## Why do we learn maths?

The ‘mastery approach’ to teaching Maths is the underlying principle of Mathematics Mastery at Ark John Archer. Instead of learning mathematical procedures by rote, we want pupils to build a deep conceptual understanding of concepts which will enable them to apply their learning in different situations. The Mathematics Mastery curriculum is cumulative - each school year begins with a focus on the concepts and skills that have the most connections, which are then applied and connected throughout the school year to consolidate learning. This gives pupils the opportunity to ‘master maths’; by using previous learning throughout the school year, they can develop mathematical fluency and conceptual understanding

## Our approach

**Connections and links:** while we acknowledge that most pupils find difficulty in transferring knowledge and skills from one area of maths to another, explicit connections and references to prior learning are made for pupils throughout a unit to support mastery of the subject.

**Home learning:** Mathematics home learning is done using Mathletics. This website supports the curriculum in school and will guide and challenge children through their mathematical thinking. Login information and passwords are shared with parents and pupils to encourage wider reading, independent research and a collaborative approach to learning within the family environment. Children also have access to IXL where they can use online teaching material to learn more about the areas of study.

**Vocabulary is knowledge: **as part of a school-wide focus, children are exposed to challenging and innovative vocabulary at the beginning of each lesson to enrich their learning. Teachers take pupils through a deep dive into a few carefully selected words, providing opportunity to orally rehearse, apply in different contexts and construct sentences with accurate use of new terms.

## #ExcitedAboutLearning

## Year 1

Autumn 1 | Autumn 2 |
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Numbers within 10: Pupils secure their knowledge of numbers to 10. They count sets of objects, represent numbers in different ways and explore number bonds to 1-digit numbers and 10. They compare and order numbers, learn to double and half, and find 1 more/1 less than a given number, recalling key facts. Addition and subtraction (0-10): Pupils explore relationships between addition and subtraction. They learn to count on and count back to solve number problems, using practical resources to demonstrate their understanding. Shape and Patterns: Pupils explore, identify and classify 2D and 3D shapes. They learn new language to describe position, direction and movement. Pupils create and describe repeating patterns. |
Numbers to 20: Pupils draw upon their knowledge of numbers to 10 to count up/down to 20. They count sets of objects, represent numbers in different ways and explore number bonds to 2- digit numbers. They compare and order numbers, learn to double and half, and find 1 more/1 less than a given number. Addition and subtraction (0-20): Pupils explore the relationship between addition and subtraction. They learn to count on and count back when solving number problems within 20 and use known facts to support calculations. Shape and Patterns: Pupils identify and classify 2D and 3D shapes. They learn new language to describe position, direction and movement. Pupils create and describe repeating patterns. |

Spring 1 | Spring 2 |
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Time: Pupils learn to read, write and tell the time to o’clock and half past the hour on an analogue clock. They sequence daily activities. Pupils complete whole and half turns, linking direction to time. Calculation Strategies (within 20): Pupils learn to represent and explain addition and subtraction problems using practical resources, before solving these. They continue to build their mental recall of number bonds to both 10 and 20. Numbers to 50: Pupils learn to represent, sequence, explore and compare 2-digit numbers. They learn to skip count in 2s, 5s and 10s, establishing recall of multiplication tables and repeated addition. Pupils describe and complete number patterns up to 50. |
Addition and Subtraction (within 50): Pupils learn to represent and explain equations in a range of ways using concrete and pictorial representations. They apply the ‘make ten’ strategy to solve problems. Pupils learn to use the correct language to calculate, explain and compare difference between totals. Fractions: Pupils learn to identify a half and a quarter of shapes, objects and amounts. They demonstrate this using shading and grouping. They link their understanding to doubles and halves. Measures – Length and Mass: Pupils learn to measure lengths using cm, and mass using kg. They make comparisons between measurements. Pupils double and half in the context of measurement. |

Summer 1 | Summer 2 |
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Numbers (50-100 and beyond): Pupils learn to recognise place value in numbers to 100, using this to read, write, represent, compare and order numbers. They learn to find one more/less and ten more/less than a 2-digit number, as well as how to identify number patterns. Addition and Subtraction: Pupils explore methods for adding and subtracting 2- digit and 1-digit numbers. They learn to represent and explain their methods using regrouping. Pupils investigate number bonds within 20 and begin to apply these when calculating. Money: Pupils identify the value of coins and notes before learning to represent values using other coin combinations. They learn how to calculate change. |
Money: Pupils identify the value of coins before learning to represent values in different ways and finding change. Multiplication and Division: Pupils learn to share equally into groups, using times tables to check their answers back. They learn to double confidently and begin to link halving to fractions. Pupils explore arrays as a way of representing facts. Measures - Capacity and Volume: Pupils learn to compare capacities, volumes and lengths using the correct units of measurement. They link understanding of fractions to capacity, finding wholes, halves and quarters of amounts. Pupils explore relationships between millilitres and litres with practical examples. |

