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Meadowdale Academy Mastery Maths Curriculum Our Intention We believe every child can succeed in maths. These plans are based on the Schemes of Work from White Rose and PD Materials form NCETM and cover all National Curriculum Objectives. We use the concrete, pictorial, abstract approach, allowing pupils plenty of time with objects and manipulatives to build their understanding of a concept, looking at the why and how initially. Building to pictorial representations to aid pupils’ reasoning and problems solving before moving onto the abstract methods or more complex calculations. These plans set out the small sequential steps necessary for a deep and lasting understanding. These steps are taken at the necessary pace of the class, teachers will use their judgement and only move on when they are confident the majority of pupils have grasped the small step. We believe these small steps will avoid cognitive overload and help us to cover the depth necessary for a greater understanding - depth before breadth so we can learn more and remember more. The Medium Term plans also show the connections or links between topics, that are necessary for understanding and building on key skills that are essential for fluency, reasoning and problem solving. We encourage pupils to ask, ‘What do I know already?’ before tackling any problem and look for efficient methods of calculations, as well as, being able to check their own work and prove their thinking. Fluency, reasoning and problem solving should be an integrated part of every lesson. Allowing plenty of time for children to talk and explain their thinking. Pupils need to be aware that the journey in maths in the most important, the process and strategies used to solve a problem, drawing on known facts. It is not always essential to find a solution or, on occasions, many solutions may be possible.
Implementation Long Term Forecast 2020 – 2021 Pupils will be taught to: The national curriculum for mathematics aims to ensure that all pupils: National Curriculum Mathematics become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Key stage 1 – Years 1 and 2 The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources [for example, concrete objects and measuring tools]. At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency. Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1. White Rose Long Term Planning NCETM Mastery Professional Development Primary Materials Identifies Ready-to-progress criteria from DfE Mathematics guidance: key stages 1 and 2 Here
Year Autumn 2020 Spring 2021 Summer 2021 Number: Place Value (within 10) Consolidation Consolidation Week 1-4 Week 1 Week 1 Sort, represent and count objects – cardinal Number: Addition and Subtraction (within 20) Number: Multiplication & Division (Reinforce One more and one less Week 2-4 multiple of 2, 5, & 10) Add by counting on – Augmentation Week 2-4 Compare and order groups, objects and numbers Number bonds to 20 Count in 10s Number: Addition and Subtraction (within 10) Make doubles Week 5-9 Subtraction, not crossing 10 and crossing 10 Make equal groups – grouping, then sharing Number bonds with 10 and to 10 Related facts Number: Fractions Adding together and adding more Week 5-6 Number: Place Value (within 50) – introduce Subtracting finding parts, counting back Find a half multiples of 2, 5, & 10 and finding the difference Find a quarter Week 5-7 Fact families and comparing addition and Numbers to 50, including Tens and Ones Geometry: Position & Direction subtraction Week 7 One more, One less Geometry: Shape Compare & Order numbers and objects Describe turns 1 Week 10 Count in 2s & 5s Describe position Recognising, naming and sorting 3-D shapes Measurement: Length & Height Number: Place Value (within 100) Recognising, naming and sorting 2-D shapes Week 8-9 Week 8-9 Patterns with 3-D and 2-D shapes Compare length and height Counting to 100 & positioning numbers Measure length and height Comparing & ordering numbers Number: Place Value (within 20) Week 11-12 Add and Subtract lengths One more, one less Numbers from 11-20 Measure Weight & Volume Measurement: Money Tens and Ones Week 10-11 Week 10 Introduce weight and mass Recognise coins One more, One less Measure and compare mass Recognise notes Compare & Order objects and numbers Introduce capacity and volume Count coins Measure & Compare capacity Consolidation Week 13 Measurement: Time Consolidation Week 11-12 Week 12 Before & after, including dates Time to the hour & half hour Writing & comparing time
