Author: Sandra Leach

Calculation Policy

This policy has been written using White Rose schemes of learning for Early Years, Year One and Two. It is designed to support the teaching of key concepts of number, focussing on small steps in order to support children to succeed.
S. Leach 2021 Reviewed December 2023 J Martines, R, Stokes and C Petretta

Key Representations
Concrete – children should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
Pictorial – alongside this children should use pictorial representations. These representations can then be used to help reason and solve problems.
Abstract – both concrete and pictorial representations should support children’s understanding of abstract methods.

Place value counters

Bar Model

Dienes

Multilink Cubes

Part Whole Model

Number Lines

Numicon

In order for teachers to successfully teach early mathematics, the 5 counting principles need to be considered and the barriers children can experience and how to overcome them. Counting Principles
The One to One Principle: This involves children assigning one number name to each object that is being counted. Children need to ensure that they count each object only once ensuring they have counted every object.
Barriers to learning: missing a number out or counting one object more than once. Therefore encourage children to line objects up and slowly touch each one saying one name per object.
The Stable Order Principle: Children understand when counting, the numbers have to be said in a certain order.
Barriers to learning: not knowing all the number names for the amount in the group they are counting. Therefore encourage children to count out loud to larger numbers without expecting them to count objects immediately.
The Cardinal Principle: Children understand that the number name assigned to the final object in a group is the total number of objects in that group.
Barriers to learning: children have not grasped the One to One and Stable Order Principle. Therefore encourage children to continue practise the above principles.
Abstraction Principle: This involves children understanding that anything can be counted including things that cannot be touched including sounds and movements e.g. jumps.
Barriers to learning: children rely heavily on only counting things they can touch. Therefore on a daily basis practise counting claps/clicks/jumps.
The Order-irrelevance Principle: This involves children understanding that the order we count a group of objects is irrelevant. There will still be the same number. Barriers to learning: if the amount an rearranged children believe there is a different amount there. Therefore encourage children to count left to right, right to left, top to bottom, bottom to top.

Commutative: This is when 2 numbers are added and the same answer will be found, no matter the order.
Subitisation: Instantly recognise a small quantity, without having to count how many there are.
Cardinal: the number that indicates how many there are in a set.
Ordinal: A number denoting the position in a sequence e.g. 1st, 2nd, 3rd, 4th…
Conservation (of number): The recognition that the number stays the same if none have been added or taken away, even if the arrangement of the quantity changes.
Inverse: Inverse means the opposite in effect. The reverse of. The inverse of addition is subtraction. The inverse of multiplication is division.

Key Language

Addition

Expected Year Group		How it will look	Resources
Counting Forwards / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		In order for a child to successfully count, they must have mastered the Five Counting principles. / Children should have lots of varied experiences from singing counting songs, counting jumps and movements, to counting objects that can be moved and manipulated. Children should learn to count forwards and backwards from small numbers progressing to larger numbers. / In the Summer Term children should learn to count beyond 10 . They should be encouraged to count on and back from different starting points	Concrete representation: Five and ten frames, compare bears, natural objects, numicon / Pictorial representation: pictures of fingers, dots and dice spots, number track and pictures / Abstract representation: Numicon number line to support number recognition and in Summer Term 100 Square. / Songs– five Monkeys jumping on the bed. 10 in the bed / Books– Squash and a Squeeze. Room on the Broom
Subitisation / Reception / Autumn– to 5 Spring– to 10 Summer– recap to 10		Subitisation is an important part of learning to count but is not the same as counting. It means a child is able to quickly recognise and name the number in a group without counting and recognising smaller quantities in larger amounts. This skill begins at a young age when children as young as two can identify they have 2 shoes without counting them. / Reception children should begin with using small quantities in familiar patterns, playing games which involve quickly revealing and hiding numbers of objects. Children should be familiarised with the five and ten frame, prompting children to subitise first.	Concrete representation: Compare bears, numicon, unifix, multilink, five frame and ten frame. Pots and pencils (there needs to be 6 pencils in the pot), knives and forks (at lunchtime) / Pictorial representation: Dice, paper plates and spots, dominoes, pictures of fingers.

Addition

Expected Year Group		How it will look	Resources
Comparing / Numbers / Reception Autumn– to 5 Spring– to 10 Summer– to 20		Children begin by comparing amounts, they should practise lining objects up and using 1:1 correspondence. They learn that a quantity can be more, less or the same as another quantity. Provide lots of opportunities for children to count two sets and compare them. These should start by counting identical objects: / And then move on to counting non-identical objects of varying size and shape. This supports children's understanding that quantity does not correlate with size or shape.	Concrete representation: Five and ten frames, compare bears, natural objects, numicon / Pictorial representation: pictures of fingers, dots and dice spots, number track and pictures / Abstract representation: Numicon number line to support number recognition.
Composition of numbers / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		Initially teachers should focus on composition of 2, 3, 4 and 5 before moving onto larger numbers 6, 7, 8, and 9. Children will practise counting out from a larger group and to represent numbers in a variety of ways including using numicon, dots, dice, drawing pictures, writing the number, part whole model. They will develop the understanding that all numbers are made up of two small numbers. / Children will explore arranging groups and objects for numbers to 10 and will be encouraged to subitise. / Songs– 5 little Monkeys, 10 fat sausages, Noah’s Ark, / Number Blocks– whole of me / Books– Kipper’s Toy Box, What the Ladybird Heard	Concrete representation: Five and ten frames, compare bears, natural objects, numicon, bead strings. / Pictorial representation: pictures of fingers, ladybird spots, dots and dice spots, number track and pictures, Part Whole model. / Abstract representation: Numicon number line to support number recognition and in Summer Term 100 Square.
Combing two groups / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		This is the children’s first experience of addition. The children learn to find the total of two small sets/groups/amounts by counting them into a straight line. / 2 + 3 / 2 + 3 1 + 4	Concrete representation: Five and ten frames, numicon pieces, large hoops and objects, dominoes, rolling 2 dice, 2 different coloured multilink and counting fingers. / Pictorial representation: Picture stories and first, then, now stories.

