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NC AT Framework Strand Assessment Focus Ma1

Using & Applying

Mathematics

Using & Applying Mathematics

Problem-solving

Communicating

Reasoning

Ma2 Number & Algebra

Counting & Understanding Number

Numbers & the Number System

Fractions, Decimals, Percentages & Ratio

Knowing & Using Number Facts

Operations & the Relationship Between Them

Mental Methods

CalculatingSolving Numerical Problems

Written & Calculator Methods

Ma3 Shape, Space & Measures

Understanding ShapeProperties of Shape

Properties of Position & Movement

Measuring Measures

Ma4 Handling Data Handling Data

Processing

Representing

Interpreting

Block StrandA

Counting, partitioning, calculating

Using & applying mathematicsCounting & understanding numberCalculating

BSecuring number facts, understanding shape

Using & applying mathematicsKnowing & using number factsUnderstanding Shape

CHandling data &

Measures

Using & applying mathematicsMeasuringHandling Data

DCalculating, measuring & understanding shape

Using & applying mathematicsCalculatingMeasuringUnderstanding Shape

ESecuring number facts,

calculating & relationships

Using & applying mathematicsCounting & understanding numberKnowing & using number factsCalculating

Ma 1 Using and Applying MathematicsLevel 1

Pupils use mathematics as an integral part of classroom activities. They represent their work with objects or pictures and discuss it. They recognise and use a simple pattern or relationship.

Problem solving Communicating Reasoning

1c7

Use mathematics as an integral part of classroom activities, with some support

With support, use objects to show how they solved a problem and say how the objects help

Continue simple repeating patterns e.g. when only the shape or the colour are changing as in circle, square, circle, square or blue, red, blue, red

1b9

Use given practical apparatus to solve problems, with some support

With support, represent their work with pictures and discuss it with prompting

Draw simple conclusions from their work with support

1a11

Use developing mathematical ideas and methods to solve practical problems

Use mental strategies to solve simple problems

Use pictures to help explain what they did

Create or continue simple repeating patterns with shapes, pictures or objects e.g. when both the shape and colour are changing e.g. red triangle, blue oblong, green square, red triangle, blue oblong, green square

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Typically, with support, they: Engage with practical mathematical activities

involving sorting, counting, measuring by direct comparison

Typically, with support, they: Refer to the materials they have used

and talk about what they have done

Typically, with support, they: Describe how they have sorted objects Copy and continue a simple pattern


Pupils select the mathematics in some classroom activities. They discuss their work using some mathematical language and are beginning to represent it using symbols and simple diagrams. They explain why an answer is correct


2c13

Use a suggested model or approach to tackle an activity

Discuss their work using familiar mathematical vocabulary

Begin to represent their work using symbols and simple diagrams

Decide whether examples satisfy given conditions or make sense

2b15

Select the mathematics they use in some classroom activities

Present solutions in a organised way using simple mathematical conventions

Explain why an answer is correct

2a17

Choose and use appropriate operations to solve problems

Explain decisions, methods and results in pictorial, written or oral form, using mathematical language and number sentences

Make predictions and test these with examples

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Typically, with support, they: Use apparatus, diagrams, role play etc to

represent and clarify a problem Find a relevant starting point, identifying key

facts/ relevant information Move between different representations of a

problem, e.g. a situation described in words or as a diagram

Adopt a suggested model or systematic approach

Make connection and apply their knowledge to similar situations

Typically, with support, they: Describe the strategies and methods

used in their work Listen to others’ explanations, try to

make sense of them. Compare… evaluate…

Use pictures, diagrams and symbols to communicate their thinking, or demonstrate practically a solution or process

Begin to appreciate the need to record and develop their own methods of recording

Typically, with support, they: Predict what comes next in a simple

number, shape or spatial pattern or sequence and give reasons for their opinions

Test true or false statements e.g. if a number ends in 2 then it is even


Pupils try different approaches and find ways of overcoming difficulties that arise when they are solving problems. They are beginning to organise their work and check results. Pupils discuss their mathematical work and are beginning to explain their thinking. They use and interpret mathematical symbols and diagrams. Pupils show that they understand a general statement by finding particular examples that match it.

Problem solving Communicating Reasoning3c19

Choose and use appropriate operations to solve problems and check the solution in the context of the problem

Use and interpret mathematical symbols and diagrams such as + - = < >, Venn and Carroll diagrams

Make a generalisation assisted by probing questions

3b21

Represent the information in a puzzle pr problem using numbers, images or diagrams and use these to find a solution

Beginning to organise their work and check results using some appropriate mathematical conventions

Identify patterns and relationships involving numbers or shapes and come to a simple conclusion

3a23

Persevere to find different approaches and find ways of overcoming difficulties that arise when solving problems

Discuss their work and are beginning to explain their thinking using appropriate vocabulary

Show understanding of a general statement by finding particular examples that match it

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Typically they: Solve a range of problems and

investigations from a variety of contexts, using mathematical content from L2 and 3

Use classroom discussions to break not a problem, recognising similarities to previous work

Put the problem into their own words Choose their own equipment appropriate

to the task, including calculators Check their work and make appropriate

corrections, e.g. decide that 2 numbers less than 100 cannot give a total more than 200

Use simple patterns in results to find other possible outcomes

Typically they: Record in ways that may be modelled by

the teacher Develop own ways of recording Use appropriate vocabulary, e.g.

vocabulary that relates to mathematical content at level 2 or 3

Develop an organised approach as they get into recording their work on a problem

Talk about their work on a problem Talk about their findings by referring to

their written work

Typically they: Make a generalisation with the assistance

of probing questions and prompts Respond to ‘What if?’ questions Are beginning to look for patterns as they

work When they have solved a problem, pose a

similar problem for their partner


Pupils are developing their own strategies for solving problems and are using these strategies both in working within mathematics and in applying mathematics to practical contexts. They present information and results in a clear and organised way. They search for a solution by trying out ideas of their own


4c25

Begin to recognise how a method can be applied to solve similar problems

When prompted, can simplify a problem by trying simpler cases

Present information in a clear and organised way, using tables and lists

Begin to recognise patterns in mathematical problems and actively search for them