Number: Place Value Number: Multiplication and Division Measurement: Length and Height Week 1-4 Week 1-4 Week 1-2 Measure length Count, represent, read, write compare & Recognise & make equal groups – Compare & order length order numbers to 20, 50, then 100 sharing & grouping Four operations with length Tens and ones with part-whole, addition & PV Multiplication sentences, 2, 5 & 10 chart, within 50, then 100 times-table Geometry: Position and Direction Count 2s, 5s, 10s and 3s Odd and even Numbers Week 3-4 Describe position Divide by 2, 5 and 10 Describe Movement Number: Addition and Subtraction Week 5-9 Describe turns Statistics Making patterns with shapes Number bonds to 20, including Week 5-6 comparing, then to 100 (tens and ones) Make tally charts Problem solving and efficient methods Add and subtract, 1s, 10s, 1-digit & 2- Draw & interpret pictograms Week 5-6 digit numbers Consolidate any necessary learning to date Block diagrams Investigate open ended questions, build 2 Add three 1-digit numbers resilience and maths confidence Recap Geometry: Property of Shape in red Measurement: Money Week 5-6 Measurement: Time Week 10-11 Week 7-8 Recognise, count & select money – pence, pounds, Recognise, describe & draw 2-D shapes Telling the time to the hour & half hour notes and coins O’clock, half past, quarter past & quarter to Lines of Symmetry Find the total, difference & change Telling time to 5 minutes Recognise & describe 3-D shapes Two-step problems Find & compare durations of time, including Number: Fractions hours & days Number: Multiplication and Division Week 9-12 Measurement: Mass, Capacity and Temperature Week 12 Make equal parts Weeks 9-11 Find & recognise a half, quarter & third Recognise and make equal groups, including Compare mass & measure in grams & kilograms Unit & non-unit fractions, including redistributing to unequal groups Compare volume & measure in millilitres & equivalence litres Add equal groups Temperature Make arrays Consolidation Consolidation Week 12 Week 13
Lower key stage 2 – Years 3 and 4 The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling. Year Autumn 2020 Spring 2021 Summer 2021 Number: Place Value Number: Multiplication and Division Number: Fractions Week 1-3 Week 1-3 Week 1-3 Represent numbers to 100 2, 4 & 8 times-tables Unit and non-unit fractions Tens & Ones using addition Related calculations Counting in tenths & tenths as decimals 100s, 10s and 1s, including finds 1, Multiply & Divide 2-digits by 1-digit Fractions of a set of objects 10 or 100 more or less Scaling Equivalent fractions Represent, compare & order numbers Compare & order fractions to 1,000 Measure: Money 3 Recap Week 4 Add and subtract fractions Count in 50s in red Count money in pence & pounds Measure: Time Number Addition and Subtraction Convert pounds and pence Week 4-6 Week 4-8 O’clock, half past, quarter past & quarter to Add and subtract 1 & 2-digit numbers Add and Subtract money Months, years, hours and telling the time Add and Subtract up to 3-digit numbers Give change Finding and comparing durations Spot the pattern Measuring time in seconds Statistics Estimate and check answers to calculations Week 5-6 Geometry: Properties of Shape – week 7-8 Make tally charts Number: Multiplication and Division Pictograms Turns, angles including right-angles
Week 9-12 Bar Charts Tables Parallel and perpendicular Multiplication – equal groups Recognise & describe 2-D & 3-D Multiply and Divide by 2, 5 & 10 Measure: Length and Perimeter shapes Multiply and Divide by 3, 4 & 8 Week 7-9 Measure & Compare lengths Geometry: Properties of Shape The 3, 4 & 8 times table Week 7-8 Add & Subtract lengths Consolidation Right angles & comparing angles Week 13 Measure & Calculate perimeter Measure accurately (straight lines) Number: Fractions Week 10-11 Horizontal, vertical, Parallel & perpendicular Making equal parts Recognise, describe & make 2-D & 3- Recognise a half, a quarter and a D shapes third Measure: Mass and Capacity Unit and non-unit fractions Week 9-11 Beginning equivalence Measure & compare mass Measure & compare capacity Consolidation Add and subtract mass & capacity Week 12 Compare volume Temperature Consolidation Week 12 Number: Place Value Number: Multiplication and Division Number: Decimals Week 1-4 Week 1- 3 Week 1-2 Bonds to 10 and 100 Represent numbers to 1,000 11 and 12 times table Make a whole & write decimals Compare, order and round decimals Count in 1,000s, 100s, 10s and 1s Multiply 3 different numbers, Factor 4 pairs Halves and Quarters Recap Round to the nearest 10, 100 and 1000 in red Multiply and divide 2-digits by 1-digit Measurement: Money Negative numbers Week 3-4 Multiply and divide 3-digits by 1-digit Ordering & Estimating money Roman Numerals Convert pounds and pence Correspondence problems Add & subtract money, including finding Number: Addition and Subtraction change Measurement: Area Week 5-7