Addition

Year Group and Skill		How it will look	Resources
Symbols / Reception and Year 1 in Autumn Term		The children are introduced to the addition and equals symbol and learn language associated with it. Such as “add” “plus” “combine”, “altogether”. Children learn that = means “equal to” or the “same as”. Initially children focus on a specific order to the number sentence a + b = c Children use first, now, then stories as well as concrete and pictorial resources to support their understanding. / Although not explicitly stated in the Early Years Foundation Stage, children should be exposed and begin to use the correct symbols + = when they are ready.	Abstract representation: / Scaffold to support order of using symbols within a number sentence, this could be laminated in Reception for children to write numbers in the boxes.
Counting on Practically / Reception-Early learning Goal / Year 1		Children move on from counting all to counting on. In order to count on to find the total amount the children must have mastered the skill of counting forward from a given number and can confidently compare numbers to identify the largest and smallest amount. / As the children grow in confidence with using concrete manipulatives move towards abstract representation of counting on in their heads.	Concrete representation: Counters, ten frame, numicon, Part Whole model, large number tiles to make number line on the floor. / Pictorial representation: Picture stories for children to interpret / Abstract representation: Numicon number line to support number recognition. Counting on in their heads.
Adding Together using Part Model / Year 1		Children understand that any number can be partitioned and that 2 smaller numbers make a larger number. They use the part whole model to support their understanding and become confident in using the language of part and whole.	Concrete representation: unifix, numicon shapes, coloured pegs on top of numicon, ten frame and double sided counters / Pictorial representation: Part-whole model in different orientations, Pictures to stories. / Abstract representation: Scaffold to support recording number sentence. / Stem sentence / The whole is ___ / ____ is a part and ___ is a part

12 13 14 15 16

Addition

Expected Year Group		How it will look	Resources
Composition of Smaller Numbers (within 10) / (Recap from Reception) / Year 1		Children build on their initial number sentences to begin to look at addition fact families. They learn that all numbers are made up of 2 smaller numbers and learn number bonds for 2,3,4,5,6,7,8,9. Children learn that the order of the number sentence can be varied (c = b + a) and they begin to discover that addition is commutative. At this stage children are also introduced to work systematically to identify all number bonds for that number.	Concrete representation: Unifix cubes/multilink, bead strings, double sided counters, ten frame and fives frame. / Pictorial representation: Part-whole model, dots and dice spots, number track and pictures. / Abstract representation: Addition sentences
Number Bonds to 10		Starting with the number 10 children look at finding 2 parts that make up the whole number (10). They are encouraged to work systematically, starting with the whole. / Children should use a variety of representations including part-whole and bar model, should see the number sentence alongside these.	Concrete representation: ten frames, unifix and multilink, numicon, and bead strings. / Pictorial representation: Dice spots, part-whole model, bar model / Abstract representation: Addition sentences
Comparing Number Bonds / Year 1		Children use their knowledge of place value and number bonds to compare numbers and number sentences. They learn to use the correct language– greater than, less than and use inequality symbols > < = to compare. (Note– this is not in the National Curriculum for Year 1. Therefore if children are not ready to use the symbols they can verbally compare)	Concrete representation: Ten frame and counters, unifix cubes, counters. Children should be initially given laminated inequality symbols to physically manipulate. / Pictorial representation: pictures of amounts to compare with statements, / Abstract representation: using the inequality symbols.
Missing Number (Find a Part) / Year 1		Children should apply their knowledge of number bonds to 10 to solve missing number problems. Building from counting on, children should start from the given part and count on to the whole, to find the missing part. Children should be encourage to use subitisation also to quickly recognise the part.	Concrete representation: Ten frame and counters, unifix cubes, counters, multilink. / Pictorial representation: part-whole model, bar model.

Progression of Skills– Addition

Progression of Skills– Addition

Expected Year Group		How it will look	Resources
Number Bonds to 20 / Year 1		Children see that working systematically helps them to find all the possible number bonds to 20 They will use their knowledge of number bonds to 10 to find number bonds to 20 Using examples such as, 7 + 3, 17 + 3 or 7 + 13 encourages children to see the link between bonds to 10 and bonds to 20 and reinforces their understanding of place value.	Concrete representation: Unifix cubes, multilink, bead strings, coloured counters, ten frame. / Pictorial representation: Part-whole model, bar model. / Abstract representation: Scaffold for recording number sentences
Add by Making 10 / Year 1		Children add numbers within 20 using their knowledge of number bonds. It is important children work practically using ten frames and coloured counters or number lines to support them with this concept. Children use scaffolds that remind them to always make 10 first on a ten frame. / They will gradually move towards using this as mental strategy but is not a requirement at this stage.	Concrete representation: Double sided counters, ten frame, numicon and pegs. / Pictorial representation: Part-whole model, bar model. Picture stories to interpret. / Abstract representation: Blank calculations to complete.
Number bonds to 20 / Year 2		Children apply their understanding of known additions facts within 20 to identify all related facts. / Using part-whole model and bar model can support and deepen children’s understanding. / During this stage, children should also be given the opportunity to check addition calculations using the inverse as well as number lines and concrete resources.	Concrete representation: Numicon, coloured counters and ten frames, / Pictorial representation: Part-whole model, bar model. / Abstract representation: Addition number sentences
Compare Number sentences (within 20) / Year 2		Children should use numbers within 20 to explore mathematical relationships. This will give children the confidence and allow them to spot patterns because they are working within the context of familiar numbers. Children should compare similar calculations using greater than, less than and equal to.	Concrete representation: Ten frame and counters, unifix cubes, counters. Children should be initially given laminated inequality symbols to physically manipulate. / Pictorial representation: pictures of amounts to compare with statements, / Abstract representation: using the inequality symbols.

Addition

Expected Year Group		How it will look	Resources
Related Facts / Year 2		Children should have an understanding of calculations with smaller digits to help them relate this to larger calculations. For example, 2 + 5 = 70 so 20 + 50 = 70. / At this stage children need to have confident understanding of partitioning and tens and ones to aid their understanding of related facts.	Concrete representation: Unifix cubes, multilink, bead strings, double sided counters, ten frames. / Pictorial representation: Part-whole model, bar model. / Abstract representation: Addition and subtraction number sentences
Bonds within 100 / Year 2		At this stage, it focusses on adding with multiples of ten up to and within 100. Links should be made with single digit bonds and ten bonds. Children can also use their knowledge of number bonds to 10 to identify missing numbers in larger calculations.	Concrete representation: dienes, ten frame, double sided counters, place value counters / Pictorial representation: Part-whole model, bar modes, picture stories / Abstract representation: Addition and subtraction number sentences
Add by Making 10 / Year 2		THIS IS A RECAP FROM YEAR 1. / Children add numbers within 20 using their knowledge of number bonds. It is important children work practically using ten frames and coloured counters or number lines to support them with this concept. They will move towards this being a mental strategy.	Ten frame and coloured counters. Part-model to support partitioning a large number in to two smaller numbers to make ten.
Add 2 digit and 1 digit number (crossing 10) / Year 2		Before crossing the ten when adding, children need to have a strong understanding of place value. The idea that ten ones is the same as one ten is essential to aid understanding. Children also need to be able to count to 20 and need to be able to partition a two digit number in order to add them. Additionally children need to understand the difference between a 2 digit and 1 digit number so they can line them up in columns. / Children will then progress onto using number lines (including empty number lines). In order to do this children will need to be secure with their number bonds. For example, 17 + 5– if you partition 5 into 2 and 3, you can bridge the ten, to make 20 and then add 2.	Concrete representation: dienes, ten frame and double sided counters / Pictorial representation: Scaffold for column method, number line (including an empty one), part-whole model / Abstract representation: Addition and subtraction number sentences

