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TRANSCRIPT
1
Contents Introduction
Introduction 1
Using the Plans 2
Autumn 1 7
Autumn 2 19
Spring 1 45
Spring 2 61
Summer 1 81
Basic Skills 99
Progression 111
The Liverpool Maths team have developed a medium term planning documentto support effective implementation of the new National Curriculum.
In order to develop fluency in mathematics, children need to secure aconceptual understanding and efficiency in procedural approaches.
Our materials highlight the importance of making connections betweenconcrete materials, models and images, mathematical language, symbolicrepresentations and prior learning.
There is a key focus on the teaching sequence to ensure that children haveopportunities to practise the key skills whilst building the understanding andknowledge to apply these skills into more complex application activities.
For each objective, there is a breakdown which explains the key componentsto be addressed in the teaching and alongside this there are a series ofsample questions that are pitched at an appropriate level of challenge foreach year group.
The non-statutory guidance is also included for reference purposes.
An additional section provides a list of key, basic skills that children must continually practise as they form the building blocks of mathematicallearning.
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Using the plans
This is not a scheme but it is more than a medium term planThe programme of study has been split into four domains:
• Number • Measurement• Geometry • Statistics
As a starting point, we have taken these domains and allocated them into five half terms:
These allocations serve only as a guide for the organisation of the teaching.Other factors such as term length, organisation of the daily maths lesson,prior knowledge and cross-curricular links may determine the way in whichmathematics is prioritised, taught and delivered in your school.
Year 4Autumn 1 Number
- number and place value- addition and subtraction
Autumn 2 Number - multiplication and division- fractions
Spring 1 MeasurementSpring 2 Geometry
- properties of shapes- position and direction
Summer 1 Statistics
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Using the plans
Within each half term, are some new objectives and some continuousobjectives:
The new objectives vary in length but cover the new learning for that halfterm, they will not appear again in their entirety.
If the objective is in italics, it has been identified as an area that, once taught,should be re-visited and consolidated through basic skills sessions as thesekey skills form the building blocks of mathematical learning (see appendix 1).
The continuous objectives build up as you move through each half term.These objectives cover all the application aspects in mathematics. It iscrucial that they are woven into the teaching continually during the year, so that once fluent in the fundamentals of mathematics, children can applytheir knowledge rapidly and accurately to problem solving.
As before, the timings allocated and the organisation and frequency ofdelivery of these continuous objectives is flexible and will vary from school to school.
Please note that Summer 2 has deliberately been left free for the testingperiod traditionally carried out at the end of summer 1. This also allows theflexibility to allocate time in Summer 2 to target specific areas identifiedthrough the assessment process as needing additional teaching time.
There are 2 appendices attached:
Appendix 1 - List of key basic skills with guidance notes
Appendix 2 - Progression through the domains across the key stages
Year 4New objectives Continuous objectives
Autumn 1 9 3Autumn 2 12 5Spring 1 5 7Spring 2 7 7Summer 1 2 7
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YEAR 4 PROGRAMME OF STUDY
DOMAIN 1 – NUMBER
NEW OBJECTIVES – AUTUMN 1
NUMBER AND PLACE VALUE
Objectives(statutory requirements)
Count in multiples of 6,7, 9, 25 and 1000
Find 1000 more or lessthan a given number
Count backwardsthrough zero to includenegative numbers
What does this mean?
Count out loud forwards andbackwards from different startingpoints and in steps of different sizes
When presented with numbers up tofour digits, children can say thenumber that is 1000 more or less
Build on the counting skills identifiedpreviously to include bridging zerointo negative numbers
Using different starting points, countbackwards beginning with steps ofone and progressing to increasedstep sizes bridging zero
Notes and guidance(non-statutory)
Using a variety of representations,including measures, pupils becomefluent in the order and place value ofnumbers beyond 1000, includingcounting in tens and hundreds, andmaintaining fluency in other multiplesthrough varied and frequent practice.
They begin to extend their knowledgeof the number system to include thedecimal numbers and fractions thatthey have met so far.
They connect estimation and roundingnumbers to the use of measuringinstruments.
Roman numerals should be put in theirhistorical context so pupils understandthat there have been different ways towrite whole numbers and that theimportant concepts of zero and placevalue were introduced over a period of time.
Example questions
Tell me all the multiples of 6 between 28 and 60
If I count in steps of 9 from zero, how manynumbers will I have said by the time I get to 56?
Tell me which multiples of 25 are between 386 and 471
How many multiples of 1000 are there between 2500 and 9600?
Give four digit cards (e.g. 3, 8, 0, 2) can theymake number 1000 more or less?
8, 6, 4 …
-7, -3, 1…
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Recognise the placevalue of each digit in afour-digit number(thousands, hundreds,tens and ones)
Order and comparenumbers beyond 1000
Have an understanding of thenumber system up to four-digitnumbers in different contexts
Understanding of zero as a place holder
Be able to talk about the relative size of numbers, a number biggerthan, less than, in between
Order consecutive and non-consecutive numbers inascending and descending order with particular focus on crossingboundaries and the use of zero as a place holder
Repeating this with units of measureand money
Give four digit cards (e.g. 3,6, 8, 0) can theymake number bigger than, smaller than,between?
Look at these numbers (e.g. 5004, 3352, 865,511) tell me what the 5 digit represents in each
Place 2368 on a number line from 1000 to5000
Think of a number that lies in between 2890and 2975
Order these numbers from smallest to largestand largest to smallest 1302, 998, 1071, 1001,909
Order these lengths from smallest to largestand largest to smallest 1120g, 1kg, 998g,1009g, 1.1kg
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Identify, represent andestimate numbers usingdifferent representations
Round any number tothe nearest 10, 100 or1000
Read Roman numerals to 100 (I to C) and knowthat over time, thenumeral system changedto include the concept ofzero and place value
Present number lines in different waysand in different contexts (horizontalnumber line, vertical scale etc.) andplace random numbers between twodemarcations on a number line
Have an understanding of thenumber system up to four-digitnumbers in different contexts
Children can build on place valueknowledge by practising exchange(e.g. ten bundles of 100 for one 1000)
On a number line with 3000 and 5000 marked,place the number 4500 accurately
Using apparatus such as Numicon, bundles ofstraws, Deines and place value counters, beable to estimate a number and then identify it
Children can work with apparatus to represent numbers accurately
Consider the number 2089, round it to thenearest 10, 100 and then 1000
Is 2847 nearer to 2000 or 3000? Explain howyou know
Tell me all the numbers that round to 3440 asthe nearest 10
Tell me any three numbers that round to 1700as the nearest 100
XII in Roman numerals represents whichnumber?
Using any number up to four digits,be able to round to one or more ofthe three criteria, 10, 100 or 1000
On a clock face, label numbers withequivalent Roman numerals
Ensure children can match Romannumerals to numbers
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NEW OBJECTIVES – AUTUMN 1
ADDITION AND SUBTRACTION
Add and subtractnumbers with up to fourdigits, using formalwritten methods ofcolumnar addition andsubtraction whereappropriate
Teaching to be in line with schoolCalculation Policy
Methods:• Expanded columnar
• Column
Progression shown through:
THTU + HTU (no bridging)
THTU + HTU (bridging 10)
THTU + HTU (bridging 100)
THTU + THTU (no bridging)
THTU + THTU (bridging 10)
THTU + THTU (bridging 100)
THTU + THTU (bridging 10 and 100)
Same progression as above forsubtraction
Refer to the calculation sequence inthe continuous objectives section toensure children are givenopportunities to apply thesecalculation skills
Pupils continue to practise both mentalmethods and columnar addition andsubtraction with increasingly largenumbers to aid fluency (see Mathematics Appendix 1).
