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Progression in Mathematics
EYFSYear 1Year 2Year 3Year 4Year 5Year 6
Number, Addition and SubtractionCount within 5 using the five principles of counting in a range of contexts (E1)
Count within 10 using the five principles of counting in a range of contexts
Count within 20 using the five principles of counting in a range of contexts
Reason about and solve problems involving saying which number is one more or one less / fewer (E2) than a given number
Using quantities and objects reason about and solve problems involving adding and subtracting 2 singledigit numbers and counting on or back to find the answer
Partition each of the numbers from 15 in different ways systematically (1:1)
Partition each of the numbers from 610 in different ways systematically in a range of contexts (1:2)
For any number within 10, be able to say what is one more / fewer / less(E2) in a range of contexts
For any number within 20, be able to say what is one more / fewer / less in a range of contexts
Find and reason about the sum of two 1 digit addends in concrete and pictorial aggregation and augmentation contexts including using the + and = signs (1:3)
Find and reason about the difference between two 1 digit numbers in concrete and pictorial contexts including using the and = signs
Within 10, where one addend is known, find the other addend in a range of contexts
Within 10, find the minuend or subtrahend where the difference is known in a range of contexts (1:4)
Partition 2 digit numbers into Tens and Ones in a range of contexts
Add and subtract 1 digit and 2 digit numbers within 20 concretely, pictorially and with missing number contexts. Partition any twodigit number into different combinations of tens and ones, explaining their thinking verbally, in pictures or using apparatus
Add and subtract any 2 twodigit numbers using an efficient strategy, explaining their method verbally, in pictures or using apparatus (e.g. 48 + 35; 72 17)
Recall all number bonds to and within 10 and use these to reason with and calculate bonds to and within 20, recognising other associated additive relationships (e.g. If 7 + 3 = 10, then 17 + 3 = 20; if 7 3 = 4, then 17 3 = 14; leading to if 14 + 3 = 17, then 3 + 14 = 17, 17 14 = 3 and 17 3 = 14)
GD (TAF) Read scales where not all numbers on the scale are given and estimate points in between
Use reasoning about numbers and relationships to solve more complex problems and explain their thinking (e.g. 29 + 17 = 15 + 4 + ; together Jack and Sam have 14. Jack has 2 more than Sam. How much money does Sam have? etc.)
Reason about and solve problems involving partitioning 3 digit numbers into Hundreds, Tens and Ones
Reason about and solve problems involving partitioning 3 digit numbers into groups of 50, 25 and 20 in a range of contexts (1:2)
Reason about when to use a partitioning, compensation or redistribution strategy when mentally adding or subtracting (3:1)
Reason about and solve problems involving comparison and ordering numbers up to 1000 in a range of contexts
Add and subtract 3 digit numbers using column addition and subtraction with regrouping in a range of reasoning and problem solving contexts including missing number problems. (3:2)Reason about and solve problems involving partitioning 4 digit numbers into Thousands, Hundreds, Tens and Ones in different contexts (1:2)
Reason about and solve problems (particularly in graphing and measures) involving partitioning 4 digit numbers into groups of 500, 250 and 200
Reason about when to use a partitioning, compensation or redistribution strategy when mentally adding or subtracting (3:1)
Use rounding to the nearest 10, 100 or 1,000 to approximate answers to problems in a range of contexts
Reason about and solve problems involving comparison and ordering numbers up to and greater than 1000 in a range of contexts
Add and subtract 4 digit numbers using column addition and subtraction with regrouping in a range of reasoning and problem solving contexts including missing number problems
Reason about and solve problems involving partitioning numbers into integers and decimal fractions (0.1 / 0.01 / 0.001)
Use the understanding that 1p is 0.01 of 1 to solve problems involving moneyLink the partitioning of up to 6 digit numbers to the relationships between Hundreds, Tens and Ones in a range of contexts (1:2)
Reason about and solve problems involving partitioning up to 6 digit numbers into 2,4 and 5 equal parts in a range of contexts
Reason about when to use a partitioning, compensation or redistribution strategy when mentally adding or subtracting larger numbers (3:1)
Add and subtract up to 6 digit numbers using column addition and subtraction with regrouping in a range of reasoning and problem solving, including multi step, contexts including missing number problems (3:2)
Use strategies involving equal difference to make calculations easier to solve with and without using a written method.
Solve problems (particularly in coordinate and graphing contexts) involving the use of negative numbers and calculation across 0
Order and compare larger numbers by using the value of the digits in order in a range of contexts (1:2)
Demonstrate that fluent calculation involves making sensible decisions about when to use particular mental strategies and when to use written methods in a range of contexts including in problems which require more than one type of operation (6:1)
Multiplication and DivisionReason about and solve problems involving doubling, halving and sharing
Solve one step problems involving counting in groups of 2,10 and 5 in concrete and pictorial contexts.