Addition

Expected Year Group		How it will look	Resources
Add two digit numbers together / (Part 1– not crossing 10 / Part 2 crossing 10) / Year 2		Part 1 not crossing tens– this is a pre-requisite before children add 2 digits numbers with exchange. To support understanding teachers should focus on the language of tens and ones. Children should look at different methods as well as the column method. Children must learnt o start by adding ones when adding using the column method. / Part 2 crossing tens– children use dienes and partitioning to add together 2 digit numbers including exchange. To aid understanding, encourage children to draw dienes alongside the column method. At this stage children need to confident in exchanging 10 ones for 1 ten.	Concrete representation: dienes, ten frame and double sided counters / Pictorial representation: Scaffold for column method, number line (including an empty one), part-whole model, 100 square / Abstract representation: Addition and subtraction number sentences
Number Bonds to 100 / Year 2		Children build on their earlier experiences of number bonds to 100 with tens, together with their number bonds to 10 and 20. They use their knowledge of exchange to find bonds to 100 with tens and ones. / For example, using a 100 square- 40 squares are shaded how many are not? Or using dienes– Tommy is making 100 using dienes, he has 34– how many more does he need? Children to place their dienes on top of 100 piece to help them calculate.	Concrete representation: dienes, bead strings, ten frame and double sided counters / Pictorial representation: 100 square, pictures of dienes / Abstract representation: addition number sentences
Add 3 1 digit numbers / Year 2		Children use their knowledge of commutativity (when 2 numbers are added and the same answer will be found, no matter the order) to find the most efficient way of adding three-one digit numbers. Children practise using their knowledge of number bonds to 10 or making doubles, to help them to add efficiently. / Children can also compare number sentences using > < and =	Concrete representation: Ten frames and 3 different colours of counters, numicon and pegs. / Pictorial representation: Picture stories to interpret / Abstract representation: addition number sentences

Subtraction

Expected Year Group		How it will look	Resources
Counting Backwards / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		In order for a child to successfully count, they must have mastered the Five Counting principles. / Children should have lots of varied experiences from singing counting songs, counting jumps and movements, to counting objects that can be moved and manipulated. Children should learn to count forwards and backwards from small numbers progressing to larger numbers. / In the Summer Term children should learn to count beyond 10. They should be encouraged to count on and back from different starting points / Songs– five Monkeys jumping on the bed. 10 in the bed / Books– Squash and a Squeeze. Room on the Broom	Concrete representation: Five and ten frames, objects such as compare bears/natural objects, numicon, pictures of fingers, dots and dice spots, number track. / Pictorial representation: In Summer Term– larger numbers on number track and 100 square, Numicon number line to support number recognition.
Subitisation / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		This will be a recap from when the children were introduced to subitisation during addition. / Within subtraction the children can use subitisation to identy the quantity that is left after taking an amount away. / Provide children with plenty of opportunities for them to continually practise subitising through out the year. This will then be built upon in Year 1.	Concrete representation: compare bears, numicon, unifix, multilink, five frame and ten frame. / Pictorial representation: Dice, paper plates and spots, dominoes, ladybird spots, numicon, five frames
Taking away / Reception / Autumn– to 5 Spring– to 10 Summer– to 20		Children use real objects to see that the quantity of a group can be changed by taking items away. Encourage children to count out all the items at the start, take away the require amount practically and then subitise or recount to see how many are left. / Adults to provide different opportunities for children take away from a larger group including, first, now, then model structure to tell simple math stories.	Concrete representation: Five frame and ten frame, number track, numicon, compare beards, multilink, pebbles, natural materials, coins. / Pictorial representation: pictures of fingers, numicon, picture stories, five and ten frames.

Subtraction

Expected Year Group		How it will look	Resources
Symbols / Reception and Year 1 in Autumn Term		The children are introduced to the subtraction and equals symbol and learn language associated with it. Such as “take away” “subtract” “less”, Children learn that = means “equal to” or the “same as”. Initially children focus on a specific order to the number sentence b - a = c Children use first, now, then stories as well as concrete and pictorial resources to support their understanding. / Although not explicitly stated in the Early Years Foundation Stage, children should be exposed and begin to use the correct symbols - = when they are ready.	Scaffold to support order of using symbols within a number sentence, this could be laminated in Reception for children to write numbers in the boxes.
Counting back / Reception—Early learning Goal / Autumn– to 5 Spring– to 10 Summer– to 20 / Year 1		Children move on from taking an amount away to counting back. In order to count back to find the total amount left, children must have mastered the skill of counting backwards from a given number and can confidently compare numbers to identify the largest and smallest amount. / When counting backwards children should be taught that first they must identify the largest amount putting this amount in their head, next using resources make the smallest number and count back. / 17 - 5	Concrete representation: Numicon, double sided counters, ten frame, large number tiles to make number line on the floor. / Pictorial representation: Part Whole model, bar model, number line, 100 square / Abstract representation: Counting back in their heads without resources
How many are left? / Year 1		Children recap learning from Reception and look at subtraction as “taking away”. It is used in a variety of real life and fun contexts like eating! The use of zero is important so children learn that when nothing is taken away the whole remains same. First, then, now story representations can be used which children will be familiar with from Reception. For example, first there were 7 birds in the tree, then 3 flew away, now there are 4.	Concrete representation: counters, ten frames, numicon, compare bears / Pictorial representation: Part-whole model, first, then and now stories with pictures, / Abstract representation: scaffold for setting out number sentences