## Year 2

Autumn 1 | Autumn 2 |
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Number (0-100): Pupils explore place value to secure their knowledge within 2- digit numbers up to 100. They develop their understanding of numbers up to 100, through partitioning, comparison and ordering. Pupils explore number patterns and develop mental methods for finding 1 more/fewer and 10 more/ fewer than a 2-digit number, recalling key facts and calculations at speed. Addition and Subtraction: Pupils apply their knowledge of place value and number bonds to 20 to add and subtract 2-digit numbers, three 1-digit numbers and multiples of ten. They learn to represent calculations using physical resources and bar models, drawing upon these representations to solve problems, check answers and explain their thinking. |
Measures – Length: Pupils learn to draw and measure lengths accurately using a scale of centimetres. They use < > and = symbols to compare and order lengths using both centimetres and metres. Graphs: Pupils learn to represent and interpret data using pictograms, block diagrams, tables and tally charts. They extract key data, making comparisons and simple inferences from the results. Multiplication & division (2,5,10): Pupils calculate the times tables of 2, 5 and 10 using skip counting. They relate the 2 times table to doubling and recall key doubles mentally. Pupils explore different pictorial representations of multiplication and division and discover how the rule of commutativity can support their mental recall of key facts. |

Spring 1 | Spring 2 |
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Time: Pupils learn to tell the time on an analogue clock, including quarter past, quarter to and 5-minute intervals. They sequence daily events and calculate durations of time in minutes and seconds. Pupils recall the number of minutes in an hour and hours in a day in order to make conversions. Fractions: Pupils explore part-whole relationships and relate this to division, identifying fractions as part of a whole or whole set. They start to explore equivalent fractions. Addition and Subtraction (2-digit): Pupils learn to illustrate, represent and explain addition and subtraction calculations, drawing upon regrouping, rounding and adjusting and near doubles strategies. |
Money: Pupils learn to recognise coins and notes of different denominations. They explore the relationship between pence and pounds and begin to use these with accuracy. Pupils learn to add and subtract amounts and calculate change within and bridging the pound. Shapes and Patterns: Pupils explore, sort, describe and compare 2-D and 3-D shapes. They learn to identify lines of symmetry. Pupils use correct language to describe position, direction and rotation to follow or describe a route. Arithmetic: Pupils learn to add and subtract 2-digit numbers mentally (up to 100). They recall multiplication facts and division facts for the 2, 5 and 10 times tables, applying these to solve problems |

Summer 1 | Summer 2 |
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Numbers (within 1000): Pupils learn to recognise place value in numbers up to 1000, using this to read, write, represent, compare and order numbers. They learn to read different scales using these numbers and skip counting. Measures - Capacity and Volume: Pupils learn to read and measure temperature, using different scales. They explore the measuring of capacity and volume using millilitres and litres, making estimates before taking accurate measurements. Pupils compare and order their findings. Measures - Mass: Pupils draw upon their learning from the previous unit to estimate, measure and compare masses in kilograms and grams. They continue to build accuracy in reading scales. |
Exploring Calculation Strategies: Pupils learn to apply the addition and subtraction strategies they have learnt to solve equations, both illustrating and explaining their calculations using column method. They draw upon a secure knowledge of pace value to check their methods for accuracy, using the inverse operation to check answers. Multiplication and Division (3 and 4): Pupils learn to recall multiplication and division facts for the 3 & 4 times tables, recognising the inverse relationship. They look for patterns, such as relating the 4 times table to doubling the 2 times table. Pupils learn to describe, interpret and represent facts using array and bar models, using this to solve problems. |