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Expanded columnar
Column
Column
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CONTINUOUS OBJECTIVES – AUTUMN 1
Solve number andpractical problems thatinvolve all of the aboveand with increasinglylarge positive numbersnumber and place value
Be able to use known facts in order toexplore others. Include commutativityand inverse and other relationshipsbetween numbers:
• 14 x 4 is also 7 x 8 because oneside of the multiplication is halved,the other side is doubled
Starting with 8 x 5 = 40:• 5 x 8 = 40 (and 40 = 5 x 8,40 = 8 x 5)• Understanding the inverse relationshipbetween multiplication and divisionleads to equivalent statements, suchas 8 = 40 ÷ 5 and 40 ÷ 8 = 5• Knowing division is notcommutative, so 8 ≠ 5 ÷ 40
Be able to answer word and reasoningproblems linked to place value
Using a variety of representations,including measures, pupils becomefluent in the order and place value ofnumbers beyond 1000, includingcounting in tens and hundreds, andmaintaining fluency in other multiplesthrough varied and frequent practice.
They begin to extend their knowledgeof the number system to include thedecimal numbers and fractions thatthey have met so far.
They connect estimation and roundingnumbers to the use of measuringinstruments.
Roman numerals should be put in theirhistorical context so pupils understandthat there have been different ways towrite whole numbers and that theimportant concepts of zero and placevalue were introduced over a period of time.
Are all these statements true?
• If 14 x 7 = 98 then 98 ÷ 7 = 14• If 14 x 7 = 98 then 98 ÷ 14 = 7• If 14 x 7 = 98 then 7 ÷ 98 = 14• If 14 x 7 = 98 then 140 x 70 = 980
Convince me that the number half way between12 and 40 is 26
Fill in the missing numbers:
6 x = 600
÷ 100 = 6
0.6 x = 60
Find the numbers that could fit the following clues:• Less than 100• Not a multiple of 5• Not odd• Tens digit is double the units digit
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Estimate and useinverse operations tocheck answers to acalculation
Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations and methodsto use and why
Working with numbers up to fourdigits, ensure that children haveopportunities to:
• Estimate the answer
• Evidence the skill of additionand/or subtraction
• Prove the inverse using the skill ofaddition and/or subtraction
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing boxrepresents a digit or represents anumber
• Solve problems including thosewith more than one step
• Solve open-ended investigations
Following the calculation sequence:
• Estimate 1245 + 1123
• Calculate 1245 + 1123
• Prove 2368 – 1123 = 1245
• Calculate 2368m – 1123m
• 2368cm - = 1245cm
• I have 2368ml of water in one jug and 1123mlin another jug, how much do I have altogether?I drink 450ml, how much is now left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that isodd/even etc.
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YEAR 4 PROGRAMME OF STUDY
DOMAIN 1 – NUMBER
NEW OBJECTIVES – AUTUMN 2
MULTIPLICATION AND DIVISION
Objectives(statutory requirements)
Recall multiplication anddivision facts formultiplication tables upto 12 x 12
What does this mean?
Include chanting of multiplicationtables both consecutively and non-consecutively
Explore commutativity ofmultiplication
Identify multiples of 6, 7 and 9, 11and 12
Recall related division facts andexplore the inverse relationship ofmultiplication and division
Know that to multiply by 12 is thesame as multiplying by 3 then doubleand double again. Explore othersimilar patterns within multiplicationtables
Notes and guidance(non-statutory)
Example questions
Recall of facts such as 6 x 8, 12 x 7, 40 ÷ 5
Knowing that 8 x 7 is the same as 7 x 8 andthat multiplication (without brackets) can bedone in any order
48 is a multiple of which numbers?
If 7 x 8 = 56, what are the related division facts?Using x and ÷, 7, 8 and 56, write down somenumber sentences
Sam multiplies two numbers together and getsthe answer 36, what could his two numbers be?15 x 12 = 15 x 3 doubled and doubled again
Use the knowledge of 7 x 8 = 56 to derive70 x 8 = 560 and 7 x 80 = 560
To find 400 ÷ 8 =, use knowledge that 40 ÷ 8= 5
When calculating 16 x 3, understand that this isthe same as 8 x 6, as you have halved onenumber and doubled the other
Pupils continue to practise recallingand using multiplication tables andrelated division facts to aid fluency.
Pupils practise mental methods andextend this to three-digit numbers toderive facts, (for example 600 ÷ 3 =200 can be derived from 2 x 3 = 6).
Pupils practise to become fluent inthe formal written method of shortmultiplication and short division withexact answers (see MathematicsAppendix 1).
Pupils write statements about theequality of expressions (for example,use the distributive law 39 × 7 = 30× 7 + 9 × 7 and associative law (2 ×3) × 4 = 2 × (3 × 4)). They combinetheir knowledge of number facts andrules of arithmetic to solve mental andwritten calculations for example, 2 x 6 x 5 = 10 x 6 = 60.
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Use place value, knownand derived facts tomultiply and dividementally, including:multiplying by 0 and 1;dividing by 1; multiplyingtogether three numbers
Recognise and usefactor pairs andcommutativity in mentalcalculations
Can apply knowledge ofmultiplication and division facts toderive answers to other calculationsthat include multiples of 10
Understand the effects of doublingand halving when multiplying anddividing and use this as an aid tosolve calculations
Use the knowledge that whenmultiplying three or more numbers,order is not important
Know that multiplying or dividing by 1,gives an answer that is the same asthe starting number, and multiplyingby 0 always gives an answer of 0
When calculating mentally ensurethat children:
• use factors to simplify amultiplication calculation
• know that when carrying out amultiplication calculation, the orderof the numbers is not important
• from a two-digit number, can findall factor pairs
Pupils solve two-step problems incontexts, choosing the appropriateoperation, working with increasinglyharder numbers.
This should include correspondencequestions such as the numbers ofchoices of a meal on a menu, or threecakes shared equally between 10children.
To calculate 8 x 2 x 9 =, rather than 16 x 9 =re-order so the calculation is double 72
17 x 1 = 17 25 ÷ 1 = 25 19 x 0 = 0
56 x 6 is the same as 8 x 7 x 6 is the same as4 x 2 x 7 x 2 x 3
To calculate 8 x 2 x 9, do 16 x 9 or re-order todouble 72
Factor pairs of 24 are 1 and 24, 2 and 12, 3and 8, 4 and 6
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Multiply two-digit andthree-digit by a one-digit number usingformal written layout
Teaching to be in line with schoolCalculation Policy
Methods for X:
• Expanded (grid)• Short
Progression shown through:
TU x U
HTU x U
Methods for ÷:
• Grouping on a number line to show progression from repeatedsubtraction
• Grouping on a number line to show links with multiplication
• Short
Progression shown through:
TU ÷ U
HTU ÷ U
Refer to the calculation sequence inthe continuous objectives section toensure children are given opportunitiesto apply these calculation skills
Expanded (grid)
Short
Short
Grouping (repeated subtraction)
Grouping (repeated addition)
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NEW OBJECTIVES – AUTUMN 2
FRACTIONS
Recognise and show,using diagrams,families of commonequivalent fractions
Include fractions with alldenominators to 10
Ensure children are making links with the denominator and fractionfamilies
Include hundredths, ensuring that the connection between tenths andhundredths is established
Use this understanding to establishother equivalents (e.g. = )
Pupils should connect hundredths totenths and place value and decimalmeasure.
They extend the use of the numberline to connect fractions, numbers and measures.
Pupils understand the relationbetween non-unit fractions andmultiplication and division of quantities,with particular emphasis on tenths and hundredths.
Pupils make connections betweenfractions of a length, of a shape andas a representation of one whole orset of quantities. Pupils use factorsand multiples to recognise equivalentfractions and simplify whereappropriate (for example = or = )
Pupils continue to practise adding andsubtracting fractions with the samedenominator, to become fluent througha variety of increasingly complexproblems beyond one whole.