12 13 14 15 16

Subtraction

Expected Year Group		How it will look	Resources
Partitioning a number in to 2 smaller numbers / Year 1 / Autumn Term		Building on children’s experiences of partitioning within addition, children are introduced to partitioning in subtraction. Children continue to understand what is meant by “whole” and “parts” when referring to partitioning a number. / To support children’s understanding they use concrete and pictorial representations.	Concrete representation: large hoops and bean bags, counters and ten frame, numicon and coloured pegs, unifix cubes. / Pictorial representation: picture stories for children to interpret and record as a number sentence. Part-whole model / Abstract representation: scaffold to support children recording number sentence correctly.
Fact Families– The 8 facts / Year 1 / Autumn Term		This is the first time children will be introduced to subtraction and addition and the link between them. Children will learn the relationships between addition and subtraction as the inverse. Using pictorial representations children will explore finding all 8 facts. For example, / Children may struggle to find 4 calculations for subtraction and should us concrete resources to support.	Concrete representation: Numicon, ten frame and counters, unifix / Pictorial representation: Picture stories to be interpreted, part whole model with numerals or pictures used to represent parts or the whole. / Abstract representation: A scaffold of the 8 number sentences the children need to identify.
Counting back / Reception and Year 1 / Autumn Term		Counting backwards is an important skill to support children to work in the abstract. Initially this may be tricky for children and concrete resources should be used to support children with counting backwards. As well as the use of number line or 100 square to support children to identify the next number to say. A common mistake children will make is including the starting number when counting. Therefore it is helpful to get children to practise putting the starting number in their head, which initially may mean touching their head and saying this number!	Concrete representation: Ten frame and counters, unifix / Pictorial representation: Number line with “jumps” included already for children to practise counting backwards / Abstract representation: Number sentences for children to solve mentally (this is the final step and not all children will achieve this initially)

Subtraction

Expected Year Group		How it will look	Resources
Find the Difference / Year 1 / Autumn Term		Children explore finding the difference as a form of subtraction. Often children can struggle with this skill as both parts are given and previously children’s experience of subtraction has been identifying the missing part or what is left. Children can use the skill of counting on or back to help them find the difference. Alternatively they can make both amounts, using concrete representations, and visually see how many more/less a number is.	Concrete representation: Unifix towers, numicon shapes on top of each other. / Pictorial representation: picture stories for children to visually see the difference. / Abstract representation: counting on or back to identify the difference between two numbers.
Compare Statements / Year 1 / Autumn Term		Initially children use the inequality symbols ( > < =) to compare statements. A + B < C For example, / 3 + 1 is greater than ___ / 3 + 1 is less than ___ / Next children move on to comparing two calculations. A +B < D + E / Children should also recap that = means “equal to” and use it to compare two calculations which are equal/the same.	Concrete representation: Ten frame and counters, unifix cubes, counters. Children should be initially given laminated inequality symbols to physically manipulate. / Pictorial representation: pictures of amounts to compare with statements, / Abstract representation: using the inequality symbols. / Stem Sentences / ____ is greater than _____ / ___ is less than _____
Subtraction not crossing 10 / Year 1 / Autumn Term 2 and Spring 1		Children build on the language of subtraction with numbers within 20. The use of is important so children know when nothing is taken away, the number they began with is the number which remains or when the whole group is taken away there is nothing left. Children should use part– whole model alongside practical equipment to reinforce number bonds within 20.	Concrete representation: Ten frame and counters, unifix cubes, numicon shapes to put on top or coloured pegs. / Pictorial representation: first, now, then stories and pictures for children to interpret into calculations to solve. Number lines, part whole model / Abstract representation: Scaffold for children to complete to support them with how to write a calculation correctly.

Subtraction

Expected Year Group		How it will look	Resources
Subtraction making 10 / Year 1 / Spring 1		This step focuses on the strategy of partitioning to make 10. For example, with the calculation 12 - 5, children partition 5 into 2 and 3, and take the 2 away from 12 leaving them with the calculation 10 - 3. This allows children to use their knowledge of number bonds to find the answer. / This strategy will be tricky for children without scaffolds and concrete manipulatives to support.	Concrete representation: Ten frames and coloured counters / Pictorial representation: part-whole model scaffold to be used in conjunction with partitioning the smaller number to make ten. / Abstract representation: Using a number line children begin by jumping back to ten and then counting backwards in 1s to the answer.
Related Facts / Year 1 / Spring 1		Children explore number bonds within 20 for addition and subtraction. They should work using concrete and pictorial representations to support children making links between addition and subtraction calculations. At this stage, children should be confident in knowing addition and subtraction are inverse operations. They will also learn that addition is commutative but subtraction is not.	Concrete representation: Ten frames and coloured counters, pegs and numicon shapes, unifix / Pictorial representation: part-whole model, bar model, picture stories. / Abstract representation: empty number sentences for children to complete.
Compare number sentences / Year 1 / Spring 1		Children compare calculations within 20 using the inequality symbols. Children will likely need to still use concrete manipulatives at this stage to help them compare calculations.	Concrete representation: Children make 2 calulations using numicon, ten frames and compare using laminated inequality symbols to manipulate. / Pictorial representation: pictures of amounts to compare with statements, / Abstract representation: using the inequality symbols

Subtraction

Expected Year Group		How it will look	Resources
Number Bonds to 20 / Year 2 / Autumn 1		Children apply their understanding of known addition and subtraction facts within 20 to identify all related facts. Children will build on their experiences in Year 1 and should understand the purpose of the equals sign as well as addition and subtraction signs. / Children should also be given time to check calculations using the inverse. Although checking calculations should not be limited to this.	Concrete representation: Ten frames and coloured counters. / Pictorial representation: part-whole model, bar model. / Abstract representation: blank calculations to support children to find all related facts. Calculations in which some are incorrect, children have to use their knowledge to identify which.
Add and Subtract 1’s / Year 2 / Autumn 1		Children should start to identify the pattern, when you add or subtract 1, commenting on what has happened to the number. This is the step before finding ten more and ten less. The pattern should be highlighted for adding 2 (by adding another one) and then adding 3.	Concrete representation: Ten frames and coloured counters, dienes, unifix, bead strings. / Pictorial representation: picture stories, part-whole model using pictures. / Abstract representation: missing numbers on a number track/100 square.
10 more and 10 less / Year 2 / Autumn 1		At the stage, teaching should be focussed on the importance of the tens digit within a number. Children explore using a 100 square to see what happens to the numbers in the columns. Children learn that when adding or subtracting ten, the tens digit changes whilst the ones digit remains the same. To support children, they need to see how the number changes using concrete materials before moving on to the abstract.	Concrete representation: Ten frames and coloured counters, dienes, unifix, bead strings. / Pictorial representation: picture stories, part-whole model using pictures. / Abstract representation: missing numbers on a number track/100 square.