Check a solution meets given criteria4b27

In new contexts, apply their own strategies to solve problems

Sometimes has more than one way of finding a solution

Begin to ask probing questions of their own

Discuss confidently their working, using mathematical vocabulary accurately

Search for a solution by trying out ideas of their own

Investigate a general statement to see if it is always, sometimes or never true

4a29

Use mental estimates of the answers to check results

Recognise how a method can be applied to solve similar problems

Explain how and why a known method can be applied to solve other similar problems

Can examine findings and make a general statement about them

Begin to use mathematical language and notation to create a written general statement

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investigations from a variety of contexts, using level 3 and 4 mathematics

Make their own suggestions of ways to tackle a range of problems

Make connections to previous work Pose and answer questions related to a

problems Check answers and ensure solutions

make sense in the context of the problem Review their work and approaches

Typically they: Organise written work e.g. record results

in order Are likely to work in an organised way

from the start Consider appropriate units Use appropriate vocabulary confidently

e.g. vocabulary that relates to mathematical content at level 3 or 4

Typically they: Check their methods and justify answers Identify patterns as they work and form

their own generalisations/ rules in words


In order to carry through tasks and solve mathematical problems, pupils identify and obtain necessary information. They check their results, considering whether these are sensible. Pupils show understanding of situations by describing them mathematically using symbols, words and diagrams. They draw simple conclusions of their own and give an explanation of their reasoning.


5c31

When having difficulty, can stop, re-evaluate and try a different approach

Compare different methods and solutions and decide which is more efficient

Make choices when presenting something and justify why method is effective

Begin to tabulate systematically

Discuss their working in order to justify choices and solutions

5b33

Independently solve problems by breaking down complex calculations into simpler steps

Break down more complex problems, with some prompting, into simpler steps before attempting a solution

Show understanding of situations by describing them mathematically using symbols, words and diagrams

Draw simple conclusions of their own and give an explanation of their reasoning

Search for patterns or reasons why things work out as they do

5a35

With increasing independence, persevere with longer and more complex problems, using a broad range of strategies

Present and interpret solutions in the context of problems, with precise use of language, notation, symbols and diagrams

Begin to justify simple mathematical statements by drawing on previous knowledge

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investigations from a variety of contexts, using mathematical content drawn from level 4 and 5

Recognise the information that is important in solving a problem, determine what is missing and use this to develop a line of enquiry

Break a several-step problem or investigation into simpler steps

Use previous experiences to choose and use efficient methods, that are appropriate to the context

Check as they work, reviewing methods, spotting and correcting errors

Draw knowledge and skills from across the maths curriculum and apply in a new context

Choose the appropriate unit for calculation

Try alternative approaches to overcome difficulties

Typically they: Look for ways to record systematically

e.g. when finding all possibilities Decide how best to represent conclusions

using appropriate recording e.g. tables, diagrams, words and symbols

Express a solution using the appropriate unit

Begin to use simple formulae and symbols to represent problems

Use vocabulary accurately when explaining a solution e.g. vocabulary that relates to mathematical content at level 4 or 5

Typically they: Explain and justify their methods and

solution using their own words and some mathematical vocabulary e.g. how systematic recording helps to prove that all possibilities have been found

Identify more complex sequences, patterns and relationships, and make predictions

Interpret results to draw simple conclusions

Find examples and counter examples to justify conclusions e.g. finding the pattern in the sum of consecutive numbers

Ma 2 Number and AlgebraLevel 1

Pupils count, order, add and subtract numbers when solving problems involving up to 10 objects. They read and write the numbers involved.Calculating

Counting & understanding numbers Knowing and using number factsNumbers & the number

systemFractions, decimals,

percentages and ratio

Operations & relationships between them

Mental methods Solving numerical problems

Written & calculator methods

1c7

Read most numbers up to 10 in familiar contexts

Count on and back in 1s from and to 0.

Understand addition as finding the total of two or more sets of objects in practical situations

Find one or two more or less than a number less than 10, by counting on or back or using practical resources

Solve simple addition problems involving numbers less than 10, using objects, pictures or practical apparatus

Record their work with objects, counters, tokens or mark-making

1b9

Count, read and order numbers (including ordinal numbers) up to 10 in a range of settings

Write numbers up to 10 with increasing accuracy

Understand subtraction as taking away objects from a set and finding how many are left

Add and subtract numbers of objects to 10

Compare two sets to find a numerical difference

Recognise coin values to 10p

Record their work with pictures or diagrams

Begin to use number tracks to calculate

1a11

Record numbers from 0 to 10 and associate them with the number of objects they have counted

Count from 0 to 20 Read and order numbers 0-

20 Recognise 0 as none and 0 in

stories and rhymes and when counting and ordering

Begin to use the fraction one-half

Understand the operations of addition and subtraction as ‘take away’ and ‘difference’ and use related vocabulary

Combine two groups by ‘counting on’ from one of the numbers

Begin to know some addition facts, such as doubles of numbers to 5

Solve addition and subtraction problems, involving up to 10 objects

Begin to use + and = to record additions

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Typically they: Estimate and check a number Read and write numbers to

10, with some reversals Say what number comes next,

what is one more/ less Count back to zero Place one to 10 in ascending

order Point to the first, second…

object etc and begin to use ordinal language

Typically they: Halve shapes

including folding paper shapes, lengths of string

Put water into a clear container so that it is about half-full

Halve an even number of objects

Typically they: Relate their understanding

of addition and subtraction to practical contexts involving groups of objects

Typically they: Use objects, fingers, bead

strings, number tracks and number lines to support mental addition and subtraction

Typically they: When given a number,

work out ‘how many more make…’

Choose which of given pairs of numbers add up to a given total

Solve measuring problems such as how many balance with

Solve simple money problems

Typically they: Use a range of visual

strategies for recording work Begin to use mathematical

symbols to record an addition number sentence


Pupils count sets of objects reliably and use mental recall of addition and subtraction facts to 10. They begin to understand the place value of each digit in a number and use it to order numbers to 100. They choose the appropriate operation when solving addition and subtraction problems. They use the knowledge that subtraction is the inverse of addition. They use mental calculation strategies to solve number problems involving money and measures. They recognise sequences of numbers, including odd and even numbers.