Add and subtract 1s, 10s, 100s and 1000s Week 4 Four operations and money Add and subtract two 3-digit numbers What is area and counting squares Add and subtract two 4-digit numbers Making shapes Measurement: Time Estimate and check answers Comparing area Week 5-6 Telling the time to 5 & 1 minute Measurement: Length and Perimeter Number: Fractions Using a.m, p.m. & the 24-hour clock Week 8-9 Week 5-8 Hours, minutes, seconds, years, months, Equivalent lengths, m, cm & mm weeks & days Unit and non-unit fractions Add and subtract lengths Analogue to digital time, 12 & 24 hour Kilometres Tenths Statistics Perimeter on a grid Equivalent fractions Week 7 Fractions greater than one Perimeter of rectangles and rectilinear Interpret charts shapes Add and subtract fraction within one Comparison, sum & difference whole Number: Multiplication and Division Introducing line graphs Week 10-12 Add and subtract fraction bridging one whole Geometry: Properties of Shape Multiply and divide by 10 and 100 Calculate fractions of sets, objects & quantity Week 8-9 Multiply by 1 and 0, divide by 1 and Number: Decimals Right-angles & comparing angles itself Week 9-10 Identify, compare & order angles Multiply and divide by 3 Recognise tenths and hundredths Show tenths and hundredths as decimals, in a Recognise & describe 2-D shapes Times table and division facts for 6, place value chart & on a number line 9 and 7 Divide 1 and 2-digits by 10 and 100 Triangles and Quadrilaterals Symmetry, Lines of symmetry Consolidation Consolidation Week 13 Week 11 Geometry: Position and Direction Week 10-11 Activity Week Describe position Week 12 Draw and move on a grid Describe movement on a grid Consolidation Week 12
Upper key stage 2 – Years 5 and 6 The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them. By the end of year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils should read, spell and pronounce mathematical vocabulary correctly. Year Autumn 2020 Spring 2021 Summer 2021 Number: Place Value Number: Multiplication and Division Consolidation Week 1-3 Week 1-3 Week 1 Numbers to 1,000 Multiplying up to 4-digits by 1 digit Number: Decimals Numbers to one million Multiplying 2, 3 and 4-digits by 2-digits Week 2-4 Add and subtract decimals within 1 Round to nearest 10, 100 up to nearest Dividing up to 3-digits by 1 digit Add and subtract decimals with the same and million different number of decimal places Dividing 4-digits by 1 digit Negative numbers & Roman numerals Add and subtract wholes and decimals Divide with remainders Decimals sequences 5 Number Addition and Subtraction Recap Week 4-5 Multiply and divide decimals by 10, 100 in red Add & subtract two 4-digit numbers Number: Fractions and 1,000 Add and subtract numbers with more then 4- Week 4-9 Unit and non-unit fractions Geometry: Properties of Shape digits Week 5-7 Round to estimate & approximate and inverse Equivalent fractions, compare and order fractions Identify and compare angles Measurement: Perimeter Week 6 *Please note this is a different order to WR Improper fractions and mixed numbers Measure and draw angles accurately Measure perimeter Number sequences Calculate angles on a straight line and Perimeter of rectangles and rectilinear shapes around a point Calculate perimeter Add and subtractions with the same denominators and different denominators Triangles and Quadrilaterals
Statistics Multiply fractions and mixed numbers by an Regular and irregular shapes Week 7-8 integer 3-D shapes Interpret tables, charts and graphs Calculated fractions of quantities and Geometry: Position and Direction Read and interpret line graphs amounts Week 8-9 Draw and use line graphs Describe position and draw on a grid Number: Decimals and Percentage Two-way tables and timetables Translation with coordinates Week 10-11 Lines of symmetry Number Multiplication and Division Decimals up to 2 d.p. Reflection with coordinates Week 9-11 Rounding, order and compare decimals Measurement: Converting Units Multiples, Factors and Primes Percentages Week 10-11 Square and Cube numbers Equivalent fractions, decimals and Kilometres, Kilograms, Millimetres percentages Multiply and divide by 10, 100 and 1,000 Metric units Consolidation Efficient methods of multiplication Imperial units Week 12 Measurement: Area Converting units of time and timetables Week 12 *Please note this is a different order to WR Counting squares Measurement: Volume Week 12 Area of rectangles and compound shapes Volume and compare volume Area of irregular shapes Estimate volume Estimate capacity Consolidation Week 13