## Year 3

Autumn 1 | Autumn 2 |
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Number Sense and Exploring Calculation Strategies: Pupils deepen understanding of place value in 3-digit numbers, using the symbols < > and = to make comparisons. They learn to add and subtract 2-digit numbers with and without regrouping. Pupils use mental methods to add and subtract; rounding and adjusting; near doubles; adding on. Place Value: Pupils identify, name and represent 3-digit numbers, learning to partition in different ways. They order and compare numbers, add and subtract ten and one hundred mentally at pace, and round 2-digit and 3-digit numbers to the nearest ten and hundred. Pupils develop an increasing bank of known facts that can be recalled mentally. |
Addition & Subtraction: Pupils develop and use a range of mental calculation strategies. They create and use pictorial representations and transfer principles from these to illustrate and explain formal written methods (column). Length & Perimeter: Pupils learn to measure and draw lengths with increasing accuracy, using scales with intervals of 2 and 5. They make direct comparisons of different lengths. Pupils learn to add and subtract lengths and apply their new learning to real-life problems. They calculate perimeter of shapes and spaces using centimetres and metres. Graphs: Pupils collect, interpret and present data using charts and tables. They extract key information from data. |

Spring 1 | Spring 2 |
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Multiplication & Division: Pupils discover multiplication and division facts for 2, 3, 4, 5, 6, 8 and 10 through exploration and investigation. They explore different multiplicative structures: including equal groups/parts; change and comparison; correspondence problems. Pupils explore relationships defined by commutativity and inverse operations. Deriving Multiplication & Division Facts: Pupils learn to multiply and divide by 10 and 100. They multiply 2-digit numbers by 2, 3, 4 and 5 and solve corresponding division calculations. Pupils learn to divide 2-digit numbers by a 1-digit number using pictorial and written methods, using known mental facts at pace to complete calculations. |
Time: Pupils learn to tell, record, write and order the time using both analogue and digital representations. They learn to recognise the 12-hour clock, using a.m. and p.m. to represent the time of day. Pupils learn to measure, calculate and compare durations within the hour. Fractions: Pupils explore the part-whole relationship using concrete resources and visual representations. They learn to recognise fractions as part of a whole or whole set, and as a number. Pupils learn to add, subtract, compare and order fractions with increasing accuracy. Arithmetic: Pupils apply multiplication facts to create associated division facts. They learn to divide one/two-digit numbers by 10 using mental methods. |

Summer 1 | Summer 2 |
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Angles and Shape: Pupils learn to define and identify angles; right angles, acute and obtuse. They recognise right angles as a quarter of a turn and use this to give directions. Pupils learn to recognise and draw parallel and perpendicular lines. They classify and compare 2-D and 3-D shapes, as well as measuring perimeter. Measures: Pupils learn to read scales with different intervals when measuring mass and volume, drawing upon their knowledge of times tables and skip counting. They weigh and compare masses and capacities with mixed units, learning to convert when necessary. Pupils estimate before measuring with accuracy. |
Measures: Pupils weigh and compare mass and capacity with mixed units, learning to convert when necessary. Pupils use their knowledge to estimate before measuring using accurate scales. Securing Multiplication & Division: Pupils learn to recall the 6 and 8 times tables at speed. They use multiplication and division facts with fluency, using the inverse to support their calculations and check back their answers. Pupils draw upon these facts to solve problems. Exploring Calculation Strategies: Pupils add and subtract mentally with increasing speed and accuracy. They find 10, 100 and 1000 more/less, order and compare numbers beyond 1000 and round numbers to the nearest hundred. |

## Year 4

Autumn 1 | Autumn 2 |
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Reasoning with 4-digit numbers: Pupils secure their knowledge of place value in 4-digit numbers. They compare and order numbers beyond 1000 and learn to add/subtract 1000 to/from any number. Pupils learn to round any number to the nearest 10/100/1000, and find 10/100/1000 more or less. Addition and Subtraction: Pupils use known facts to derive addition and subtraction facts. They learn to use column method for adding and subtracting 4-digit numbers, and choose appropriate strategies when solving mentally. Pupils use bar models to represent a problem and draw upon this to find a solution. |
Multiplication & Division: Pupils explore and investigate the distributive property of multiplication, including multiplying three 1-digit numbers. They rehearse mental strategies to multiply and divide using place value and known/derived facts. Pupils learn the written method of short multiplication and division. Discrete & continuous data: Pupils learn to read and interpret pictograms, bar charts and time graphs, before learning to construct their own to best represent sets of data. They use representations of data to identify information, make comparisons and draw conclusions. Times Tables: Pupils continue to learn and practise their times tables up to 12x12. They use known facts and commutative law to recall at speed. |