CalculatingCounting & understanding numbers Knowing and using number facts

Numbers & the number system Fractions, decimals, percentages and ratio

Operations & relationships between

them



2c13

Count sets of objects up to 20 reliably

Count, read, write and order 2-digit numbers, showing an understanding of the place value of each digit

Recognise odd & even numbers to 20 and other simple number sequences

Understand the concept of a half and begin to find half of shapes, small numbers and even multiples of ten

Know that adding increases a total and subtracting decreases a total

Identify doubles and some halves using numbers up to 20

Have mental recall of addition & subtraction facts to 10 and begin to use these to solve other calculations

Solve simple addition and subtraction problems with the support of self-chosen practical apparatus

Can read and understand +, - and = in the context of a number sentence

2b15

Recognise and complete or continue simple sequences of numbers, including odd & even numbers, to about 50, adding 2s or adding 10s

Begin to understand concept of ½ and ¼

Find halves of two-digit numbers

Know subtraction is the inverse of addition and use this to solve addition & subtraction problems

Understand halving as the inverse of doubling

solve simple addition and subtraction problems using a range of strategies, such as counting, addition, subtraction, doubling and halving

Know by heart facts for 2x & 10x tables

Recognise 1p, 2p, 5p, 10p, 20p & 50p, and choose coins to make amounts up to 50p.

Solve simple money problems involving coins and pence, and simple measures problems

Solve simple multiplication problems by grouping practically

Can read, interpret and use + and – and = to record number sentences

Show addition and subtraction using informal methods such as a numbered number line

2a17

Count on and back in 2s, 5s and 10s

Recognise, complete or continue more sophisticated number sequences

Identify halves and quarters of shapes and begin to identify quarters of numbers

Begin to understand the relationship between multiplication and division

Use mental recall of addition facts up to 10 to add and subtract whole numbers, including multiples of 10.

Know by heart facts for 2x, 5x & 10x tables

Use the knowledge that addition can be done in any order.

Understand the operation of multiplication as repeated addition, or as describing an array, and of division as repeated subtraction or sharing

Understand and use £ and p notation for money

Can read, interpret and use x and ÷ and = to record number sentences

Use informal methods such as a numbered number line to show addition, subtraction, multiplication or division

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Typically, they: demonstrate their knowledge of

numbers using a range of models and images, for example, bead strings, rulers, 100 squares & number line

Know to group objects into sets in order to count larger numbers of objects

Typically, they: Shade one half or one

quarter of a given shape, including those divided into squares

Typically, they: know that subtract 6

‘undoes’ add 6 Understand addition

and subtraction as inverse operations e.g. given 14, 6 and 8 they can make related number sentences:

6 + 8 = 14 14 – 8 = 68 + 6 = 14 14 – 6 = 8

Typically they: Use knowledge of number

facts to 10 and place value to add or subtract multiples of 10, e.g. use

3 + 7 = 10 to work out 30 + 70 = 100

Typically they: Solve whole number

problems involving addition and subtraction, using one- and two=digit numbers and bridging tens e.g. a ribbon is 56cm long, 9 cm is cut off, how much is left?

Typically they: Use informal jottings,

pictures, words, numbers and signs to support their mental calculations


Pupils show understanding of place value in numbers up to 1000 and use this to make approximations. They begin to use decimal notation and to recognise negative numbers, in contexts such as money and temperature. Pupils use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers. They add and subtract numbers with two digits mentally and numbers using written methods. They use mental recall of the 2, 3, 4, 5 and 10 multiplication tables and derive the associated division facts. They solve whole-number problems involving multiplication and division, including those that give rise to remainders. They use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent.


Numbers & the number system

Fractions, decimals, percentages and ratio




3c19

Read, write and order numbers up to 1000

Count on or back in 10’s or 100’s from a two or three digit number

Recognise unit fractions such as ½, ¼ 1/3, 1/5, 1/10,

Use simple fractions that are several parts of a whole

Understand division as the inverse of multiplication

Recall addition and subtraction facts up to 20

Use mental recall of addition and subtraction facts to 20 in solving problems involving multiples of 10

Choose an appropriate strategy from a range of informal pencil and paper methods to record all four operations, such as empty number lines or partitioning and recombining

3b21

Show understanding of place value up to 1000 and use this to make approximations

Begin to use decimal notation in the context of money

Derive associated division facts from known multiplication facts

Use mental recall of 2, 3, 4, 5 and 10 multiplication tables and derive the associated division facts

Use mental recall of addition and subtractions facts to 20 in solving problems involving larger numbers

Solve whole number problems involving x and ÷ where the result is an integer

Add and subtract with 3 digits using expanded written methods

Begin to use a systematic method such as grid method multiplication to multiply two- digit numbers by a single digit

Use informal methods to divide by a single digit

3a23

Recognise negative numbers in contexts such as temperature

Use decimal notation for tenths and hundredths

Recognise when two simple fractions are equivalent

Use symbols correctly including less than (<), greater than (>) and equals (=)

Add and subtract numbers with 2 digits mentally

Begin to know multiplication facts for 6x, 7x, 8x and 9x tables

Solve whole number problems involving x and ÷ including those that give rise to remainders

Add and subtract with 3 digits using standard written methods

Use an efficient method multiplication effectively to multiply two- digit numbers by a single digit

Use chunking to divide by a single integer

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Typically they: Multiply and divide integers

by 10, where the answers are also integers

Continue whole number sequences forwards and backwards

Use number lines, number squares, base 10 and other models of numbers to represent and compare numbers

Typically they: Find unit fractions of

shapes and sets of objects

Know that 306p is the same as £3.06

Order decimals with one decimal place, two decimal places in the context of money

Typically they: Use inverses to find missing

whole numbers, e.g. I think of a number, double it and add 5. The answer is 35. What was my number?