This image shows that and are the same37
614
Look at these two images, the first is dividedinto 10 equal sections, so the shading shows
The second is divided into 100 equal sections,so the shading shows
This proves that is equivalent to
Can you use these images to tell mesomething about and ?
is equivalent to 110
10100
110
10100
110
10100
210
310
69
231
428
30100
310
25
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Count up and down inhundredths; recognisethat hundredths arisewhen dividing an objectby a hundred anddividing tenths by ten
Include different starting points,count forwards and backwards fromdifferent starting points inhundredths
Understand that is the same asdividing by 100 and the explicit link of tenths with hundredths
Pupils are taught throughout thatdecimals and fractions are differentways of expressing numbers andproportions.
Pupils’ understanding of the numbersystem and decimal place value isextended at this stage to tenths and then hundredths. This includesrelating the decimal notation to divisionof whole number by 10 and later 100.
They practise counting using simplefractions and decimals, both forwardsand backwards.
Pupils learn decimal notation and thelanguage associated with it, including in the context of measurements. Theymake comparisons and order decimalamounts and quantities that areexpressed to the same number ofdecimal places.
They should be able to representnumbers with one or two decimalplaces in several ways, such as onnumber lines.
As the children count, show images to supportunderstanding
Using different shapes that are divided intohundredths, ask questions such as, ‘How manyhundredths are shaded here?’
1100
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Add and subtractfractions with the samedenominator
Recognise and writedecimal equivalents ofany number of tenths orhundredths
Recognise and writedecimal equivalents to
and
Use denominators up to 10, ensureaccurate notation used and calculations extend beyond one whole
Build on the knowledge of placevalue columns to include tenths andhundredths
the same as
Reinforce the relationship betweenthe place value columns i.e. is tentimes bigger than
Build on the relationship betweentenths and hundredths to showcommon fraction equivalents
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1100
110
1100
110
1100
10100
x 10 = = 110
14
34
12
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Find the effect ofdividing a one or two-digit number by 10 and100, identifying thevalue of the digits in theanswer as units, tenthsand hundredths
Round decimals withone decimal place tothe nearest wholenumber
Understand that when dividing anumber by ten, we are making thatnumber ten times smaller, so wemove each digit one place to the right
Understand that when dividing anumber by one hundred, we aremaking that number one hundredtimes smaller, so we move each digittwo places to the right
Ensure that the importance of zeroas a place holder is emphasised
Using the knowledge that 0.5 is thesame as ½, children work withdecimals to round up or down tonearest whole number
This image represents three bars of chocolateeach divided by ten
This image represents three chocolate bars,each divided by 100
If I divide £5.00 between ten people, eachperson will get 50p. How much would eachperson get if £5.00 was divided between 100people?
Round 5.3 to the nearest whole number
5.3 is less that 5.5 so round down to 5
5.8 is larger than 5.5 so round up to 6
3 ÷ 100 = or 0.033100
3 ÷ 10 = or 0.3310
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Compare numbers withthe same number ofdecimal places up totwo decimal places
Using number lines with differentdemarcations and using thelanguage of bigger, smaller, nearer to,children can place numbers on anumber line with increasing degreesof accuracy
On a number line marked from 2 to 6, place 2.7 and 2.9
On a number line marked from 3 to 7, place 5.1 and 6.7
On a number line marked from 1 to 2, place 1.35 and 1.78
Can you think a number that would be betweenthese two numbers, that is larger than thisnumber, that is smaller than this number?
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CONTINUOUS OBJECTIVES – AUTUMN 2
Solve number andpractical problems thatinvolve all of the aboveand with increasinglylarge positive numbersnumber and place value
Be able to use known facts in order toexplore others, commutativity andinverse but also the relationshipbetween numbers:
• 14 x 4 is also 7 x 8 because oneside of the multiplication is halved,the other side is doubled
Starting with 8 x 5 = 40:
• 5 x 8 = 40 (and 40 = 5 x 8, 40 = 8 x 5)• Understanding the inverserelationship between multiplicationand division leads to equivalentstatements, such as 8 = 40 ÷ 5 and40 ÷ 8 = 5
• Knowing division is notcommutative, so 8 ≠ 5 ÷ 40
Be able to answer word, logic andreasoning problems linked to place value
Are all these statements true?
• If 14 x 7 = 98 then 98 ÷ 7 = 14• If 14 x 7 = 98 then 98 ÷ 14 = 7• If 14 x 7 = 98 then 7 ÷ 98 = 14• If 14 x 7 = 98 then 140 x 70 = 980
Convince me that the number half way betwee12 and 40 is 26
Fill in the missing numbers:
Find the numbers that could fit the following clues:• Less than 100• Not a multiple of 5• Not odd• Tens digit is double the units digit
6 x = 600
÷ 100 = 6
0.6 x = 60
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Estimate and useinverse operations tocheck answers to acalculation
Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations and methodsto use and why
Working with numbers up to fourdigits, ensure that children haveopportunities to:
• Estimate the answer
• Evidence the skill of addition and/or subtraction
• Prove the inverse using the skill ofaddition and/or subtraction
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questions includingthose where missing box represents adigit or represents a number
• Solve problems including those with more than one step
• Solve open-ended investigations
Following the calculation sequence:
• Estimate 1245 + 1173
• Calculate 1245 + 1173
• Prove 2368 – 1123 = 1245
• Calculate 2368m – 1123m
• 2368cm - = 1245cm
• I have 2368ml of water in one jug and1123ml in another jug, how much do I havealtogether? I drink 450ml, how much is now left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that isodd/even etc.
37
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Solve problemsinvolving multiplyingand adding, includingusing the distributivelaw to multiply two digitnumbers by one digit,integer scalingproblems and hardercorrespondenceproblems such as nobjects are connectedto m objects
Working with numbers up TU x U(where the answer is a 2–digitnumber) and TU ÷ U, ensure thatchildren have opportunities to:
• Estimate the answer
• Evidence the skill of multiplicationand division
• Prove the inverse using the skill ofmultiplications and division
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing boxrepresents a digit or represents anumber
• Solve problems including thosewith more than one step
• Solve open-ended investigations
• Estimate 14 x 7 =
• Calculate 14 x 7 =
• Prove 98 ÷ 7 = 14
• Calculate 14 ml x 7 =
• 98 ÷ = 14
• One full barrel holds 14 litres and there are 7full barrels, how much do I have altogether? Isell 2 barrels, how many litres do I have left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is a multiple of 5 etc.
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Solve problemsinvolving increasinglyharder fractions tocalculate quantities, and fractions to dividequantities, includingnon-unit fractions wherethe answer is a wholenumber
Solve simple measureand money problemsinvolving fractions anddecimal problems to twodecimal places
Building on the skill of using divisionto find unit fractions of quantities, use multiplication to calculate non-unit fractions
Increase in complexity to use allnumerators and denominators up to 10
Adding fractions with the samedenominator when the answer is morethan one
Finding fractions of quantities
Comparing fractions of quantities
Addition and subtraction of numberswith up to two decimal places thathave the same number of decimalplaces
There are 32 sheep in the field and escape,how many are left?
of the sweets in my jar is 15, what is the total number of sweets in my jar?
I ate of one pizza and of another, how muchpizza did I eat altogether?
From a bottle containing 240ml of juice, I pourout into a glass, how much is in the glass?
Which is larger, of £100 or of £80?
I spent £7.64 in the shop, how much change doI get from a £10 note?
There are two fences in the garden, onemeasures 2.54m and the other measures3.75m. What is the total length of fence in the garden?
41
45
35
35
35
58
14
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YEAR 4 PROGRAMME OF STUDY
DOMAIN 2 – MEASUREMENT
NEW OBJECTIVES - SPRING 1
Objectives(statutory requirements)
Convert betweendifferent units ofmeasure
Measure and calculatethe perimeter of arectilinear figure(including squares) incentimetres and metres
What does this mean?
