy-gb	Dylid hefyd gyfeirio dysgwyr at adnoddau ymchwil ar-lein sy’n cynnig gwybodaeth am gyrsiau a chynnydd, er mwyn eu helpu i ddeall yr amrywiaeth o gyﬂeoedd dysgu sydd ar gael, ac i helpu i godi eu dyheadau a chynnig sail iddynt allu gwneud penderfyniadau gwybodus.

en-gb	Relationships and sexuality education
cy-gb	Addysg cydberthynas a rhywioldeb

en-gb	When preparing mathematics sessions we must be aware that reinforcing any stereotype around gender is potentially restricting.
cy-gb	Wrth baratoi sesiynau mathemateg, rhaid i ni fod yn ymwybodol y gall atgyfnerthu unrhyw stereoteip o ran rhywedd fod yn gyfyngol.

en-gb	Effective mathematics instruction must be conducted in an environment that encourages equal achievement in mathematics for boys and girls. 
cy-gb	Rhaid ymgymryd â chyfarwyddyd mathemateg effeithiol mewn amgylchedd sy’n annog cyﬂawniad cyfartal i fechgyn a merched mewn mathemateg. 

en-gb	Teachers must ensure that there are equal opportunities for participation and that the classroom setting is a positive factor in achievement.
cy-gb	Rhaid i athrawon sicrhau bod cyﬂeoedd cyfartal i gymryd rhan a bod yr ystafell ddosbarth yn ffactor cadarnhaol o ran sicrhau cyﬂawniad.

en-gb	When introducing famous mathematicians, care should be taken to ensure that both female and male mathematicians are presented to learners, in order to promote equality and gender positivity.
cy-gb	Wrth gyﬂwyno mathemategwyr enwog, dylid sicrhau y caiff mathemategwyr benywaidd a gwrywaidd eu cyﬂwyno i ddysgwyr, er mwyn hyrwyddo cydraddoldeb ac agweddau cadarnhaol mewn perthynas â rhywedd. 

en-gb	Teachers should choose activities connecting mathematics activities to careers in ways that do not reinforce existing gender stereotypes and select activities that spark initial curiosity about mathematics.
cy-gb	Dylai athrawon ddewis gweithgareddau sy’n cysylltu gweithgareddau mathemateg â gyrfaoedd mewn ffyrdd nad ydynt yn atgyfnerthu stereoteipiau rhywedd sy’n bodoli eisoes a dylent ddewis gweithgareddau sy’n tanio chwilfrydedd cychwynnol tuag at fathemateg.

en-gb	Teachers of all age-groups should be encouraging gender equality within mathematics and promoting career choices which show no bias.
cy-gb	Dylai athrawon pob grŵp oedran annog cydraddoldeb rhwng y rhywiau mewn mathemateg  a hyrwyddo dewisiadau gyrfa diduedd. 

en-gb	Enrichment and experiences
cy-gb	Cyfoethogi a phroﬁadau

en-gb	Throughout the Mathematics and Numeracy Area of Learning and Experience there is an emphasis on actively engaging learners in their mathematical learning by reference to, for example, exploring, investigating, playing and deducing. 
cy-gb	Ym mhob rhan o’r Maes Dysgu a Phroﬁad Mathemateg a Rhifedd ceir pwyslais ar sicrhau bod dysgwyr yn ymgysylltu’n weithredol â’u dysgu mathemategol drwy gyfeirio, er enghraifft, at archwilio, ymchwilio, chwarae a diddwytho. 

en-gb	The approach suggested through the experiences outlined in the descriptions of learning is to engage learners in meaningful problem-solving in all areas of mathematics, set in the contexts of real-world local and global situations. 
cy-gb	Drwy’r proﬁadau a amlinellir yn y disgriﬁad o’r dysgu, awgrymir y dylid sicrhau bod dysgwyr yn ymwneud â gweithgareddau datrys problemau ystyrlon ym mhob maes mathemategol, wedi’u gosod yng nghyd-destunau sefyllfaoedd lleol a byd-eang go iawn. 

en-gb	This will promote thelearners’ own desire for learning, by making its value clearer and more relevant.
cy-gb	Bydd hyn yn hyrwyddo awydd y dysgwyr eu hunain i ddysgu, drwy sicrhau bod gwerth y dysgu hwnnw yn gliriach ac yn fwy perthnasol.

en-gb	The achievement outcomes refer in multiple places to the resources that could and should be used to enhance understanding and enrich the mathematical experiences of learners. 
cy-gb	Mae’r deilliannau cyﬂawniad yn cyfeirio mewn sawl man at yr adnoddau y gellid ac y dylid eu defnyddio er mwyn gwella dealltwriaeth a chyfoethogi proﬁadau mathemategol dysgwyr. 

en-gb	The appropriate use of a range of digital technologies, manipulables, everyday objects, and concrete and abstract representations of mathematical objects helps the learners to engage with mathematical concepts from more than one perspective.
cy-gb	Mae defnydd priodol o amrywiaeth o dechnolegau digidol, eitemau hydrin, gwrthrychau pob-dydd, a chynrychioliadau diriaethol a haniaethol o wrthrychau mathemategol yn helpu’r dysgwyr i ymgysylltu â chysyniadau mathemategol o fwy nag un persbectif.

en-gb	In mathematics, learners sometimes collaborate to solve problems together in groups. 
cy-gb	Mewn mathemateg, mae dysgwyr weithiau’n cydweithio er mwyn datrys problemau gyda’i gilydd mewn grwpiau. 

en-gb	For example, some mathematics depends on generating several sources of data, forms of representation, and separate steps of multi-step tasks which can be shared within a group. 
cy-gb	Er enghraifft, mae rhai agweddau ar fathemateg yn dibynnu ar greu sawl ffynhonnell ddata, mathau o gynrychioli, a chamau unigol ar gyfer tasgau aml-gam y gellir eu dosrannu o fewn grŵp. 

en-gb	All can, therefore, contribute to completion of something beyond that which any individual might have done alone. 
cy-gb	Felly, gall pob un gyfrannu at gwblhau rhywbeth y tu hwnt i’r hyn y gallai unrhyw unigolyn fod wedi’i gyﬂawni ar ei ben ei hun. 

en-gb	As they work together, they engage actively in mathematical thinking and working, communicating about mathematics. 
cy-gb	Wrth iddynt gydweithio, maent yn ymwneud yn weithredol â dulliau meddwl a gweithio mathemategol, gan gyfathrebu am fathemateg. 

en-gb	This can aid the development of their own understanding, and enhance their own experience of mathematics. 
cy-gb	Gall hyn helpu i feithrin a gwella eu dealltwriaeth, a’u proﬁad personol o fathemateg. 

en-gb	However, it is also important in mathematics to encourage independent and individual work, with learners taking responsibility for their own learning. 
cy-gb	Fodd bynnag, mae hefyd yn bwysig mewn mathemateg i annog gwaith annibynnol ac unigol, gan roi cyfrifoldeb i ddysgwyr am eu dysgu eu hunain. 

en-gb	They need time to think without being swamped by others’ talk; time to internalise methods, facts, etc. 
cy-gb	Mae angen amser arnynt i feddwl, heb gael eu llethu gan syniadau eraill, i fewnoli dulliau, ffeithiau, ac ati. 

en-gb	A balanced diet of group and individual working will enrich the learners’ experience. 
cy-gb	Bydd cydbwysedd addas o waith grŵp a gwaith unigol yn cyfoethogiproﬁad dysgwyr.

en-gb	The learning of mathematics will be further enriched by the use of meaningful and substantial tasks, from modelling real-life numerical problems, perhaps involving ﬁnancial calculations, to relating patterns in nature to mathematical sequences, to using the data-handling cycle to investigate their own research questions.
cy-gb	Caiff y broses o ddysgu mathemateg ei chyfoethogi ymhellach drwy ddefnyddio tasgau ystyrlon a sylweddol, o fodelu problemau rhifyddol go iawn yn ymwneud, o bosibl, â chyfriﬁadau ariannol, i gysylltu patrymau ym myd natur â dilyniannau mathemategol, i ddefnyddio’r cylch trin data i ymchwilio i’w cwestiynau ymchwil eu hunain.

en-gb	Putting the area of learning and experience into practice
cy-gb	Rhoi’r maes dysgu a phroﬁad ar waith

en-gb	The Mathematics and Numeracy curriculum will need to be used by schools to design school-level provision, with the four purposes of the curriculum central to the planning of experiences that learners will encounter. 
cy-gb	Bydd angen i ysgolion ddefnyddio’r cwricwlwm Mathemateg a Rhifedd i gynllunio darpariaeth ar lefel ysgolion, gyda phedwar diben y cwricwlwm yn greiddiol i’r broses o gynllunio’r proﬁadau a gynigir i’r dysgwyr. 

en-gb	Important decisions will need to be taken about the structure and sequence of mathematics and numeracy topics, and these decisions should be informed by the hierarchic and connected nature of mathematics concepts, in order to ensure foundations are built upon and experiences are connected.
cy-gb	Bydd angen gwneud penderfyniadau pwysig am strwythur a dilyniant agweddau mathemateg a rhifedd, a dylai’r penderfyniadau hyn fod yn seiliedig ar natur hierarchaidd a chysylltiedig cysyniadau mathemategol, er mwyn sicrhau yr adeiledir ar sylfeini a bod cyswllt rhwng y proﬁadau.

en-gb	Deep understanding in mathematics and numeracy should develop through planning for all ﬁve of the mathematical proﬁciencies, and the connection and application of these in a range of contexts. 
cy-gb	Dylai dealltwriaeth gadarn o fathemateg a rhifedd ddatblygu drwy gynllunio ar gyfer pob un o’r pum hyfedredd mathemategol, a thrwy’r cysylltiad rhyngddynt a’r ffordd y cânt eu defnyddio mewn amrywiaeth o gyd-destunau. 

en-gb	Schools will have the autonomy to determine the length of time spent on particular aspects of mathematics and numeracy, and formative assessment should drive decisions about planning in the short term. 
cy-gb	Gall ysgolion unigol benderfynu faint o amser i’w dreulio ar agweddau mathemateg a rhifedd penodol, a dylai’r drefn asesu ffurﬁannol lywio penderfyniadau cynllunio yn y byrdymor. 

en-gb	In planning over longer periods of time, schools will need to ensure that systems of mapping and tracking provision across year groups are robust.
cy-gb	Wrth gynllunio dros gyfnodau hwy o amser, bydd angen i ysgolion sicrhau bod y systemau mapio a’r ddarpariaeth olrhain ar draws grwpiau blwyddyn yn rhai cadarn.

en-gb	The Mathematics and Numeracy curriculum does not prescribe one particular pedagogy, rather it requires practitioners to collaborate and make informed decisions to ensure that progress is achieved.
cy-gb	Nid yw’r cwricwlwm Mathemateg a Rhifedd yn rhagnodi un addysgeg benodol, ond mae’n ei gwneud yn ofynnol i ymarferwyr gydweithredu a gwneud penderfyniadau gwybodus er mwyn sicrhau cynnydd.

en-gb	Glossary Draft Curriculum for Wales 2022: 
cy-gb	Geirfa Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 18
cy-gb	Mathemateg a Rhifedd 19

en-gb	WHAT MATTERS IN MATHEMATICS AND NUMERACY
cy-gb	YR HYN SY’N BWYSIG MEWN MATHEMATEG A RHIFEDD

en-gb	The number system is used to represent and compare relationships between numbers and quantities.
cy-gb	Defnyddir y system rifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau.

en-gb	Numbers are the symbol system for describing and comparing quantities. 
cy-gb	Rhifau yw’r system o symbolau ar gyfer disgriﬁo a chymharu meintiau. 

en-gb	This is the ﬁrst abstract concept that learners meet in mathematics, and it helps to establish the principles of logical reasoning. 
cy-gb	Dyma’r cysyniad haniaethol cyntaf y bydd dysgwyr yn dod ar ei draws ym mathemateg, ac mae’n fodd i sefydlu egwyddorion rhesymu rhesymegol. 

en-gb	In mathematics the number system provides a basis for algebraic, statistical, probabilistic and geometrical reasoning, as well as for ﬁnancial calculation and decision-making.
cy-gb	Ym mathemateg, mae’r system rifo’n sail i resymu o ran algebra, ystadegau, tebygolrwydd a geometreg, yn ogystal ag o ran cyfrifo ariannol a gwneud penderfyniadau.

en-gb	Knowledge of, and competence in, number and quantities are fundamental to conﬁdent participation in the world, and provide a foundation for further study and for employment. 
cy-gb	Mae gwybodaeth a gallu ym maes rhifau a meintiau yn hanfodol ar gyfer cyfrannu i’r byd, ac yn cynnig sylfaen ar gyfer astudio pellach a chyﬂogaeth. 

en-gb	Computational ﬂuency is essential for problem-solving and progressing in all areas of learning and experience. 
cy-gb	Mae rhuglder o ran cyfriﬁannu yn allweddol i ddatrys problemau a gwneud cynnydd ym mhob maes dysgu a phroﬁad. 

en-gb	Fluency is developed through using the four basic arithmetic operations and acquiring an understanding of the relationship between them. 
cy-gb	Datblygir rhuglder drwy ddefnyddio’r pedwar gweithrediad rhifyddeg sylfaenol a datblygu dealltwriaeth o’r berthynas rhyngddynt. 

en-gb	This leads to preparing the way for using algebraic symbolisation successfully.
cy-gb	Mae hyn yn arwain at baratoi’r ffordd ar gyfer defnyddio symbolau algebra yn llwyddiannus.

en-gb	Learning
cy-gb	Dysgu

en-gb	Principles of progression
cy-gb	Egwyddorion cynnydd

en-gb	Principles of progression are the basis on which the achievement outcomes have been developed and should guide the progression of learning within the area of learning and experience.
cy-gb	Egwyddorion cynnydd yw’r sail ar gyfer datblygu’r deilliannau cyﬂawniad a dylent lywio dilyniant y dysgu o fewn y maes dysgu a phroﬁad.

en-gb	The following interdependent proﬁciencies 6 have been used to formulate the achievement outcomes and are central to progression at each stage of mathematics learning.
cy-gb	Defnyddiwyd y hyfedreddau cyd-ddibynnol canlynol 6 wrth greu’r deilliannau cyﬂawniad ac maent  yn greiddiol i gynnydd yn ystod pob cam o ddysgu mathemategol.

en-gb	Numeracy involves applying and connecting these proﬁciencies in a range of real-life contexts,across and beyond the curriculum.
cy-gb	Mae rhifedd yn golygu cymhwyso a chysylltu’r hyfedreddau hyn mewn amrywiaeth o gyd-destunau go iawn, ym mhob rhan o’r cwricwlwm a’r tu hwnt iddo.

en-gb	Conceptual understanding: 
cy-gb	Dealltwriaeth gysyniadol: 

en-gb	Mathematical concepts and ideas should be dwelt on, built on, and connected together as learners experience increasingly complex mathematical ideas. 
cy-gb	Dylid myfyrio ar syniadau a chysyniadau mathemategol, ynghyd â’u datblygu a’u cysylltu â’i gilydd, wrth i ddysgwyr gael proﬁad o syniadau mathemategol cynyddol gymhleth. 

en-gb	Learners demonstrate conceptual understanding by explaining and expressing concepts, ﬁnding examples (or non-examples) and by representing a concept in a variety of ways, including verbal, concrete, visual, digital and abstract representations.
cy-gb	Mae dysgwyr yn dangos dealltwriaeth gysyniadol drwy egluro a mynegi cysyniadau, dod o hyd i enghreifftiau (neu anenghreifftiau) a thrwy gynrychioli cysyniad mewn gwahanol ffyrdd, gan gynnwys cynrychioliadau llafar, diriaethol, gweledol, digidol a haniaethol.

en-gb	Communication with symbols: 
cy-gb	Cyfathrebu â symbolau: 

en-gb	Learners should understand that the symbols they are using are abstract representations and should develop greater ﬂexibility in their application and manipulation of an increasing range of symbols, understanding the conventions of the symbols they are using.
cy-gb	Dylai dysgwyr ddeall bod y symbolau y maent yn eu defnyddio yn gynrychioliadau haniaethol a dylent ddatblygu mwy o hyblygrwydd wrth iddynt gymhwyso a defnyddio amrywiaeth gynyddol o symbolau, gan ddeall confensiynau’r symbolau y maent yn eu defnyddio.

en-gb	Strategic competence: 
cy-gb	Cymhwysedd strategol: 

en-gb	(i.e. formulating problems mathematically in order to solve them) Learners should become increasingly independent in recognising and applying the underlying mathematical structures and ideas within a problem, in order to be able to solve them.
cy-gb	(h.y. gosod problemau allan mewn ffurf fathemategol er mwyn eu datrys) Dylai dysgwyr ddod yn gynyddol annibynnol wrth adnabod a chymhwyso’r strwythurau a’r syniadau mathemategol sydd wrth wraidd problem, er mwyn gallu ei datrys.

en-gb	Logical reasoning: 
cy-gb	Rhesymu rhesymegol: 

en-gb	As learners experience increasingly complex concepts, they should also develop an understanding of the relationships between and within these concepts. 
cy-gb	Wrth i ddysgwyr broﬁ cysyniadau cynyddol gymhleth, dylent hefyd feithrin dealltwriaeth o’r berthynas rhwng y cysyniadau hyn ac o fewn y cysyniadau hyn. 

en-gb	They should apply logical reasoning about these relationships and be able to justify and prove them. 
cy-gb	Dylent gymhwyso dulliau rhesymu rhesymegol wrth ymdrin â’r perthnasau hyn a gallu eu cyﬁawnhau a’u proﬁ.

en-gb	Justiﬁcations and proof should become increasingly abstract, moving from verbal, visual or concrete explanations to representations involving symbols and conventions.
cy-gb	Dylai’r cyﬁawnhad a’r dystiolaeth ddod yn gynyddol haniaethol, gan symud o esboniadau llafar, gweledol neu ddiriaethol i gynrychioliadau haniaethol sy’n cynnwys symbolau a chonfensiynau.

en-gb	Fluency: 
cy-gb	Rhuglder: 

en-gb	As learners experience, understand and apply increasingly complex concepts and relationships, ﬂuency in remembering facts, relationships and techniques should grow. 
cy-gb	Wrth i ddysgwyr broﬁ, deall a chymhwyso cysyniadau a pherthnasau sy’n gynyddol fwy cymhleth, dylai eu rhuglder wrth goﬁo ffeithiau, perthnasau a thechnegau wella. 

en-gb	As a result, facts, relationships and techniques learned previously should become ﬁrmly established, memorable and usable.
cy-gb	O ganlyniad, dylai ffeithiau, perthnasau a thechnegau a ddysgwyd ynghynt fod wedi’u hymsefydlu’n gadarn, yn goﬁadwy ac yn ddefnyddiadwy.

en-gb	6 Based on Adding It Up: 
cy-gb	6 Yn seiliedig ar Adding It Up: 

en-gb	Helping Children Learn Mathematics by Kilpatrick, Swafford and Findel (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics gan Kilpatrick, Swafford a Findel (National Research Council, 2001)

en-gb	and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
cy-gb	ac wedi’u haddasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen, 2018.