Round up or down after division, depending on context

Complete number sentences such as 7 x 10 = 82 - □ , 6 + 18 < 4 x □ , or 40 ÷ 5 > 20 - □

Typically they: Multiply a 2-digit

number by 2, 3, 4 or 5 Calculate complements

to 100 e.g. 24 + □ = 100

Typically they: Select an appropriate

method to solve a problem e.g. mental, with written recording, or using apparatus

Solve one step whole number problems using any of the 4 operations as described in L2&3

Solve two-step problems involving addition and subtraction

Typically they: Add and subtract 3-digit

numbers where bridging through either a ten or hundred is required

Add and subtract decimals in the context of money where bridging is not required


Pupils use their understanding of place value to multiply and divide whole numbers by 10 or 100. In solving number problems, pupils use a range of mental methods of computation with the four operations, including mental recall of multiplication facts up to 10 x 10 and quick derivation of corresponding division facts. They use efficient written methods of addition and subtraction and of short multiplication and division. They add and subtract decimals to two places and order decimals to three places. In solving problems with or without a calculator, pupils check the reasonableness of their results by reference to their knowledge of the context or to the size of the numbers. They recognise approximate proportions of a whole and use simple fractions and percentages to describe these. Pupils recognise and describe number patterns, and relationships including multiple, factor and square. They begin to use simple formulae expressed in words. Pupils use and interpret coordinates in the first quadrant.


Numbers & the number system Fractions, decimals, percentages and ratio

Operations & relationships between

them



4c25

Use place value to multiply and divide whole numbers by 10 or 100

Convert mixed numbers to improper fractions and vice versa

Understand the role of = to complete a missing number problem where they need to decide the starting point e.g. 20 + □ = 100 ÷ 4

Recall most multiplication facts up to 10 x 10

Use and interpret co-ordinates in the first quadrant

Carry out simple calculations involving negative numbers in context e.g. what temperature is 8ºC higher than -2ºC

Use efficient written methods of addition and subtraction of integers

Use a method such as grid multiplication to multiply pairs of two-digit numbers efficiently

Use chunking effectively to divide by a single digit

4b27

Round a number with one or two decimal places to the nearest integer

Recognise approximate proportions of a whole and use simple fractions and percentages to describe these

Use inverse operations to find missing numbers, including decimals, using a calculator where appropriate

Recall all multiplication facts up to 10x10

Use a range of mental methods of computation with the four operations to solve number problems

Use and interpret co-ordinates in the first and second quadrant

Interpret calculator displays correctly in the context of money or measures when solving problems

Solve two-step problems choosing the appropriate operations

Add and subtract decimals to 2 decimal places

Use short multiplication and division written methods when multiplying or dividing by a single digit.

4a29

Order decimals to 3 decimal places Recognise and describe number

patterns and relationships including multiple, factor and square

Relate fractions to division and their decimal representation

Derive quickly division facts corresponding to tables up to 10 x 10

Extend mental calculations to include fractions, decimals and percentages

Use and interpret co-ordinates in the first, second and third quadrant

Begin to use simple formulae expressed in words

Check the reasonableness of their results by reference to their knowledge of the context or to the size of the numbers

Use efficient written methods of multiplication and division, including long multiplication for TU x TU

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Typically they: Continue sequences forwards and

backwards which involve decimals, negative numbers or two operations e.g. the rule for a number sequence is double and add 1’ fill in the missing numbers: …, 11, 23, 47, …

Find factors within multiplications tables and all factor pairs to 30

Explain the effect of multiplying or dividing by 10 or 100

Make general statements in words e.g. ‘If you multiply 5 by an even number, you always get a multiple of 10’

Typically they: Recognise equivalence

between fractions, decimals and percentages such as ½, ¼, ¾, ¹/10

Begin to understand ratio and proportion, e.g. four biscuits cost 20p altogether. How much do 12 biscuits cost?

Typically they: ‘Undo’ two- or three-step

problems e.g. Josh thinks of a number. He adds 4 the multiples the result by 3. Then he takes away 9. His final answers are 90. What number did Josh start with?

Understand the use of brackets in simple calculations, e.g. 3x(5+6)=

Typically they: Calculate complements to 1000

e.g. 347 + □ = 1000 Use their knowledge of tables and

place value to calculate e.g. 60 x 7, 180 ÷ 3

Use a range of mental methods of computation with the four operations e.g. 3000-1997=; divide by 4 using halving; £3.60 ÷ 4=, multiply by 12 by multiplying by 10, multiplying by 2 and adding the products together

Typically they: Understand two-step problems

and choose appropriate operations e.g. number skills and knowledge described in levels 3 and 4

Deal with two constraints simultaneously e.g. Sapna and Robbie have 14 biscuits altogether. Sapna has 2 more than Robbie. How many do they have each?

Typically they: Use efficient methods for

addition and subtraction of 4-digit numbers e.g. 1202+45+367=, 3572-1496=

Multiply a 4-digit number and divide a 3-digit number by a single digit

Multiply decimal numbers by a single digit

Use a calculator to solve number problems e.g.

□□ X □= 378

Ma 2 Number and Algebra Level 5

Pupils use their understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000. They order, add and subtract negative numbers in context. They use all four operations with decimals to two places. They reduce a fraction to its simplest form by cancelling common factors and solve simple problems involving ratio and direct proportion. They calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. Pupils understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three-digit number by any two-digit number. They check their solutions by applying inverse operations or estimating using approximations. They construct, express in symbolic form, and use simple formulae involving one or two operations. They use brackets appropriately. Pupils use and interpret coordinates in all four quadrants.