Progression of Skills– Subtraction

Expected Year Group		How it will look	Resources
Add and Subtract 10 / Year 2 / Autumn 1		Building on the previous step of finding 10 more and 10 less, children begin to add and subtract 10s. Children are reminded of the importance of the tens digit changing whilst the ones digit remains the same. / Children should be provided with lots of opportunities to add and subtracts tens using concrete and pictorial representations before moving on to abstract.	Concrete representation: dienes, ten frames, numicon. / Pictorial representation: picture stories for children to interpret and record as a calculation, tens and ones column to support adding/subtracting tens. / Abstract representation: Using the column method.
RECAP / Subtraction making 10 / Year 2		THIS IS A RECAP FROM YEAR 1 / This step focuses on the strategy of partitioning to make 10. For example, with the calculation 12 - 5, children partition 5 into 2 and 3, and take the 2 away from 12 leaving them with the calculation 10 - 3. This allows children to use their knowledge of number bonds to find the answer. / This strategy will be tricky for children without scaffolds and concrete manipulatives to support.	Concrete representation: Ten frames and coloured counters / Pictorial representation: part-whole model scaffold to be used in conjunction with partitioning the smaller number to make ten. / Abstract representation: Using a number line children begin by jumping back to ten and then counting backwards in 1s to the answer.
Subtract 1 digit from 2 digit– crossing ten / Year 2		To be successful at this stage, children need to have a strong understanding of Place Value and number bonds. Children need to be able to count to 20 and be able to partition two-numbers in order to subtract from them. They need to understand the difference between one digit and two digit number in order to line them up correctly in columns.	Concrete representation: dienes, ten frame and counters / Pictorial representation: Part whole model, place value frame / Abstract representation: column method, calculations to solve

Subtraction

Expected Year Group		How it will look	Resources
Subtract 2 digit from 2 digit (Part 1 not crossing tens boundary) / Year 2 / Autumn		It is important children explore subtracting 2 digit numbers without crossing the tens boundary before moving on to part 2. Children need to use concrete manipulatives but also draw images of dienes so they can independently solve problems. Using first, then, now stories alongside pictorial representations such as pictures of dienes will support children and their understanding. For example,	Concrete representation: dienes, ten frames, Numicon. / Pictorial representation: drawing images to represent dienes, part-whole model, first, then, now stories. / Abstract representation: calculations to solve, column method.
Subtract 2 digit from 2 digit (Part 2 crossing tens boundary) / Year 2 / Autumn		Children use their knowledge that one ten is the same as one ten to exchange when crossing a ten in subtraction. Children should continue to use concrete manipulatives (dienes) and pictorial representations (number lines and part-whole models) to develop understanding.	Concrete representation: dienes, ten frames, Numicon. / Pictorial representation: drawing images to represent dienes, part-whole model, empty number line. / Abstract representation: calculations to solve, column method.

Multiplication

Expected Year Group		How it will look	Resources
Doubling / Reception / Spring 1 / and Summer 1 / Spring– to 10 Summer– to 20		Children will learn that double means “twice as many”. They should be given opportunities to build doubles using real objects and mathematical equipment. Building using the pair wise patterns on ten frame helps children to see doubles. Encourage children to say the doubles as they build them, e.g. Double 2 is 4. Provide children with doubles and non doubles for them to compare.	Concrete representation: mirrors and counters, natural materials, ten frame and counters, numicon shapes, multilink and unifix. / Pictorial representation: Picture stories, art painting doubles on butterfly wings, drawing doubles, fingers, playing snap with playing cards/dots. / Abstract representation: Recording as a calculation, use a scaffold to support children with this.
Sharing and Grouping / Reception / Spring 1 / and Summer 1 / Spring– to 10 Summer– to 20		The language of sharing is something most children will already have experiences of and will be able to talk about needing to make it “fair” when we share! Let children explore sharing real objects such as gingerbread man and buttons, pencils into pots and discuss how each has to be “equal” or the same. Children also need to be given experiences of sharing where there are not equal groups and so they can discuss and resolve this.	Concrete representation: At this stage it is real life experiences. Such as handing out snack at snack time, button on to gingerbread man, goldilocks and three bears plates and cups. / Pictorial representation: Picture stories, drawing equal amounts such as 10 sweets and 2 plates.
Odd and Even / Reception / Spring 1 / and Summer 1 / Spring– to 10 Summer– to 20		Children learn that some quantities can be shared equally into two groups and some won’t. They begin to notice that some quantities can be grouped into pairs and some will have one left over. As well as real life contexts, children can also explore numicon identifying which shapes have an odd or even structure.	Concrete representation: using numicon to identify odd and even structure, ten frame and building pair wise patterns, unifix cubes, 5 friends into pairs / Pictorial representation: Picture stories, drawing equal amounts into pairs or 2 groups.

Multiplication

Expected Year Group		How it will look	Resources
Counting in 2’s / Year 1 / Spring Term– Place Value / Summer Term– Multiplication		This stage has initially been covered in Place Value and therefore is a recap. / Children will build on their previous knowledge of counting in 2’s and go beyond 20 up to 50. They will apply their previous learning of 1 more and 1 less to counting forwards and backwards in 2’s.	Concrete representation: numicon shape number 2, double sided counters on ten frame, multilink or unifix in pairs / Pictorial representation: Picture stories– pairs of socks/ gloves, pencils in pots, bunches of bananas in sets of 2, number line or number track. / Abstract representation: Repeated addition number sentences..
Counting in 5’s / Year 1 / Spring Term– Place Value / Summer Term– Multiplication		This stage has initially been covered in Place Value and therefore is a recap. / Children build on previous learning of counting in fives to go beyond 20 and up to 50 The 1-50 grid can be used to spot and discuss patterns that emerge when counting in 5s.	Concrete representation: numicon shape number 5, double sided counters on a ten frame, multilink or unifix in pairs / Pictorial representation: Picture stories– pencils in pots, hands, number line or number track and 50/100 square / Abstract representation: / Repeated addition number sentences
Counting in 10’s / Year 1 / Summer Term– Multiplication		Children count in groups of tens for the first time. Previously they have counted in 2s and 5s. They use pictures, bead strings and number lines to support their counting. Counting in 10s on a hundred square will also support children to see the similarities between the numbers when we count in tens.	Concrete representation: numicon, ten frame, multilink or unifix, bead strings, dienes / Pictorial representation: Picture stories– cakes on a tray, birds in a tree, hands, number line or number track and 50/100 square / Abstract representation: / Repeated addition number sentences