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have experienced and explored numbers in a variety of contexts and can express whole numbers in words, signs and symbols to convey size and order.
cy-gb	Rwyf wedi proﬁ ac archwilio rhifau mewn sawl cyd-destun, a gallaf fynegi rhifau cyfan mewn geiriau, arwyddion a symbolau er mwyn cyﬂeu maint a threfn.

en-gb	I can notice and read numbers in number-rich indoor and outdoor environments, experiencing cardinal, ordinal and nominal numbers.
cy-gb	Gallaf sylwi ar rifau, a’u darllen, mewn amgylcheddau sy’n frith o rifau, boed hynny dan do neu yn yr awyr agored, gan broﬁ rhifau prifol, trefnol ac enwol.

en-gb	I can use my experience of the counting sequence of numbers and of one-to-one correspondence to count sets reliably. 
cy-gb	Gallaf ddefnyddio fy mhroﬁad o drefn cyfrif rhifau ac o gyfatebiaeth un i un er mwyn cyfrif setiau’n ddibynadwy. 

en-gb	I can count objects that I can touch, and ones that I cannot.
cy-gb	Gallaf gyfrif gwrthrychau y gallaf gyffwrdd â nhw a rhai na allaf gyffwrdd â nhw.

en-gb	I can notice, read and write numbers in a range of media, through a multisensory approach, from zero to at least 20, ensuring they are correctly formed.
cy-gb	Gallaf sylwi ar rifau, a’u darllen a’u hysgrifennu, mewn amrywiaeth o gyfryngau a thrwy ddull aml-synhwyrol, a hynny o sero i 20 o leiaf, gan sicrhau eu bod wedi’u ffurﬁo’n gywir.

en-gb	I have experienced the counting sequence of numbers in different ways, counting forwards and backwards, and starting at different points.
cy-gb	Rwyf wedi cael proﬁad o drefn cyfrif rhifau, a hynny mewn gwahanol ffyrdd, gan gyfrif ymlaen ac yn ôl, a chan ddechrau ar wahanol rifau.

en-gb	I have explored composing a quantity in different ways, using combinations of objects or quantities and using the corresponding mathematical language such as words like ‘more’,‘less’, ‘most’ or ‘least’.
cy-gb	Rwyf wedi archwilio elfennu maint mewn gwahanol ffyrdd, gan ddefnyddio cyfuniadau o wrthrychau neu feintiau a chan ddefnyddio’r iaith fathemategol briodol, megis geiriau fel ‘mwy’,‘llai’, ‘mwyaf’ neu ‘leiaf’.

en-gb	I can understand that a number can be partitioned in different ways.
cy-gb	Gallaf ddeall y gellir ymrannu rhif mewn gwahanol ffyrdd.

en-gb	I have experienced grouping and sharing with objects/quantities, and I can group or share small quantities into equal-sized groups.
cy-gb	Rwyf wedi cael proﬁad o grwpio a rhannu gyda gwrthrychau/meintiau, a gallaf grwpio neu rannu meintiau bychain i grwpiau hafal eu maint.

en-gb	I can use my visual sense of number to make estimates and comparisons. 
cy-gb	Gallaf ddefnyddio fy synnwyr gweledol o rif i wneud amcangyfrifon a chymariaethau. 

en-gb	I can check estimates using counting or measuring.
cy-gb	Gallaf wirio amcangyfrifon drwy gyfrif neu fesur.

en-gb	I have used money in play and real-life situations and understand that I need to exchange money for items. 
cy-gb	Rwyf wedi defnyddio arian mewn sefyllfaoedd chwarae a bywyd go iawn, a gallaf ddeall bod angen i mi gyfnewid arian am eitemau. 

en-gb	I can use the language of money.
cy-gb	Gallaf ddefnyddio iaith arian.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can read, write and interpret numbers using ﬁgures and words up to at least 1,000.
cy-gb	Gallaf ddarllen, ysgrifennu a dehongli rhifau gan ddefnyddio fﬁgurau a geiriau hyd at 1,000, o leiaf.

en-gb	I can order and sequence numbers, including odd and even numbers, in number-rich indoor and outdoor environments, and can count on and back in uniform steps of any size.
cy-gb	Gallaf drefnu a dilyniannu rhifau, gan gynnwys odrifau ac eilrifau, mewn amgylchoedd sy’n frith o rifau, boed hynny o dan do neu yn yr awyr agored, a gallaf gyfrif ymlaen ac yn ôl mewn camau unffurf o unrhyw faint.

en-gb	I have experienced numbers below zero in practical contexts, including temperature measurements.
cy-gb	Rwyf wedi cael proﬁad o rifau is na sero mewn cyd-destunau ymarferol, gan gynnwys mesuriadau tymheredd.

en-gb	I have explored composing numbers in a variety of ways and I can understand that number value can be determined by the position of the digits used.
cy-gb	Rwyf wedi archwilio elfennu rhifau mewn amrywiol ffyrdd a gallaf ddeall sut y gall gwerth rhifau gael ei bennu gan saﬂe’r digidau a ddefnyddir.

en-gb	I have explored additive relationships using a range of representations. 
cy-gb	Rwyf wedi archwilio perthnasau adiol gan ddefnyddio amrywiaeth o gynrychioliadau. 

en-gb	I can use my understanding of additive relationships to add and subtract whole numbers using a variety of written and mental methods. 
cy-gb	Gallaf ddefnyddio fy nealltwriaeth o berthnasau adiol i adio a thynnu rhifau cyfan gan ddefnyddio amrywiaeth o ddulliau ysgrifenedig a meddyliol. 

en-gb	I can estimate and check the accuracy of my answers using inverse operations when appropriate.
cy-gb	Gallaf amcangyfrif a gwirio cywirdeb fy atebion gan ddefnyddio gweithredau gwrthdro pan fo hynny’n briodol.

en-gb	I have demonstrated an understanding of, and can recall, multiplication tables including 2, 3, 4, 5 and 10, and use the term ‘multiples’.
cy-gb	Rwyf wedi arddangos dealltwriaeth o dablau lluosi, gan gynnwys 2, 3, 4, 5 a 10, a gallaf eu coﬁo. Hefyd gallaf ddefnyddio y term ‘lluosrifau’.

en-gb	I have explored multiplicative relationships, using a range of representations (including sharing/grouping and the array), and I can use my understanding of multiplicative relationships to multiply and divide whole numbers using a variety of written and mental methods.
cy-gb	Rwyf wedi archwilio perthnasau lluosol gan ddefnyddio amrywiaeth o gynrychioliadau (gan gynnwys rhannu/grwpio a’r aráe), a gallaf ddefnyddio fy nealltwriaeth o berthnasau lluosol i luosi a rhannu rhifau cyfan a gwneud hynny mewn amrywiaeth o ddulliau ysgrifenedig a meddyliol.

en-gb	I have engaged in practical tasks and real-life problems to estimate and round numbers to the nearest 10 and 100.
cy-gb	Rwyf wedi ymgymryd â thasgau ymarferol a phroblemau bywyd go iawn i amcangyfrif a thalgrynnu i’r 10 neu’r 100 agosaf.

en-gb	I can reﬂect on how reasonable answers are in the light of estimations and I have veriﬁed calculations using inverse operations.
cy-gb	Gallaf fyfyrio ar ba mor rhesymol yw atebion yng ngoleuni amcangyfrifon ac rwyf wedi gwirio cyfriﬁadau gan ddefnyddio gweithrediadau wrthdro.

en-gb	I have demonstrated an understanding that unit fractions represent equal parts of a whole and are a way of conveying quantities and relationships.
cy-gb	Rwyf wedi arddangos dealltwriaeth fod ffracsiynau unedol yn cynrychioli rhannau cyfartal o’r cyfan a’u bod yn ffordd o gyﬂeu meintiau a pherthnasau.

en-gb	I have experienced fractions in practical situations, using a variety of representations. 
cy-gb	Rwyf wedi cael proﬁad o ffracsiynau mewn sefyllfaoedd ymarferol gan ddefnyddio amrywiaeth o gynrychioliadau.

en-gb	I have explored equivalent fractions and understand equivalent fraction relationships.
cy-gb	Rwyf wedi archwilio ffracsiynau cywerth ac rwy’n deall perthnasau ffracsiynau cywerth.

en-gb	I have demonstrated an understanding of when to count, when to measure and when to calculate to ﬁnd quantities.
cy-gb	Rwyf wedi arddangos dealltwriaeth o bryd i gyfrif, pryd i fesur a phryd i gyfrifo i ddod o hyd i feintiau.

en-gb	I can explain that money and ways to save and pay come in different forms. 
cy-gb	Gallaf esbonio bod arian a ffyrdd i gynilo a thalu yn dod ar ffurﬁau gwahanol. 

en-gb	I can make sensible ﬁnancial transactions in familiar role-play scenarios, including making informed decisions and choices about spending and saving.
cy-gb	Gallaf wneud trafodion ariannol call mewn senarios chwarae-rôl cyfarwydd, gan gynnwys gwneud penderfyniadau a dewisiadau am wario a chynilo, a hynny ar sail gwybodaeth.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have used a range of practical equipment to develop and secure my understanding of place value for positive and negative integers. 
cy-gb	Rwyf wedi defnyddio amrywiaeth o offer ymarferol i ddatblygu a chadarnhau fy nealltwriaeth o werth lle ar gyfer cyfanrifau positif a negatif. 

en-gb	I can read, write and interpret numbers, using ﬁgures and words up to at least one million.
cy-gb	Gallaf ddarllen, ysgrifennu a dehongli rhifau, gan ddefnyddio fﬁgurau a geiriau hyd at ﬁliwn, o leiaf.

en-gb	I have extended my understanding of the number system, through a range of activities using non-digital and digital manipulatives, to include decimals and fractions, and I can conﬁdently place whole numbers and fractional quantities on a number line. 
cy-gb	Rwyf wedi ymestyn fy nealltwriaeth o’r system rifau drwy amrywiaeth o weithgareddau, gan ddefnyddio trinolion digidol ac annigidol, yn cynnwys degolion a meintiau ffracsiynol, a gallaf osod yn hyderus rifau cyfan a meintiau ffracsiynol ar linellau rhif. 

en-gb	I have demonstrated my understanding that a fraction can be used as an operator, or to represent division. 
cy-gb	Rwyf wedi arddangos fy nealltwriaeth y gall ffracsiwn gael ei ddefnyddio fel gweithredydd, neu i gynrychioli rhannu. 

en-gb	I can use place value for non-integers.
cy-gb	Gallaf ddefnyddio gwerth lle ar gyfer rhifau nad ydynt yn gyfanrifau.

en-gb	I have demonstrated my understanding that fractions (including improper fractions) as well as mixed numbers, decimals and percentages, provide different ways of representing non-integer quantities.
cy-gb	Rwyf wedi arddangos dealltwriaeth o’r modd y mae ffracsiynau (gan gynnwys ffracsiynau pendrwm), ynghyd â rhifau cymysg, degolion a chanrannau, yn ffyrdd gwahanol o gynrychioli meintiau nad ydynt yn gyfanrifau.

en-gb	I have explored number patterns, connections and calculations with manipulatives and digital technology, and can demonstrate my understanding of number facts and relationships. 
cy-gb	Rwyf wedi archwilio patrymau rhifau, cysylltiadau a chyfriﬁadau gyda thrinolion a thechnoleg ddigidol, a gallaf arddangos fy nealltwriaeth o ffeithiau a pherthnasau rhifau. 

en-gb	I have used my knowledge of number facts and relationships to solve problems in mathematical and real-life contexts.
cy-gb	Rwyf wedidefnyddio’r hyn rwy’n ei wybod am ffeithiau a pherthnasau rhifau i ddatrys problemau mewn cyd-destunau mathemategol a rhai bywyd go iawn.

en-gb	I have developed, used and discussed efﬁcient and accurate methods when applying all four arithmetic operations to integers and decimals. 
cy-gb	Rwyf wedi datblygu, defnyddio a thrafod dulliau effeithlon a chywir wrth gymhwyso pob un o’r pedwar gweithrediad rhifyddeg mewn perthynas â chyfanrifau a degolion. 

en-gb	I can combine these operations, in both mathematical and real-life contexts of problem-solving.
cy-gb	Gallaf gyfuno’r pedwar, mewn cyd-destunau mathemategol a rhai bywyd go iawn, i ddatrys problemau.

en-gb	I can verify calculations and statements about number by inverse reasoning and approximation methods.
cy-gb	Gallaf wirio cyfriﬁadau a datganiadau am rifau, drwy resymu gwrthdro a dulliau amcangyfrif.

en-gb	I have explored the meaning of negative numbers in meaningful and authentic contexts. 
cy-gb	Rwyf wedi archwilio ystyr rhifau negatif mewn cyd-destunau ystyrlon a dilys. 

en-gb	I can compare the sizes of negative numbers and I can calculate the differences between any two integers. 
cy-gb	Gallaf gymharu maint rhifau negatif a gallaf gyfrifo’r gwahaniaethau rhwng unrhyw ddau gyfanrif. 

en-gb	I can check my answers.
cy-gb	Gallaf wirio fy atebion.

en-gb	I can ﬂuently recall times tables up to at least 10 x 10 and demonstrate my understanding by using them appropriately in applications and in mental and written arithmetic.
cy-gb	Gallaf goﬁo tablau lluosi a’u hadrodd yn rhugl hyd at o leiaf 10 x 10, a gallaf arddangos fy nealltwriaeth drwy eu defnyddio’n briodol mewn cymwysiadau ac mewn rhifyddeg ysgrifenedig a meddyliol.

en-gb	I have demonstrated an understanding of rounding and can solve problems requiring rounding to the nearest unit, 10, 100 and 1,000.
cy-gb	Rwyf wedi arddangos dealltwriaeth o dalgrynnu a gallaf ddatrys problemau sy’n gofyn am dalgrynnu i’r uned, y 10, y 100 a’r 1,000 agosaf.

en-gb	I have demonstrated an understanding of the equivalence of simple fractions, decimals and percentages, and I can convert between representations. 
cy-gb	Rwyf wedi arddangos dealltwriaeth o gywerthedd ffracsiynau syml, degolion a chanrannau a gallaf newid rhwng cynrychioliadau. 

en-gb	I can use my knowledge of equivalence to compare the sizes of fractions. 
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am gywerthedd i gymharu maint ffracsiynau. 

en-gb	I understand the inverse relation between the denominator of a fraction and its value.
cy-gb	Rwy’n deall y berthynas wrthdro rhwng enwadur ffracsiwn a’i werth.

en-gb	I can use my knowledge of multiplication, division, fractions and percentages to calculate proportions of a number or quantity, and to divide a number or quantity in a given ratio. 
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am luosi, rhannu, ffracsiynau a chanrannau i gyfrifo cyfrannau rhif neu faint ac i rannu rhif neu faint mewn cymhareb benodol. 

en-gb	I have solved problems involving ratio and proportion in real-life contexts, and I have used my knowledge of estimation and rounding to predict and check my answers.
cy-gb	Rwyf wedi datrys problemau sy’n ymwneud â chymhareb a chyfran mewn cyd-destunau bywyd go iawn, ac rwyf wedi defnyddio’r hyn rwy’n ei wybod am amcangyfrif a thalgrynnu i ragfynegi fy atebion,a’u gwirio.

en-gb	I have demonstrated an understanding of income and expenditure, and I can calculate proﬁt and loss. 
cy-gb	Rwyf wedi arddangos dealltwriaeth o incwm a gwariant, a gallaf gyfrifo elw a cholled. 

en-gb	I have created and evaluated budgets for activities and events.
cy-gb	Rwyf wedi creu a gwerthuso cyllidebau ar gyfer gweithgareddau a digwyddiadau.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can ﬂuently and accurately apply the four arithmetic operations, in the correct order, on integers, decimals and fractions, using written, mental and digital methods. 
cy-gb	Gallaf gymhwyso pedwar gweithrediad rhifyddeg yn rhugl ac yn gywir, a hynny yn y drefn gywir, o ran cyfanrifau, degolion a ffracsiynau, gan ddefnyddio dulliau ysgrifenedig, meddyliol a digidol. 

en-gb	I can use my sense of number to predict and check my answers.
cy-gb	Gallaf ddefnyddio fy synnwyr rhifau i ragfynegi fy atebion, a’u gwirio.

en-gb	I have demonstrated an understanding of the equivalence of fractions, decimals and percentages and I can convert ﬂuently between the different forms, using both written methods and a calculator. 
cy-gb	Rwyf wedi arddangos dealltwriaeth o gywerthedd ffracsiynau, degolion a chanrannau, a gallaf newid yn hawdd rhwng y gwahanol ffurﬁau, gan ddefnyddio dulliau ysgrifenedig a chyfriﬁannell. 

en-gb	I have used my knowledge of percentages and ratio to solve problems that involve simple interest, compound interest, depreciation, and calculating bills and budgets that include basic taxation on goods and services.
cy-gb	Rwyf wedi defnyddio’r hyn rwy’n ei wybod am ganrannau a chymhareb i ddatrys problemau sy’n ymwneud â llog syml, adlog, dibrisiad a chyfrifo biliau a chyllidebausy’n cynnwys treth sylfaenol ar nwyddau a gwasanaethau.

en-gb	I have derived and applied the rules of indices, with the exclusion of fractional indices, to calculate values and solve problems.
cy-gb	Rwyf wedi deillio a chymhwyso rheolau indecsau, ac eithrio indecsau ffracsiynol, i gyfrifo gwerthoedd a datrys problemau.

en-gb	I have consolidated my understanding of reciprocals when dividing fractions.
cy-gb	Rwyf wedi atgyfnerthu fy nealltwriaeth o gilyddion wrth rannu ffracsiynau.

en-gb	I can use standard index form to represent small and large numbers and to perform calculations in appropriate real-life and mathematical contexts.
cy-gb	Gallaf ddefnyddio ffurf indecs safonol i gynrychioli rhifau bach a mawr ac i wneud cyfriﬁadau mewn cyd-destunau mathemategol addas a rhai bywyd go iawn addas.

en-gb	I can solve problems requiring rounding or signiﬁcant ﬁgures at various stages of the calculation and give the answer, using both written and digital methods, and I can interpret the calculator outputs.
cy-gb	Gallaf ddatrys problemau sy’n gofyn am dalgrynnu neu fﬁgurau ystyrlon ar amrywiol gamau o’r gwaith cyfrifo a rhoi’r ateb, gan ddefnyddio dulliau ysgrifenedig a digidol, a gallaf ddehongli allbwn y gyfriﬁannell.

en-gb	I have demonstrated an understanding of ratio and proportion and can solve numerical problems that involve direct and inverse proportion, including expressing one quantity as a proportion of another, proportional change and problems that involve foreign currencies and exchange rates.
cy-gb	Rwyf wedi arddangos dealltwriaeth o gymhareb a chyfrannedd, a gallaf ddatrys problemau rhiﬁadol sy’n ymwneud â chyfrannedd union a gwrthdro, gan gynnwys mynegi un maint fel cyfran o un arall, newid cyfrannol a phroblemau o ran arian tramor a chyfraddau cyfnewid.

en-gb	I can use my knowledge of number to predict and check my answers.
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am rif i ragweld a gwirio fy atebion.

en-gb	I can justify choices based on value for money, personal well-being and global impact.
cy-gb	Gallaf gyﬁawnhau dewisiadau’n seiliedig ar werth am arian, lles personol ac effaith fyd-eang.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can recognise the difference between rational and irrational numbers, and apply all four arithmetic operations to them.
cy-gb	Gallaf adnabod y gwahaniaeth rhwng rhifau cymarebol a rhai anghymarebol, a chymhwyso pob un o’r pedwar gweithrediad rhifyddeg atynt.

en-gb	I have explored the relationship between powers, roots and fractional indices, and I can derive and apply the rules to simplify and decompose surds.
cy-gb	Rwyf wedi archwilio’r berthynas rhwng pwerau, israddau ac indecsau ffracsiynol, a gallaf ddeillio a gweithredu’r rheolau i symleiddio a dadelfennu syrdiau.

en-gb	I have demonstrated ﬂuency in moving between representations of numbers, including converting a given recurring decimal to a fraction.
cy-gb	Rwyf wedi arddangos rhuglder yn y modd rwy’n symud rhwng cynrychioliadau o rifau, gan gynnwys trosi degolyn cylchol penodol i ffracsiwn.

en-gb	I have demonstrated an understanding that measurements are not always accurate and are subject to tolerance and margins of error. 
cy-gb	Rwyf wedi dod i ddeall nad yw mesuriadau bob amser yn gywir a bod rhaid ystyried goddeﬁant a chyfeiliornad wrth fesur. 

en-gb	I can solve problems involving upper and lower bounds, and justify the outcome. 
cy-gb	Gallaf ddatrys problemau’n ymwneud ag arfﬁniau uchaf ac isaf, a chyﬁawnhau’r canlyniad. 