When converting, children will beusing decimal notation and using the skill of multiplication
Understand the links with multiplication and division whenconverting (e.g. there are 100cm in 1m therefore when converting metresto centimetres multiply by 100)
Include lengths (m/cm/mm); mass(kg/g); volume/capacity (l/ml)
A rectilinear shape is one with rightangles at all its vertices
Can find the perimeter of given shapes
When calculating the perimeter of a rectangle, children understand that they only need to measure onelength and one width, add thesetogether and double
Children move towards understanding the formula 2 (a + b) and use this whencalculating perimeter
Notes and guidance(non-statutory)
Pupils build on their understanding of place value and decimal notation to record metric measures, includingmoney.
They use multiplication to convert from larger to smaller units.
Perimeter can be expressedalgebraically as 2(a + b) where a and b are the dimensions in the same unit.
They relate area to arrays andmultiplication
Example questions
Using the full range of units of measure ask questions such as:
Convert 3.7m into centimetres
How many millimetres in 236cm?
Why is this not correct 1.7km = 170m?
If I was converting grams into kg, would Imultiply or divide by 10, 100 or 1000?
Calculate the perimeter of these shapes bymeasuring the sides accurately with a ruler and expressing the answer in centimetres
Calculate the perimeter of this rectangle?
In this example, perimeter =14m + 14m + 5m + 5mIt can also be expressed as 2 (14m + 5m)
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Find the area ofrectilinear shapes bycounting squares
Estimate, compare andcalculate differentmeasures, includingmoney in pounds andpence
Using rectilinear shapes, ensuresthat children are only counting wholesquares
When finding the area of a rectangleby counting squares, ensure that thelinks with arrays are made so thatthe skills of multiplication can beused to calculate area
When presented with an objectchildren can give a reasonableestimation of its length, mass andvolume/capacity using appropriateunits of measurement
When presented with a list ofmeasurements (length, mass,volume/capacity, money and time)
including mixed numbers and thosewith decimal notation, children cancompare and order them
The area of this shape is 18cm²
This can be calculated initially by counting thesquares moving towards the link with arrays6 x 3 or 3 x 6
Ensure children are given the opportunity towork practically across the full range ofmeasures
47
Order these measures (this is an example forthe measure of time, use the same model forlength, mass, volume/capacity and money)
Half past two, quarter to seven, ten past tenand twenty to six
7.15pm, 2.05am, 12.10am and 6.45pm
01:15, 14:10, 09:30 and 21:20
Twenty to eleven, 9.15pm and 17.30
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Read, write and converttime between analogueand digital, 12 and 24-hour clocks
Solve calculations including thosewith decimal notation keeping thesize of numbers in line with theprogression outlined in the additionand subtraction objective
If the calculation includes mixedunits, use the skills of conversion tokeep all units of measure the samewithin the calculation (e.g. 1.1m –57cm requires the conversion of themetres into cm first and becomes110cm – 57cm)
From a range of clock displays,children can read the time accurately
Children can alternate betweendigital and analogue including 24-hour clock displays
How much does it cost to hire a rowing boatfor three hours?
Tom pays £3.00 to hire a motor boat, he goesout at 3:20pm, by what time must he return?
Alex pours 150 millilitres of water out of thisjug, how much water will be left in the jug?
Read the time accurately and convert betweendigital, 12 and 24-hour clock notation
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51
Solve number andpractical problems thatinvolve all of the aboveand with increasinglylarge positive numbersnumber and place value
Be able to use known facts in orderto explore others, commutativity andinverse but also the relationshipbetween numbers:• 14 x 4 is also 7 x 8 because oneside of the multiplication is halved,the other side is doubled
Starting with 8 x 5 = 40:• 5 x 8 = 40 (and 40 = 5 x 8,40 = 8 x 5)
• Understanding the inverserelationship between multiplicationand division leads to equivalentstatements, such as 8 = 40 ÷ 5and 40 ÷ 8 = 5
• Knowing division is notcommutative, so 8 ≠ 5 ÷ 40
Be able to answer word, logic andreasoning problems linked to placevalue
Are all these statements true?
• If 14 x 7 = 98 then 98 ÷ 7 = 14
• If 14 x 7 = 98 then 98 ÷ 14 = 7
• If 14 x 7 = 98 then 7 ÷ 98 = 14
• If 14 x 7 = 98 then 140 x 70 = 980
Convince me that the number half way between 12 and 40 is 26
Fill in the missing numbers:
Find the numbers that could fit the following clues:• Less than 100• Not a multiple of 5• Not odd• Tens digit is double the units digit
6 x = 600
÷ 100 = 6
0.6 x = 60
CONTINUOUS OBJECTIVES – SPRING 1
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Estimate and useinverse operations tocheck answers to acalculation
Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations andmethods to use and why
Working with numbers up to fourdigits, ensure that children haveopportunities to:
• Estimate the answer
• Evidence the skill of addition and/or subtraction
• Prove the inverse using the skill ofaddition and/or subtraction
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing box represents a digit orrepresents a number
• Solve problems including thosewith more than one step
• Solve open-ended investigations
Following the calculation sequence:
• Estimate 1245 + 1173
• Calculate 1245 + 1173
• Prove 2368 – 1123 = 1245
• Calculate 2368m – 1123m
• 2368cm - = 1245cm
• I have 2368ml of water in one jug and 1123mlin another jug, how much do I have altogether?I drink 450ml, how much is now left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that isodd/even etc.
53
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55
Solve problemsinvolving multiplyingand adding, includingusing the distributivelaw to multiply two digitnumbers by one digit,integer scalingproblems and hardercorrespondenceproblems such as nobjects are connectedto m objects
Working with numbers up TU x U(where the answer is a 2–digitnumber) and TU ÷ U, ensure thatchildren have opportunities to:
• Estimate the answer
• Evidence the skill of multiplicationand division
• Prove the inverse using the skill of multiplications and division
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing box represents a digit orrepresents a number
• Solve problems including thosewith more than one step
• Solve open-ended investigations
• Estimate 14 x 7 =
• Calculate 14 x 7 =
• Prove 98 ÷ 7 = 14
• Calculate 14 ml x 7 =
• 98 ÷ = 14
• One full barrel holds 14 litres and there are 7full barrels, how much do I have altogether? Isell 2 barrels, how many litres do I have left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is a multiple of 5 etc.
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Solve problemsinvolving increasinglyharder fractions tocalculate quantities,and fractions to dividequantities, includingnon-unit fractionswhere the answer is awhole number
Solve simple measureand money problemsinvolving fractions anddecimal problems totwo decimal places
Building on the skill of using divisionto find unit fractions of quantities,use multiplication to calculate non-unit fractions
Increase in complexity to use all numerators and denominators up to 10
Adding fractions with the samedenominator when the answer ismore than one
Addition and subtraction of numberswith up to two decimal places thathave the same number of decimalplaces
There are 32 sheep in the field and escape,how many are left?
of the sweets in my jar is 15, what is the total number of sweets in my jar?
I ate of one pizza and of another, how much pizza did I eat altogether?
From a bottle containing 240ml of juice, I pourout into a glass, how much is in the glass?
Which is larger, of £100 or of £80?
I spent £7.64 in the shop, how much change do I get from a £10 note?
There are two fences in the garden, onemeasures 2.54m and the other measures3.75m What is the total length of fence in thegarden?
57
45
35
35
35
58
14
23
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59
Solve problems,involving convertingfrom hours to minutes;minutes to seconds;years to months; weeksto days
Building on conversion work, children can now apply these skillswhen solving problems
12 minutes and 5 seconds = seconds
days + 15 days = 8 weeks
It took Peter 3.5 hours to run the marathon and Mike 200 minutes, who was quicker?
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YEAR 4 PROGRAMME OF STUDY
DOMAIN 3 – GEOMETRY
NEW OBJECTIVES – SPRING 2
PROPERTIES OF SHAPES
Objectives(statutory requirements)
Compare and classifygeometric shapes,including quadrilateralsand triangles, based ontheir properties andsizes
What does this mean?