Numbers & the number system

Fractions, decimals, percentages and ratio




5c3

1

Use understanding of place value to multiply and divide whole numbers by 10, 100 and 1000

Order negative numbers in context

Recognise the decimal equivalents of fraction where the decimal is a recurring fraction

Check solutions by applying inverse operations

Add or subtract a positive number to or from a negative number in context, including crossing zero

Read and place co-ordinates in all four quadrants

Solve simple problems involving ratio and direct proportion

Calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate

Use an efficient method such as grid method to multiply decimals by an integer

5

3

Use understanding of place value to multiply and divide decimal numbers by 10, 100 and 1000

Check solutions by estimating using approximations

Order a given set of positive and negative integers

Reduce a fraction to its simplest form by cancelling common factors

Identify equivalent fractions

Use brackets appropriately

Multiply a two-digit number by a single digit e.g. 39 x 7

Use their knowledge of tables and place value to calculate e.g. 0.6 x 7, 18 ÷ 0.3

Add and subtract negative numbers in context

Use and interpret co-ordinates in all 4 quadrants

Use letter symbols to represent unknown numbers or variables

Construct , express in symbolic form, and use simple formulae involving one or two operations

Carry out addition, subtraction, short multiplication and short division of numbers involving decimals to two places

Understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any 3 digit by any 2 digit number

5

3

Use understanding of place value to multiply and divide decimal numbers by any power of 10

Begin to multiply/ divide by 0.1 and know that the result is the same as dividing/ multiplying by 10

Recognise the equivalence of percentages, fractions and decimals

Use their knowledge of equivalence to compare fractions with different denominators

Reduce a ratio to its simplest form, recognising links with fraction notation

Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arithmetic operations (BODMAS)

Use a wide range of mental strategies, drawing on knowledge of key number facts and place value, to calculate with integers and decimals quickly and accurately

Begin to add and subtract positive and negative numbers out of context

Find co-ordinates that satisfy a rule and plot them on a co-ordinate grid

Begin to construct and solve simple linear equations with an unknown on one side

Use standard methods for multiplication and division of and by decimals

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Typically they: Find two-digit prime

numbers Make generalisations

about sequences saying whether much larger numbers will be in the sequence or not

Round decimals to one decimal place

Approximate to check answers are of the correct magnitude e.g. 31.9 x 167.6 ≈ 5000

Typically they: Recognise equivalence between

fractions, such as 2/3 and 14/21 or 5/8 and 35/56

Recognise equivalence between fractions, decimals and percentages such as 1/3, 4/5, 7/10

Order decimals to 3 decimal places e.g. 3.3, 3.04, 3.404

Order fractions where the denominators are different

Typically they: Use inverse operations to

check answers Know and use the order

of operations, including brackets e.g. £7.95 + 3 x £4.50 = or (37.9+14.67) x 12 =

Create number sentences from a 2-step word problem that involves brackets e.g. what is the cost of 12 desks and chairs, when desks cost £37.90 and chairs cost £14.67 i.e. (37.9+14.67) x12=

Typically they: Calculate decimals

complements to 1 or 100 e.g. 63.8+ □ = 100, 6.34+ □ = 10

Calculate fractions or percentages of a quantity e.g. 3/8 of 400g or 60% of £300

Typically they: Understand simple

expressions using symbols e.g. ‘2 less than n’ can be written as ‘n-2’

Evaluate expressions by substituting numbers into them e.g. what is 3n + 5 when n=4?

Begin to use simple formulae expressed in symbols e.g. Perimeter of an oblong, P=2l+2w

Solve ratio and proportion problems e.g. given a recipe for 6 people, how much of each ingredient is needed for 8 people?

Typically they: Add and subtract numbers which

do not have the same number of decimal places e.g. 8.6 – 3.75 =

Multiply or divide decimal numbers by a single digit e.g. 31.62 x 7 =, 87.5 ÷ 7 =

Multiply or divide any three-digit number by a two-digit number

Find fractions or percentages of quantities e.g. 3/8 of 980, 65% of £840

Find fractions or percentages of quantities using a calculators e.g. 5/12 of 378; 24% of 525

Ma 3 Shape, Space and MeasuresLevel 1

When working with 2D and 3D shapes, pupils use everyday language to describe properties and positions. They measure and order objects using direct comparison, and order events.Understanding Shape Measuring

Level Properties of Shape Properties of Position and Movement Measures

1c7

Use language such as circle or bigger to describe the shape and size of solid and flat shapes

Distinguish between flat and solid shapes

Respond to positional language Use language such as greater, smaller, heavier or lighter to compare quantities

1b9

Recognise and name simple 2D and 3D shapes

Identify different examples of simple 2D and 3D shapes from a set e.g. matching all the circles or all the cones

Use everyday words to describe position such as behind, in front, on top, top, bottom, side

Respond to directional language

Measure and order more than two objects by length, mass and capacity, using direct comparison

Order everyday events logically and begin to use the vocabulary of time

1a11

Visualise and name some common 2D shapes and 3D solids and describe features

Use them to make patterns, pictures and models

Recognise and follow simple directional symbols such as arrows or footprints

Compare two or more lengths, masses or capacities by direct comparison

Tell the time to o’clock on an analogue clock

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Typically, with support, they: Sort shapes and say how they have

selected them Use properties such as large, small,

triangles, roll, stack Begin to refer to some features of shapes

such as side and corner

Typically, with support, they: Follow paths as instructed/ described by

an adult Find things by responding to basic

positional language Follow trails and treasure hunts using

symbols such as arrows

Typically, with support, they: Use the vocabulary of time including the

days of the week, day, night, yesterday, today, tomorrow

Check which of two objects is heavier/ lighter using a balance and begin to put three objects in order

Use comparative and superlative language when talking about quantities e.g. heavier, longest

Find objects that are longer/ shorter than a metre, heavier/ lighter than 500g, holds more/ less than 1 litre


Pupils use mathematical names for common 2-D and 3-D shapes and describe their properties, including numbers of sides and corners. They distinguish between straight and turning movements, understand angle as a measurement of turn, and recognise right angles in turns. They begin to use everyday non-standard and standard units to measure length and mass.Understanding Shape Measuring


2c13

Use the correct term for common shapes e.g. circle, triangles, cube, cylinder and describe their properties using everyday language

Begin to link everyday language with mathematical language, e.g. angle and point

Describe positions using terms such as near to, far from, next to

Use ordinal numbers to describe the position of objects in a row or line

Suggest suitable standard or uniform non-standard units of measuring equipment to estimate or measure a length, mass or capacity

Begin to tell time to half past as well as o’clock

Use a time line to order daily events and ordinal numbers to describe the order of some regular events

2b15

Use the correct terms for common shapes and recognise and describe properties of shapes such as faces, edges, sides and corners

Recognise and draw a line of symmetry or construct patterns with a line of symmetry