en-gb	I can use my knowledge of tolerance when choosing the required degree of accuracy to make real-life calculations.
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am oddeﬁant wrth ddewis faint o gywirdeb sydd ei angen i wneud cyfriﬁadau bywyd go iawn.

en-gb	I can solve problems involving repeated and inverse proportional reasoning.
cy-gb	Gallaf ddatrys problemau sy’n ymwneud â rhesymu cyfrannol ailadroddus a rhesymu cyfrannol gwrthdro.

en-gb	I can use my knowledge of annual equivalent rate (AER) and annual percentage rate (APR) to develop models to evaluate and compare ﬁnancial products.
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am gyfradd gywerth ﬂynyddol (AER) a’r gyfradd ganrannol ﬂynyddol (APR) i ddatblygu modelau i werthuso a chymharu cynnyrch ariannol.

en-gb	I can calculate income tax and understand the implications of taxation.
cy-gb	Gallaf gyfrifo treth incwm a deall goblygiadau trethu.

en-gb	Planning for learning
cy-gb	Cynllunio ar gyfer dysgu

en-gb	Links within this area of learning and experience
cy-gb	Cysylltiadau o fewn y maes dysgu a phroﬁad hwn

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across the Mathematics and Numeracy Area of Learning and Experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws Maes Dysgu a Phroﬁad Mathemateg a Rhifedd. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations.
cy-gb	Mae algebra yn defnyddio systemau symbolau i fynegi strwythurau’r perthnasau rhwng rhifau, meintiau a chydberthnasau.

en-gb	• The connections between arithmetic and algebra develop tools and skills for abstract reasoning from an early age.
cy-gb	• Mae’r cysylltiadau rhwng rhifyddeg ac algebra yn datblygu adnoddau a sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.

en-gb	• There is a strong relationship between the algorithms of arithmetic and the laws of algebra. 
cy-gb	• Mae perthynas gref rhwng algorithmau rhifyddeg a deddfau algebra. 

en-gb	• The order of operations and laws of arithmetic are followed in algebra.
cy-gb	• Dilynir trefn gweithrediadau a deddfau rhifyddeg mewn algebra.

en-gb	Geometry focuses on relationships involving properties of shape, space, and position, and measurement focuses on quantifying phenomena in the physical world . 
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	• Number is used throughout geometry to quantify shape, size and movement.
cy-gb	• Defnyddir rhifau ym mhob agwedd ar geometreg i fesur siapiau, maint a symudiad.

en-gb	• Measure is an aspect of geometrical thinking which is highly connected to number and much of the development of understanding of number can emerge through increasingly sophisticated measuring.
cy-gb	• Mae mesur yn agwedd ar feddwl geometregol sydd â chysylltiad agos â rhifau a gall cryn dipyn o’r broses o ddatblygu dealltwriaeth o rifau ddod drwy fesur cynyddol sofﬁstigedig.

en-gb	• Geometric thinking involves reasoning with proportion, which connects with development in number work.
cy-gb	• Mae meddwl geometrig yn cynnwys rhesymu â chymesuredd, sy’n cysylltu â datblygiad mewn gwaith rhifau.

en-gb	• Geometry involves lengths, areas and volumes which are expressed as numerical quantities. 
cy-gb	• Mae geometreg yn cynnwys hydoedd, arwynebeddau a chyfeintiau a fynegir fel meintiau rhifyddol.

en-gb	• Use of rules of number to calculate further values related to measurement and geometry.
cy-gb	• Defnyddio rheolau rhifau i gyfrifo gwerthoedd pellach sy’n gysylltiedig â mesur a geometreg.

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions.
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus.

en-gb	• Probability and statistics are described and manipulated by using number;  they are represented using number.
cy-gb	• Mae tebygolrwydd ac ystadegau yn cael eu disgriﬁo a’u trin drwy ddefnyddio rhifau; cânt eu cynrychioli drwy ddefnyddio rhifau.

en-gb	• Probability is expressed through number in various ways, e.g. through the use of percentages, fractions and decimals, and the connections between the representations is necessary for effective expression of probability.
cy-gb	• Mynegir tebygolrwydd drwy rifau mewn sawl ffordd, e.e. drwy ddefnyddio canrannau, ffracsiynau a degolion, ac mae angen y cysylltiadau rhwng y cynrychioliadau er mwyn mynegi tebygolrwydd yn effeithiol.

en-gb	• Statistics involves manipulation and representation of data, which involves numerical thinking.
cy-gb	• Mae ystadegau yn cynnwys trin a chynrychioli data, sy’n cynnwys meddwl rhifyddol.

en-gb	Links with other areas of learning and experience
cy-gb	Cysylltiadau â meysydd dysgu a phroﬁad eraill

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across all the areas of learning and experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws yr holl feysydd dysgu a phroﬁad. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	Expressive Arts
cy-gb	Celfyddydau Mynegiannol

en-gb	• Scale, proportion and ratio. 
cy-gb	• Graddfa, cyfrannedd a chymhareb. 

en-gb	• Fractions in music, rhythm. 
cy-gb	• Ffracsiynau mewn cerddoriaeth, rhythmau. 

en-gb	• Songs and rhymes.
cy-gb	• Caneuon a rhigymau.

en-gb	Humanities
cy-gb	Dyniaethau

en-gb	• Ratio and scale. 
cy-gb	• Graddfa a chymhareb. 

en-gb	• Finance.
cy-gb	• Cyllid.

en-gb	• Rounding. 
cy-gb	• Talgrynnu.

en-gb	• Ordering.
cy-gb	• Rhoi mewn trefn.

en-gb	Science and Technology
cy-gb	Gwyddoniaeth a Thechnoleg

en-gb	• Rounding and estimating.
cy-gb	• Talgrynnu ac amcangyfrif.

en-gb	• Laws of indices.
cy-gb	• Deddfau indecsau.

en-gb	• Reading, writing and calculating in standard index form. 
cy-gb	• Darllen, ysgrifennu a chyfrifo mewn ffurf safonol. 

en-gb	• Direct and inverse proportion.
cy-gb	• Cyfrannedd union a gwrthdro.

en-gb	Health and Well‑being
cy-gb	Iechyd a Lles

en-gb	• Understanding of estimation and rounding.
cy-gb	• Deall amcangyfrif a thalgrynnu.

en-gb	• Application to making real-life decisions including ﬁnancial ones.
cy-gb	• Cymhwyso gan wneud penderfyniadau bywyd go iawn gan gynnwys rhai ariannol. 

en-gb	• Fractions, percentages and proportions, e.g. balanced diet.
cy-gb	• Ffracsiynau, canrannau a chyfraneddau, e.e. deiet cytbwys.

en-gb	Languages, Literacy and Communication
cy-gb	Ieithoedd, Llythrennedd a Chyfathrebu

en-gb	• Songs and rhymes.
cy-gb	• Caneuon a rhigymau.

en-gb	Experiences, knowledge and skills
cy-gb	Proﬁadau, gwybodaeth a sgiliau

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• explore numbers and quantities through multisensory experiences both indoors and outdoors
cy-gb	• archwilio rhifau a meintiau drwy broﬁadau amlsynhwyraidd dan do ac yn yr awyr agored 

en-gb	• learn that the number system, and whole numbers in particular, allow us to convey size and quantity
cy-gb	• dysgu bod y system rifau, yn enwedig rhifau cyfan, yn ein galluogi i gyﬂeu maint 

en-gb	• represent and communicate with whole numbers
cy-gb	• cynrychioli a chyfathrebu â chyfanrifau

en-gb	• begin to understand that money is needed to pay for things
cy-gb	• dechrau deall bod angen arian i dalu am bethau

en-gb	• use a variety of representations to explore number, including objects, visual representations and, where appropriate, digital representations.
cy-gb	• defnyddio amrywiaeth o gynrychioliadau i archwilio rhifau, megis gwrthrychau, cynrychioliadau gweledol a, lle bo hynny’n briodol, cynrychioliadau digidol.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• extend their understanding of the number system, through experiential learning, to include large numbers, zero, negative numbers and fractions
cy-gb	• ehangu eu dealltwriaeth o’r system rifau, drwy ddysgu drwy broﬁad, i gynnwys rhifau mawr, sero,rhifau negatif a ffracsiynau

en-gb	• explore composition and equivalence of number, and learn about place value 
cy-gb	• archwilio elfennau a chywerthedd rhif, a dysgu am werth lle 

en-gb	• learn about relationships in numbers
cy-gb	• dysgu am berthnasau mewn rhifau

en-gb	• understand the additive relationship and be introduced to the multiplicative relationship, including using the array
cy-gb	• amgyffred y berthynas adiol ac fe’u cyﬂwynir i’r berthynas luosol, gan gynnwys defnyddio’r aráe

en-gb	• use their understanding of the equivalence and value of coins and notes to make appropriate transactions.
cy-gb	• defnyddio eu dealltwriaeth o gywerthedd a gwerth darnau arian ac arian papur i wneud trafodion priodol.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• extend their understanding and use of the number system, through a broad range of experiences, to include negative numbers, decimals and fractions
cy-gb	• ymestyn eu dealltwriaeth a’u defnydd o’r system rifau, drwy amrywiaeth eang o broﬁadau,i gynnwys rhifau negatif, degolion a ffracsiynau

en-gb	• further develop understanding of place value
cy-gb	• datblygu eu dealltwriaeth o werth lle ymhellach

en-gb	• explore the properties of numbers, including factors, multiples, primes, and the inverse relationship between squares and square roots
cy-gb	• archwilio priodweddau rhifau gan gynnwys ffactorau, lluosrifau, rhifau cyseﬁn, a’r berthynas wrthdro rhwng ail israddio a sgwario

en-gb	• become increasingly conﬁdent in using all four arithmetic operations in their calculations  with whole numbers and decimals, and combine these, using distributive, associative and commutative laws where appropriate
cy-gb	• datblygu’n fwyfwy hyderus wrth ddefnyddio pob un o’r pedwar gweithrediad rhifyddol yn eu  cyfriﬁadau gyda chyfanrifau a degolion, a chyfuno’r rhain, gan ddefnyddio deddfau dosbarthol,  cysylltiadol a chymudol lle bo hynny’n briodol

en-gb	• create and evaluate enterprise projects linked to their immediate and local environment.
cy-gb	• creu a gwerthuso prosiectau menter sy’n gysylltiedig â’r hyn sydd o’u cwmpas ac yn rhan o’u hamgylcheddau lleol.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• become increasingly ﬂuent in their use of number in calculations, through a broad range of  experiences, in order to interpret mathematical statements and describe quantities both with and without the use of calculators
cy-gb	• drwy amrywiaeth eang o broﬁadau, ddod yn fwyfwy rhugl yn eu defnydd o rifau o fewn cyfriﬁadau er mwyn dehongli datganiadau mathemategol a disgriﬁo meintiau gyda chyfriﬁanellau  a hebddynt

en-gb	• further develop their understanding of equivalence, appreciating that any number may be represented in many ways
cy-gb	• datblygu ymhellach eu dealltwriaeth o gywerthedd, gan werthfawrogi bod sawl ffordd o gynrychioli unrhyw rif

en-gb	• use proportional reasoning to compare two quantities using multiplicative thinking, and then apply this to a new situation
cy-gb	• defnyddio rhesymu cyfrannol i gymharu dau faint, gan ddefnyddio meddwl lluosol, ac yna’n cymhwyso hynny mewn sefyllfa newydd

en-gb	• deepen their understanding of using and comparing very big and very small numbers 
cy-gb	• magu dealltwriaeth well o ddefnyddio a chymharu rhifau mawr iawn a bach iawn

en-gb	• select and use efﬁcient mental, written and digital methods to perform calculations 
cy-gb	• dewis a defnyddio dulliau effeithlon, yn feddyliol, yn ysgrifenedig ac yn ddigidol, i wneud cyfriﬁadau

en-gb	• extend their understanding of ﬁnance to personal, local and global contexts.
cy-gb	• ymestyn eu dealltwriaeth o gyllid i gyd-destunau personol, lleol a byd-eang.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• become increasingly ﬂuent in their use of number, through a broad range of experiences,  in order to describe, interpret and communicate size, scale and comparisons, both within and beyond mathematics
cy-gb	• drwy amrywiaeth eang o broﬁadau, ddod yn fwyfwy rhugl yn eu defnydd o rifau er mwyn disgriﬁo,dehongli a chyﬂeu maint, graddfa a chymariaethau o fewn mathemateg, a thu hwnt

en-gb	• become increasingly ﬂuent in their calculations, both with and without the use of calculators, and
cy-gb	• dod yn fwyfwy rhugl yn eu cyfriﬁadau, gyda chyfriﬁanellau a hebddynt, ac yn magu dealltwriaeth

en-gb	deepen their understanding of how to use rational and irrational numbers
cy-gb	ddyfnach o ddefnyddio rhifau cymarebol ac anghymarebol

en-gb	• become critical consumers in broader ﬁnancial contexts.
cy-gb	• dod yn ddefnyddwyr beirniadol mewn cyd-destunau ariannol ehangach.

en-gb	Glossary Draft Curriculum for Wales 2022: 
cy-gb	Geirfa Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 28
cy-gb	Mathemateg a Rhifedd 29

en-gb	WHAT MATTERS IN MATHEMATICS AND NUMERACY
cy-gb	YR HYN SY’N BWYSIG MEWN MATHEMATEG A RHIFEDD

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations.
cy-gb	Mae algebra yn defnyddio systemau symbolau i fynegistrwythurau’r perthnasau rhwng rhifau, meintiau a chydberthnasau.

en-gb	Algebra is the study of structures abstracted from computations and relations, and provides a way to make generalisations. 
cy-gb	Mae algebra yn astudio’r strwythurau sydd ymhlyg mewn cyfriﬁannau a chydberthnasau, ac yn cynnig ffordd o gyffredinoli. 

en-gb	Algebraic thinking moves away from context to structure and relationships. 
cy-gb	Mae meddwl algebraidd yn symud o’r cyd-destun i’r strwythur a’r perthnasau. 

en-gb	This powerful approach provides the means to abstract important features and to detect and express mathematical structures of situations in order to solve problems. 
cy-gb	Mae’r dull gweithredu pwerus hwn yn cynnig ffordd o gyrraedd at nodweddion pwysig ac o ganfod a mynegi strwythurau mathemategol sefyllfaoedd,gyda’r nod o ddatrys problemau. 

en-gb	Algebra is a unifying thread running through the fabric of mathematics.
cy-gb	Mae algebra yn rhedeg fel llinyn cyd-gysylltiol drwy frethyn mathemateg i gyd.

en-gb	Algebraic thinking is essential for reasoning, modelling and solving problems in mathematics and in a wide range of real-world contexts, including technology and ﬁnance. 
cy-gb	Mae meddwl algebraidd yn hanfodol er mwyn rhesymu, modelu a datrys problemau mewn mathemateg ac mewn amrywiaeth eang o gyd-destunau go iawn, gan gynnwys technoleg a chyllid. 

en-gb	Making connections between arithmetic and algebra develops skills for abstract reasoning from an early age.
cy-gb	Mae gwneud y cysylltiadau rhwng rhifyddeg ac algebra yn meithrin sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.

en-gb	Learning
cy-gb	Dysgu

en-gb	Principles of progression
cy-gb	Egwyddorion cynnydd

en-gb	Principles of progression are the basis on which the achievement outcomes have been developed and should guide the progression of learning within the area of learning and experience.
cy-gb	Egwyddorion cynnydd yw’r sail ar gyfer datblygu’r deilliannau cyﬂawniad a dylent lywio dilyniant y dysgu o fewn y maes dysgu a phroﬁad.

en-gb	The following interdependent proﬁciencies 7 have been used to formulate the achievement outcomes and are central to progression at each stage of mathematics learning.
cy-gb	Defnyddiwyd y hyfedreddau cyd-ddibynnol canlynol 7 wrth greu’r deilliannau cyﬂawniad ac maent  yn greiddiol i gynnydd yn ystod pob cam o ddysgu mathemategol.

en-gb	Numeracy involves applying and connecting these proﬁciencies in a range of real-life contexts,across and beyond the curriculum.
cy-gb	Mae rhifedd yn golygu cymhwyso a chysylltu’r hyfedreddau hyn mewn amrywiaeth o gyd-destunau go iawn, ym mhob rhan o’r cwricwlwm a’r tu hwnt iddo.

en-gb	Conceptual understanding: 
cy-gb	Dealltwriaeth gysyniadol: 

en-gb	Mathematical concepts and ideas should be dwelt on, built on, and connected together as learners experience increasingly complex mathematical ideas. 
cy-gb	Dylid myfyrio ar syniadau a chysyniadau mathemategol, ynghyd â’u datblygu a’u cysylltu â’i gilydd, wrth i ddysgwyr gael proﬁad o syniadau mathemategol cynyddol gymhleth. 

en-gb	Learners demonstrate conceptual understanding by explaining and expressing concepts, ﬁnding examples (or non-examples) and by representing a concept in a variety of ways, including verbal, concrete, visual, digital and abstract representations.
cy-gb	Mae dysgwyr yn dangos dealltwriaeth gysyniadol drwy egluro a mynegi cysyniadau, dod o hyd i enghreifftiau (neu anenghreifftiau) a thrwy gynrychioli cysyniad mewn gwahanol ffyrdd, gan gynnwys cynrychioliadau llafar, diriaethol, gweledol, digidol a haniaethol.

en-gb	Communication with symbols: 
cy-gb	Cyfathrebu â symbolau: 

en-gb	Learners should understand that the symbols they are using are abstract representations and should develop greater ﬂexibility in their application and manipulation of an increasing range of symbols, understanding the conventions of the symbols they are using.
cy-gb	Dylai dysgwyr ddeall bod y symbolau y maent yn eu defnyddio yn gynrychioliadau haniaethol a dylent ddatblygu mwy o hyblygrwydd wrth iddynt gymhwyso a defnyddio amrywiaeth gynyddol o symbolau, gan ddeall confensiynau’r symbolau y maent yn eu defnyddio.

en-gb	Strategic competence: 
cy-gb	Cymhwysedd strategol: 

en-gb	(i.e. formulating problems mathematically in order to solve them) Learners should become increasingly independent in recognising and applying the underlying mathematical structures and ideas within a problem, in order to be able to solve them.
cy-gb	(h.y. gosod problemau allan mewn ffurf fathemategol er mwyn eu datrys) Dylai dysgwyr ddod yn gynyddol annibynnol wrth adnabod a chymhwyso’r strwythuraua’r syniadau mathemategol sydd wrth wraidd problem, er mwyn gallu ei datrys.

en-gb	Logical reasoning: 
cy-gb	Rhesymu rhesymegol: 

en-gb	As learners experience increasingly complex concepts, they should also develop an understanding of the relationships between and within these concepts. 
cy-gb	Wrth i ddysgwyr broﬁ cysyniadau cynyddol gymhleth, dylent hefyd feithrin dealltwriaeth o’r berthynas rhwng y cysyniadau hyn ac o fewn y cysyniadau hyn. 

en-gb	They should apply logical reasoning about these relationships and be able to justify and prove them. 
cy-gb	Dylent gymhwyso dulliau rhesymu rhesymegol wrth ymdrin â’r perthnasau hyn a gallu eu cyﬁawnhau a’u proﬁ. 

en-gb	Justiﬁcations and proof should become increasingly abstract, moving from verbal, visual or concrete explanations to representations involving symbols and conventions.
cy-gb	Dylai’rcyﬁawnhad a’r dystiolaeth ddod yn gynyddol haniaethol, gan symud o esboniadau llafar, gweledol neu ddiriaethol i gynrychioliadau haniaethol sy’n cynnwys symbolau a chonfensiynau.

en-gb	Fluency: 
cy-gb	Rhuglder: 

en-gb	As learners experience, understand and apply increasingly complex concepts and relationships, ﬂuency in remembering facts, relationships and techniques should grow. 
cy-gb	Wrth i ddysgwyr broﬁ, deall a chymhwyso cysyniadau a pherthnasau sy’n gynyddol fwy cymhleth, dylai eu rhuglder wrth goﬁo ffeithiau, perthnasau a thechnegau wella. 

en-gb	As a result, facts, relationships and techniques learned previously should become ﬁrmly established, memorable and usable.
cy-gb	O ganlyniad, dylai ffeithiau, perthnasau a thechnegau a ddysgwyd ynghynt fod wedi’u hymsefydlu’n gadarn, yn goﬁadwy ac yn ddefnyddiadwy.

en-gb	Helping Children Learn Mathematics by Kilpatrick, Swafford and Findel (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics gan Kilpatrick, Swafford a Findel (National Research Council, 2001)

en-gb	and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
cy-gb	ac wedi’u haddasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen, 2018.