A quadrilateral is any four sidedshape with straight sides that is two dimensional
Examples of regular quadrilaterals include:
parallelogram, rhombus, trapezium,rectangle, square and kite
A triangle is a two dimensional shape with three straight sides and three angles
Examples of triangles include:
equilateral, isosceles, scalene and right angled
Building on understanding of theterms parallel, perpendicular,symmetrical etc., children use this to compare and classify shapes indifferent ways
Notes and guidance(non-statutory)
Pupils continue to classify shapesusing geometrical properties,extending to classifying differenttriangles (for example, isosceles,equilateral, scalene) and quadrilaterals(for example, parallelogram, rhombus,trapezium).
Pupils compare and order angles inpreparation for using a protractor andcompare lengths and angles to decideif a polygon is regular or irregular.
Pupils draw symmetric patterns using a variety of media to become familiarwith different orientations of lines ofsymmetry; and recognise linesymmetry in a variety of diagrams,including where the line of symmetrydoes not dissect the original shape.
Example questions
61
IsocelesTwo equal sidesTwo equal angles
EquilateralThree equal sidesThree equal angles,
always 60o
ScaleneNo equal sidesNo equal angles
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63
Identify acute andobtuse angles andcompare and orderangles up to two rightangles
Identify lines ofsymmetry in 2-Dshapes presented indifferent orientations
When given a set of angles, childrencan classify according to the termsacute, obtuse and right angled andcan order them from smallest tolargest and largest to smallest(children do not need to measure the angles, just compare them)
Ensure shapes are not alwayspresented in the same orientation
Use all 2-D shapes children haveexperienced so far ensuring they can identify the line(s) of symmetry
A symmetric figure can be folded or divided into half so that the twohalves match exactly
The line of symmetry can be verticalor horizontal
When given half a shape and a lineof symmetry, children can draw theother half of the shape to complete it
Name each angle and place them in size orderfrom smallest to largest
Draw the lines of symmetry on these shapes,
Using the line of symmetry shown, draw theother half of the shape
Complete a simplesymmetric figure withrespect to a specificline of symmetry
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NEW OBJECTIVES – SPRING 2
POSITION AND DIRECTION
Describe positions on a2-D grid as coordinatesin the first quadrant
Describe movementbetween positions astranslations of a givenunit to the left/right andup/down
Children identify a given point anddescribe it as a coordinate in theformat (x, y)
Children draw both axes and labelaccurately using whole numbers writtenalongside the corresponding grid line
Children can plot given coordinatesas points in the first quadrant
From two plotted points, children candescribe how to move from one tothe other
From a given point and using a set ofinstructions, children plot the newcoordinate
Write the coordinates of points A, B and C
Having given the children a set of labelled axes,ask them to plot the points for the coordinates(4,2) and (5,6)
Ask children to construct a fully labelled set ofaxes, plot points and write the correspondingcoordinates
Describe how to move from point A (6,4) topoint B (3,1)
From point A, move up 2 and left 3, what is thenew coordinate?
65
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67
Plot specified points anddraw sides to completea given polygon
When given a set of coordinates,children can plot them accurately, join them together using a ruler, and name the polygon they haveconstructed
A, B and C are three corners of a rectangle.What are the coordinates of the fourth corner?
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CONTINUOUS OBJECTIVES – SPRING 2
Solve number andpractical problems thatinvolve all of the aboveand with increasinglylarge positive numbersnumber and place value
Be able to use known facts in orderto explore others, commutativity andinverse but also the relationshipbetween numbers:• 14 x 4 is also 7 x 8 because oneside of the multiplication is halved,the other side is doubled
Starting with 8 x 5 = 40:
• 5 x 8 = 40 (and 40 = 5 x 8, 40 = 8 x 5)
• Understanding the inverserelationship between multiplicationand division leads to equivalentstatements, such as 8 = 40 ÷ 5and 40 ÷ 8 = 5
• Knowing division is notcommutative, so 8 ≠ 5 ÷ 40
Be able to answer word, logic andreasoning problems linked to placevalue
Are all these statements true?
• If 14 x 7 = 98 then 98 ÷ 7 = 14• If 14 x 7 = 98 then 98 ÷ 14 = 7• If 14 x 7 = 98 then 7 ÷ 98 = 14• If 14 x 7 = 98 then 140 x 70 = 980
Convince me that the number half way between 12 and 40 is 26
Fill in the missing numbers:
Find the numbers that could fit the following clues:• Less than 100• Not a multiple of 5• Not odd• Tens digit is double the units digit
69
6 x = 600
÷ 100 = 6
0.6 x = 60
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71
Estimate and useinverse operations tocheck answers to acalculation
Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations andmethods to use andwhy
Working with numbers up to fourdigits, ensure that children haveopportunities to:
• Estimate the answer
• Evidence the skill of additionand/or subtraction
• Prove the inverse using the skill of addition and/or subtraction
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing boxrepresents a digit or represents a number
• Solve problems including thosewith more than one step
• Solve open-ended investigations
• Estimate 1245 + 1173
• Calculate 1245 + 1173
• Prove 2368 - 1123 = 1245
• Calculate 2368m x 1123m
• 2368cm - = 1245cm
• I have 2368ml of water in one jug and1123ml in another jug, how much do I havealtogether? I drink 450ml, how much is nowleft?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is odd/even etc.
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73
Solve problemsinvolving multiplyingand adding, includingusing the distributivelaw to multiply two digitnumbers by one digit,integer scalingproblems and hardercorrespondenceproblems such as nobjects are connectedto m objects
Working with numbers up TU x U(where the answer is a 2–digitnumber) and TU ÷ U, ensure thatchildren have opportunities to:
• Estimate the answer
• Evidence the skill of multiplicationand division
• Prove the inverse using the skill of multiplications and division
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing boxrepresents a digit or represents anumber
• Solve problems including thosewith more than one step
• Solve open-ended investigations
• Estimate 14 x 7 =
• Calculate 14 x 7 =
• Prove 98 ÷ 7 = 14
• Calculate 14 ml x 7 =
• 98 ÷ = 14
• One full barrel holds 14 litres and there are 7full barrels, how much do I have altogether? Isell 2 barrels, how many litres do I have left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is a multiple of 5 etc.
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Solve problemsinvolving increasinglyharder fractions tocalculate quantities,and fractions to dividequantities, includingnon-unit fractionswhere the answer is awhole number
Solve simple measureand money problemsinvolving fractions anddecimal problems totwo decimal places
Building on the skill of using divisionto find unit fractions of quantities,use multiplication to calculate non-unit fractions
Increase in complexity to use allnumerators and denominators up to 10
Adding fractions with the samedenominator when the answer ismore than one
Addition and subtraction of numberswith up to two decimal places thathave the same number of decimalplaces
There are 32 sheep in the field and escape,how many are left?
of the sweets in my jar is 15, what is the totalnumber of sweets in my jar?
I ate of one pizza and of another, how muchpizza did I eat altogether?
From a bottle containing 240ml of juice, I pourout into a glass, how much is in the glass?
Which is larger, of £100 or of £80?
I spent £7.64 in the shop, how much change doI get from a £10 note?
There are two fences in the garden, onemeasures 2.54m and the other measures3.75m What is the total length of fence in the garden?
75
45
35
35
35
58
14
23
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77
Solve problems,involving convertingfrom hours to minutes;minutes to seconds;years to months; weeksto days
Building on conversion work, children can now apply these skillswhen solving problems
12 minutes and 5 seconds = seconds
days + 15 days = 8 weeks
It took Peter 3.5 hours to run the marathon andMike 200 minutes, who was quicker?
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81
YEAR 4 PROGRAMME OF STUDY
DOMAIN 3 – STATISTICS
NEW OBJECTIVES - SUMMER 1
Objectives(statutory requirements)
Interpret and presentdiscrete and continuousdata using appropriategraphical methods,including bar charts andtime graphs
What does this mean?