Recall multiplication and division facts for 2, 5 and 10 and use them to solve simple problems, demonstrating an understanding of commutativity as necessary
GD (TAF) Recall and use multiplication and division facts for 2, 5 and 10 and make deductions outside known multiplication facts
Solve unfamiliar word problems that involve more than one step
Reason about and solve problems involving understanding the connections between the 2,4 and 8 times tables and the 3,6 and 9 times tables
Solve multiplication and division problems in a range of contexts including missing number problems, integer scaling problems and correspondence problems in which n objects are connected to m objects (3:3)
Solve multiplication and division problems in a range of contexts using multiplication facts up to 12 x 12
Solve problems in a range of contexts using multiplication and division by 10, 100 and 1,000
Reason about and solve problems in a range of contexts using short multiplication
Reason about and solve problems in a range of contexts using short division including with remainders
Solve multiplication and division problems, including those with multiples steps in a range of contexts
Reason about and solve problems involving the multiplication of three factors
Reason about and solve problems involving multiplication and division of decimal fractions
Reason about and solve problems involving finding factors and multiples of numbers
Reason and solve problems in a range of contexts using long multiplication
Reason and solve problems in a range of contexts using long division including with remainders
Fractions
Reason about and solve problems involving recognising and finding half as one of two equal parts and a quarter as one of four equal parts of an object, shape or quantity.
Reason about and solve problems involving finding 1/4, 1/3 , 1/2 , 2/4, 3/4, of a number or shape, and know that all parts must be equal parts of the whole Reason about and solve problems involving finding unit and nonunit fractions, including tenths, of a set of objects or a shape divided into equal sized parts in a range of contexts (3:4)
Reason about and solve problems involving finding, recognising and explaining equivalent fractions with small denominators in a range of contexts
Add and subtract fractions with the same denominator within one whole
Explain a rule for ordering fractions with the same denominator (3:5)Reason about and solve problems using factors and multiples to recognise equivalent fractions and simplify where appropriate in a range of contexts
Reason about and solve problems involving ordering fractions with denominators which are multiples of the same number in a range of contextsReason about and solve problems involving mixed numbers and improper fractions and convert from one from to the other in a range of contexts
Reason about and solve problems involving multiplication of proper fractions and mixed numbers by whole numbers in a range of contexts
Reason about and solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25Reason about and solve problems involving addition and subtraction of fractions with different denominations and mixed numbers in a range of contexts
Reason about and solve problems involving multiplication and division of pairs of proper fractions by whole number, writing the answer in its simplest form
Reason about and solve problems involving equivalences between simple fractions, decimals and percentages in a range of contexts
Measures
Use everyday language to talk about, reason about and solve problems involving size, mass (weight), capacity, position, distance, time and money, comparing quantities and objects
Know that the number of coins in a set is different from the total value of the coins and use this to solve problems in a range of contexts
Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.
Compare, describe and solve practical problems for lengths and heights for example, long/short, longer/shorter, tall/short, double/half read scales (2:1) in divisions of ones, twos, fives and tens
Reason about and solve problems involving using different coins to make the same amount
Read the time on a clock to the nearest 15 minutes
GD (TAF) Read the time on a clock to the nearest 5 minutesReason about and solve problems involving measures where scales of different sorts (3:6) are divided into 100s, 10s, 50s, 25s and 20s (e.g. length, mass, capacity and money / coins)
Tell and write the time from an analogue clock and 12hour and 24hour clocks
Reason about and solve problems involving measures where scales are divided into 1000s, 100s, 500s, 250s and 200s (e.g. length, mass, capacity) including converting between units of measurement
Reason about and solve problems involving calculation of area and perimeter in a range of contexts
Solve problems involving calculation of measures measured in negative numbers on both horizontal and vertical scalesReason and solve problems involving understanding when rounding is useful for approximation, estimation or finding averages and when a precise answer is necessary (6:2)
Reason about and solve problems involving calculating the area of parallelograms and triangles
StatisticsReason about and solve problems involving graphs and data of different sorts where the indices are divided into 100s, 10s, 50s, 25s and 20s)
Reason about and solve problems involving graphs and data of different sorts where the indices are divided into 1000s, 100s, 500s, 250s and 200s)
Reason about and solve problems involving interpretation of pie charts and line graphs
Solve problems in a range of contexts involving the calculation of the mean as an average
GeometryReason about and solve problems involving recognising, creating and describing patterns
Explore characteristics of everyday objects and shapes and use mathematical language to describe themReason about and solve problems involving the naming of 2D shapes including rectangles, squares, circles and triangles
Reason about and solve problems involving the naming of and describing the properties of 2D and 3D shapes, including number of sides, vertices, edges, faces and lines of symmetry.
GD (TAF) Describe similarities and differences of 2D and 3D shapes, using their properties (e.g. that two different 2D shapes both have only one line of symmetry; that a cube and a cuboid have the same number of edges, faces and vertices, but different dimensions).Reason about and solve problems involving identifying right angles, recognising that two right angles make a halfterm, three make three quarters of a turn and four a complete turn
Reason about and solve problems involving identifying whether angles are acute or obtuse.