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have explored patterns through a range of hands-on activities and by using a variety of concrete, visual and digital resources. 
cy-gb	Rwyf wedi archwilio patrymau drwy amrywiaeth o weithgareddau ymarferol a chan ddefnyddio amrywiaeth o adnoddau diriaethol, gweledol a digidol. 

en-gb	I can recognise, copy and generalise patterns and sequences around me. 
cy-gb	Gallaf adnabod, copïo a chyffredinoli patrymau a dilyniannau o’m cwmpas.

en-gb	I have demonstrated an understanding of the concepts of equality and inequality, using objects.
cy-gb	Rwyf wedi dangos dealltwriaeth o gysyniadau hafaledd ac anhafaledd wrth ddefnyddio gwrthrychau.

en-gb	I can talk about how sets of objects change when objects are added to and taken away from them.
cy-gb	Gallaf drafod sut y mae setiau o wrthrychau yn newid pan gaiff gwrthrychau eu hychwanegua’u tynnu oddi wrthynt.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have explored patterns of numbers and shape using concrete, paper-based and digital materials. 
cy-gb	Rwyf wedi archwilio patrymau mewn rhifau a siapiau gan ddefnyddio deunyddiau diriaethol, deunyddiau papur a deunyddiau digidol. 

en-gb	I can recognise, copy and generate sequences of numbers and visual patterns.
cy-gb	Gallaf adnabod, copïo a chynhyrchu dilyniannau o rifau a phatrymau gweledol.

en-gb	I have demonstrated an understanding of the concepts of equality and inequality within a number equation. 
cy-gb	Rwyf wedi dangos dealltwriaeth o gysyniadau hafaledd ac anhafaledd o fewn hafaliad rhif. 

en-gb	I can use the equals sign to indicate that both sides of a number sentence have the same value and I can use inequality signs when comparing quantities.
cy-gb	Gallaf ddefnyddio’r arwydd hafal i ddangos bod gan ddwy ochr brawddeg rhif yr un gwerthâ’i gilydd, a gallaf ddefnyddio arwyddion anhafaleddau wrth gymharu meintiau.

en-gb	I have explored commutativity with addition and multiplication and I can recognise when two different numerical expressions describe the same situation but are written in different ways.
cy-gb	Rwyf wedi archwilio cymuded mewn perthynas ag adio a lluosi, a gallaf adnabod pan fydd dau fynegiad rhifyddol gwahanol yn disgriﬁo’r un sefyllfa ond wedi’u hysgrifennu mewn gwahanol ffyrdd.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can recognise equalities, inequalities and equivalence of expressions, and also when commutativity, distributivity and associativity can be used to state a simple expression in a different way.
cy-gb	Gallaf adnabod hafaleddau, anhafaleddau a chywerthedd mynegiadau, a hefyd achosion lle y gellir defnyddio cymuded, dosbarthed a chysylltedd i ddatgan mynegiad syml mewn ffordd wahanol.

en-gb	I have explored patterns of numbers and shapes, using digital and non-digital methods. 
cy-gb	Rwyf wedi archwilio patrymau rhifau a siapiau, gan ddefnyddio dulliau digidol a dulliau nad ydynt yn ddigidol. 

en-gb	I can interpret, explain in words and generalise numerical sequences and spatial patterns.
cy-gb	Gallaf ddehongli, egluro mewn geiriau a chyffredinoli dilyniannau rhifyddol a phatrymau gofodol.

en-gb	I can create equations to model problems, using symbols or words to represent unknown values. 
cy-gb	Gallaf greu hafaliadau i fodelu problemau, gan ddefnyddio symbolau neu eiriau i gynrychioli gwerthoedd anhysbys. 

en-gb	I can use inverse operations to ﬁnd unknown values in simple equations using mental, written and digital methods, and manipulatives. 
cy-gb	Gallaf ddefnyddio gweithrediadau gwrthdro er mwyn dod o hyd i werthoedd anhysbys mewn hafaliadau syml, gan ddefnyddio dulliau meddyliol, ysgrifenedig a digidol, a thrinolion. 

en-gb	I can check my answers.
cy-gb	Gallaf wirio fy atebion.

en-gb	I have demonstrated an understanding of the idea of input, application of a rule (including inverse operations) and output, using a function machine or other appropriate methods.
cy-gb	Rwyf wedi dangos dealltwriaeth o’r syniad o fewnbwn, cymhwyso rheol (gan gynnwys gwrthdro) ac allbwn, gan ddefnyddio peiriant ffwythiant neu ddulliau priodol eraill.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have demonstrated an understanding of the concept of a variable and I have used letters to represent variables in forming linear algebraic expressions.
cy-gb	Rwyf wedi dangos dealltwriaeth o’r cysyniad o newidyn ac rwyf wedi defnyddio llythrennau i gynrychioli newidynnau wrth ffurﬁo mynegiadau algebraidd llinol.

en-gb	I can manipulate algebraic expressions ﬂuently by simplifying, expanding and factorising by extracting a common factor. 
cy-gb	Gallaf drin mynegiadau algebraidd yn rhugl drwy symleiddio, ehangu, a ffactorio drwy echdynnu ffactor cyffredin. 

en-gb	I can also substitute values and change the subject of a formula when the subject appears in one term.
cy-gb	Gallaf hefyd amnewid gwerthoedd a newid testun fformiwla pan fydd y testun yn ymddangos mewn un term.

en-gb	I can distinguish between algebraic expressions, equations and inequalities. 
cy-gb	Gallaf wahaniaethu rhwng mynegiadau algebraidd, hafaliadau ac anhafaleddau. 

en-gb	I have used a variety of methods, including trial and improvement where appropriate, to solve equations and inequalities in the ﬁrst degree, which may include brackets and unknowns on one or both sides. 
cy-gb	Rwyf wedi defnyddio amrywiaeth o ddulliau, gan gynnwys cynnig a gwella lle y bo’n briodol, er mwyn datrys hafaliadau ac anhafaleddau unradd, a’r rheini’n gallu cynnwys cromfachau ac anhysbysion ar un ochr neu ar y ddwy ochr. 

en-gb	I can check my answers using substitution.
cy-gb	Gallaf wirio fy atebion drwy ddefnyddio dulliau amnewid.

en-gb	I have used equations and inequalities in the ﬁrst degree to represent and model real-life situations and solve problems. 
cy-gb	Rwyf wedi defnyddio hafaliadau ac anhafaleddau unradd i gynrychioli a modelu sefyllfaoedd go iawn ac i ddatrys problemau. 

en-gb	I can interpret my answers and check that they make sense in context.
cy-gb	Gallaf ddehongli fy atebion a gwirio eu bod yn gwneud synnwyr yn eu cyd-destun.

en-gb	I can recognise linear sequences and can generalise them using algebra. 
cy-gb	Gallaf adnabod dilyniannau llinol a gallaf eu cyffredinoli gan ddefnyddio algebra. 

en-gb	I can ﬁnd, describe and use the n th term. 
cy-gb	Gallaf ddod o hyd i’r n fed term, ei ddisgriﬁo a’i ddefnyddio. 

en-gb	I can describe and use the term-to-term rule for simple iterative sequences. 
cy-gb	Gallaf ddisgriﬁo a defnyddio’r rheol term i derm ar gyfer dilyniannau iterus syml. 

en-gb	I can apply my knowledge of sequences to solve real-life and mathematical problems.
cy-gb	Gallaf gymhwyso’r hyn rwy’n ei wybod am ddilyniannau i ddatrys problemau go iawn a phroblemau mathemategol.

en-gb	I can recognise, draw, sketch and interpret linear graphs, and investigate graphs, using written and digital methods. 
cy-gb	Gallaf adnabod, lluniadu, braslunio a dehongli grafﬁau llinol, ac ymchwilio i grafﬁau, gan ddefnyddio dulliau ysgrifenedig a digidol. 

en-gb	I can demonstrate an understanding of each of the terms in the equation of a straight line. 
cy-gb	Gallaf ddangos dealltwriaeth o bob un o’r termau yn yr hafaliad ar gyfer llinell syth. 

en-gb	I can explore the effect on the line when the constant or coefﬁcient is changed.
cy-gb	Gallaf archwilio effaith newid y cysonyn neu’r cyfernod ar y llinell.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can ﬂuently manipulate algebraic expressions by expanding double brackets, factorising quadratic expressions and changing the subject of a formula where the subject appears in more than one term. 
cy-gb	Gallaf drin mynegiadau algebraidd yn rhwydd drwy ehangu cromfachau dwbl, ffactorio mynegiadau cwadratig a newid testun fformiwla pan fydd y testun yn ymddangos mewn mwy nag un term. 

en-gb	I can simplify and manipulate algebraic fractions.
cy-gb	Gallaf symleiddio a thrin ffracsiynau algebraidd.

en-gb	I can solve a range of linear and higher-order equations, and inequalities, including simultaneous, quadratic and trigonometric equations, using numerical, graphical and algebraic methods where appropriate. 
cy-gb	Gallaf ddatrys amrywiaeth o hafaliadau llinol, hafaliadau trefn uwch ac anhafaleddau, yn cynnwys hafaliadau cydamserol, cwadratig a thrigonometrig, gan ddefnyddio dulliau rhifyddol, grafﬁgol ac algebraidd lle y bo’n briodol. 

en-gb	I can then interpret the meaning of the answer, or answers, checking for reasonableness.
cy-gb	Gallaf wedyn ddehongli ystyr yr ateb, neu’r atebion, gan eu gwirio er mwyn sicrhau eu bod yn rhesymol.

en-gb	I have used equations and inequalities, and relevant graphs, to model and solve problems in real-life and mathematical contexts, including those which describe proportion and exponentiation, and I can use my knowledge of the real world and number sense to predict and check my interpretations of these.
cy-gb	Rwyf wedi defnyddio hafaliadau ac anhafaleddau, a grafﬁau perthnasol, i fodelu a datrys problemau mewn cyd-destunau go iawn a chyd-destunau mathemategol, gan gynnwys y rheini sy’n disgriﬁo cyfrannedd a thwf esbonyddol, a gallaf ddefnyddio’r hyn rwy’n ei wybod am y byd go iawn a’m synnwyr rhifau i ragfynegi a gwirio fy nehongliadau ohonynt.

en-gb	I can recognise and generalise simple non-linear sequences using algebra.
cy-gb	Gallaf adnabod a chyffredinoli dilyniannau aﬂinol syml gan ddefnyddio algebra.

en-gb	I can understand the concept of an identity and can translate statements describing mathematical relationships into algebraic models, using expressions and equations.
cy-gb	Gallaf ddeall y cysyniad o unfathiant a gallaf drosi datganiadau sy’n disgriﬁo perthnasau mathemategol yn fodelau algebraidd, gan ddefnyddio mynegiadau a hafaliadau.

en-gb	I have investigated a variety of non-linear graphs (including quadratic, cubic and reciprocals), using written and digital methods. 
cy-gb	Rwyf wedi ymchwilio i amrywiaeth o grafﬁau aﬂinol (gan gynnwys cwadratig, ciwbig a chilyddiol), gan ddefnyddio dulliau ysgrifenedig a digidol. 

en-gb	I can demonstrate an understanding of the effect of the coefﬁcients, indices and constants on the shape of the graph. 
cy-gb	Gallaf ddangos dealltwriaeth o effaith y cyfernodau, yr indecsau a’r cysonion ar siâp y graff. 

en-gb	I can determine the gradient at a point and the area under a graph, and understand what these represent. 
cy-gb	Gallaf ddarganfod graddiant ar bwynt a’r arwynebedd o dan graff, a deall beth y maent yn ei gynrychioli. 

en-gb	I can use graphs to solve problems.
cy-gb	Gallaf ddefnyddio grafﬁau i ddatrys problemau.

en-gb	Planning for learning
cy-gb	Cynllunio ar gyfer dysgu

en-gb	Links within this area of learning and experience
cy-gb	Cysylltiadau o fewn y maes dysgu a phroﬁad hwn

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across the Mathematics and Numeracy Area of Learning and Experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws Maes Dysgu a Phroﬁad Mathemateg a Rhifedd. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	The number system is used to represent and compare relationships between numbers and quantities.
cy-gb	Defnyddir y system rhifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau.

en-gb	• The connections between arithmetic and algebra develop tools and skills for abstract reasoning from an early age.
cy-gb	• Mae’r cysylltiadau rhwng rhifyddeg ac algebra yn datblygu adnoddau a sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.

en-gb	• There is a strong relationship between the algorithms of arithmetic and the laws of algebra. 
cy-gb	• Mae perthynas gref rhwng algorithmau rhifyddeg a deddfau algebra. 

en-gb	• The order of operations and laws of arithmetic are followed in algebra.
cy-gb	• Dilynir trefn gweithrediadau a deddfau rhifyddeg mewn algebra.

en-gb	Geometry focuses on relationships involving properties of shape, space, and position, and measurement focuses on quantifying phenomena in the physical world.
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	• Algebra and geometry are connected principally through the expression of shape, measure and movement through algebraic expressions, equations and formulae.
cy-gb	• Mae algebra a geometreg yn gysylltiedig â’i gilydd yn bennaf drwy fynegi siapiau, mesur a symudiad drwy fynegiadau, hafaliadau a fformiwlâu algebraidd.

en-gb	• An equation is an algebraic concept, which, when graphed, becomes a geometric concept. 
cy-gb	• Cysyniad algebraidd yw hafaliad, sydd o’i droi’n graff, yn dod yn gysyniad geometrig. 

en-gb	The variables within the equation refer to geometric concepts.
cy-gb	Mae’r newidynnau yn yr hafaliad yn cyfeirio at gysyniadau geometrig.

en-gb	• Co-ordinates, geometrically represented on the Cartesian plane, are deﬁned by algebraic functions.
cy-gb	• Difﬁnnir cyfesurynnau, a gynrychiolir yn geometrig ar y plân Cartesaidd drwy ffwythiannau algebraidd.

en-gb	• Functions and mappings in algebra can be used to describe transformations.
cy-gb	• Gellir defnyddio ffwythiannau a mapio mewn algebra i ddisgriﬁo trawsffurﬁadau.

en-gb	• Algebraic formulae and equations are used to connect the geometric concepts of triangles with measures of angles and sides.
cy-gb	• Defnyddir fformiwlâu a hafaliadau algebraidd i gysylltu cysyniadau geometrig trionglau â mesuriadau onglau ac ochrau.

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions.
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus.

en-gb	• Algebra is used within probability and statistics to express generalities and develop formulae.
cy-gb	• Defnyddir algebra ym maes tebygolrwydd ac ystadegau i fynegi cyffredinolrwydd a datblygu fformiwlâu.

en-gb	• In probability, algebra allows us to use the concept of a variable and we can apply this in probability by using a random variable; this is a parameter or event with a random outcome.
cy-gb	• Mewn tebygolrwydd, mae algebra yn rhoi cyﬂe i ni ddefnyddio cysyniad newidyn a gallwn  gymhwyso hwn mewn tebygolrwydd drwy ddefnyddio hapnewidyn, sef paramedr neu ddigwyddiad ac iddo hapganlyniad.

en-gb	• In statistics, general formulae are written using algebra.
cy-gb	• Mewn ystadegau, caiff fformiwlâu cyffredinol eu hysgrifennu drwy ddefnyddio algebra.

en-gb	• Algebra and statistical analysis are interlinked; 
cy-gb	• Mae algebra a dadansoddiad ystadegol yn gydgysylltiedig; 

en-gb	use of algorithms and formulae to calculate further statistical measures to analyse data.
cy-gb	defnyddio algorithmau a fformiwlâu i gyfrifo mesurau ystadegol pellach i ddadansoddi data.

en-gb	Links with other areas of learning and experience
cy-gb	Cysylltiadau â meysydd dysgu a phroﬁad eraill

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across all the areas of learning and experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws yr holl feysydd dysgu a phroﬁad. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	Expressive Arts
cy-gb	Celfyddydau Mynegiannol

en-gb	• Sequences and patterns.
cy-gb	• Dilyniannau a phatrymau.

en-gb	Science and Technology 
cy-gb	Gwyddoniaeth a Thechnoleg

en-gb	 • Concept of the variable. 
cy-gb	• Cysyniad y newidyn.

en-gb	• Equations and formulae. 
cy-gb	• Hafaliadau a fformiwlâu. 

en-gb	• Direct and inverse proportion. 
cy-gb	• Cyfrannedd union a gwrthdro. 

en-gb	• Patterns and graphs.
cy-gb	• Patrymau a grafﬁau.