Distinguish between straight and turning movements

Describe positions using a wider range of terms such as ‘at the corner of’ or ‘further away from’

Become familiar with standard units of measurement

Begin to use standard units to measure length and mass

Tell time to o’clock and half past

2a17

Identify common shapes by their properties and describe them in terms of their properties

Sort one collection of 2D or 3D shapes in more than one way

Identify right angles in 2D and 3D shapes and the environment

Identify lines of symmetry in simple shapes and recognise shapes with no lines of symmetry

Show an understanding of right angles through movement, including using clockwise and anti-clockwise

Understand angle as a measure of turn Tell the time using hours, half hour and

quarter hour units and use the vocabulary related to time

Begin to use standard units of length (cm, m); mass (g, kg) and capacity (l) to measure and compare quantities and objects

Compare events and time scales using an appropriate standard unit of time (hour, minute, second)

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Typically they: Make and talk about shapes referring to

their properties using mathematical language e.g. corner, face, flat, pointed, circular

Sort shapes according to a criterion e.g. shapes that are pentagons or shapes with four sides and justify their choices

Recognise that properties are the same even when a shape is enlarged, e.g. comparing different size squares, circles, similar triangles, cubes or spheres

Typically they: Distinguish between left and right and

clockwise and anti-clockwise and use these when giving directions

Instruct a programmable robot, combining straight-line movements and turns, to move along a defined path or reach a target destination

Recognise that a shape stays the same even when it is held up in different orientations

Typically they: Make whole-, half- and quarter-turns Make and use a ‘right angle checker’ Begin to understand that numbers can be

used not only to count discrete objects but also to describe continuous measures such as length e.g., recognise that a length could be more than 1m but not as much as 2m

Know what measuring tools to use to measure different things

Read scales labelled in ones or tens to the nearest labelled division

Ma 3 Shape, Space and Measures

Level 3

Pupils classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes. They use non-standard units, standard metric units of length, capacity and mass, and standard units of time, in arrange of contextsUnderstanding Shape Measuring


3c19

Recognise a wider range of 3-D shapes, including prisms

Draw and complete shapes with reflective symmetry

Identify lines of symmetry by folding 2D shapes

Recognise when shape does not have a line of symmetry

Draw and complete patterns with reflective symmetry

Describe position and movement

Use units of time and know the relationship between them (second, minute, hour, day, week, month, year)

Use non-standard and standard metric units of length in a range of contexts

Use non-standard and standard metric units of mass in a range of contexts

3b21

Classify 2-d shapes in various ways using mathematical properties, such as reflective symmetry for 2D shapes

Begin to understand the terms ‘regular’ and ‘irregular’

Draw the reflection of a shape with a horizontal or vertical mirror line touching the shape

Use standard units of time in a range of contexts

Read to the nearest division and half-division, scales that are numbered; use the information to measure and draw to a suitable degree of accuracy

3a23

Classify 3-d shapes in various ways using mathematical properties

Relate 3-D shapes to drawings and photographs of them, including from different viewpoints

Recognise right-angled and equilateral triangles

Draw the reflection of a shape with a horizontal or vertical mirror line when the shape is not touching the mirror line

Read to the nearest division, scales that are partially numbered

Use non-standard and standard metric units of capacity in a range of contexts

Recognise angles as a measure of turn and know that one whole turn is 360º

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Typically they: Recognise common 3-D shapes e.g.

triangular prism, square-based pyramid Begin to recognise nets of familiar 3-D

shapes e.g. cube, cuboid, triangular prism, square-based pyramid

Demonstrate a shape is symmetrical by folding

Begin to understand the term regular when describing and sorting shapes

Recognise irregular 2-D shapes Recognise angles bigger/ smaller than 90º

and beginning to know the vocabulary acute and obtuse

Sort objects using more than one criterion, e.g. pentagon, not pentagon and all edges same length/ not same length

Typically they: Recognise shapes in different orientations Use terms such as left/ right, clockwise/

anti-clockwise, quarter turn/ 90º to give directions along a route

Typically they: Measure a length to the nearest ½ cm Read simple scales e.g. in increments of

2, 5 or 10 Read a 12-hour clock and calculate time

durations that do not bridge across the hour

Begin to understand area as a measure of surface and perimeter as a measure of length

Find areas of shapes by counting squares and explain area as a number of squares, even if not using standard units such as cm² or m²


Pupils make 3-D mathematical models by linking given faces or edges, draw common 2-D shapes in different orientations on grids. They reflect simple shapes in a mirror line. They choose and use appropriate units and instruments, interpreting, with appropriate accuracy, numbers on a range of measuring instruments. They find perimeters of simple shapes and find areas by counting squares.Understanding Shape Measuring


4c25

Recognise and name most quadrilaterals Recognise oblique lines of symmetry in

shapes

Draw the reflection of a shape in an oblique mirror line, when the shape is touching the mirror

Find areas by counting squares and part squares

Find perimeters of simple shapes Calculate time intervals that go over the

hour Read and calculate digital time using the

24-hour clock

4b27

Recognise and name right-angles, scalene, equilateral and isosceles triangles

Make 3D mathematical models by linking faces or edges

Draw the reflection of a shape in an oblique mirror line, when the shape is not touching the mirror

Draw common 2D shapes in different orientations on grids

Know and use the relationships between familiar units of length, mass and capacity

Use the terms ‘area’ and ‘perimeter’ accurately and consistently

Read and interpret timetables Convert times between 12- and 24-hour

clocks

4a29

Use a widening range of mathematical vocabulary, such as horizontal, vertical, congruent (same size, same shape), parallelogram

Visualise shapes and recognise them in different orientations

Translate shapes horizontally or vertically Begin to rotate a simple shape or object

about its centre or a vertex

Choose and use appropriate units and instruments, interpreting with appropriate accuracy, numbers on a range of instruments

Understand area measured in square centimetres; understand and use the formula in words ‘length x breadth’ for the area of a rectangle

Begin to find the area of compound shapes that can be divided into rectangles

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Typically they: Recognise and name shapes such as

trapezium, rhombus, parallelogram Understand properties of shapes, e.g. why

a square is a special rectangle

Typically they: Are beginning to use distances from the

mirror line to reflect shapes more accurately

Complete shapes on a grid in different orientations, e.g. complete a rectangle which has 2 sides drawn at an oblique angle to the grid