Spring 1 | Spring 2 |
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Securing Multiplication Facts: Pupils draw upon their learning in Autumn Term to identify and explore patterns in the multiplication tables (including 7 and 9). They consolidate their recall and application of the times tables at pace. Fractions: Pupils explore different interpretations and representations of fractions, making comparisons of size and identifying equivalence. They learn to represent fractions greater than one as mixed numbers and improper fractions. Pupils learn to add/subtract fractions with the same denominator, including those greater than one. Arithmetic: Pupils practise their methods of finding fractions of quantities using known multiplication facts at pace. |
Time: Pupils learn to recognise time on both analogue and digital clocks using the 12-hour and 24-hour. They learn to convert between units of time to identify durations, bridging the half and full hour. Decimals and Fractions: Pupils learn to identify decimal equivalents to tenths, quarters and halves. They compare and order numbers with the same number of decimal places. Pupils learn to multiply and divide by 10 and 100, including decimals with increasing mental fluency. Area and Perimeter: Pupils learn to calculate the perimeter of rectangles and rectilinear figures. They calculate the area of rectangles and rectilinear shapes and make direct comparisons. Pupils investigate area and perimeter. |

Summer 1 | Summer 2 |
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Measures and Money Problems: Pupils learn to convert between different units of measurement with accuracy. They select appropriate units and apparatus to carry out measurements. Pupils learn to use a range of strategies for investigating problems; organising using lists and tables; trial and improvement; working systematically and in sequence. Shape and Symmetry: Pupils learn to classify, compare and order angles on a range of shapes and lines. They compare and classify 2-D shapes with a deeper understanding of their properties. Pupils learn to visualise and identify lines of symmetry in shapes and objects and to reflect these with accuracy. |
Position and Direction: Pupils learn to describe and plot coordinates before using these to describe translations. Reasoning with Pattern and Sequences: Pupils learn to read and record Roman numerals up to 100. They explore patterns in place value and investigate other number systems. Pupils use their knowledge of number to identify patterns and sequences, using these to solve problems, make predictions and estimates, and explain their thinking. 3-D Shapes: Pupils draw upon their prior learning of shape to describe properties to a greater depth. They learn to identify 3-D shapes from 2-D representations. Pupils use nets to recognise, construct and represent 3-D shapes. |

## Year 5

Autumn 1 | Autumn 2 |
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Reasoning with large numbers: Pupils secure their knowledge of place value in 5-digit and 6-digit numbers. They compare and order numbers and learn to round to the nearest 1000/10,000/ 100,000. Pupils apply this knowledge to solving number problems. They also investigate Roman Numerals up to one thousand, learning to read and compare to our number system. Problem solving with integer addition and subtraction: Pupils use rounding to estimate answers and a range of mental strategies to partition for adding and subtracting. They add and subtract multiples of 10, 100, 1000, 10,000 and 100,000. Pupils use column method to add and subtract large whole numbers. |
Multiplication & Division: Pupils learn to identify multiples and factors and investigate prime numbers. They multiply and divide by 10, 100 and 1000 (integers) and use derived facts to support their calculations. Pupils learn to illustrate and explain formal multiplication and division strategies (long and short) and use a range of mental strategies at increasing pace. Perimeter & Area: Pupils investigate the perimeter and area of rectilinear shapes. They estimate measurements before calculating using specific formulae. Line Graphs & Timetables: Pupils read complete and interpret data presented in line graphs. They interpret timetables, calculating intervals between times. |

Spring 1 | Spring 2 |
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Fractions and Decimals: Pupils learn to read, write, order and compare decimal numbers, as well as rounding decimals to the nearest whole number. They represent, identify name, write, order and compare fractions (including improper fractions and mixed numbers). Pupils learn to calculate fractions of amounts with increasing accuracy. Angles: Pupils learn to classify, compare and order angles. They measure and draw angles using a protractor with increasing accuracy. Pupils understand and use angle facts in order to calculate missing angles presented in a problem. Arithmetic: Pupils learn to multiply proper fractions and mixed numbers by whole numbers, using known facts at pace to complete their calculations. |
Fractions and Percentages: Pupils learn to add and subtract fractions with denominators that are multiples of the same number. They multiply fractions and mixed numbers by a whole number. Pupils explore the relationships between fractions, percentages and decimals through equivalence and proportion. Transformations: Pupils learn to identify coordinates in all four quadrants, gaining the skills to translate and reflect shapes images. They calculate intervals across zero as context for negative numbers. Arithmetic: Pupils learn to divide numbers up to 4-digits by a 1-digit number using formal written methods, recording with a remainder. They divide whole numbers by 10, 100 and 1000. |