Multiplication

Expected Year Group		How it will look	Resources
Making Equal Groups / Year 1 Summer Term / Year 2 Autumn Term		Children begin by using stories which link to pictures and concrete manipulatives to explore making equal groups and write statements such as ‘there are ___ groups of ___.’ They will recognise and explain how they know when they are equal or not. Children see equal groups that are arranged differently so they understand that the groups look different but can still be equal in number. At this stage children do not explore multiplication formally.	Concrete representation: numicon, unifix/multilink, counters / Pictorial representation: picture stories / Abstract representation: Stem sentence: there are ___ groups of ___ / Repeated addition (see next step)
Add Equal Groups / Year 1 Summer Term / Year 2 Autumn Term		Children use equal groups to find a total. They focus on counting equal groups of 2, 5 and 10 and explore this within 50. Children could begin by linking this to real life, for example animal legs, wheels, flowers in vases etc. Stem sentences alongside number sentences can help children link the calculation with the situation. Ensure children have the opportunity to say their sentences aloud.	Concrete representation: numicon, unifix/multilink, double sided counters and ten frame / Pictorial representation: picture stories, number line or number track / Abstract representation: Stem sentence: there are ___ groups of ___ / Repeated addition (provide children with scaffold to support recording repeated addition)
Make Arrays / Year 1 Summer Term		Children begin to make arrays by making equal groups and building them up in columns or rows. They use a range of concrete and pictorial representations alongside sentence stems to support their understanding. Children also explore arrays built incorrectly and recognise the importance of columns and rows.	Concrete representation: unifix/multilink, double sided counters and ten frame, Lego/Duplo / Pictorial representation: picture stories– sweets/cakes/buttons in a rows and columns / Abstract representation: Stem sentences: / There are ____ columns / There are ___ rows

Multiplication

Expected Year Group		How it will look	Resources
Making Doubles / Year 1 Summer Term / Year 2 Autumn Term		Children explore doubling with numbers up to 20. Reinforce understanding that ‘double’ is two groups of a number or an amount. Children show and explain what doubling means using concrete and pictorial representations. They record doubling using the sentence, ‘Double ___ is ____’ and use repeated addition to represent doubles in the abstract. They look at representations to decide whether that shows doubling or not.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– hands, numicon, fruit, sweets, dice / Abstract representation: Stem sentence: / Double ___ is ____ / Repeated addition
Making Equal Groups / Year 2 Autumn Term		Children should be able to make equal groups to demonstrate their understanding of the word ‘equal’. With the examples provided to the children, it is important that they are exposed to numerals and words, as well as multiple representations.	Concrete representation: numicon, unifix/multilink, counters and ten frames, dienes, / Pictorial representation: picture stories of numicon, ten frames, dienes, coins, plates of food. / Abstract representation: Numerals and words. / Stem sentence: there are ___ groups of ___ / Repeated addition (see next step)
Add Equal Groups / Year 2 Autumn Term		Children begin to connect equal groups to repeated addition. At this point children have added 3 one digit numbers together, therefore they can add up to 3 equal groups when each group is any one digit number. If there are more than 3 equal groups, the examples must be limited to 2s, 5s, 10s and 3s.	Concrete representation: numicon, unifix/multilink, double sided counters and ten frame / Pictorial representation: picture stories, number line or number track / Abstract representation: / Stem sentence: there are ___ equal groups of ___ / Repeated addition (provide scaffolds for those children who are struggling to record as a repeated addition)

Multiplication

Expected Year Group		How it will look	Resources
The Multiplication Symbol / Year 2 Autumn Term		Children are introduced to the multiplication symbol for the first time. They should link repeated addition and multiplication together, using stem sentences to support their understanding. They should also be able to interpret mathematical stories and create their own involving multiplication. The use of concrete resources and pictorial representations is still vital for understanding.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– hands, numicon, fruit, sweets, dice / Abstract representation: Stem sentence: / There are ___ equal groups with ____ in each group / Repeated addition and multiplication
Multiplication from Pictures / Year 2 Autumn Term		Children will use the multiplication symbol and work out the total from pictures. They should also be able to interpret a multiplication word problem by drawing images to help them solve it. Coins could be used within this small step too.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– hands, numicon, fruit, sweets, dice / Abstract representation: Stem sentence: / ___ lots of ___ = ___ / ____ multiplied by ___= ___
Using Arrays / Year 2 Autumn Term		Children explore arrays to see the commutativity of multiplication facts e.g. 5 × 2 = 2 × 5 / The use of the array could be used to help children calculate multiplication statements. The multiplication symbol and language of ‘lots of’ should be used interchangeably.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: pictures in rows and columns / Abstract representation: Scaffolds of repeated addition and multiplication sentences for children to complete

Multiplication

Expected Year Group		How it will look	Resources
Making Doubles / Year 2		This is a recap from Year 1 / Children explore doubling with numbers up to 20. Reinforce understanding that ‘double’ is two groups of a number or an amount. Children show and explain what doubling means using concrete and pictorial representations. They record doubling using the sentence, ‘Double ___ is ____’ and use repeated addition to represent doubles in the abstract. They look at representations to decide whether that shows doubling or not.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– hands, numicon, fruit, sweets, dice / Abstract representation: Stem sentence: / Double ___ is ____ / Repeated addition
2 times table / Year 2		Children should be comfortable with the concept of multiplication so they can apply this to multiplication tables. Images, as well as number tracks, should be used to encourage children to count in twos. Resources such as cubes and number pieces are important for children to explore equal groups within the 2 times-table.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– 2 fingers, numicon, fruit, sweets, dice, number tracks with missing numbers / Abstract representation: Multiplication sentences (scaffolds for those who need support )
5 times table / Year 2		Children can already count in 5s from any given number. They will also have developed understanding of the 2 times table. This small step is focused on the 5 times table and it is important to include the use of zero. Children should see the = sign at both ends of the calculation to understand that it means ‘equals to’.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories– hands, numicon, fruit, sweets, dice, number tracks with missing numbers / Abstract representation: Multiplication sentences (scaffolds for those who need support )

Multiplication

Expected Year Group		How it will look	Resources
10 times table / Year 2		Children have counted in 10s from any given whole number. This small step is focused on the 10 times-table and it is important to include the use of zero. Children should see the = sign at both ends of the calculation to understand what it means.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories, number tracks with missing numbers, bar model / Abstract representation: Multiplication sentences (scaffolds for those who need support )