Discrete data is counted and canonly take certain values and answersthe question, ‘How many?’
Continuous data is measured andcan take any value within a rangeand answers the question, ‘How much?’
Discrete data:
When given examples of constructedbar charts, children can identify thekey features and answer simplequestions including examples usingan increased variety of scales (Year3 is in increments of 2, 5 and 10)
Notes and guidance(non-statutory)
Pupils understand and use a greaterrange of scales in their representations.
Pupils begin to relate the graphicalrepresentation of data to recordingchange over time.
Example questions
Which country won the most/least medals?
How many more medals did USA win than Germany?
What was the total number of silver medals won?
Give children just the bar chart and ask them to construct the frequency table or vice versa
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Using data given in a tally chart orfrequency table, children canconstruct a bar chart with accuratelabels and scaling (remember toinclude questions where the child isrequired to use a variety of scales)
Children should be able to select and use the most appropriate scale
Continuous data:
When given examples of constructedtime graphs, children can identify thekey features and answer simplequestions
When given a set of data, childrencan construct a time graph withaccurate labels and scaling
How many months on the graph show atemperature between 10°c and 20°c?
Find the difference in temperature betweenJuly and August
Construct a bar chart using this data
Construct a time graph using this data
83
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85
Solve comparison, sum and differenceproblems usinginformation presentedin bar charts,pictograms, tables and other graphs
Building on understanding of barcharts, pictograms, time graphs andtables, children apply these skills toanswer increasingly complexquestions
Sue jumped 212cm, draw her result on the graph
Use the graph to estimate how much furtherSam jumped than Jan
Estimate how many birthday cards were sold
How many more ‘thank you’ cards than ‘get well’cards were sold?
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CONTINUOUS OBJECTIVES – SUMMER 1
Solve number andpractical problems thatinvolve all of the aboveand with increasinglylarge positive numbersnumber and place value
Be able to use known facts in orderto explore others, commutativity andinverse but also the relationshipbetween numbers:• 14 x 4 is also 7 x 8 because oneside of the multiplication is halved,the other side is doubled
Starting with 8 x 5 = 40:
• 5 x 8 = 40 (and 40 = 5 x 8, 40 = 8 x 5)
• Understanding the inverserelationship between multiplicationand division leads to equivalentstatements, such as 8 = 40 ÷ 5and 40 ÷ 8 = 5
• Knowing division is notcommutative, so 8 ≠ 5 ÷ 40
Be able to answer word, logic andreasoning problems linked to placevalue
Are all these statements true?
• If 14 x 7 = 98 then 98 ÷ 7 = 14• If 14 x 7 = 98 then 98 ÷ 14 = 7• If 14 x 7 = 98 then 7 ÷ 98 = 14• If 14 x 7 = 98 then 140 x 70 = 980
Convince me that the number half way between12 and 40 is 26
Fill in the missing numbers:
Find the numbers that could fit the following clues:• Less than 100• Not a multiple of 5• Not odd• Tens digit is double the units digit
87
6 x = 600
÷ 100 = 6
0.6 x = 60
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89
Estimate and useinverse operations tocheck answers to acalculation
Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations andmethods to use and why
Working with numbers up to fourdigits, ensure that children haveopportunities to:
• Estimate the answer
• Evidence the skill of addition and/or subtraction
• Prove the inverse using the skill ofaddition and/or subtraction
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing box represents a digit orrepresents a number
• Solve problems including thosewith more than one step
• Solve open-ended investigations
Following the calculation sequence:
• Estimate 1245 + 1173
• Calculate 1245 + 1173
• Prove 2368 – 1123 = 1245
• Calculate 2368m – 1123m
• 2368cm - = 1245cm
• I have 2368ml of water in one jug and 1123mlin another jug, how much do I have altogether?I drink 450ml, how much is now left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that isodd/even etc.
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Solve problemsinvolving multiplyingand adding, includingusing the distributivelaw to multiply two digitnumbers by one digit,integer scalingproblems and hardercorrespondenceproblems such as nobjects are connectedto m objects
Working with numbers up TU x U(where the answer is a 2–digitnumber) and TU ÷ U, ensure thatchildren have opportunities to:
• Estimate the answer
• Evidence the skill of multiplicationand division
• Prove the inverse using the skill of multiplications and division
• Practice calculation skill includingunits of measure (m, cm, mm, kg, g,l, ml, hours, minutes and seconds)
• Solve missing box questionsincluding those where missing box represents a digit orrepresents a number
• Solve problems including thosewith more than one step
• Solve open-ended investigations
• Estimate 14 x 7 =
• Calculate 14 x 7 =
• Prove 98 ÷ 7 = 14
• Calculate 14 ml x 7 =
• 98 ÷ = 14
• One full barrel holds 14 litres and there are 7full barrels, how much do I have altogether? Isell 2 barrels, how many litres do I have left?
• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is a multiple of 5 etc.
91
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93
Solve problemsinvolving increasinglyharder fractions tocalculate quantities,and fractions to dividequantities, includingnon-unit fractionswhere the answer is awhole number
Solve simple measureand money problemsinvolving fractions anddecimal problems totwo decimal places
Building on the skill of using divisionto find unit fractions of quantities,use multiplication to calculate non-unit fractions
Increase in complexity to use allnumerators and denominators up to 10
Adding fractions with the samedenominator when the answer ismore than one
Addition and subtraction of numberswith up to two decimal places thathave the same number of decimalplaces
There are 32 sheep in the field and escape,how many are left?
of the sweets in my jar is 15, what is the totalnumber of sweets in my jar?
I ate of one pizza and of another, how muchpizza did I eat altogether?
From a bottle containing 240ml of juice, I pourout into a glass, how much is in the glass?
Which is larger, of £100 or of £80?
I spent £7.64 in the shop, how much change doI get from a £10 note?
There are two fences in the garden, onemeasures 2.54m and the other measures3.75m What is the total length of fence in the garden?
45
35
35
35
58
14
23
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Solve problems,involving convertingfrom hours to minutes;minutes to seconds;years to months; weeksto days
Building on conversion work, childrencan now apply these skills whensolving problems
12 minutes and 5 seconds = seconds
days + 15 days = 8 weeks
It took Peter 3.5 hours to run the marathon and Mike 200 minutes, who was quicker?
95
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SKILLS
Count from zero in multiples of 6, 7, 9, 25 and 1000 using bridgingstrategies as appropriate
Use knowledge of complements to 100 to find change from whole pounds
Use knowledge of complements to 60 to calculate time within an hour
Recall multiplication facts and related division facts for tables up to 12 x 12
Read and write numbers up to 10 000 and recognise the place value of each digit
Recognise the place value of each digit in a four-digit number
Compare and order numbers up to 10 000
GUIDANCE NOTES
If children are not secure in reciting their 9 times tables they should use abridging strategy, (for example 27 + 9 = 27 + 3 + 6)
Know that there are 100 pence in one pound, use this to calculate £1 –60p, £1 – 35p etc.
Know that there are 60 minutes in one hour, use this to calculate 1 hour –40 minutes etc.
Chanting forwards and backwards from different starting points as well asrecalling random, non-consecutive multiplication and division facts
Use structured apparatus and place value grid to support conceptualunderstanding of place value.
Play place value games to reinforce this concept
What is the value of the 5 digit in these three numbers, 1025, 5123, 2510and 2258.
Play place value games to reinforce this concept (e.g. if I add 200 to thenumber 2510, which digit would change, what would the new digit be?)
