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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
Ma 1 Using and Applying MathematicsLevel 2
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
Problem solving Communicating Reasoning
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
Ma 1 Using and Applying MathematicsLevel 3
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
Ma 1 Using and Applying MathematicsLevel 4
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
Problem solving Communicating Reasoning
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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Typically they: Solve a range of problems and
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
Ma 1 Using and Applying MathematicsLevel 5
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.
Problem solving Communicating 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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Typically they: Solve a range of problems and
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
Ma 2 Number and AlgebraLevel 2
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
Mental methods Solving numerical problems
Written & calculator methods
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
Ma 2 Number and AlgebraLevel 3
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.
CalculatingCounting & understanding numbers Knowing and using number facts
Numbers & the number system
Fractions, decimals, percentages and ratio
Operations & relationships between them
Mental methods Solving numerical problems
Written & calculator methods
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
Ma 2 Number and AlgebraLevel 4
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.
CalculatingCounting & understanding numbers Knowing and using number facts
Numbers & the number system Fractions, decimals, percentages and ratio
Operations & relationships between
them
Mental methods Solving numerical problems
Written & calculator methods
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.
CalculatingCounting & understanding numbers Knowing and using number facts
Numbers & the number system
Fractions, decimals, percentages and ratio
Operations & relationships between them
Mental methods Solving numerical problems
Written & calculator methods
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
Ma 3 Shape, Space and MeasuresLevel 2
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
Level Properties of Shape Properties of Position and Movement Measures
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
Level Properties of Shape Properties of Position and Movement Measures
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
Ma 3 Shape, Space and MeasuresLevel 4
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
Level Properties of Shape Properties of Position and Movement Measures
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
Ma 3 Shape, Space and MeasuresLevel 5
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
Level Properties of Shape Properties of Position and Movement Measures
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
Ma 4 Handling DataLevel 2
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
Ma 4 Handling DataLevel 3
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?
Ma 4 Handling DataLevel 4
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.
Processing Representing Interpreting
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
Ma 4 Handling DataLevel 5
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.
Processing Representing Interpreting
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