en-gb	Experiences, knowledge and skills
cy-gb	Proﬁadau, gwybodaeth a sgiliau

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• explore, copy, repeat, continue and generate a range of simple patterns and sequences using a multisensory approach
cy-gb	• archwilio, copïo, ailadrodd a llunio amrywiaeth o batrymau a dilyniannau syml a pharhau â nhw gan ddefnyddio dull amlsynhwyraidd

en-gb	• start to predict what will come next, through shared stories, pictures and rhymes that have a pattern element
cy-gb	• dechrau rhagfynegi beth fydd yn dod nesaf, drwy rannu straeon, lluniau a rhigymau ag elfen o batrwm ynddynt

en-gb	• through active experience, demonstrate an understanding of equality and inequality, and how these can be preserved when numbers are changed, using the language of comparison and equality.
cy-gb	• drwy broﬁad gweithredol, dangos dealltwriaeth o hafaledd ac anhafaledd, ac o sut y gellir eu gwarchod pan gaiff rhifau eu newid, gan ddefnyddio iaith cymharu a hafaledd.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• express and use, through experiential learning, general laws and rules of arithmetic
cy-gb	• drwy ddysgu drwy broﬁad, fynegi a defnyddio deddfau a rheolau cyffredinol rhifyddeg 

en-gb	 • explore and describe sequences of whole numbers with a common difference between terms
cy-gb	• archwilio a disgriﬁo dilyniannau o rifau cyfan sydd â gwahaniaeth cyffredin rhwng y termau 

en-gb	 • ﬁnd missing terms and continue sequences
cy-gb	• dod o hyd i dermau coll a pharhau â dilyniannau

en-gb	• understand that Robert Recorde’s equals sign is placed between two or more expressions that have the same value
cy-gb	• deall bod arwydd hafal Robert Recorde yn cael ei osod rhwng dau neu fwy o fynegiadau sydd â’r un gwerth â’i gilydd

en-gb	• recognise commutativity of addition and multiplication, using objects, diagrams and numbers 
cy-gb	• adnabod cymuded adio a lluosi, gan ddefnyddio gwrthrychau, diagramau a rhifau 

en-gb	• reason logically, using equality and the laws of arithmetic.
cy-gb	• rhesymu mewn ffordd resymegol gan ddefnyddio hafaledd a deddfau rhifyddeg.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences, describe relations which depend on equality, equivalence and the commutative, associative and distributive laws
cy-gb	• drwy amrywiaeth eang o broﬁadau, ddisgriﬁo perthnasau sy’n dibynnu ar hafaledd, cywerthedd a’r deddfau cymudol, cysylltiol a dosbarthol

en-gb	• describe and generate, in words, visual patterns and numerical sequences
cy-gb	• disgriﬁo a llunio, mewn geiriau, patrymau gweledol a dilyniannau rhifyddol

en-gb	• model simple problem situations, using words and symbols to create equations from which they can ﬁnd an unknown value
cy-gb	• modelu sefyllfaoedd sy’n cynnwys problemau syml gan ddefnyddio geiriau a symbolau er mwyn creu hafaliadau y gallant eu defnyddio i ddod o hyd i werth anhysbys

en-gb	• understand that a function can transform a set of numbers to a new set of numbers, according to a rule
cy-gb	• deall y gall ffwythiant drawsnewid set o rifau i set newydd o rifau yn unol â rheol

en-gb	• move between concrete, visual and abstract representations throughout their mathematical work.
cy-gb	• symud rhwng cynrychioliadau diriaethol, gweledol a haniaethol drwy gydol eu gwaith mathemategol.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences, appreciate the power of mathematics to express relationships concisely and in forms that are universally understood
cy-gb	• drwy amrywiaeth eang o broﬁadau, werthfawrogi pŵer mathemateg i fynegi perthnasau mewn ffordd gryno ac mewn ffurﬁau a gaiff eu deall yn gyffredinol

en-gb	• express the laws of arithmetic using algebraic notation, developing their conceptual understanding of a variable
cy-gb	• mynegi deddfau rhifyddeg, gan ddefnyddio nodiant algebraidd a chan feithrin eu dealltwriaeth gysyniadol o newidyn

en-gb	• explore, generate, identify and represent linear patterns in a variety of contexts
cy-gb	• archwilio, llunio, adnabod a chynrychioli patrymau llinol mewn amrywiaeth o gyd-destunau

en-gb	• model real-life situations, using equations and inequalities to solve problems, checking the reasonableness of their solutions
cy-gb	• modelu sefyllfaoedd go iawn, gan ddefnyddio hafaliadau ac anhafaleddau i ddatrys problemau, a chan ystyried rhesymolrwydd eu hatebion

en-gb	• explore equations graphically, using digital technologies
cy-gb	• archwilio hafaliadau ar ffurf grafﬁau, gan ddefnyddio technolegau digidol 

en-gb	 • explore numerical and physical sequences, using written and digital methods 
cy-gb	• archwilio dilyniannau rhifyddol a fﬁsegol, gan ddefnyddio dulliau ysgrifenedig a digidol 

en-gb	• investigate linear graphs in realistic situations.
cy-gb	• ymchwilio i grafﬁau llinol mewn sefyllfaoedd realistig.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences, create multiple representations of a mathematical concept
cy-gb	• drwy amrywiaeth eang o broﬁadau, greu sawl cynrychioliad o gysyniad mathemategol

en-gb	• explore connections between equations and expressions with geometric, numerical and graphical representations, and understand their equivalence
cy-gb	• archwilio’r cysylltiadau rhwng hafaliadau a mynegiadau sydd â chynrychioliadau geometrig,rhifyddol a grafﬁgol, ac yn deall eu cywerthedd

en-gb	• explore, generate and identify non-linear patterns, and express them algebraically and graphically
cy-gb	• archwilio, llunio ac adnabod patrymau aﬂinol, ac yn eu mynegi ar ffurf algebraidd a grafﬁgol

en-gb	• develop and apply their knowledge of a range of methods such as factorisation, simpliﬁcation and inverse functions to change the subject of formulae involving two or more variables
cy-gb	• datblygu a chymhwyso’r hyn y maent yn ei wybod am amrywiaeth o ddulliau, megis ffactorio, symleiddio a ffwythiannau gwrthdro, er mwyn newid testun fformiwlâu sy’n cynnwys dau newidyn neu fwy

en-gb	• model real-life situations, identifying variables and constructing polynomials.
cy-gb	• modelu sefyllfaoedd go iawn gan adnabod y newidynnau a llunio polynomialau.

en-gb	What Matters in Mathematics and Numeracy Draft Curriculum for Wales 2022: 
cy-gb	Geirfa Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 37
cy-gb	Mathemateg a Rhifedd 38

en-gb	WHAT MATTERS IN MATHEMATICS AND NUMERACY
cy-gb	YR HYN SY’N BWYSIG MEWN MATHEMATEG A RHIFEDD

en-gb	Geometry focuses on relationships involving properties of shape, space and position, and measurement focuses on quantifying phenomena in the physical world.
cy-gb	Mae geometreg yn canolbwyntio ar berthnasausy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	Geometry involves playing with, manipulating, comparing, naming and classifying shapes and structures. 
cy-gb	Mae geometreg yn ymwneud â chwarae â siapiau a strwythurau, eu trin, eu cymharu, eu henwi a’u dosbarthu. 

en-gb	The study of geometry encourages the development and use of conjecture, deductive reasoning and proof. 
cy-gb	Mae astudio geometreg yn annog dysgwyr i ddatblygu a defnyddio dulliau dyfalu, rhesymu diddwythol a phrawf. 

en-gb	Measurement allows the magnitude of spatial and abstract features to be quantiﬁed, using a variety of standard and non-standard units, and can support the development of numerical reasoning.
cy-gb	Mae mesur yn golygu y gellir meintioli graddau nodweddion gofodol a haniaethol, gan ddefnyddio amrywiaeth o unedau safonol ac ansafonol, a gall ategu’r broses o ddatblygu dulliau rhesymu rhifyddol.

en-gb	Reasoning about the sizes and properties of shapes and their surrounding spaces helps us to make sense of the physical world and the world of mathematical shapes. 
cy-gb	Mae rhesymu ynghylch meintiau a phriodweddau siapiau a’r gofod o’u hamgylch yn cynnig modd i ni wneud synnwyr o’r byd fﬁsegol a byd siapiau mathemategol. 

en-gb	Geometry and measurement have applications in many ﬁelds, including art, construction, science and technology, engineering, and astronomy.
cy-gb	Gellir cymhwyso geometreg a mesur mewn sawl maes, gan gynnwys celf, adeiladu, gwyddoniaeth a thechnoleg, peirianneg, a seryddiaeth.

en-gb	Learning
cy-gb	Dysgu

en-gb	Principles of progression
cy-gb	Egwyddorion cynnydd

en-gb	Principles of progression are the basis on which the achievement outcomes have been developed and should guide the progression of learning within the area of learning and experience.
cy-gb	Egwyddorion cynnydd yw’r sail ar gyfer datblygu’r deilliannau cyﬂawniad a dylent lywio dilyniant y dysgu o fewn y maes dysgu a phroﬁad.

en-gb	The following interdependent proﬁciencies 8 have been used to formulate the achievement outcomes and are central to progression at each stage of mathematics learning.
cy-gb	Defnyddiwyd y hyfedreddau cyd-ddibynnol canlynol 8 wrth greu’r deilliannau cyﬂawniad ac maent  yn greiddiol i gynnydd yn ystod pob cam o ddysgu mathemategol.

en-gb	Numeracy involves applying and connecting these proﬁciencies in a range of real-life contexts,across and beyond the curriculum.
cy-gb	Mae rhifedd yn golygu cymhwyso a chysylltu’r hyfedreddau hyn mewn amrywiaeth o gyd-destunau go iawn, ym mhob rhan o’r cwricwlwm a’r tu hwnt iddo.

en-gb	Conceptual understanding: 
cy-gb	Dealltwriaeth gysyniadol: 

en-gb	Mathematical concepts and ideas should be dwelt on, built on, and connected together as learners experience increasingly complex mathematical ideas. 
cy-gb	Dylid myfyrio ar syniadau a chysyniadau mathemategol, ynghyd â’u datblygu a’u cysylltu â’i gilydd, wrth i ddysgwyr gael proﬁad o syniadau mathemategol cynyddol gymhleth. 

en-gb	Learners demonstrate conceptual understanding by explaining and expressing concepts, ﬁnding examples (or non-examples) and by representing a concept in a variety of ways, including verbal, concrete, visual, digital and abstract representations.
cy-gb	Mae dysgwyr yn dangos dealltwriaeth gysyniadol drwy egluro a mynegi cysyniadau, dod o hyd i enghreifftiau (neu anenghreifftiau) a thrwy gynrychioli cysyniad mewn gwahanol ffyrdd, gan gynnwys cynrychioliadau llafar, diriaethol, gweledol, digidol a haniaethol.

en-gb	Communication with symbols: 
cy-gb	Cyfathrebu â symbolau: 

en-gb	Learners should understand that the symbols they are using are abstract representations and should develop greater ﬂexibility in their application and manipulation of an increasing range of symbols, understanding the conventions of the symbols they are using.
cy-gb	Dylai dysgwyr ddeall bod y symbolau y maent yn eu defnyddio yn gynrychioliadau haniaethol a dylent ddatblygu mwy o hyblygrwydd wrth iddynt gymhwyso a defnyddio amrywiaeth gynyddol o symbolau, gan ddeall confensiynau’r symbolau y maent yn eu defnyddio.

en-gb	Strategic competence: 
cy-gb	Cymhwysedd strategol: 

en-gb	(i.e. formulating problems mathematically in order to solve them) Learners should become increasingly independent in recognising and applying the underlying mathematical structures and ideas within a problem, in order to be able to solve them.
cy-gb	(h.y. gosod problemau allan mewn ar ffurf fathemategol er mwyn eu datrys) Dylai dysgwyr ddod yn gynyddol annibynnol wrth adnabod a chymhwyso’r strwythuraua’r syniadau mathemategol sydd wrth wraidd problem, er mwyn gallu ei datrys.

en-gb	Logical reasoning: 
cy-gb	Rhesymu rhesymegol: 

en-gb	As learners experience increasingly complex concepts, they should also develop an understanding of the relationships between and within these concepts. 
cy-gb	Wrth i ddysgwyr broﬁ cysyniadau cynyddol gymhleth, dylent hefyd feithrin dealltwriaeth o’r berthynas rhwng y cysyniadau hyn ac o fewn y cysyniadau hyn. 

en-gb	They should apply logical reasoning about these relationships and be able to justify and prove them. Justiﬁcations and proof should become increasingly abstract, moving from verbal, visual or concrete explanations to representations involving symbols and conventions.
cy-gb	Dylent gymhwyso dulliau rhesymu rhesymegol wrth ymdrin â’r perthnasau hyn a gallu eu cyﬁawnhau a’u proﬁ.Dylai’r cyﬁawnhad a’r dystiolaeth ddod yn gynyddol haniaethol, gan symud o esboniadau llafar, gweledol neu ddiriaethol i gynrychioliadau haniaethol sy’n cynnwys symbolau a chonfensiynau.

en-gb	Fluency: 
cy-gb	Rhuglder: 

en-gb	As learners experience, understand and apply increasingly complex concepts and relationships, ﬂuency in remembering facts, relationships and techniques should grow. 
cy-gb	Wrth i ddysgwyr broﬁ, deall a chymhwyso cysyniadau a pherthnasau sy’n gynyddol fwy cymhleth, dylai eu rhuglder wrth goﬁo ffeithiau, perthnasau a thechnegau wella. 

en-gb	As a result, facts, relationships and techniques learned previously should become ﬁrmly established, memorable and usable.
cy-gb	O ganlyniad, dylai ffeithiau, perthnasau a thechnegau a ddysgwyd ynghynt fod wedi’u hymsefydlu’n gadarn, yn goﬁadwy ac yn ddefnyddiadwy.

en-gb	8 Based on Adding It Up: 
cy-gb	8 Yn seiliedig ar Adding It Up: 

en-gb	Helping Children Learn Mathematics by Kilpatrick, Swafford and Findel (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics gan Kilpatrick, Swafford a Findel (National Research Council, 2001)

en-gb	and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
cy-gb	ac wedi’u haddasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen, 2018.

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can understand and apply the language of time in relation to my daily life and in relation to events that happen around me, including naming the days of the week, the months of the year and the seasons, all in meaningful contexts.
cy-gb	Gallaf ddeall a chymhwyso iaith amser mewn perthynas â’m bywyd beunyddiol ac mewn perthynas â digwyddiadau sy’n digwydd o’m cwmpas, gan gynnwys enwi dyddiau’r wythnos, misoedd y ﬂwyddyn a’r tymhorau, a’r cyfan mewn cyd-destunau ystyrlon.

en-gb	I have used a variety of objects to measure lengths, masses and capacities, and I can understand the need to repeat the same physical unit without any gaps when measuring.
cy-gb	Rwyf wedi defnyddio amrywiaeth o wrthrychau i fesur hydoedd, masau a chynwyseddau, ac, wrth fesur, gallaf ddeall yr angen i ailadrodd yr un gwrthrych (uned) heb unrhyw fylchau.

en-gb	I can make estimates and comparisons with measures. 
cy-gb	Gallaf amcangyfrif a chymharu â mesurau. 

en-gb	I can use language and non-standard units to discuss my sense of size.
cy-gb	Gallaf ddefnyddio iaith ac unedau ansafonol i drafod fy ymdeimlad o faint.

en-gb	I have explored shapes through investigative play, and I can categorise and sort shapes using their properties. 
cy-gb	Rwyf wedi archwilio siapiau drwy chwarae ymchwiliol, a gallaf gategoreiddio a didoli siapiau gan ddefnyddio eu priodweddau. 

en-gb	I can use the language of shapes to describe objects.
cy-gb	Gallaf ddefnyddio iaith siapiau i ddisgriﬁo gwrthrychau.

en-gb	I have explored movements and directions, both physically and by using digital technology, and I can use mathematical language to describe position.
cy-gb	Rwyf wedi archwilio symudiadau a chyfeiriadau, drwy ddull fﬁsegol a chan ddefnyddio technoleg ddigidol, a gallaf ddefnyddio iaith fathemategol i ddisgriﬁo saﬂe.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can tell the time on an analogue clock (in at least 15-minute intervals) and I can connect this to time displayed digitally. 
cy-gb	Gallaf ddweud yr amser ar gloc analog (mewn cyfnodau o 15 munud, o leiaf) a gallaf gysylltu hyn â’r amser ar ffurf ddigidol. 

en-gb	I have explored and used different ways of showing the passing of time, including calendars, timelines, simple timetables and schedules.
cy-gb	Rwyf wedi archwilio ac wedi defnyddio gwahanol ffyrdd o ddangos treigl amser, gan gynnwys calendrau, llinellau amser, amserlenni syml a rhestrau digwyddiadau.

en-gb	I have estimated and measured length, volume, capacity, mass, temperature and time in practical situations, using non-standard units.
cy-gb	Rwyf wedi amcangyfrif ac wedi mesur hyd, cyfaint, cynhwysedd, màs, tymheredd ac amser mewn sefyllfaoedd ymarferol, gan ddefnyddio unedau ansafonol.

en-gb	I have used a variety of measuring devices from different starting points.
cy-gb	Rwyf wedi cael proﬁad o ddefnyddio amrywiaeth o ddyfeisiau mesur o fannau cychwyn gwahanol.

en-gb	I can apply standard units in practical situations to measure length, volume, capacity, mass, temperature and time accurately.
cy-gb	Gallaf gymhwyso unedau safonol mewn sefyllfaoedd ymarferol i fesur hyd, cyfaint, cynhwysedd, màs, tymheredd ac amser yn gywir.

en-gb	I have explored and named two-dimensional and three-dimensional shapes in a range of contexts. 
cy-gb	Rwyf wedi archwilio ac wedi enwi siapiau dau ddimensiwn a tri dimensiwn mewn amrywiaeth o gyd-destunau. 

en-gb	I can sort and categorise regular and irregular two-dimensional shapes in different ways, according to their properties. 
cy-gb	Gallaf ddidoli a chategoreiddio siapiau dau ddimensiwn rheolaidd ac afreolaidd mewn gwahanol ffyrdd yn ôl eu priodweddau. 

en-gb	I can sketch two-dimensional shapes and make models of three-dimensional objects.
cy-gb	Gallaf fraslunio siapiau dau ddimensiwn ac yn gwneud modelau o wrthrychau tri dimensiwn.

en-gb	I can identify reﬂective symmetry in a range of contexts and can identify symmetry in two-dimensional shapes.
cy-gb	Gallaf adnabod cymesuredd adlewyrchol mewn amrywiaeth o gyd-destunau a gallaf adnabod cymesuredd mewn siapiau dau ddimensiwn.

en-gb	I have explored the concept of rotation, both physically and using digital technology, and can use simple fractions of a complete rotation to describe turns.
cy-gb	Rwyf wedi archwilio’r cysyniad o gylchdroi, drwy ddull fﬁsegol a chan ddefnyddio technoleg ddigidol, a gallaf ddefnyddio ffracsiynau syml mewn perthynas â chylchdro cyﬂawn i ddisgriﬁo troeon.

en-gb	I have described and quantiﬁed the position of objects relative to other objects through active learning experiences, using appropriate language, including the words ‘left’ and ‘right’.
cy-gb	Rwyf wedi disgriﬁo ac wedi meintioli saﬂe gwrthrychau mewn perthynas â gwrthrychau eraill drwy broﬁadau dysgu gweithredol, gan ddefnyddio iaith briodol, gan gynnwys y geiriau ‘chwith’ a ‘dde’.

en-gb	I can follow and create instructions related to movement, using a range of approaches and resources (including digital technologies) to demonstrate my understanding.
cy-gb	Gallaf ddilyn a llunio cyfarwyddiadau sy’n ymwneud â symudiad gan ddefnyddio amrywiaeth o ddulliau ac adnoddau (gan gynnwys technolegau digidol) er mwyn dangos fy nealltwriaeth.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can read analogue and digital clocks accurately and I can make calculations involving the passing of time. 
cy-gb	Gallaf ddarllen clociau analog a digidol yn gywir a gallaf wneud cyfriﬁadau sy’n gysylltiedig â threigl amser. 

en-gb	I have used timetables and schedules to make calculations involving time.
cy-gb	Rwyf wedi defnyddio amserlenni a rhestrau digwyddiadau i wneud cyfriﬁadau sy’n gysylltiedig ag amser.

en-gb	I have estimated and measured length, capacity, mass, temperature and time, using appropriate standard units.
cy-gb	Rwyf wedi amcangyfrif ac wedi mesur hyd, cynhwysedd, màs, tymheredd ac amser, gan ddefnyddio unedau safonol priodol.

en-gb	I can convert between metric units in mathematical and real-life problem-solving contexts, and I can check my answers to make sure they make sense.
cy-gb	Gallaf drosi rhwng unedau metrig mewn cyd-destunau datrys problemau mathemategol a rhai bywyd go iawn, a gallaf wirio fy atebion er mwyn sicrhau eu bod yn gwneud synnwyr.

en-gb	I have explored properties of two-dimensional shapes, using concrete, paper-based and digital resources, and I can use mathematical language to describe and compare the properties (including number of sides and symmetry) of given shapes, and to classify them accordingly. 
cy-gb	Rwyf wedi archwilio priodweddau siapiau dau ddimensiwn gan ddefnyddio adnoddau diriaethol, adnoddau papur ac adnoddau digidol, a gallaf ddefnyddio iaith fathemategol i ddisgriﬁo a chymharu’r priodweddau (gan gynnwys nifer yr ochrau a chymesuredd siapiau penodedig) ac i’w dosbarthu’n briodol. 

en-gb	I can name different types of triangles.
cy-gb	Gallaf enwi gwahanol fathau o drionglau.

en-gb	I have explored vertices, edges and faces of three-dimensional shapes and I can use these characteristics to describe a three-dimensional shape. 
cy-gb	Rwyf wedi archwilio fertigau, ymylon a wynebau siapiau tri dimensiwn a gallaf ddefnyddio’r nodweddion hyn i ddisgriﬁo siâp tri dimensiwn. 

en-gb	I have explored the relationship between a three-dimensional shape and two-dimensional nets, using concrete, paper-based and digital resources, and I can recognise nets of common three-dimensional shapes.
cy-gb	Rwyf wedi archwilio’r berthynas rhwng siâp tri dimensiwn a rhwydi dau ddimensiwn, gan ddefnyddio adnoddau diriaethol, adnoddau papur ac adnoddau digidol, a gallaf adnabod rhwydi siapiau tri dimensiwn cyffredin.