Typically they: Measure a length using mm to within 2mm Read scales with fewer labelled

increments, e.g. read 550g on a scale with increments every 50g and labelled every 200g

Measure and draw angles to the nearest 5º, when one edge is horizontal or vertical

Know 1kg=1000g, 1 litre=1000ml, 1km=1000m and 1 cm=10mm and use these to convert between units e.g. 1.2kg=1200g, 15.6cm=156mm


When constructing models and when drawing or using shapes, pupils measure and draw angles to the nearest degree, and use language associated with angle. Pupils know the angle sum of a triangle and that of angles at a point. They identify all the symmetries of 2-D shapes. They know the rough metric equivalents of imperial units still in daily use and convert one metric unit to another. They make sensible estimates of a range of measures in relation to everyday situations. Pupils understand and use the formula for the area of a rectangle.Understanding Shape Measuring


5c31

Identify parallel and perpendicular lines and faces in 2D and 3D shapes

Know and use the angle sum of a triangle Have a secure knowledge of the properties of

different types of triangle and quadrilateral

Identify some of the symmetries of 2d shapes- reflection and rotation symmetry (for rotation symmetry- see KS3 PoS)

Reflect shapes which cross the mirror line

Use the language associated with angle, e.g. acute, obtuse, reflex, complementary, supplementary

calculate the area of a rectangle by using the formula efficiently, and distinguish area from perimeter

5b33

Know the sum of angles at a point and on a straight line

Recognise opposite equal angles in quadrilaterals and other 2D shapes

Identify all the symmetries of 2D shapes- reflection and rotation symmetry

Translate shapes along an oblique line Rotate shapes through 90º or 180º when the

centre of rotation is a vertex of the shape, and recognise such rotations

Reason about shapes, positions and movement

Make a sensible estimates of a range of measures in relation to everyday situations

Measure and draw angles to the nearest degree

Calculate the area and perimeter of compound shapes that can be split into rectangles, when some of the measurements are given

5a35

Construct a wide range of quadrilaterals, including trapezium, kite and parallelogram, and begin to describe their properties using appropriate vocabulary, e.g. opposite, adjacent, parallel, perpendicular, equal, complementary, acute, obtuse

Reflect shapes not presented on a grid, by measuring perpendicular distances to/from the mirror line

Rotate shapes through 90º or 180º around the origin or another point outside of the shape

Know the rough metric equivalents of imperials units still in daily use and convert one metric unit to another

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Typically they: Calculate missing angles in triangles, including

isosceles triangles or right angled triangles, where only one angle is given

Calculate angles on a straight line or at a point, e.g. the angle between the hands of a clock, or find an angles around the central point of a regular hexagon

Reason about special triangles and quadrilaterals, e.g. given the perimeter and one side of an isosceles triangle, find both possible triangles

Classify quadrilaterals, including trapezium and kite, using their properties, e.g. number of parallel sides

Draw a trapezium of a given area on a square grid

Given the co-ordinates of three vertices of a parallelogram, find the fourth

Typically they: Visualise where patterns drawn on a 3D

shape will occur on its net Draw shapes with a fixed number of lines of

symmetry e.g. a pentagon with one line of symmetry, a hexagon with 2 lines of symmetry

Reflect shapes in two mirror lines, where the shape is not parallel or perpendicular to either mirror

Recognise the order of rotation symmetry Visualise a 3-D shape from its net and match

vertices that will be joined Visualise where patterns shown on a 3-D

shape will occur on its net, e.g. when shown a cube with patterns on two or three faces, create the net to make the cube

Typically they: Measure and draw angles to the nearest

degree, including reflex angles, when neither edge is horizontal or vertical

Construct a triangle given the length of 2 sides and the angle between them (accurate to 1mm and 2º)

Solve problems involving the conversion of units, including imperial measures, e.g. 1.5kg+30g= set within a problem, or approximately how many km are equivalent to 20 miles?

Find the length of a rectangle given its perimeter and width

Read and interpret scales on a range of measuring instruments, explaining how to read values between labelled divisions

Ma 4 Handling DataLevel 1

Pupils sort objects and classify them, demonstrating the criterion they have used.Processing Representing Interpreting

1c7

Sort objects/ pictures using one criterion Represent their work using the objects they have sorted as a record

Say what criterion governs a set e.g. all round, all green

1b9

Sort objects/ pictures into disjoint sets Draw a simple picture of the sets they create

Respond to questions about how they have sorted objects and justify simple choices

1a11

Sort objects/ pictures into a large-scale Venn or Carroll diagram

Use objects or pictures to create a simple block graph

Make direct comparisons between two sets using the language most and least, more or less

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Typically they: Sort by finding all the objects matching one

criterion, e.g. find all the red ones, find all the boys, find all the cones

Separate a group of objects into two disjoint sets, such as boy/ girl, long/ short, soft/ hard

Place objects or pictures on a simple Venn or Carroll diagram

Typically they: Use concrete and pictorial strategies as

a way of recording their work Use given scaffolds such as large-scale

Venn & Carroll diagrams, large-scale axes for creating simple block graphs

Always use one object or picture to represent one unit

Typically they: State the criterion they have chosen to

sort by Give simple explanations of their

choices e.g. ‘the cardboard tube goes here because I can roll it’ or ‘The box can’t go in this set because it isn’t round’

Make simple comparisons and respond to questions such as ‘Which set has most/ least?’, when looking a two disjoint sets such as boy/ girl


Pupils sort objects and classify them using more than one criterion. When they have gathered information, pupils record results in simple lists, tables and block graphs, in order to communicate findings

Processing Representing Interpreting

2c13

Use lists and diagrams to sort objects Understand simple vocabulary relating to

handling data

Record information in simple lists Communicate their findings using the simple list they have recorded

explain choices using appropriate language, including ‘not’

2b15

Use lists, tables and diagrams to sort objects explain choices using appropriate language,

including ‘not’

Record results in simple tables Communicate their findings using the simple table they have recorded

explain choices using appropriate language, including ‘not’

2a17

Sort objects and classify them using more than one criterion

Record results in simple block graphs Communicate their findings using the simple block they have recorded

Discuss and explain their results

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Typically they: Collect and sort data to test a simple

hypothesis e.g. Count a show of hands to test the hypothesis ‘Most children in our class are in bed by 7:30pm’

Understand vocabulary relating to handling data e.g. sort, group, set, list, table, most common, most popular

Enter data into a simple computer database

Typically they: Present information in lists, tables,

pictograms or block graphs where one symbol or block represents one unit

Typically they: Respond to questions about the data

they have presented e.g. How many of our names have five letters?