Number: Place Value Number Fractions – continued from Autumn Geometry: Properties of Shape Week 1-2 Week 1 Week 1-3 Multiply unit fraction & non-unit fractions by Describe angles in degrees Represent compare & order numbers integers to 1 million Multiply fraction by fractions Measure and draw lines & angles Represent, compare & order numbers to 10 Divide fraction by integers Angles on a straight line & around a point million Four rules with fractions Fractions of an amount and find the whole Vertically opposite angles Round any number Number: Decimals Angles in a triangle, special quadrilateral Negative numbers in context Week 2-3 & regular polygons Number: Addition and Subtraction Decimals up to 2 d.p. Draw shapes accurately Week 3-4 *Please note this is a different order to WR Understanding thousandths & Three Draw nets for 3-D shapes Add & subtract whole numbers with more than decimal places 4-digits Consolidation & SATs Preparation Inverse operations Multiply & divide decimals by 10, 100 & Weeks 4-5 1,000 Related facts using compensation Multiply & divide decimals by integers Consolidation, Investigations & Preparation for 6 properties Decimals as fractions & fraction to decimals KS3 Multi-step problems and efficient methods Week 6-12 Recap in red Number Percentage Measurement: Perimeter Week 4-5 Week 5 *Please note this is a different order to WR Understand percentage Perimeter on a grid & of a rectangle Equivalent & order fractions, decimals and Perimeter of rectilinear shapes percentages Calculate perimeter Percentage of amounts Percentage missing values Number Multiplication and Division Week 6-8 *Please note this is a different order to Number: Algebra WR Week 6-7 Multiply by 1-digit, up to 3-digits by 2-digits Find a rule, one & two-steps Multiply 4-digit 2-digits Forming expressions Divide 4-digits by 1-digit, including remainders Substitution Short division by 2-digits Formulae & forming equations Division using factors Solve one & two-step equations Long division Factors, Common factors, Primes to 100, Square Find pairs of values and Cube numbers Order of Operations Measurement: Converting Units Week 8 Mental calculations & reasoning from Convert & calculate with metric measures
known facts Miles & kilometres Imperial measures Measurement: Area and Volume Week 9 *Please note this is a different order to WR Number: Ratio Week 9-10 Area of rectangles Ration & fractions and introducing the Area of triangles ration symbol Area of parallelogram Calculating ratio Volumes counting cubes and of a cuboid Using & calculating scale factor Number Fractions Week 10-13 & Spring week 1 Ration & proportion problems Unit and non-unit fraction Statistics Equivalent fractions and simplifying Week 11 fractions Read, interpret & draw line graphs Improper fraction and mixed numbers Circles Read, interpret & draw pie charts Compare and order fractions The mean Add and subtract fractions, including mixed numbers Geometry: Positions and Direction Week 12 *Please note this is a different order to WR The first quadrant Four quadrants Translations Reflections
Key stage 2 – Years 7 and 8 KS3 National Curriculum Mathematics Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects. Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on. Higher Strand challenge Year Autumn 2020 Spring 2021 Summer 2021 Place Value & Ordering Addition & Subtraction Constructing, Measuring & Using Geometric *Please note this is a different order to WR Week 1-2 Notation Week 1-3 Mental strategies for addition & subtraction Week 1-3 Recognise the place value of any whole number Formal methods for whole and decimal Draw & measure line segments including or decimal up to one billion & write in words and numbers geometric figures figures Choose the most appropriate methods Classify, measure and draw angles Work out intervals and place integers on a Perimeter Identify perpendicular and parallel number line Solve problems involving Finance, timetables, Recognise types of triangle, quadrilateral and 7 Round integers to the nearest power of 10 & to frequency trees and graphs polygons up to decagon Recap 1 significant figure Construct triangles and complex polygons in red Compare and order integers, using =, ≠, , ≤, ≥ Add and subtract number given in standard Interpret and draw simple pie charts Find the range & medium form Developing Geometric Reasoning Write 10, 100, 1,000 etc. As powers of 10 Multiplication & Division Week 4-6 Week 3-5 Understand and use the sum of angles at a Write whole number and decimals in the Understand and use factors & multiples point, angles on a straight line and use form A x 10n Multiply & divide integers & decimals by powers vertically opposite angles of 10 Know and apply sum of angles in a triangles Investigate negative powers