en-gb	I have used a range of hands-on activities to explore the perimeter and area of shapes. 
cy-gb	Rwyf wedi defnyddio amrywiaeth o weithgareddau ymarferol i archwilio perimedr ac arwynebedd siapiau. 

en-gb	I have derived the respective formulae for ﬁnding the area of a rectangle and of a right-angled triangle, and have applied them in mathematical and real-life problem-solving contexts, using estimation to predict and check my answers.
cy-gb	Rwyf wedi deillio’r fformiwlâu priodol yn eu tro ar gyfer dod o hyd i arwynebedd petryal a thriongl ongl sgwâr, ac wedi eu cymhwyso mewn cyd-destunau datrys problemau mathemategol a rhai bywyd go iawn, gan ddefnyddio dulliau amcangyfrif i ragfynegi a gwirio fy atebion.

en-gb	I can demonstrate my understanding of angle as a measure of rotation and I can recognise, name and describe types of angles.
cy-gb	Gallaf ddangos fy mod yn deall onglau fel ffordd o fesur cylchdro, a gallaf adnabod, enwi a disgriﬁo mathau o onglau.

en-gb	I have developed an understanding of why we need co-ordinates and I can use them to locate and plot points in the ﬁrst quadrant of the Cartesian plane. 
cy-gb	Rwyf wedi dod i ddeall pam mae angen cyfesurynnau arnom, a gallaf ddefnyddio cyfesurynnau i leoli a phlotio pwyntiau ym mhedrant cyntaf y plân Cartesaidd. 

en-gb	I can use my knowledge of co-ordinates to solve problems involving shape, length, angle and position in mathematical and real-life contexts.
cy-gb	Gallaf ddefnyddio’r hyn rwy’n ei wybod am gyfesurynnau i ddatrys problemau sy’n ymwneud â siâp, hyd, ongl a saﬂe, a hynny mewn cyd-destunau mathemategol a go iawn.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can represent and use compound measures, using standard units, and I can demonstrate an understanding of the relationship between a formula representing a measurement and the units used.
cy-gb	Gallaf gynrychioli a defnyddio mesurau cyfansawdd, gan ddefnyddio unedau safonol, a dangos dealltwriaeth o’r berthynas rhwng fformiwla sy’n cynrychioli mesuriad a’r unedau a ddefnyddiwyd.

en-gb	I can create and use conversion graphs to solve problems set in local and global contexts.
cy-gb	Gallaf greu a defnyddio grafﬁau trawsnewid er mwyn datrys problemau wedi’u gosod o fewn cyd-destunau lleol a byd-eang.

en-gb	I have explored symmetries and other properties of regular and irregular two-dimensional and three-dimensional shapes. 
cy-gb	Rwyf wedi archwilio cymesuredd a phriodweddau eraill siapiau dau ddimensiwn a thri dimensiwn rheolaidd ac afreolaidd. 

en-gb	I can construct two-dimensional representations of three-dimensional shapes in order to investigate properties further. 
cy-gb	Gallaf lunio cynrychioliadau dau ddimensiwn o siapiau tri dimensiwn er mwyn ymchwilio ymhellach i’w priodweddau. 

en-gb	I can classify two-dimensional and three-dimensional shapes according to their mathematical properties.
cy-gb	Gallaf ddosbarthu siapiau dau ddimensiwn a thri dimensiwn yn ôl eu priodweddau mathemategol.

en-gb	I have explored all four transformations of two-dimensional shapes, using a variety of approaches, including digital technology. 
cy-gb	Rwyf wedi archwilio’r pedwar trawsffurﬁad o ran siapiau dau ddimensiwn, gan ddefnyddio amrywiaeth o ddulliau gweithredu, gan gynnwys technoleg ddigidol. 

en-gb	I can use my understanding to predict and describe how shapes will change under a given transformation.
cy-gb	Gallaf ddefnyddio fy nealltwriaeth i ragfynegi a disgriﬁo sut y bydd siapiau yn newid o dan drawsffurﬁad penodol.

en-gb	I can use co-ordinates to plot points in the four quadrants and deduce the location of additional points.
cy-gb	Gallaf ddefnyddio cyfesurynnau i blotio pwyntiau yn y pedwar pedrant a diddwytho lleoliad pwyntiau ychwanegol.

en-gb	I can use a protractor to measure and draw angles. 
cy-gb	Gallaf ddefnyddio onglydd i fesur a llunio onglau. 

en-gb	I have modelled and solved problems involving bearings. 
cy-gb	Rwyf wedi modelu ac wedi datrys problemausy’n cynnwys cyfeiriannau. 

en-gb	I can use reasoning to calculate the size of angles in triangles and quadrilaterals. 
cy-gb	Gallaf ddefnyddio dulliau rhesymu i gyfrifo maint onglau mewn trionglau a phedrochrau. 

en-gb	I have explored angles formed by parallel lines and by a transversal, and I can use my understanding to calculate angles in these contexts. 
cy-gb	Rwyf wedi archwilio onglau a luniwyd gan linellau paralel ac ardrawslin, a gallaf ddefnyddio fy nealltwriaeth i gyfrifo onglau yn y cyd-destunau hyn.

en-gb	I have calculated the areas or surface areas of two-dimensional and three-dimensional simple and compound shapes, including circles, and have demonstrated an understanding of pi ( π ) as the ratio of the circumference of a circle to its diameter. 
cy-gb	Rwyf wedi cyfrifo arwynebeddau neu arwynebeddau arwyneb siapiau dau ddimensiwn a thri dimensiwn syml a chyfansawdd, gan gynnwys cylchoedd, ac wedi dangos dealltwriaeth o pi ( π ) fel cymhareb cylchedd cylch i’w ddiamedr. 

en-gb	I have derived the formulae for the volume of simple three-dimensional prisms and I can calculate the volumes of three-dimensional shapes to solve problems. 
cy-gb	Rwyf wedi deillio’r fformiwlâu ar gyfer cyfaint prismau tri dimensiwn syml, a gallaf gyfrifo cyfeintiau siapiau tri dimensiwn er mwyn datrys problemau.

en-gb	I have demonstrated an understanding of the relationship between right-angled triangles and squares in the context of Pythagoras’ theorem, and I have used it to solve problems in mathematical and real-life contexts.
cy-gb	Rwyf wedi dangos dealltwriaeth o’r berthynas rhwng trionglau ongl sgwâr a sgwariau yng nghyd-destun theorem Pythagoras, ac rwyf wedi defnyddio’r theorem honno i ddatrys problemau mewn cyd-destunau mathemategol a chyd-destunau go iawn.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can explain why two or more shapes are similar, congruent, or neither. 
cy-gb	Gallaf egluro pam mae dau siâp neu fwy yn gyﬂun, yn gyfath, neu heb fod yn un o’r ddau. 

en-gb	I have used my knowledge of congruency and similarity to solve problems involving angles and lengths, both in mathematical and real-life contexts.
cy-gb	Rwyf wedi defnyddio’r hyn rwy’n ei wybod am gyfathiant a chyﬂunedd i ddatrys problemau sy’n ymwneud ag onglau a hydoedd, a’r rheini wedi’u gosod mewn cyd-destunau mathemategol a rhai bywyd go iawn.

en-gb	I can calculate the perimeter, area or surface area and volume of compound two-dimensional and three-dimensional shapes, and I can rearrange formulae to ﬁnd missing lengths. 
cy-gb	Gallaf gyfrifo perimedr, arwynebedd neu arwynebedd arwyneb a chyfaint siapiau dau ddimensiwn a thri dimensiwn cyfansawdd, a gallaf ail-drefnu fformiwlâu er mwyn dod o hyd i hydoedd coll. 

en-gb	I have demonstrated an understanding of the effect of scale when comparing measurements and shapes in all three dimensions, and I have used my knowledge of scale and ratio to calculate the lengths and areas of fractions of shapes, including arcs and segments of circles.
cy-gb	Rwyf wedi dangos dealltwriaeth o effaith graddfa wrth gymharu mesuriadau a siapiau ym mhob un o’r tri dimensiwn ac rwyf wedi defnyddio’r hyn rwy’n ei wybod am raddfa a chymarebau i gyfrifo hydoedd ac arwynebeddau ffracsiynau o siapiau, gan gynnwys arcau a segmentau o gylchoedd.

en-gb	I have located and described the locus of points deﬁned by a range of different criteria, using
cy-gb	Rwyf wedi lleoli ac wedi disgriﬁo locws pwyntiau a ddifﬁniwyd gan amrywiaeth o wahanol feini

en-gb	digital and non-digital technologies.
cy-gb	prawf, gan ddefnyddio technolegau digidol a thechnolegau nad ydynt yn ddigidol. 

en-gb	I have demonstrated an understanding of trigonometric ratios in right-angled triangles and I have used, in mathematical and real-life contexts, my knowledge of the trigonometric ratios to solve problems involving lengths, angles and area of any triangle.
cy-gb	Rwyf wedi dangos dealltwriaeth o gymarebau trigonometrig mewn trionglau ongl sgwâr ac rwyf wedi defnyddio, mewn cyd-destunau mathemategol a rhai bywyd go iawn, yr hyn rwy’n ei wybod am y cymarebau trigonometrig i ddatrys problemau sy’n cynnwys hydoedd, onglau ac arwynebedd unrhyw driongl.

en-gb	I have used reasoning and logical arguments, along with my knowledge of polygons, intersecting lines, angle and the circle theorems, to solve problems, deduce and calculate angles and lengths in diagrams that involve combinations of these.
cy-gb	Rwyf wedi defnyddio dulliau rhesymu a dadleuon rhesymegol, ynghyd â’r hyn rwy’n ei wybod am bolygonau, llinellau sy’n croestorri, onglau a’r theoremau cylch, i ddatrys problemau, diddwytho a chyfrifo onglau a hydoedd mewn diagramau sy’n cynnwys cyfuniadau o’r elfennau hyn.

en-gb	What Matters in Mathematics and Numeracy Draft Curriculum for Wales 2022: 
cy-gb	Yr Hyn sy’n Bwysig mewn Mathemateg a Rhifedd Draft C w ur r r i i c c w ul w um m f D or ra W fft a i le G s y 2 m 0 r 2 u 2 2 : 

en-gb	Mathematics and Numeracy 42
cy-gb	0 M 2 a 2 t : h M em at a h t e ic m s a a t n e d g n a u R m h e if r e a d c d y 44

en-gb	Planning for learning
cy-gb	Cynllunio ar gyfer dysgu

en-gb	Links within this area of learning and experience
cy-gb	Cysylltiadau o fewn y maes dysgu a phroﬁad hwn

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across the Mathematics and Numeracy Area of Learning and Experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws Maes Dysgu a Phroﬁad Mathemateg a Rhifedd. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	The number system is used to represent and compare relationships between numbers and quantities.
cy-gb	Defnyddir y system rhifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau.

en-gb	• Number is used throughout geometry to quantify shape, size and movement.
cy-gb	• Defnyddir rhifau ym mhob agwedd ar geometreg i fesur siapiau, maint a symudiad.

en-gb	• Measure is an aspect of geometrical thinking which is highly connected to number and much of the development of understanding of number can emerge through increasingly sophisticated measuring.
cy-gb	• Mae mesur yn agwedd ar feddwl geometregol sydd â chysylltiad agos â rhifau a gall cryn dipyn o’r broses o ddatblygu dealltwriaeth o rifau ddod drwy fesur cynyddol sofﬁstigedig.

en-gb	• Geometric thinking involves reasoning with proportion, which connects with development in number work.
cy-gb	• Mae meddwl geometrig yn cynnwys rhesymu â chymesuredd, sy’n cysylltu â datblygiad mewn gwaith rhifau.

en-gb	• Geometry involves lengths, areas and volumes which are expressed as numerical quantities. 
cy-gb	• Mae geometreg yn cynnwys hydoedd, arwynebeddau a chyfeintiau a fynegir fel meintiau rhifyddol.

en-gb	• Use of rules of number to calculate further values related to measurement and geometry.
cy-gb	• Defnyddio rheolau rhifau i gyfrifo gwerthoedd pellach sy’n gysylltiedig â mesur a geometreg.

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations.
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	• Algebra and geometry are connected principally through the expression of shape, measure and movement through algebraic expressions, equations and formulae
cy-gb	• Mae algebra a geometreg yn gysylltiedig â’i gilydd yn bennaf drwy fynegi siapiau, mesur a symudiad drwy fynegiadau, hafaliadau a fformiwlâu algebraidd.

en-gb	• An equation is an algebraic concept, which, when graphed, becomes a geometric concept. 
cy-gb	• Cysyniad algebraidd yw hafaliad, sydd o’i droi’n graff, yn dod yn gysyniad geometrig. 

en-gb	The variables within the equation refer to geometric concepts.
cy-gb	Mae’r newidynnau yn yr hafaliad yn cyfeirio at gysyniadau geometrig.

en-gb	• Co-ordinates, geometrically represented on the Cartesian plane, are deﬁned by algebraic functions.
cy-gb	• Difﬁnnir cyfesurynnau, a gynrychiolir yn geometrig ar y plân Cartesaidd drwy ffwythiannau algebraidd.

en-gb	• Functions and mappings in algebra can be used to describe transformations.
cy-gb	• Gellir defnyddio ffwythiannau a mapio mewn algebra i ddisgriﬁo trawsffurﬁadau.

en-gb	• Algebraic formulae and equations are used to connect the geometric concepts of triangles with measures of angles and sides.
cy-gb	• Defnyddir fformiwlâu a hafaliadau algebraidd i gysylltu cysyniadau geometrig trionglau â mesuriadau onglau ac ochrau.

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions.
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus.

en-gb	• Geometry involves graphical thinking which is central to statistical representations and analysis.
cy-gb	• Mae geometreg yn cynnwys meddwl yn grafﬁgol sy’n ganolog i gynrychioliadau a dadansoddi ystadegol.

en-gb	• Graphs are used to convert from one value to another, and to represent statistical information including spread, quantity and central tendency.
cy-gb	• Defnyddir grafﬁau i drosi o un gwerth i un arall, a chynrychioli gwybodaeth ystadegol, gan gynnwys ymlediad, nifer a chanolduedd.

en-gb	• Graphical techniques are used to make connections between different sets of data. 
cy-gb	• Defnyddir technegau grafﬁgol i greu cysylltiadau rhwng gwahanol setiau o ddata.

en-gb	• Data generated by measure can be analysed using statistics.
cy-gb	• Gall data a gynhyrchir drwy fesur gael eu dadansoddi drwy ddefnyddio ystadegau.

en-gb	What Matters in Mathematics and Numeracy Draft Curriculum for Wales 2022: 
cy-gb	Yr Hyn sy’n Bwysig mewn Mathemateg a Rhifedd Draft C w ur r r i i c c w ul w um m f D or ra W fft a i le G s y 2 m 0 r 2 u 2 2 : 

en-gb	Mathematics and Numeracy 43
cy-gb	0 M 2 a 2 t : h M em at a h t e ic m s a a t n e d g n a u R m h e if r e a d c d y 45

en-gb	Links with other areas of learning and experience
cy-gb	Cysylltiadau â meysydd dysgu a phroﬁad eraill

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across all the areas of learning and experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws yr holl feysydd dysgu a phroﬁad. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	Expressive Arts
cy-gb	Celfyddydau Mynegiannol

en-gb	• Shape symmetry in movement and artwork. 
cy-gb	• Cymesuredd siâp mewn symudiadau a chelfwaith. 

en-gb	• Scale.
cy-gb	• Graddfa.

en-gb	• Use of appropriate equipment to measure accurately.
cy-gb	• Defnyddio offer priodol i fesur yn gywir.

en-gb	Humanities
cy-gb	Dyniaethau

en-gb	• Use of appropriate equipment to measure accurately. 
cy-gb	• Defnyddio offer priodol i fesur yn gywir. 

en-gb	• Scale.
cy-gb	• Graddfa.

en-gb	• Time and chronological ordering.
cy-gb	• Amser a threfn gronolegol.

en-gb	Science and Technology
cy-gb	Gwyddoniaeth a Thechnoleg

en-gb	• Use of appropriate equipment to measure accurately.
cy-gb	• Defnyddio offer priodol i fesur yn gywir.

en-gb	• Units – use of appropriate unit, converting between units, and links between units and formulae. 
cy-gb	• Unedau – defnyddio’r uned briodol, trosi rhwng unedau, a’r cysylltiadau rhwng unedau a fformiwlâu.

en-gb	• Scale.
cy-gb	• Graddfa.

en-gb	Health and Well‑being
cy-gb	Iechyd a Lles

en-gb	• Use of appropriate equipment to measure accurately.
cy-gb	• Defnyddio offer priodol i fesur yn gywir.

en-gb	Languages, Literacy and Communication
cy-gb	Ieithoedd, Llythrennedd a Chyfathrebu

en-gb	• Use of prepositions to describe the location of selves and objects.
cy-gb	• Defnyddio arddodiaid i ddisgriﬁo eu lleoliad nhw eu hunain a lleoliad gwrthrychau.

en-gb	What Matters in Mathematics and Numeracy Draft Curriculum for Wales 2022: 
cy-gb	Yr Hyn sy’n Bwysig mewn Mathemateg a Rhifedd Draft C w ur r r i i c c w ul w um m f D or ra W fft a i le G s y 2 m 0 r 2 u 2 2 : 

en-gb	Mathematics and Numeracy 44
cy-gb	0 M 2 a 2 t : h M em at a h t e ic m s a a t n e d g n a u R m h e if r e a d c d y 46

en-gb	Experiences, knowledge and skills
cy-gb	Proﬁadau, gwybodaeth a sgiliau

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through exploring situations in their everyday life, develop an understanding of measurement, using non-standard units with developing accuracy
cy-gb	• drwy archwilio sefyllfaoedd o fewn eu bywydau pob-dydd, ddatblygu dealltwriaeth o ddulliau mesur, gan ddefnyddio unedau ansafonol gyda chywirdeb cynyddol

en-gb	• through play and discovery, categorise and recognise shapes 
cy-gb	• drwy chwarae a darganfod, gategoreiddio ac adnabod siapiau

en-gb	• use the language of direction, location and position.
cy-gb	• defnyddio iaith cyfeiriad, lleoliad a saﬂe.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through experiential learning and solving problems in real-life and more abstract contexts, develop an understanding of standard measurement and of the properties of shapes
cy-gb	• drwy ddysgu drwy broﬁad a datrys problemau o fewn cyd-destunau bywyd go iawn a rhai mwy haniaethol, ddatblygu dealltwriaeth o fesuriadau safonol ac o briodweddau siapiau

en-gb	• select and use appropriate equipment and units to measure accurately 
cy-gb	• dethol a defnyddio offer ac unedau priodol i fesur yn gywir

en-gb	• describe location, movement and position, using mathematical terminology.
cy-gb	• disgriﬁo lleoliad, symudiad a saﬂe, gan ddefnyddio terminoleg fathemategol.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences and through solving problems in real-life and abstract  contexts, reﬁne their understanding of standard measurement and the relationship between  units of measure
cy-gb	• drwy amrywiaeth eang o broﬁadau a thrwy ddatrys problemau o fewn cyd-destunau bywyd go iawn a rhai haniaethol, ﬁreinio eu dealltwriaeth o fesuriadau safonol a’r berthynas rhwng  unedau mesur

en-gb	• select and use appropriate equipment and units to measure accurately
cy-gb	• dethol a defnyddio offer ac unedau priodol i fesur yn gywir 

en-gb	• reﬁne their understanding of the properties of shapes
cy-gb	• mireinio eu dealltwriaeth o briodweddau siapiau

en-gb	• use the mathematical concepts of angle, co-ordinates and distance to describe location, movement and position.
cy-gb	• defnyddio cysyniadau mathemategol am onglau, cyfesurynnau a phellter i ddisgriﬁo lleoliad,symudiad a saﬂe.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences and through solving problems within real-life and abstract contexts, develop their understanding of standard and compound measurement, the properties of shapes and solids, and location, movement and position
cy-gb	• drwy amrywiaeth eang o broﬁadau a thrwy ddatrys problemau o fewn cyd-destunau bywyd  go iawn a rhai haniaethol, ddatblygu eu dealltwriaeth o fesuriadau safonol a chyfansawdd,  priodweddau siapiau a solidau, a lleoliad, symudiad a saﬂe

en-gb	• select and use appropriate equipment and units to measure accurately
cy-gb	• dethol a defnyddio offer ac unedau priodol i fesur yn gywir

en-gb	 • use digital technologies to explore shape and space, developing and testing conjectures
cy-gb	• defnyddio technolegau digidol i archwilio siâp a gofod, gan ddatblygu a phroﬁ dyfaliadau

en-gb	• use angle and shape facts to deduce further features and relationships
cy-gb	• defnyddio ffeithiau am onglau a siapiau i ddiddwytho nodweddion a pherthnasau pellach

en-gb	• recognise pi ( π ) as the ratio of the circumference of a circle to its diameter and appreciate the signiﬁcance of William Jones’s contribution.
cy-gb	• adnabod pi ( π ) fel cymhareb cylchedd cylch i’w ddiamedr a gwerthfawrogi arwyddocâd cyfraniad William Jones.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences, describe, represent, analyse and explain properties of shapes in two-dimensional and three-dimensional space
cy-gb	• drwy amrywiaeth eang o broﬁadau, ddisgriﬁo, cynrychioli, dadansoddi ac egluro priodweddau siapiau mewn gofod dau ddimensiwn a thri dimensiwn

en-gb	• use digital technologies to explore shape and space, movement and position, developing and testing conjectures
cy-gb	• defnyddio technolegau digidol i archwilio siâp a gofod, symudiad a saﬂe, gan ddatblygu a phroﬁ dyfaliadau

en-gb	• work in real-life and mathematical contexts, using local examples where possible.
cy-gb	• gweithio mewn cyd-destunau bywyd go iawn a rhai mathemategol, gan ddefnyddio enghreifftiau lleol lle y bo’n bosibl.