Division

Expected Year Group		How it will look	Resources
Sharing and Grouping / Reception / Spring 1 / and Summer 1 / Spring– to 10 Summer– to 20		The language of sharing is something most children will already have experiences of and will be able to talk about needing to make it “fair” when we share! Let children explore sharing real objects such as gingerbread man and buttons, pencils into pots and discuss how each has to be “equal” or the same. Children also need to be given experiences of sharing where there are not equal groups and so they can discuss and resolve this.	Concrete representation: At this stage it is real life experiences. Such as handing out snack at snack time, button on to gingerbread man, goldilocks and three bears plates and cups. / Pictorial representation: Picture stories, drawing equal amounts such as 10 sweets and 2 plates.
Sharing and Grouping / Reception / Spring 1 / and Summer 1 / Spring– to 10 Summer– to 20		The language of sharing is something most children will already have experiences of and will be able to talk about needing to make it “fair” when we share! Let children explore sharing real objects such as gingerbread man and buttons, pencils into pots and discuss how each has to be “equal” or the same. Children also need to be given experiences of sharing where there are not equal groups and so they can discuss and resolve this.	Concrete representation: At this stage it is real life experiences. Such as handing out snack at snack time, button on to gingerbread man, goldilocks and three bears plates and cups. / Pictorial representation: Picture stories, drawing equal amounts such as 10 sweets and 2 plates.
Make Equal groups– Grouping / Year 1– Summer Term		Children start with a given total and make groups of an equal amount. They record their understanding in sentences, not through formal division at this stage. Children can develop their understanding of equal groups by also being exposed to numbers which do not group equally	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories / Abstract representation: / Stem sentence: / There are ____ equal groups of ____. / There are ____ altogether.

Division

Expected Year Group		How it will look	Resources
Make Equal Groups– Sharing / Year 1– Summer Term		Children explore sharing as a model of division. They use 1 : 1 correspondence to share concrete objects into equal groups. Children also need to be given the opportunity to see when a number of objects cannot be shared equally into equal groups.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories, part whole model / Abstract representation: / Stem sentence: / ___ shared equally between ___ is ____
Make Equal groups– Grouping / Year 2– Spring Term		This is a recap from Year 1 / See previous step
Make Equal Groups– Sharing / Year 2– Spring Term		Children divide by sharing objects into equal groups using one-to-one correspondence. They need to do this using concrete manipulatives in different contexts, then move on to pictorial representations. Children will be introduced to the ‘÷’ symbol. They will begin to see the link between division and multiplication.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories, number lines / Abstract representation: / Stem sentences: / ___ shared equally between ___ / ___ groups of ____ make ____ / Division sentences
Divide by 2 / Year 2– Spring Term		Children should be secure with grouping and sharing. They will use this knowledge to help them divide by 2 They will be secure with representing division as an abstract number sentence using the division and equals symbol. Children should be able to count in 2s and know their 2 times table.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories, number line / Abstract representation: / Division sentences / Stem sentences: / There are ____ groups. / There are ____ in each group.

Division

Expected Year Group		How it will look	Resources
Odd and Even Numbers / Year 2– Spring Term		Building on from Year 1, children should be able to recognise odd and even numbers. They will use concrete manipulatives to explore odd and even numbers and the structure of these. Questions: what makes this number odd? How can you find out if ___ is odd or even number?	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: pictures of dienes, coins, numicon, bead strings, fingers, hands, socks / Abstract representation: / Numerals and words
Divide by 5 / Year 2– Spring Term		During this step, children focus on efficient strategies and whether they should use grouping or sharing depending on the context of the question. They use their knowledge of the five times table to help them divide by 5 They will continue to see the = sign both before and after the calculation.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: pictures stories to solve, number lines / Abstract representation: / Division and multiplication sentences
Divide by 10 / Year 2– Spring Term		Children should already be able to multiply by 10 and recognise multiples of 10. They will need to use both grouping and sharing to divide by 10 depending on the context of the problem. Children start to see that grouping and counting in 10s is more efficient than sharing into 10 equal groups.	Concrete representation: numicon, double sided counters and 2 ten frames, unifix/multilink / Pictorial representation: picture stories, number lines / Abstract representation: / Division and multiplication sentences. / Word problems.

Fractions

Expected Year Group		How it will look	Resources
Exploration of cutting shapes / Reception– Summer Term		As a pre-requisite to halving– let children explore cutting up shapes looking at what new shapes they can make such as when you half a square you can make 2 triangles or 2 rectangles! The language of “half” and “whole” to be introduced to the children. This is an exploration of making new shapes from halving a whole shape and there is no formal recording at this stage.	Concrete representation: playdough, cutters and scissors, coloured gummed paper / Pictorial representation: pictures of halved shapes– can you find the other half? / Abstract representation: / Language of half
Find half of a shape / Year 1-Summer Term		Children explore finding a half for the first time using shapes and sets of objects. They will use the vocabulary ‘half’ and ‘whole’. Children will not at this stage use the fractional notation of ½. It is important that they know that a half means ‘one of two equal parts’ and are able to count them.	Concrete representation: shapes to cut in half / Pictorial representation: pictures of food, shapes and objects to half / Abstract representation: / Language of half, whole
Find half of a quantity / Year 1-Summer Term		Children use their understanding of finding half of an object or shape and apply this to finding half of a small quantity. It is important that children find the total amount and can then show how this number can be shared equally into two. The use of concrete manipulatives such as counters can help children to find a half.	Concrete representation: double sided counters and 2 ten frames, unifix/multilink, bead strings, halving mat / Pictorial representation: picture stories, / Abstract representation: / Stem sentences: / Half of ___ is ___ / For those who are ready– introduce the fraction half