Reason about and solve problems involving comparison and classification of shapes, including quadrilaterals and triangles, based on their properties and sizes in a range of contexts
Reason about and solve problems involving Identifying lines of symmetry in 2D shapes presented in different orientations (4:1)
Draw given angles and measure them in degrees in a range of problem solving contexts
Solve problems involving naming parts of circles, including radius, diameter and circumference and knowing that the diameter is twice the radius.
Reason about and solve problems involving drawing and translating shapes on the coordinate plane and reflecting them in the axes
Reason about and solve problems involving recognising angles where they meet at a point, are on a straight line, or are vertically opposite, and finding missing angles.
AlgebraUse simple formulae
Ratio and proportionSolve problems involving unequal sharing and grouping using knowledge of fractions and multiples
E1 The five principles of counting are: The one to one principle, the stable order principle, the cardinal principle, the abstraction principle and the order irrelevance principle. If you need further information about these, please ask your Maths Subject Leader.
E2 Less refers to an amount and fewer to a number e.g. you can have less water, not fewer water, you can have fewer marbles, not less marbles.
1:1 Systematically means that they should find all of the ways to make the numbers, understanding that they should begin at the smallest number and build to the largest or vice versa
1:2 In a range of contexts means that, in order to say that this statement has been achieved, it should be seen in different types of contexts with different demands of the type of reasoning or problem solving skill required. Just seeing it in one way will not be enough. This is at the heart of the small steps to depth approach so it is assumed that more time needs to be spent on seeing this range of contexts.
1:3 Addends are the numbers which are added to achieve the sum. In the equation 3 + 4 = 7, 3 and 4 are addends and 7 is the sum. Aggregation is when two sets are added to each other e.g. Dave has 2 and Sally has 3. How many have they got altogether? Augmentation is where a quantity is added to another e.g. Sally had 3 and then she found another 2. We define these so that we know that we are using a range of contexts for addition.
1:4 The minuend is the number to be subtracted from. The subtrahend is the number being subtracted. The difference is the answer.
2:1 The scale can be in the form of a number line, a practical situation or a graph axis.
3:1 Partitioning is when the number to be added or subtracted is partitioned first (e.g. 345 + 124 as 300 + 100 = 400, 40 + 20 = 60 so 460 and then 5 + 4 = 9 so 469). Compensation can be used when a number to be added or subtracted is near to a boundary number such as a multiple of 10 (e.g. 365 129 can be seen as 365130 = 235 and then add on the one that was subtracted at the beginning = 236). Redistribution is a strategy that involves adding or subtracting from both numbers to take them to ones which are easier to deal with (e.g. 27135 can be seen as 270 34. 279+65 can be seen as 280 + 64). Its important that children have strategies such as these so that they can weigh up which approach is best to solve any problem rather than only opting for a written method.
3:2 Regrouping means when there are too many or too few in one column so they have to be exchanged for ten of the previous or next column.
3:3 Integer scaling problems are those in which one whole number factor is x times the other (e.g. Dave has 3 sweets. Sally has three times as many. How many does she have?). Problems in which n objects are connected to m objects are a context for multiplication where we are told a factor, often in a menu e.g. red sweets are 5p, yellow sweets are 6p and blue sweets are 7p, and we are asked to multiply that factor by another in the context) e.g. If I buy 6 red sweets, how much do I pay?).
3:4 Children should be able to answer questions such as what are 2/5 of 35 in different contexts but they should also be able to answer questions such as (in a shape divided into 24 equal sized pieces) shade in 1/6 and explain why 6 parts shaded is not 1/6.
3:5 When the denominators are the same, the bigger the numerator, the bigger the fraction and explain why
3:6 Scales of different sorts can be number lines, rulers, weighing scales, measuring containers and, for money, 50p, 20p and 10p pieces)
4:1 It is important that shapes are shown in different orientations and not just in the way that we are used to seeing them in order to focus on the symmetry and not simply the shape.
6:1 It is important by Y6 that children have a range of problem solving strategies at their disposal so that they can confidently use different strategies depending on the type of question rather than relying on only using written methods. This makes them better mathematicians and also saves time in tests such as SATs on using written methods for questions where they might complete them more efficiently by using known facts or mental strategies
6:2  Rounding can be used for approximation (where a precise answer is not needed e.g. 1,125,642 might be described as over a million) , estimation ( 316,543 + 293,875 should be roughly 600,000) or finding averages (e.g. the average attendance at a stadium over a year might be 50,000). Children should understand these different purposes for rounding and when a precise answer is necessary
Greater Depth
In Year 2, the requirements of the Teacher Assessment Framework need to be seen for a child to be seen as working at Greater Depth
As we have discussed, there is no hard and fast rule for what is Greater Depth in other year groups. Our current view is that a child is working at greater depth if they consistently successfully tackle questions which show:
Greater complexity of reasoning than that expected from all children
A greater number of steps which make the question more complex (as opposed to simple steps of the same type)
When finding all the possibilities, a range of starting points or another constraint.
A conflation of two or more aspects of maths
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