Pose similar simple questions about their data for others to answer


Pupils extract and interpret information presented in simple tables and lists. They construct bar charts and pictograms, where the symbol represents a group of units, to communicate information they have gathered, and they interpret information presented to them in these forms.

Processing Representing Interpreting3c19

Gather a specified set of data Construct bar charts and pictograms Extract information presented in tables, lists and pictograms

3b21

Make appropriate choices for ways of recording data

Decide on an appropriate scale for a graph or pictogram

Extract and interpret information presented in simple tables and lists

3a23

identify what data to collect in order to answer a given question

Decide how best to represent data to show the information most clearly

Extract and interpret information presented as bar charts and pictograms

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Typically they: Gather data in ways such as lists, tally

charts, frequency tables Identify the data that a question is seeking

Typically they: Choose and construct bar charts, Venn

and Carroll diagrams, pictograms etc Choose how many a symbol will represent

or in what steps a scale will be labelled Use Venn and Carroll diagrams to sort to

one and two criteria Use ICT where appropriate to present

data

Typically they: Read scales labelled in twos, fives or

tens, including reading between labelled divisions, e.g. halfway between 40 and 50 or 8 and 10

Use a key to interpret represented data Compare data e.g. say how many more…

than… and recognise the category that has most/ least

Respond to questions about the whole data set e.g. How many children took part in this survey altogether?


Pupils collect discrete data and record them using a frequency table. They understand and use the mode and range to describe sets of data. They group data, where appropriate, in equal class intervals, represent collected data in frequency diagrams and interpret such diagrams. They construct and interpret simple line graphs.


4c25

Formulate hypotheses and questions to investigate, identifying what data to collect and carrying out the investigation efficiently

Construct frequency tables, pictograms and bar graphs to represent the frequency of events and changes over time

Find the mode of a set of data

4b27

Predict possible solutions for problems requiring the collection and analysis of data

Construct simple line graphs Interpret simple line graphs Find the range of a set of data

4a29

Group data, where appropriate, in equal class intervals

represent collected data in frequency diagrams

Use the language of probability to describe outcomes and events, justifying their reasoning

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Typically they: Test a hypothesis about the frequency of an

event by collecting data quickly e.g. from a science experiment, likelihood of rolling a 6 with a dice

Group data during or after collection, e.g. children’s heights

Given a problem that can be addressed by collecting and analysing data, suggest possible answers

Typically they: Decide how best to represent data e.g.

a line graph, bar chart, Venn diagram, pictogram etc to show the information most clearly

Decide upon an appropriate scale for a graph or pictogram e.g. labelled divisions/ symbol representing 2, 5, 10, 100

Use Venn and Carroll diagrams to record their sorting and classifying of information (typical of level 3 and 4 mathematics e.g. sorting numbers according to properties such as multiples of 8 and multiples of 6) using 2 criteria

Typically they: Interpret simple pie charts Interpret the scale on bar graphs and

line graphs, reading between the labelled divisions e.g. reading 17 on a scale labelled in fives

Compare data sets and respond to questions e.g. how does our data about favourite television programmes compare to the data from Y3 children?

Are beginning to understand the language of probability, e.g. more likely, equally likely, fair, unfair, certain

Use mode and range to describe a set of data e.g. a set of shoe sizes


Pupils understand and use the mean of discrete data. They compare two simple distributions, using the range and one of the mode, median or mean. They interpret graphs and diagrams, including pie charts, and draw conclusions. They understand and use the probability scale from 0 to 1. Pupils find and justify probabilities, and approximations to these, by selecting and using methods based on equally likely outcomes and experimental evidence, as appropriate. They understand that different outcomes may result from repeating an experiment.


5c31

Design a data collection sheet, grouped where appropriate into equal class intervals, or a questionnaire to use in a simple survey

Understand and use the probability scale from 0 to 1

Understand and use the mean of discrete data

Interpret graphs and diagrams, including pie charts, and draw conclusions

5b33

Understand that different outcomes may result from repeating an experiment

Create line graphs with increasing accuracy

Understand and use the median of discrete data

5a35

Select methods based on equally likely outcomes and experimental evidence, as appropriate

Find and justify probabilities, and find approximations to these, by selecting and using methods based on equally likely outcomes and experimental evidence, as appropriate

Compare two simple distributions, using the range and one of the mode, median or mean

Draw conclusions and identify further questions to ask

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Typically they: Understand that the results of an experiment

may not be the same if it were repeated e.g. tossing a coin ten times

Understand the more an experiment is repeated, the better the estimate of probability

Discuss a problem that can be addressed by collecting and analysing data, identifying related questions to explore

Decide which data would be relevant for an enquiry and possible sources e.g. surveying a group of people, an experiment involving observation, counting or measuring

Typically they: Create line graphs where the

intermediate values have meaning, choosing suitable scales and labelling axes e.g. conversion between pound and Euros

Complete a 2-way table, given some of the data

Compare two spinners e.g. to find which is more likely to show an even number

Typically they: Describe and compare two sets of data

e.g. football results, by using the range and mode

Interpret bar graphs involving grouped data and pie charts (not requiring the use of a protractor)

Interpret the scale on bar and line graphs to find differences between two points, involving reading/ estimating between the labelled divisions e.g. reading 34 on a scale labelled in tens or 3.7 on a scale labelled in ones, and using this to answer, ‘How much more…?’

Recognise when information is presented in a misleading way e.g. comparing two pie charts where the sample sizes are different

Describe and predict outcomes from data using the language of chance or likelihood

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