Summer 1 | Summer 2 |
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Converting Units of Measure: Pupils learn to convert between units of time and metric units of length, mass and capacity with accuracy. They learn to recall and use approximate conversions between imperial and metric values. Pupils use this knowledge to investigate different measurements; solve problems using conversion; give accurate answers. Calculating with Whole Numbers and Decimals: Pupils learn mental strategies and formal written methods for adding and subtracting involving decimals. They learn to multiply and divide numbers by 10, 100 and 1000 mentally involving decimals. Pupils derive multiplication facts involving decimals and us |
2-D and 3-D Shapes: Pupils learn to classify 2-D and 3-D shapes based on their increasing knowledge of shape properties, creating 2-D representations of 3-D shapes. They learn to distinguish between regular and irregular polygons, reasoning with this knowledge. Pupils investigate properties of quadrilaterals. Volume: Pupils learn to use cube numbers and notation to estimate and measure volume. They learn to convert accurately between units of volume. Problem Solving: Pupils solve problems involving negative numbers, calculating intervals across zero. They calculate the mean accurately, interpret remainders and investigate number with confidence; consecutive, palindromic and multiples. |

## Year 6

Autumn 1 | Autumn 2 |
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Integers and decimals Pupils learn to read and write 7-digit numbers in words and numerals. They compare numbers up to 10 million using the symbols < > and =. Pupils order numbers in ascending and descending order. They round to an appropriate degree of accuracy to support their calculations. Multiplication and division: Pupils use their knowledge of place value in decimal numbers to multiply and divide by 10, 100 and 1000, and to multiply by any whole number. They explore common multiples and common factors and use these to describe properties of numbers. Pupils use written methods of short and long multiplication and division to solve real world problems. |
Calculation Problems: Pupils learn the importance of brackets. They use this knowledge to carry out calculations with the correct order of operation and to generate and describe linear number sequences. Pupils learn to express missing number problems using algebra and use this understanding to solve equations with unknown values. Fractions: Pupils deepen understanding of equivalence. They order, simplify and compare fractions, including those greater than one. Pupils mentally recall equivalence between common fractions and decimals, and find decimal quotients using short division. Missing Angles and Length: Pupils use angle facts to find missing angles. |

Spring 1 | Spring 2 |
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Coordinates and Shapes: Pupils learn to draw a range of geometric shapes using given dimensions and angles. They describe, draw, translate and reflect shapes on a co-ordinate plane. Pupils name and illustrate parts of a circle. Fractions: Pupils learn to represent multiplication involving fractions. They learn to multiply two proper fractions and divide a fraction by an integer. Decimals and Measure: Pupils use, read and write standard units of measure, converting between units of mass, time, length, money and volume, as well as imperial units. They estimate and calculate the area of parallelograms and triangles, as well as calculating and comparing the volume of cuboids. |
Percentages and Statistics: Pupils learn to calculate and compare percentages of amounts. They identify connections and patterns between percentages, fractions and decimals, by exploring equivalence. Pupils construct, analyse and interpret line graphs and pie charts, as well as learning to calculate the mean. Proportion Problems: Pupils learn to use fractions, decimals and percentages as a way of expressing proportion. They identify ratio as a relationship between quantities and as a scale factor. Pupils explore unequal sharing involving ratio. Decimals and Measure: Pupils estimate and calculate the area of parallelograms and triangles, as well as calculating and comparing the volume of cuboids. |

Summer 1 | Summer 2 |
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Pupils consolidate their understanding and fluency in the following areas of the Mathematics curriculum. As they grow in confidence, pupils apply key concepts, formal methods and mental strategies with independence to solve problems and investigate mathematical concepts. Calculation strategies: Addition, division, subtraction, multiplication involving whole numbers, decimal numbers, fractions, percentages. Pupils consider the order of operations for calculations. They improve their accuracy in all areas. Decimals, Percentages and Fractions: Equivalence; expressing proportion and ratio; converting accurately between units; comparing; ordering; calculating area, perimeter, volume, money, length. |
Pupils consolidate their understanding and fluency in the following areas of the Mathematics curriculum. As they grow in confidence, pupils apply key concepts, formal methods and mental strategies with independence to solve problems and investigate mathematical concepts. Calculation strategies: Addition, division, subtraction, multiplication involving whole numbers, decimal numbers, fractions, percentages. Pupils consider the order of operations when carrying out calculations. |