en-gb	Glossary Draft Curriculum for Wales 2022: 
cy-gb	Geirfa Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 46
cy-gb	Mathemateg a Rhifedd 48

en-gb	WHAT MATTERS IN MATHEMATICS AND NUMERACY
cy-gb	YR HYN SY’N BWYSIG MEWN MATHEMATEG A RHIFEDD

en-gb	Statistics represent data, probability models chance, and both support informed inferences and decisions.
cy-gb	Mae ystadegau yn cynrychioli data, mae tebygolrwydd yn modelu siawns, ac mae’r ddau yn cefnogi casgliadau a phenderfyniadau gwybodus.

en-gb	Statistics is the practice of collecting, manipulating and analysing data, allowing representation and generalisation of information. 
cy-gb	Ystadegau yw’r arfer o gasglu, trin a dadansoddi data er mwyn gallu cynrychioli a chyffredinoli gwybodaeth. 

en-gb	Probability is the mathematical study of chance, enabling predictions of the likelihood of events occurring. 
cy-gb	Tebygolrwydd yw’r broses fathemategol o astudio siawns, er mwyn gallu rhagfynegi’r tebygrwydd y bydd rhywbeth yn digwydd. 

en-gb	Statistics and probability rely on the application and manipulation of number and algebra.
cy-gb	Mae ystadegau a thebygolrwydd yn dibynnu ar gymhwyso a thrin rhifau ac algebra.

en-gb	Managing data and representing information effectively provides the means to test hypotheses, draw conclusions and make predictions. 
cy-gb	Mae rheoli data a chynrychioli gwybodaeth yn effeithiol yn cynnig ffordd o broﬁ rhagdybiaethau, dod i gasgliadau a gwneud rhagfynegiadau. 

en-gb	Reasoning with statistics and probability, and evaluating their reliability, develops critical thinking and analytical skills that are fundamental to making ethical and informed decisions.
cy-gb	Mae rhesymu gan ddefnyddio ystadegau a thebygolrwydd, a gwerthuso eu dibynadwyedd, yn meithrin y sgiliau dadansoddi a meddwl beirniadol sy’n hollbwysig wrth wneud penderfyniadau egwyddorol a gwybodus.

en-gb	Learning
cy-gb	Dysgu

en-gb	Principles of progression
cy-gb	Egwyddorion cynnydd

en-gb	Principles of progression are the basis on which the achievement outcomes have been developed and should guide the progression of learning within the area of learning and experience.
cy-gb	Egwyddorion cynnydd yw’r sail ar gyfer datblygu’r deilliannau cyﬂawniad a dylent lywio dilyniant y dysgu o fewn y maes dysgu a phroﬁad.

en-gb	The following interdependent proﬁciencies 9 have been used to formulate the achievement outcomes and are central to progression at each stage of mathematics learning.
cy-gb	Defnyddiwyd y hyfedreddau cyd-ddibynnol canlynol 9 wrth greu’r deilliannau cyﬂawniad ac maent  yn greiddiol i gynnydd yn ystod pob cam o ddysgu mathemategol.

en-gb	Numeracy involves applying and connecting these proﬁciencies in a range of real-life contexts,across and beyond the curriculum.
cy-gb	Mae rhifedd yn golygu cymhwyso a chysylltu’r hyfedreddau hyn mewn amrywiaeth o gyd-destunau go iawn, ym mhob rhan o’r cwricwlwm a’r tu hwnt iddo.

en-gb	Conceptual understanding: 
cy-gb	Dealltwriaeth gysyniadol: 

en-gb	Mathematical concepts and ideas should be dwelt on, built on, and connected together as learners experience increasingly complex mathematical ideas. 
cy-gb	Dylid myfyrio ar syniadau a chysyniadau mathemategol, ynghyd â’u datblygu a’u cysylltu â’i gilydd, wrth i ddysgwyr gael proﬁad o syniadau mathemategol cynyddol gymhleth. 

en-gb	Learners demonstrate conceptual understanding by explaining and expressing concepts, ﬁnding examples (or non-examples) and by representing a concept in a variety of ways, including verbal, concrete, visual, digital and abstract representations.
cy-gb	Mae dysgwyr yn dangos dealltwriaeth gysyniadol drwy egluro a mynegi cysyniadau, dod o hyd i enghreifftiau (neu anenghreifftiau) a thrwy gynrychioli cysyniad mewn gwahanol ffyrdd, gan gynnwys cynrychioliadau llafar, diriaethol, gweledol, digidol a haniaethol.

en-gb	Communication with symbols: 
cy-gb	Cyfathrebu â symbolau: 

en-gb	Learners should understand that the symbols they are using are abstract representations and should develop greater ﬂexibility in their application and manipulation of an increasing range of symbols, understanding the conventions of the symbols they are using.
cy-gb	Dylai dysgwyr ddeall bod y symbolau y maent yn eu defnyddio yn gynrychioliadau haniaethol a dylent ddatblygu mwy o hyblygrwydd wrth iddynt gymhwyso a defnyddio amrywiaeth gynyddol o symbolau, gan ddeall confensiynau’r symbolau y maent yn eu defnyddio.

en-gb	Strategic competence: 
cy-gb	Cymhwysedd strategol: 

en-gb	(i.e. formulating problems mathematically in order to solve them) Learners should become increasingly independent in recognising and applying the underlying mathematical structures and ideas within a problem, in order to be able to solve them.
cy-gb	(h.y. gosod problemau allan mewn ffurf fathemategol er mwyn eu datrys) Dylai dysgwyr ddod yn gynyddol annibynnol wrth adnabod a chymhwyso’r strwythurau a’r syniadau mathemategol sydd wrth wraidd problem, er mwyn gallu ei datrys.

en-gb	Logical reasoning: 
cy-gb	Rhesymu rhesymegol: 

en-gb	As learners experience increasingly complex concepts, they should also develop an understanding of the relationships between and within these concepts. 
cy-gb	Wrth i ddysgwyr broﬁ cysyniadau cynyddol gymhleth, dylent hefyd feithrin dealltwriaeth o’r berthynas rhwng y cysyniadau hyn ac o fewn y cysyniadau hyn. 

en-gb	They should apply logical reasoning about these relationships and be able to justify and prove them. Justiﬁcations and proof should become increasingly abstract, moving from verbal, visual or concrete explanations to representations involving symbols and conventions.
cy-gb	Dylent gymhwyso dulliau rhesymu rhesymegol wrth ymdrin â’r perthnasau hyn a gallu eu cyﬁawnhau a’u proﬁ.Dylai’r cyﬁawnhad a’r dystiolaeth ddod yn gynyddol haniaethol, gan symud o esboniadau llafar, gweledol neu ddiriaethol i gynrychioliadau haniaethol sy’n cynnwys symbolau a chonfensiynau.

en-gb	Fluency: 
cy-gb	Rhuglder: 

en-gb	As learners experience, understand and apply increasingly complex concepts and relationships, ﬂuency in remembering facts, relationships and techniques should grow. 
cy-gb	Wrth i ddysgwyr broﬁ, deall a chymhwyso cysyniadau a pherthnasau sy’n gynyddol fwy cymhleth, dylai eu rhuglder wrth goﬁo ffeithiau, perthnasau a thechnegau wella. 

en-gb	As a result, facts, relationships and techniques learned previously should become ﬁrmly established, memorable and usable.
cy-gb	O ganlyniad, dylai ffeithiau, perthnasau a thechnegau a ddysgwyd ynghynt fod wedi’u hymsefydlu’n gadarn, yn goﬁadwy ac yn ddefnyddiadwy.

en-gb	9 Based on Adding It Up: 
cy-gb	9 Yn seiliedig ar Adding It Up: 

en-gb	Helping Children Learn Mathematics by Kilpatrick, Swafford and Findel (National Research Council, 2001)
cy-gb	Helping Children Learn Mathematics gan Kilpatrick, Swafford a Findel (National Research Council, 2001)

en-gb	and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
cy-gb	ac wedi’u haddasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen, 2018.

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have investigated and collected data found in my environment. 
cy-gb	Rwyf wedi ymchwilio i ddata yn fy amgylchedd ac wedi casglu’r data hynny. 

en-gb	I can record data, giving meaning to marks which represent number and where each quantity corresponds to something in the real world, keeping simple records which include tallying and pictograms.
cy-gb	Gallaf gofnodi data, gan roi ystyr i farciau sy’n cynrychioli rhif a lle y bo pob maint yn cyfateb i rywbeth yn y byd go iawn, gadw cofnodion syml, rhai ohonynt ar ffurf marciau rhifo a phictogramau.

en-gb	I have grouped sets of objects or pictures into categories, through practical experiences, and I can classify by one criterion or more. 
cy-gb	Rwyf wedi grwpio setiau o wrthrychau neu luniau yn gategorïau, drwy broﬁadau ymarferol, a gallaf eu dosbarthu yn ôl un neu fwy o feini prawf. 

en-gb	I can talk about the rule(s) I have used and can reclassify according to new criteria.
cy-gb	Gallaf drafod y rheol(au) a ddefnyddiwyd gennyf a gallaf ailddosbarthu yn ôl meini prawf newydd.

en-gb	I can present data using non-digital and digital methods. 
cy-gb	Gallaf gyﬂwyno data gan ddefnyddio dulliau digidol a dulliau nad ydynt yn ddigidol. 

en-gb	I have created simple charts and graphs and I have talked about what they mean.
cy-gb	Rwyf wedi creu siartiau a grafﬁau syml ac rwyf wedi trafod eu hystyr.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I can collect and organise data for posing and answering questions in relevant situations.
cy-gb	Gallaf gasglu a threfnu data er mwyn gofyn ac ateb cwestiynau mewn sefyllfaoedd perthnasol.

en-gb	I can sort and classify using more than one criterion, using Venn diagrams and Carroll diagrams in practical situations.
cy-gb	Gallaf ddidoli a dosbarthu gan ddefnyddio mwy nag un maen prawf, a chan ddefnyddio diagramau Venn a diagramau Carroll mewn sefyllfaoedd ymarferol.

en-gb	I have used digital and non-digital methods to record and present data in a variety of ways, including the use of tally charts, frequency tables, and block graphs when appropriate axes and scales are provided.
cy-gb	Rwyf wedi defnyddio dulliau digidol a dulliau nad ydynt yn ddigidol i gofnodi a chyﬂwyno data mewn amrywiaeth o ffyrdd, gan gynnwys defnyddio siartiau marciau rhifo, tablau amlder, a grafﬁau bloc lle y darperir echelinau a graddfeydd priodol.

en-gb	I can interpret and analyse graphs, charts and data.
cy-gb	Gallaf ddehongli a dadansoddi grafﬁau, siartiau a data.

en-gb	I can explain what I have found out, justify my reasoning and I can evaluate how well my method worked.
cy-gb	Gallaf egluro fy nghanfyddiadau, cyﬁawnhau fy rhesymeg a gallaf werthuso llwyddiant fy null gweithredu.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have used a sequential data-handling cycle to ask and answer appropriate questions in meaningful situations.
cy-gb	Rwyf wedi defnyddio cylch trin data dilyniannol er mwyn gofyn ac ateb cwestiynau priodol mewn sefyllfaoedd ystyrlon.

en-gb	I can pose and answer sensible questions and I have demonstrated an understanding of the importance of collecting relevant data that can be used to answer my questions.
cy-gb	Gallaf ofyn ac ateb cwestiynau synhwyrol, ac rwyf wedi dangos dealltwriaeth o bwysigrwydd casglu data perthnasol y gellir eu defnyddio i ateb fy nghwestiynau.

en-gb	I have demonstrated an understanding of the kinds of data I need, including discrete and continuous data.
cy-gb	Rwyf wedi dangos dealltwriaeth o’r mathau o ddata sydd eu hangen arnaf, gan gynnwys data arwahanol a di-dor.

en-gb	I can ﬁnd and use the mean of a simple set of data in meaningful contexts.
cy-gb	Gallaf ddod o hyd i gymedr set syml o ddata a’i ddefnyddio mewn cyd-destunau ystyrlon.

en-gb	I have used appropriate methods to answer my questions by collecting, analysing and summarising my data and interpreting my results. 
cy-gb	Rwyf wedi defnyddio dulliau priodol er mwyn ateb fy nghwestiynau drwy gasglu, dadansoddi a chrynhoi fy nata a dehongli fy nghanlyniadau. 

en-gb	I can evaluate my methods and suggest different or better ways to approach investigations in the future.
cy-gb	Gallaf werthuso fy nulliau ac awgrymu gwahanol ffyrdd neu well ffyrdd o gynnal ymchwiliadau yn y dyfodol.

en-gb	I have represented information by creating a variety of appropriate charts of increasing complexity, including tally charts, frequency tables, bar graphs, line graphs, with and without the use of digital technologies. 
cy-gb	Rwyf wedi cynrychioli gwybodaeth drwy greu amrywiaeth o siartiau priodol o ddyfnder cynyddol, gan gynnwys siartiau cyfrif, tablau amlder, grafﬁau bar a grafﬁau llinell, gan ddefnyddio technolegau digidol a thechnolegau eraill. 

en-gb	I have created pie charts using digital technology.
cy-gb	Rwyf wedi creu siartiau cylch gan ddefnyddio technoleg ddigidol.

en-gb	I can use different scales on axes to extract and interpret information from a range of diagrams, tables (including databases) and graphs, including pie charts with simple fractions and proportions.
cy-gb	Gallaf ddefnyddio gwahanol raddfeydd ar echeliniau i echdynnu a dehongli gwybodaeth o amrywiaeth o ddiagramau, tablau (gan gynnwys cronfeydd data) a grafﬁau, gan gynnwys siartiau cylch â ffracsiynau a chyfraneddau syml.

en-gb	I have investigated simple statistics, presented in the media and elsewhere, to support an argument and I can explain how the statistics do or do not support the argument.
cy-gb	Rwyf wedi ymchwilio i ystadegau syml a gyﬂwynwyd yn y cyfryngau ac mewn mannau eraill er mwyn ategu dadl, a gallaf egluro sut mae’r ystadegau yn llwyddo neu beidio i ategu’r ddadl.

en-gb	I can recognise validity and trends, and can discuss how anomalies may affect conclusions when evaluating results.
cy-gb	Gallaf adnabod dilysrwydd a thueddiadau, a gallaf drafod sut y gall anomaleddau effeithio ar gasgliadau wrth werthuso canlyniadau.

en-gb	I have explored the possibility of given outcomes and have used the language of probability to describe the chance of an event occurring.
cy-gb	Rwyf wedi archwilio posibilrwydd canlyniadau penodedig ac wedi defnyddio iaith tebygolrwydd i ddisgriﬁo’r siawns y bydd rhywbeth yn digwydd.

en-gb	I have played games that involve ﬂipping coins, rolling dice and using spinners in order to simulate and discuss chance.
cy-gb	Rwyf wedi chwarae gemau sy’n cynnwys taﬂu darnau arian, rholio dis a defnyddio troellwyr,er mwyn efelychu a thrafod siawns.

en-gb	I have hypothesised and anticipated outcomes of chance experiments in a range of contexts,
cy-gb	Rwyf wedi rhagdybiaethu ac wedi rhagweld canlyniadau arbroﬁon siawns mewn amrywiaeth

en-gb	recording my ﬁndings in a systematic and appropriate way.
cy-gb	o gyd-destunau, gan gofnodi fy nghanfyddiadau mewn ffordd systemataidd a phriodol.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have used a sequential data-handling cycle to ask and answer appropriate questions.
cy-gb	Rwyf wedi defnyddio cylch trin data dilyniannol er mwyn gofyn ac ateb cwestiynau priodol.

en-gb	I can choose a sensible hypothesis to investigate and I have demonstrated an understanding of the methods I can use to collect appropriate data.
cy-gb	Gallaf ddewis rhagdybiaeth synhwyrol er mwyn ymchwilio ac rwyf wedi dangos dealltwriaetho’r dulliau y gallaf eu defnyddio i gasglu data perthnasol a phriodol.

en-gb	I can design and have critiqued questionnaires to ensure that the data to be collected will enable the sequential data-handling cycle to be used.
cy-gb	Gallaf ddylunio holiaduron a’u trafod yn feirniadol, er mwyn sicrhau y bydd y data a gesglir yn caniatáu defnydd o’r cylch trin data dilyniannol.

en-gb	I can calculate the mean, median, mode and range of a set of data and I have made comparisons between small sets of data using summary statistics.
cy-gb	Gallaf gyfrifo cymedr, canolrif, modd ac amrediad set o ddata, ac rwyf wedi cymharu setiau bach o ddata gan ddefnyddio ystadegau crynhoi.

en-gb	I can select and justify an appropriate way to use my data to investigate my hypothesis. 
cy-gb	Gallaf ddethol a chyﬁawnhau ffordd briodol o ddefnyddio fy nata er mwyn ymchwilio i’m rhagdybiaeth. 

en-gb	I have explored different ways to understand and summarise my data, including using averages to make comparisons between large data sets, with grouped frequency distributions for discrete and continuous data. 
cy-gb	Rwyf wedi archwilio gwahanol ffyrdd o ddeall a chrynhoi fy nata, gan gynnwys defnyddio cyfartaleddau er mwyn cymharu setiau data mawr, gyda dosraniadau amlderwedi’u grwpio ar gyfer data arwahanol a data di-dor. 

en-gb	I can use a scatter diagram to analyse two sets of variables and investigate correlation between them. 
cy-gb	Gallaf ddefnyddio diagram gwasgariad i ddadansoddi dwy set o newidynnau ac i ymchwilio i’r cydberthyniad rhyngddynt. 

en-gb	I can make predictions and identify trends and anomalies in data sets.
cy-gb	Gallaf ragfynegi ac adnabod tueddiadau ac anomaleddau mewn setiau data.