Comparing two four-digit numbers, children can say which is the bigger, thesmaller, they also use the < and > signs. Children can order consecutiveand non-consecutive numbers both forwards and backwards
YEAR 4BASIC SKILLS
99
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101
Partition numbers into place value columns
Partition numbers in different ways
Round any four-digit number to the nearest 10, 100 and 1000
Use rounding to support estimation and calculation
Use knowledge of place value to derive new addition and subtraction facts
Use knowledge of inverse to derive associated addition and subtractionfacts and check answers
Double any number between 1 and 100 and find all corresponding halves
Add and subtract mentally THTU ± U, THTU ± T, THTU ± H, TU ± TU andHTU ±TU
Multiply numbers including decimals by 10 and 100
Children can partition four-digit numbers (for example 3164 = 3000 + 100+ 60 + 4)
3164 is 3000 + 100 + 60 + 4 and is also 2000 + 1100 + 50 + 14 etc.
2234 is 2230 (to the nearest 10) 2200 (to the nearest 100) and 2000 (to the nearest 1000)
2234 + 68 is approximately 2300
If I know 7 + 8 = 15, I know 70 + 80 = 150, 700 + 800 = 1500,0.7 + 0.8 = 1.5
If I know 15 + 5 = 20, then 20 – 5 must be 15 and 2 – 0.5 must be 1.5
Use partitioning to double 65 so that it becomes double 60 + double 5.Halve 130 by partitioning it into 100, 20 and 10 then halving each andrecombining
Children need to be secure with the skills of bridging, partitioning, doublingand know their number pairs up to ten to add and subtract mentally
1236 + 4 1236 + 40 1236 + 400 36 + 57 136 + 23
1236 + 7 1236 + 70 1236 + 700 36 + 57 136 + 57
Understand that when multiplying a number by ten, its digits move oneplace to the left (as that place value column is ten times bigger) and zero isused as a place holder. When multiplying a number by 100, its digits movetwo places to the left (understanding that the hundreds column is ten timesbigger than the tens column) and zeros are needed as place holders
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Divide decimal numbers (to one decimal place) by 10
Divide four–digit whole numbers by 100
Use knowledge of inverse to derive associated multiplication and division facts
Use known facts to derive new facts
Use known facts to derive equivalent facts
Count up and down in tenths and hundredths and recognise the equivalentdecimal values
Recall fraction and decimal pairs to 1
Understand that when dividing a number by ten, its digits move one place tothe right (as that place value column is ten times smaller) and zero may beneeded as a place holder
Understand that when dividing a number by 100, its digits move two placesto the right (understanding that the tens column is ten times smaller thanthe hundreds column)
If I know 4 × 8 = 32, I know 8 x 4 = 32, 32 ÷ 8 = 4, 32 ÷ 4 = 8
If I know 5 × 8 = 40, I know 5 × 80 = 400 and then 50 x 80 = 4000
Also 5 x 0.8 = 4.0
If I know 80 + 80 = 160, I know 70 + 90 = 160
If I want to know 16 x 8, I can use factor knowledge e.g. 4 x 4 x 4 x 2
Children count forwards and backwards, from different starting points,consecutively and non-consecutively (e.g. ) and make connectionswith the decimal equivalents
Include fraction pairs ( + decimal pairs (0.2 + 0.8) and mixed
decimal/fraction pairs (0.2 + )
103
48
48810
3100
4100
5100
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105
Identify fractions greater or less than a half
Identify equivalent fractions
Order, add and subtract fractions with the same denominator
Recognise decimal equivalents of fractions with a denominator of ten and onehundred and also decimal equivalents of half, one quarter and three quarters
Round decimals with one decimal place to the nearest whole number
Tell and write the time from a 12-hour analogue clock and a clock withRoman numerals and a digital clock display
Read, tell and write the time from a 24-hour clock
Convert between 12 and 24-hour clocks
Children can say whether fractions such as and are more or less than ahalf, they also use the < and > signs
Children see the links between fraction families and can say that ,and are equivalent
Comparing two fractions, children can say which is the bigger, the smaller,they also use the < and > signs.
For fractions with the same denominator, children can order consecutiveand non-consecutive fractions both forwards and backwards, they can alsoadd and subtract
Match decimals to fraction equivalents and vice versa ( = 0.3, 0.03 = )
8.6 rounded to 9, 18.6 rounded to 19, 158.6 rounded to 159
Children can alternate between stating the time from a clock display anddrawing or showing a clock display to match a given time
Children can read the time as ‘Twenty five past four’ when shown 16:25,knowing that this is 4:25 pm
Children can alternate between saying the time as 16:25 and 4:25 pm andvice versa
24
12
3100
310
48
26
46
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Convert between money and measures including time
Recognise right angles, straight angles, half and full turns and relate the turnto a measurement in degrees
Identify different types of angles including acute and obtuse
Children can convert m to cm and cm to mm, kg to g, l to ml, hours tominutes and minutes to seconds and vice versa to include decimals
Children can identify simple angles from pictures or practical experiencesthey can also state the corresponding turns for these angles and know howmany degrees the angle is equal to (e.g. a right angle is a quarter turn and = 90°)
Using pictures or working practically, children can compare two anglesstating whether they are < or > than a right angle and knowing that < aright angle is acute and > a right angle is obtuse
107
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Y3
count from 0 in multiples of 4, 8, 50 and 100;find 10 or 100 more or less than a given number
recognise the place value of each digit in athree-digit number (hundreds, tens, ones)
compare and order numbers up to 1000
identify, represent and estimate numbers usingdifferent representations
read and write numbers up to 1000 in numeralsand in words
solve number problems and practical problemsinvolving the ideas from number and place value
Y5
read, write, order and compare numbers to at least1 000 000 and determine the value of each digit
count forwards or backwards in steps of powersof 10 for any given number up to 1 000 000
interpret negative numbers in context, countforwards and backwards with positive andnegative whole numbers including through zero
round any number up to 1 000 000 to thenearest 10, 100, 1000, 10 000 and 100 000
solve number problems and practical problemsthat involve all of the above
read Roman numerals to 1000 (M) and recogniseyears written in Roman numerals
PROGRESSION THROUGH THE DOMAINS
NUMBER AND PLACE VALUE
Y4
count in multiples of 6, 7, 9, 25 and 1000
find 1000 more/ less than a given number
count backwards through zero to includenegative numbers
recognise the place value of each digit in a four-digitnumber (thousands, hundreds, tens, and ones)
order and compare numbers beyond 1000
identify, represent and estimate numbers usingdifferent representations
round any number to the nearest 10, 100 or 1000
solve number and practical problems thatinvolve all of the above and with increasinglylarge positive numbers and place value
read Roman numerals to 100 (I to C) and knowthat over time, the numeral system changed toinclude the concept of zero and place value
111
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113
Y3
add and subtract numbers mentally, including:
a three-digit number and ones a three-digit number and tens a three-digit number and hundreds
add and subtract numbers with up to threedigits, using formal written methods of columnaraddition and subtraction
estimate the answer to a calculation and useinverse operations to check answers
solve problems, including missing numberproblems, using number facts, place value, andmore complex addition and subtraction
Y5
add and subtract whole numbers with more than 4 digits, including using formal written methods(columnar addition and subtraction)
add and subtract numbers mentally withincreasingly large numbers
use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
solve addition and subtraction multi-step problemsin contexts, deciding which operations andmethods to use and why
ADDITION AND SUBTRACTION
Y4
add and subtract numbers with up to four digitsusing the formal written methods of columnaraddition and subtraction where appropriate
estimate and use inverse operations to checkanswers to a calculation
solve addition and subtraction two-stepproblems in contexts, deciding which operationsand methods to use and why
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Y3
recall and use multiplication and division factsfor the 3, 4 and 8 multiplication tables
write and calculate mathematical statements for multiplication and division using themultiplication tables that they know, including for two-digit numbers times one-digit numbers,using mental and progressing to formal written methods
solve problems, including missing numberproblems, involving multiplication and division,including integer scaling problems andcorrespondence problems in which n objects are connected to m objects
Y5
identify multiples and factors, including finding allfactor pairs of a number, and common factors oftwo numbers
know and use the vocabulary of prime numbers,prime factors and composite (non-prime) numbers
establish whether a number up to 100 is prime andrecall prime numbers up to 19
multiply numbers up to 4 digits by a one- or two-digit number using a formal written method,including long multiplication for two-digit numbers
multiply and divide numbers mentally drawing uponknown facts