Sequencing and quadrilateral Week 4-6 Multiply by 0.1 and 0.01 Solve complex angle problems Describe & continue a sequence Convert between metric units Represent a sequence in tabular and graphical Formal methods for whole and decimals Find and use angle sum of any polygon forms numbers Recognise the difference between linear & non- Understand and use order of operations Understand and use parallel line angles linear sequences Area of rectangles, parallelograms, triangles and rules Explain the term to term rule trapeziums Use known facts to obtain simple proofs Find missing numbers within sequences Solve problems using the mean Developing Number Sense Algebraic Notation explore multiplication & division in Week 7-8 Week 7-9 algebraic expressions Know and use mental arithmetic strategies for Find input and outputs for a single & two-step integers, decimal and fractions function machines Fraction & Percentages of Amounts Use factors to simplify calculations Use diagrams & letters to with single & two-step Week 6 Use estimation to check mental calculations function machines Find fraction & percentage of a given amount Use known facts to derive others facts Substitute values into one & two-step Use a given fraction to find the whole and/or Use known algebraic facts to derive other facts expressions other fractions Know when to use a mental strategy, formal Generate sequences given an algebraic rule written method or a calculator Represent one & two-step functions graphically Solve problems with fraction and percentages greater than 1 and 100% Sets & Probability Equality and Equivalence Week 9-10 Week 10-11 Direct Number Identify and represent sets Understand & use fact families, numerically & Week 7-9 Interpret and create Venn diagrams algebraically Order, add, subtract, multiply and divide direct Understand and use the intersection & union numbers (whole or decimal, positive or of sets Solve one-step linear equations with all four negative) operations Use a calculator Understand and use the complement of Understand and use terminology of equality, equivalence, like & unlike terms Use direct numbers in algebraic equations, sets Simplify algebraic equations by collecting like including two-step equations Know and use vocabulary of probability terms Use order of operations Generate sample space & calculate probability of a single event Roots of positive numbers Understand and use the probability scale, Fractions, Percentages & Decimals Week 12-13 knowing the sum of probabilities of all possible Explore higher powers and roots outcomes is 1 Represent tenths & hundredths as diagrams & on a number line Addition & Subtraction of Fractions Convert between fractions, decimals and Prime Numbers and Proof Week 10-12 Week 11-12 percentages Understand representation of fractions & Use & interpret Pie charts Recognise and identify multiples, factors, convert between mixed number and fractions prime numbers, square & triangle numbers Identify & use simple equivalent fractions Add and subtract fractions, improper fractions Find common factors & multiples (HCF & LCM) and mixed numbers
Understand and use equivalent fractions Write a number as a product of its prime Explore fraction above one as decimals and Use fractions in algebraic context factors percentages Add and subtract decimals and fractions Use a Venn diagram to calculate HCF & Add and subtract simple algebraic fractions LCM Make, test & disprove conjectures
Impact Assessment strategies are used daily and are ongoing. Teachers as constantly assessing, through their questioning, discussions and book looks. This informs necessary planning, interventions, pre teaching or groupings for future lessons. We try to complete regular low-stakes quizzes to aid retrieval of current and known facts. Little and often. Pre Learning Checks are used to assess what pupils know already, to aid planning the sequential steps to follow and set individual targets. Post Leaning Checks are used to assess retention, check targets and inform planning for future steps. More formal assessments are used termly to monitor progress and inform planning. Resources NCETM National Curriculum Resource Tool – every Topic, every Year Group Curriculum Explained, Links & Resources (Making connections, Articles, Activities, Exemplification & Videos) Here NCETM Video presentation by Debbi Morgan CBE (Director of Primary) explaining the Mastery approach: Here NCETM Example Lessons Videos: Here NCETM Progression Maps – for each topic, see where it is taught throughout Y1-6: Here NCETM Progression Maps Reasoning – for each topic, see where it is taught throughout Y1-6 with reasoning suggestions: See Planning File NCETM Calculation Guide. This is very detailed, our Calculation Policy was reduced to 4 pages to make it manageable for parents Here NCETM Primary Assessment Materials – a written guide giving example questions and an idea of the expectation for each year group: Here 2018 KS1 Mathematics Exemplification – demonstration of work to the expected standard: Here 2016 KS2 Mathematics Exemplification - demonstration of work to the expected standard: Here Free videos (RebeccaTheMathsLady) explaining how to teach primary maths: Here Third Space Learning guide to teaching mental maths strategies: Here
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