en-gb	I have presented my data in the form of appropriate graphs, charts and tables, and I have used digital technologies, taking into account the purpose of the data and nature of the audience. 
cy-gb	Rwyf wedi cyﬂwyno fy nata ar ffurf grafﬁau, siartiau a thablau priodol, ac rwyf wedi defnyddio technoleg ddigidol, gan ystyried pwrpas y data a natur y gynulleidfa. 

en-gb	I have discussed the relative advantages and disadvantages of each presentation method, and I can justify my choice of method.
cy-gb	Rwyf wedi trafod manteision ac anfanteision cymharol pob dull cyﬂwyno a gallaf gyﬁawnhau fy newis o ddull.

en-gb	I have used my data to draw conclusions about my hypotheses and I have communicated my ﬁndings clearly. 
cy-gb	Rwyf wedi defnyddio fy nata er mwyn dod i gasgliadau am fy rhagdybiaethau, ac rwyf wedi cyﬂeu fy nghanfyddiadau yn glir. 

en-gb	I can critique my own methods and ﬁndings, and consider what I may have done differently or better at each stage of the sequential data-handling cycle.
cy-gb	Gallaf drafod fy nulliau a’m canfyddiadau’n feirniadol ac ystyried beth y gallwn fod wedi’i wneud yn wahanol neu’n well yn ystod pob cam o’r cylch trin data dilyniannol.

en-gb	I have critically analysed statistics published in the media and elsewhere to consider what it means and how it does, or does not, support any ﬁndings reported. 
cy-gb	Rwyf wedi cynnal dadansoddiad beirniadol o ystadegau a gyhoeddwyd yn y cyfryngau ac mewn mannau eraill er mwyn ystyried beth y maent yn ei olygu a sut maent yn llwyddo neu’n methu ag ategu unrhyw ganfyddiadau a nodwyd. 

en-gb	I can pose relevant questions to check the credibility of the ﬁndings.
cy-gb	Gallaf ofyn cwestiynau perthnasol er mwyn cadarnhau hygrededd y canfyddiadau.

en-gb	I can explain randomness, and I have investigated chance by modelling and by comparing theoretical and experimental probabilities.
cy-gb	Gallaf egluro haprwydd, ac rwyf wedi ymchwilio i siawns, drwy fodelu a chymharu tebygolrwyddau damcaniaethol ac arbrofol.

en-gb	I have explored all the possible mutually exclusive outcomes of successive and combined events. 
cy-gb	Rwyf wedi archwilio’r holl ganlyniadau cydanghynhwysol posibl sy’n gysylltiedig â digwyddiadau dilynol a chyfunol. 

en-gb	I can work systematically making use of lists and sample space diagrams, and I have shown an understanding that the sum of probabilities of all mutually exclusive outcomes is 1. 
cy-gb	Gallaf weithio mewn ffordd systematig gan ddefnyddio rhestrau a diagramau gofod enghreifftiol, ac rwyf wedi dangos fy mod yn deall mai mainttebygolrwyddau’r holl ganlyniadau cydanghynhwysol yw 1. 

en-gb	I have demonstrated an understanding of when it is appropriate to add or multiply probabilities.
cy-gb	Rwyf wedi dangos dealltwriaeth o ran pryd y mae’n briodol adio neu luosi tebygolrwyddau.

en-gb	I can make meaningful real-life judgements based on outcomes of experimental data and risk.
cy-gb	Gallaf lunio barn ystyrlon go iawn yn seiliedig ar ganlyniadau data arbrofol a risg.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Achievement outcomes
cy-gb	Deilliannau cyﬂawniad

en-gb	I have used a sequential data-handling cycle to ask and answer appropriate questions.
cy-gb	Rwyf wedi defnyddio cylch trin data dilyniannol er mwyn gofyn ac ateb cwestiynau priodol.

en-gb	I have explored different sampling methods and I have demonstrated an understanding of the need to select a sample when collecting data. 
cy-gb	Rwyf wedi archwilio gwahanol ddulliau samplu ac rwyf wedi dangos dealltwriaeth o’r angen i ddethol sampl wrth gasglu data. 

en-gb	I can evaluate, choose and use different sampling techniques, including random sampling, stratiﬁed sampling and systematic sampling.
cy-gb	Gallaf werthuso, dewis a defnyddio gwahanol dechnegau samplu, gan gynnwys samplu ar hap, samplu haenedig a samplu systematig.

en-gb	I have experimented with different approaches to presenting data, including cumulative frequency, box and whisker, and histograms, to interpret measures of central tendency and measures of spread. 
cy-gb	Rwyf wedi arbroﬁ â gwahanol ddulliau o gyﬂwyno data, gan gynnwys dulliau amlder cronnus, blwch a blewyn, a histogramau, er mwyn dehongli mesurau canolduedd a mesurau o wasgariad. 

en-gb	I can select appropriate approaches when comparing data sets, justifying and evaluating my choices.
cy-gb	Gallaf ddethol dulliau gweithredu priodol wrth gymharu setiau data, gan gyﬁawnhau a gwerthuso fy newisiadau.

en-gb	I have critically analysed statistics in the media, considering how data is presented, its reliability, and whether and how the data has been manipulated to tell a particular story. 
cy-gb	Rwyf wedi cynnal dadansoddiad beirniadol o ystadegau yn y cyfryngau, gan ystyried sut y caiff data eu cyﬂwyno, eu dibynadwyedd, a’r modd, os o gwbl, y mae’r data wedi cael eu trin i adrodd stori benodol. 

en-gb	I can make informed decisions based on statistical evidence, identifying bias and anomalies.
cy-gb	Gallaf wneud penderfyniadau gwybodus yn seiliedig ar dystiolaeth ystadegol, gan adnabod rhagfarn ac anomaleddau.

en-gb	I can solve problems involving probabilities of mutually exclusive, independent and dependent events in real-life and mathematical contexts. 
cy-gb	Gallaf ddatrys problemau sy’n ymwneud â thebygolrwyddau digwyddiadau cydanghynhwysol, annibynnol a dibynnol mewn cyd-destunau bywyd go iawn a rhai mathemategol. 

en-gb	I can use a variety of strategies, including using Venn and tree diagrams, to solve problems in local and wider contexts. 
cy-gb	Gallaf ddefnyddio amrywiaeth o strategaethau, gan gynnwys defnyddio diagramau Venn a diagramau canghennog i ddatrys problemau mewn cyd-destunau lleol a rhai ehangach.

en-gb	I have played and created games to understand the relationship between relative frequency and theoretical probabilities, making judgements on outcomes of experimental data and risk.
cy-gb	Rwyf wedi chwarae a chreu gemau er mwyn deall y berthynas rhwng amlder cymharol a thebygolrwyddau damcaniaethol, gan lunio barn ar ganlyniadau data arbrofol a risg.

en-gb	I can use probabilistic arguments, drawing on theory, information, research and experimentation to support my conclusion.
cy-gb	Gallaf ddefnyddio dadleuon tebygoliaethol sy’n seiliedig ar ddamcaniaethau, gwybodaeth,gwaith ymchwil ac arbroﬁon er mwyn ategu fy nghasgliad.

en-gb	Planning for learning
cy-gb	Cynllunio ar gyfer dysgu

en-gb	Links within this area of learning and experience
cy-gb	Cysylltiadau o fewn y maes dysgu a phroﬁad hwn

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across the Mathematics and Numeracy Area of Learning and Experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws Maes Dysgu a Phroﬁad Mathemateg a Rhifedd. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	The number system is used to represent and compare relationships between numbers and quantities.
cy-gb	Defnyddir y system rhifau i gynrychioli a chymharu’r perthnasau rhwng rhifau a meintiau.

en-gb	• Probability and statistics are described and manipulated by using number; they are represented using number.
cy-gb	• Mae tebygolrwydd ac ystadegau’n cael eu disgriﬁo a’u trin drwy ddefnyddio rhifau; cânt eu cynrychioli drwy ddefnyddio rhifau.

en-gb	• Probability is expressed through number in various ways, e.g. through the use of percentages, fractions and decimals, and the connections between the representations is necessary for effective expression of probability.
cy-gb	• Mynegir tebygolrwydd drwy rifau mewn sawl ffordd, e.e. drwy ddefnyddio canrannau, ffracsiynau a degolion, ac mae angen y cysylltiadau rhwng y cynrychioliadau er mwyn mynegi tebygolrwydd yn effeithiol.

en-gb	• Statistics involves manipulation and representation of data, which involve numerical thinking.
cy-gb	• Mae ystadegau’n cynnwys trin a chynrychioli data, sy’n cynnwys meddwl rhifyddol.

en-gb	Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations.
cy-gb	Mae algebra yn defnyddio systemau symbolau i fynegi strwythurau’r perthnasau rhwng rhifau, symiau a chydberthnasau.

en-gb	• Algebra is used within probability and statistics to express generalities and develop formulae.
cy-gb	• Defnyddir algebra ym maes tebygolrwydd ac ystadegau i fynegi cyffredinolrwydd a datblygu fformiwlâu.

en-gb	• In probability, algebra allows us to use the concept of a variable and we can apply this in probability by using a random variable; this is a parameter or event with a random outcome.
cy-gb	• Mewn tebygolrwydd, mae algebra yn rhoi cyﬂe i ni ddefnyddio cysyniad newidyn a gallwn  gymhwyso hwn mewn tebygolrwydd drwy ddefnyddio hapnewidyn; sef paramedr neu ddigwyddiad ac iddo hapganlyniad.

en-gb	• In statistics, general formulae are written using algebra.
cy-gb	• Mewn ystadegau, caiff fformiwlâu cyffredinol eu hysgrifennu drwy ddefnyddio algebra.

en-gb	• Algebra and statistical analysis are interlinked; 
cy-gb	• Mae algebra a dadansoddiad ystadegol yn gysylltiedig â’i gilydd; 

en-gb	use of algorithms and formulae to calculate further statistical measures to analyse data.
cy-gb	defnyddio algorithmau a fformiwlâu i gyfrifo mesurau ystadegol pellach i ddadansoddi data.

en-gb	Geometry focuses on relationships involving properties of shape, space, and position, and measurement focuses on quantifying phenomena in the physical world.
cy-gb	Mae geometreg yn canolbwyntio ar berthnasau sy’n ymwneud â phriodweddau siâp, gofod a saﬂe, ac mae mesur yn canolbwyntio ar feintioli ffenomena yn y byd fﬁsegol.

en-gb	• Geometry involves graphical thinking which is central to statistical representations and analysis.
cy-gb	• Mae geometreg yn cynnwys meddwl yn grafﬁgol sy’n ganolog i gynrychioliadau a dadansoddi ystadegol.

en-gb	• Graphs are used to convert from one value to another, and to represent statistical information including spread, quantity and central tendency.
cy-gb	• Defnyddir grafﬁau i drosi o un gwerth i un arall, a chynrychioli gwybodaeth ystadegol, gan gynnwys ymlediad, nifer a chanolduedd.

en-gb	• Graphical techniques are used to make connections between different sets of data. 
cy-gb	• Defnyddir technegau grafﬁgol i greu cysylltiadau rhwng gwahanol setiau o ddata.

en-gb	• Data generated by measure can be analysed using statistics.
cy-gb	• Gall data a gynhyrchir drwy fesur gael eu dadansoddi drwy ddefnyddio ystadegau.

en-gb	Links with other areas of learning and experience
cy-gb	Cysylltiadau â meysydd dysgu a phroﬁad eraill

en-gb	This section suggests where learning can be enriched through drawing links between other what matters statements across all the areas of learning and experience. 
cy-gb	Mae’r adran hon yn awgrymu lle gellid cyfoethogi dysgu drwy wneud cysylltiadau rhwng y datganiadau o’r hyn sy’n bwysig ar draws yr holl feysydd dysgu a phroﬁad. 

en-gb	It also suggests where different elements of learning could be considered together in order to support more holistic learning.
cy-gb	Mae hefyd yn awgrymu ymhle gellid ystyried gwahanol elfennau o ddysgu gyda’i gilydd er mwyn cefnogi dysgu sy’n fwy holistaidd.

en-gb	Humanities
cy-gb	Dyniaethau

en-gb	• Sorting and classifying.
cy-gb	• Didoli a dosbarthu.

en-gb	• Lines of best ﬁt.
cy-gb	• Llinellau fﬁt orau.

en-gb	• Analysing and inferring from data. 
cy-gb	• Dadansoddi data a gwneud casgliadau yn eu sgil. 

en-gb	• Spotting trends and anomalies. 
cy-gb	• Adnabod tueddiadau ac anomaleddau. 

en-gb	• Averages and range.
cy-gb	• Cyfartaleddau ac amrediad.

en-gb	• Drawing and interpreting a range of graphs.
cy-gb	• Llunio a dehongli amrywiaeth o grafﬁau.

en-gb	Science and Technology
cy-gb	Gwyddoniaeth a Thechnoleg

en-gb	• Sorting and classifying.
cy-gb	• Didoli a dosbarthu.

en-gb	• Lines of best ﬁt.
cy-gb	• Llinellau fﬁt orau.

en-gb	• Analysing and inferring from data. 
cy-gb	• Dadansoddi data a gwneud casgliadau yn eu sgil. 

en-gb	• Spotting trends and anomalies. 
cy-gb	• Adnabod tueddiadau ac anomaleddau. 

en-gb	• Averages and range.
cy-gb	• Cyfartaleddau ac amrediad.

en-gb	• Drawing and interpreting a range of graphs.
cy-gb	• Llunio a dehongli amrywiaeth o grafﬁau.

en-gb	• Sorting and classifying.
cy-gb	Iechyd a Lles

en-gb	Health and Well‑being
cy-gb	• Didoli a dosbarthu.

en-gb	• Lines of best ﬁt.
cy-gb	• Llinellau fﬁt orau.

en-gb	• Analysing and inferring from data. 
cy-gb	• Dadansoddi data a gwneud casgliadau yn eu sgil. 

en-gb	• Spotting trends and anomalies. 
cy-gb	• Adnabod tueddiadau ac anomaleddau. 

en-gb	• Averages and range.
cy-gb	• Cyfartaleddau ac amrediad.

en-gb	• Drawing and interpreting a range of graphs.
cy-gb	• Llunio a dehongli amrywiaeth o grafﬁau.

en-gb	Experiences, knowledge and skills
cy-gb	Proﬁadau, gwybodaeth a sgiliau

en-gb	Progression step 1
cy-gb	Cam cynnydd 1

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through play and discovery in stimulating and relevant local contexts, collect and sort a variety of simple data and answer questions
cy-gb	• drwy chwarae a darganfod o fewn cyd-destunau lleol perthnasol ac ysgogol, gasglu a didoli amrywiaeth o ddata syml ac ateb cwestiynau

en-gb	• use appropriate digital and non-digital methods to represent and interpret data 
cy-gb	• defnyddio dulliau digidol priodol a dulliau priodol nad ydynt yn ddigidol i gynrychioli a dehongli data 

en-gb	• talk about their results.
cy-gb	• trafod eu canlyniadau.

en-gb	Progression step 2
cy-gb	Cam cynnydd 2

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through experiential learning in stimulating and relevant local contexts, use a sequential data-handling cycle to pose questions, then collect and sort a variety of purposeful data to answer questions
cy-gb	• drwy ddysgu drwy broﬁad o fewn cyd-destunau lleol perthnasol ac ysgogol, ddefnyddio cylch trin  data dilyniannol i ofyn cwestiynau, wedyn casglu a didoli amrywiaeth o ddata pwrpasol er mwyn ateb cwestiynau

en-gb	• use appropriate digital and non-digital methods to analyse, represent and interpret data
cy-gb	• defnyddio dulliau digidol priodol a dulliau priodol nad ydynt yn ddigidol i ddadansoddi, cynrychioli a dehongli data 

en-gb	 • explain their results and evaluate their methods.
cy-gb	• egluro eu canlyniadau a gwerthuso eu dulliau.

en-gb	Progression step 3
cy-gb	Cam cynnydd 3

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences in stimulating and relevant local and global contexts, use a sequential data-handling cycle to pose questions, collect and sort a variety of purposeful data 
cy-gb	• drwy amrywiaeth eang o broﬁadau o fewn cyd-destunau lleol a byd-eang perthnasol ac ysgogol,  ddefnyddio cylch trin data dilyniannol i ofyn cwestiynau, casglu a didoli amrywiaeth o ddata pwrpasol

en-gb	• use appropriate digital and non-digital methods to analyse, summarise, represent and interpret data
cy-gb	• defnyddio dulliau digidol priodol a dulliau priodol nad ydynt yn ddigidol i ddadansoddi, crynhoi, cynrychioli a dehongli data 

en-gb	 • through using different approaches, compare, check and evaluate their results, explaining what they have found
cy-gb	• drwy ddefnyddio gwahanol ddulliau, cymharu, gwirio a gwerthuso eu canlyniadau, gan egluro’r hyn y maent wedi’i ganfod

en-gb	• experiment with chance.
cy-gb	• arbroﬁ â siawns.

en-gb	Progression step 4
cy-gb	Cam cynnydd 4

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences in stimulating and relevant local and global contexts, use a sequential data-handling cycle to pose questions, collect and sort a variety of purposeful data
cy-gb	• drwy amrywiaeth eang o broﬁadau o fewn cyd-destunau lleol a byd-eang perthnasol ac ysgogol,  ddefnyddio cylch trin data dilyniannol i ofyn cwestiynau, casglu a didoli amrywiaeth o ddata pwrpasol

en-gb	 • use appropriate digital and non-digital methods to analyse, summarise, represent and interpret data to draw conclusions
cy-gb	• defnyddio dulliau digidol priodol a dulliau priodol nad ydynt yn ddigidol i ddadansoddi, crynhoi, cynrychioli a dehongli data er mwyn dod i gasgliadau

en-gb	• check and evaluate their results and recognise anomalies and trends in data
cy-gb	• gwirio a gwerthuso eu canlyniadau, ac adnabod anomaleddau a thueddiadau yn y data

en-gb	• extend their understanding of chance by expressing theoretical probability numerically.
cy-gb	 • ehangu eu dealltwriaeth o siawns drwy fynegi tebygolrwydd damcaniaethol ar ffurf rifyddol.

en-gb	Progression step 5
cy-gb	Cam cynnydd 5

en-gb	Learners need to experience, to know or be able to:
cy-gb	Mae angen i ddysgwyr broﬁ, deall neu allu:

en-gb	• through a broad range of experiences in stimulating and relevant local and global contexts, use a sequential data-handling cycle to pose questions, select a sample, and collect and sort a variety of purposeful data
cy-gb	• drwy amrywiaeth eang o broﬁadau o fewn cyd-destunau lleol a byd-eang perthnasol ac ysgogol,  ddefnyddio cylch trin data dilyniannol i ofyn cwestiynau, dethol sampl a chasglu a didoli amrywiaeth o ddata pwrpasol

en-gb	• use appropriate digital and non-digital methods to analyse, summarise, represent and interpret data to draw conclusions
cy-gb	• defnyddio dulliau digidol priodol a dulliau priodol nad ydynt yn ddigidol i ddadansoddi, crynhoi, cynrychioli a dehongli data er mwyn dod i gasgliadau

en-gb	• check and evaluate their results
cy-gb	• gwirio a gwerthuso eu canlyniadau

en-gb	• engage critically with statistics in the media
cy-gb	• ymwneud yn feirniadol ag ystadegau yn y cyfryngau

en-gb	• calculate probabilities of combined events and consider probabilities of real-life events.
cy-gb	• cyfrifo tebygolrwyddau digwyddiadau cyfunol ac ystyried tebygolrwyddau digwyddiadau bywyd go iawn.

en-gb	GLOSSARY
cy-gb	GEIRFA

en-gb	Word/phrase Deﬁnition
cy-gb	Gair/ymadrodd Difﬁniad

en-gb	Draft Curriculum for Wales 2022: 
cy-gb	Cwricwlwm Drafft i Gymru 2022: 

en-gb	Mathematics and Numeracy 60
cy-gb	Mathemateg a Rhifedd 63

en-gb	© Crown copyright 2019   WG35002 
cy-gb	© Hawlfraint y Goron 2019   WG35002