Fractions

Expected Year Group		How it will look	Resources
Quarter a shape / Year 1-Summer Term		Children explore quarters for the first time. They will develop their understanding of equal parts and non-equal parts and relate this to a shape or object being split up into four equal parts. Children will use the words quarters and parts at this stage but will not use the fractional notation of ¼	Concrete representation: shapes to cut in quarter / Pictorial representation: pictures of quartered shapes– / Abstract representation: / Language of quarter, whole
Quarter a quantity / Year 1-Summer Term		Children find a quarter of a small quantity through equal sharing. It is important they can show the groups clearly by drawing around quantities or by physically sharing into something. Children will use the word quarters and parts at this stage but will not use the fractional notation of ¼. They also begin to describe capacity using the terminology ‘a quarter full’.	Concrete representation: double sided counters and 2 ten frames, unifix/multilink, bead strings, quartering mat / Pictorial representation: pictures of food, shapes and objects to quarter / Abstract representation: / Stem sentences: / Quarter of ___ is ___ / For those who are ready– introduce the fraction quarter
Make Equal Parts / Year 2– Autumn and Spring Term		Children understand the concept of a whole as being one object or one quantity. Children explore making and recognising equal and unequal parts. They should do this using both real life objects and pictorial representations of a variety of shapes and quantities.	Concrete representation: numicon, unifix/multilink, double sided counters and ten frames / Pictorial representation: picture stories– identify which are equal or unequal, part whole model / Abstract representation: / Stem sentences: / Equal groups of ___

Fractions

Expected Year Group		How it will look	Resources
Recognise a Half / Year 2– Autumn and Spring Term		Children understand that halving is splitting a whole into two equal parts. They are introduced to the notation ½ for the first time and will use this alongside sentence stems and ‘half’ or ‘halves’. They should be introduced to the language of numerator, denominator and what these represent. Children must explore halves in different contexts, for example, half of a length, shape or set object.	Concrete representation: double sided counters and 2 ten frames, unifix/multilink, bead strings, halving mat / Pictorial representation: pictures of quartered shapes, quantities and objects / Abstract representation: Written fraction for a half / Stem sentences: / The whole is split into ___ equal parts
Find a half / Year 2– Autumn and Spring Term		In this small step children find a half of a set of objects or quantity. Links should be made here to dividing by 2. Children may need to use the concept of sharing to find a half. Paper plates, hoops and containers can be used to share objects into 2 equal groups.	Concrete representation: double sided counters and 2 ten frames, unifix/multilink, bead strings, halving mat, paper plates, hoops and containers / Pictorial representation: picture stories of shapes, quantities and objects halved. / Abstract representation: Written fraction for a half / Stem sentences: Half of ___ is ___ / ____ is shared into 2 equal groups
Recognise a Quarter / Year 2– Autumn and Spring Term		Children extend their knowledge of the whole and halves to recognise quarters of shapes, objects and quantities. They continue to work concretely and pictorially, understanding that they are splitting the whole into 4 equal parts and that each part is one quarter.	Concrete representation: unifix/multilink, bead strings, quartering mat, counters / Pictorial representation: picture stories of shapes, quantities and objects / Abstract representation: / Written fraction for a quarter / Stem sentences: / The whole is split into ___ equal parts

Fractions

Expected Year Group		How it will look	Resources
Find a Quarter / Year 2– Autumn and Spring Term		Children find quarters of shapes, objects and quantities. They begin by physically sharing amounts into four equal groups, or drawing around quantities then move towards working in the abstract. The link between the concrete, pictorial and abstract representations should be made explicit. Support children in seeing the relationship between half of an amount and a quarter of an amount.	Concrete representation: unifix/multilink, bead strings, quarter mat, paper plates, hoops and containers / Pictorial representation: picture stories of objects, quantities or shapes in quarters / Abstract representation: Written fraction for a quarter / Stem sentences: Half of ___ is ___ / ____ is shared into 4 equal groups
Recognise a third / Year 2– Autumn and Spring Term		Children apply understanding of fractions to finding thirds. They continue to use the language of ‘whole’ and ‘equal parts’ and understand that one third is equal to one part out of three equal parts. They write one third as a fraction and explain what each of the digits represents in the fractional notation.	Concrete representation: double sided counters and 3 ten frames, unifix/multilink, bead strings, shapes / Pictorial representation: picture stories, shapes, objects and quantities split into thirds / Abstract representation: Written fraction for a third / Stem sentences: / ____ equal groups
Find a Third / Year 2– Autumn and Spring Term		Children build on their understanding of a third and three equal parts to find a third of a quantity. They use their knowledge of division and sharing in order to find a third of different quantities using concrete and pictorial representations to support their understanding.	Concrete representation: unifix/multilink, counters, bead strings, double sided counters / Pictorial representation: picture stories, shapes, objects and quantities split into thirds / Abstract representation: / The fraction ¼ / Stem sentences: / One third of ____ is ____

Fractions

Expected Year Group		How it will look	Resources
Unit Fractions / Year 2– Autumn and Spring Term		Children understand the concept of a unit fraction by recognising it as one equal part of a whole. They link this to their understanding of recognising and finding thirds, quarters and halves. Children also need to understand that the denominator represents the number of parts that a shape or quantity is split into.	Concrete representation: unifix/multilink, bead strings / Pictorial representation: picture stories of objects, quantities or shapes / Abstract representation: Written fractions
Non-Unit Fractions / Year 2– Autumn and Spring Term		Children are introduced to the non-unit fractions 2/3 and ¾ for the first time. They also need to look at fractions where the whole is shaded and how these fractions are written. Children see that the numerator and denominator are the same when the fraction is equivalent to one whole	Concrete representation: double sided counters and 3 ten frames, unifix/multilink, / Pictorial representation: picture representations of different fractions / Abstract representation: non unit fractions
Equivalence of a half and 2 quarters / Year 2– Autumn and Spring Term		Children explore the equivalence of two quarters and one half of the same whole and understand that they are the same. Children tackle this practically, using strips of paper and concrete apparatus (e.g. counters, Cuisenaire rods, number pieces).	Concrete representation: strips of paper, counters, unifix/multilink, shapes to colour / Pictorial representation: picture stories, shapes, objects and quantities, bar model / Abstract representation: / The fractions ¼ ½ 2/4

Fractions

Expected Year Group		How it will look	Resources
Find three quarters / Year 2– Autumn and Spring Term		Children use their understanding of quarters to find three quarters of a quantity. They work concretely and pictorially to make connections to the abstract. Children should be encouraged to spot patterns and relationships between quarters of amounts.	Concrete representation: strips of paper, counters, unifix/multilink, shapes to colour, hoops, plates, containers / Pictorial representation: picture stories of objects, quantities or shapes / Abstract representation: Written fractions
Count in Fractions / Year 2– Autumn and Spring Term		Using their knowledge of halves, thirds and quarters, children count in fractions from any number up to 10. They begin to understand that fractions can be larger than one whole. Teachers can use a number line, counting stick or hoop to support them in counting in fractions.	Concrete representation: double sided counters, unifix/multilink, counting stick / Pictorial representation: picture stories, number lines, counting sticks / Abstract representation: Written fractions

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