divide numbers up to 4 digits by a one-digit numberusing the formal written method of short division andinterpret remainders appropriately for the context
multiply and divide whole numbers and thoseinvolving decimals by 10, 100 and 1000
recognise and use square numbers and cubenumbers, and the notation for squared (2) andcubed (3)
MULTIPLICATION AND DIVISION
Y4
recall multiplication and division facts formultiplication tables up to 12 × 12
use place value, known and derived facts tomultiply and divide mentally, including:multiplying by 0 and 1; dividing by 1; multiplyingtogether three numbers
recognise and use factor pairs andcommutativity in mental calculations
multiply two-digit and three-digit numbers by aone-digit number using formal written layout
solve problems involving multiplying and adding,including using the distributive law to multiplytwo digit numbers by one digit, integer scalingproblems and harder correspondence problemssuch as n objects are connected to m objects
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117
Y3 Y5
solve problems involving multiplication and divisionwhere larger numbers are used by decomposingthem into their factors
solve problems involving addition, subtraction,multiplication and division and a combination ofthese, including understanding the meaning of theequals sign
solve problems involving multiplication and division,including scaling by simple fractions and problemsinvolving simple rates
ADDITION AND SUBTRACTION
Y4
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Y3
count up and down in tenths; recognise thattenths arise from dividing an object into 10 equal parts and dividing one-digit numbers orquantities by 10
recognise, find and write fractions of a discreteset of objects: unit fractions and non-unitfractions with small denominators
recognise and use fractions as numbers: unitfractions and non-unit fractions with smalldenominators
recognise and show, using diagrams, equivalentfractions with small denominators
add and subtract fractions with the samedenominator within one whole
compare and order unit fractions, and fractionswith the same denominators
solve problems involving fractions
Y5
compare and order fractions whose denominatorsare all multiples of the same number
identify, name and write equivalent fractions of agiven fraction, represented visually, including tenthsand hundredths
recognise mixed numbers and improper fractionsand convert from one form to the other and writemathematical statements > 1 as a mixed number(for example + = = 1 )
add and subtract fractions with the samedenominator and multiples of the same number
multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
read and write decimal numbers as fractions (for example 0.71 = )
recognise and use thousandths and relate them totenths, hundredths and decimal equivalents
round decimals with two decimal places to thenearest whole number and to one decimal place
FRACTIONS (INCLUDING DECIMALS Y4 AND PERCENTAGES Y5)
Y4
recognise and show, using diagrams, families of common equivalent fractions
count up and down in hundredths; recognisethat hundredths arise when dividing an object bya hundred and dividing tenths by ten
solve problems involving increasingly harderfractions to calculate quantities, and fractions todivide quantities, including non-unit fractionswhere the answer is a whole number
add and subtract fractions with the samedenominator
recognise and write decimal equivalents of anynumber of tenths or hundredths
recognise and write decimal equivalents to , ,
find the effect of dividing a one- or two-digitnumber by 10 and 100, identifying the value ofthe digits in the answer as units, tenths andhundredths
round decimals with one decimal place to thenearest whole number
119
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12
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25
45
65
15
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121
Y3 Y5
read, write, order and compare numbers with up tothree decimal places
solve problems involving number up to threedecimal places
recognise the per cent symbol (%) and understandthat per cent relates to “number of parts perhundred”, and write percentages as a fraction withdenominator hundred, and as a decimal
solve problems which require knowing percentageand decimal equivalents of , , , , andthose with a denominator of a multiple of 10 or 25
FRACTIONS (INCLUDING DECIMALS Y4 AND PERCENTAGES Y5)
Y4
compare numbers with the same number ofdecimal places up to two decimal places
solve simple measure and money problemsinvolving fractions and decimals to two decimalplaces
12
14
15
25
45
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Y3
measure, compare, add and subtract: lengths(m/cm/mm); mass (kg/g); volume/capacity (l/ml)
measure the perimeter of simple 2-D shapes
add and subtract amounts of money to givechange, using both £ and p in practical contexts
tell and write the time from an analogue clock,including using Roman numerals from I to XII,and 12-hour and 24-hour clocks
estimate and read time with increasing accuracyto the nearest minute; record and compare timein terms of seconds, minutes, hours and o’clock;use vocabulary such as a.m./p.m., morning,afternoon, noon and midnight
know the number of seconds in a minute andthe number of days in each month, year and leap year
compare durations of events, for example tocalculate the time taken by particular events or tasks
Y5
convert between different units of metric measure(e.g. kilometre and metre; centimetre and metre;centimetre and millimetre; gram and kilogram; litreand millilitre)
understand and use appropriate equivalencesbetween metric units and common imperial unitssuch as inches, pounds and pints
measure and calculate the perimeter of compositerectilinear shapes in centimetres and metres
calculate and compare the area of squares andrectangles including using standard units, squarecentimetres (cm2) and square metres (m2) andestimate the area of irregular shapes
estimate volume (for example using 1 cm3 blocksto build cuboids(including cubes) and capacity (forexample using water)
solve problems involving converting between units of time
use all four operations to solve problems involvingmeasure (for example length, mass, volume,money) using decimal notation including scaling
MEASUREMENT
Y4
convert between different units of measure
measure and calculate the perimeter of arectilinear figure (including squares) incentimetres and metres
find the area of rectilinear shapes by counting squares
estimate, compare and calculate differentmeasures, including money in pounds and pence
read, write and convert time between analogueand digital, 12 and 24-hour clocks
solve problems involving converting from hoursto minutes; minutes to seconds; years tomonths; weeks to days
123
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125
Y3
Properties of shapes
draw 2-D shapes and make 3-D shapes usingmodelling materials; recognise 3-D shapes indifferent orientations and describe them
recognise that angles are a property of shape or a description of a turn
identify right angles, recognise that two rightangles make a half-turn, three make threequarters of a turn and four a complete turn;identify whether angles are greater than or lessthan a right angle
identify horizontal and vertical lines and pairs ofperpendicular and parallel lines
Y5
Properties of shapes
identify 3-D shapes, including cubes and othercuboids, from 2-D representations
know angles are measured in degrees: estimateand compare acute, obtuse and reflex angles
draw given angles, and measure them in degrees (o )Identify: • angles at a point and one whole turn (total 360o)• angles at a point on a straight line and a turn(total 180o) • other multiples of 90o
use the properties of rectangles to deduce relatedfacts and find missing lengths and angles
distinguish between regular and irregular polygonsbased on reasoning about equal sides and angles
Position and direction
identify, describe and represent the position of ashape following a reflection or translation, usingthe appropriate language, and know that the shapehas not changed
GEOMETRY
Y4
Properties of shapes
compare and classify geometric shapes,including quadrilaterals and triangles, based ontheir properties and sizes
identify acute and obtuse angles and compareand order angles up to two right angles
identify lines of symmetry in 2-D shapespresented in different orientations
complete a simple symmetric figure with respect to a specific line of symmetry
Position and direction describe positions on a 2-D grid as coordinatesin the first quadrant describe movement between positions astranslations of a given unit to the left/right andup/down plot specified points and draw sides to completea given polygon
12
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Y3
interpret and present data using bar charts,pictograms and tables
solve one-step and two-step questions such as‘How many more?’ and ‘How many fewer?’ usinginformation presented in scaled bar charts andpictograms and tables
Y5
solve comparison, sum and difference problemsusing information presented in a line graph
complete, read and interpret information in tables,including timetables
STATISTICS
Y4
interpret and present discrete and continuousdata using appropriate graphical methods,including bar charts and time graphs
solve comparison, sum and difference problemsusing information presented in bar charts,pictograms, tables and other graphs
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For more information please contact:
School Improvement LiverpoolE-mail: [email protected] Telephone: 0151 233 3901
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