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Maths PlansYear 5

SIL Maths Plans Year 5_Layout 1 11/06/2014 11:50 Page 2

1

Contents Introduction

Introduction 1

Using the Plans 2

Autumn 1 7

Autumn 2 21

Spring 1 53

Spring 2 75

Summer 1 96

Basic Skills 115

Progression 125

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.

An additional section (see appendix 1) provides a list of key, basic skills thatchildren must continually practise as they form the building blocks ofmathematical learning.


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 5Autumn 1 Number

- number and place value- addition and subtraction

Autumn 2 Number - multiplication and division- fractions (including decimals and percentages)

Spring 1 MeasurementSpring 2 Geometry

- properties of shapes- position and direction

Summer 1 Statistics

2


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

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 5New objectives Continuous objectives

Autumn 1 7 3Autumn 2 18 8Spring 1 5 10Spring 2 7 10Summer 1 2 10

3


4


Autumn


6


7

YEAR 5 PROGRAMME OF STUDY

DOMAIN 1 – NUMBER

NEW OBJECTIVES – AUTUMN 1

NUMBER AND PLACE VALUE

Objectives(statutory requirements)

Read, write, order andcompare numbers to atleast 1 000 000 anddetermine the value ofeach digit

What does this mean?

Be able to recognise and recordnumbers in words and figures

Be able to talk about the relative sizeof numbers, a number bigger than,less than, in between

Place 23 683 on a number line from 23 000 to 24 000

Think of a number that lies in between 23 490and 23 890

Order consecutive and non-consecutive numbers inascending and descending order with particular focus on crossingboundaries and the use of zero as a place holder

Present number lines in differentways and in different contexts(horizontal number line, vertical scale etc.) and place randomnumbers between two demarcationson a number line

Order these numbers from smallest to largestand largest to smallest 23 542, 23 045, 23005, 23 504

Notes and guidance(non-statutory)

Pupils identify the place value in largewhole numbers.

They continue to use number incontext, including measurement.Pupils extend and apply theirunderstanding of the number systemto the decimal numbers and fractionsthat they have met so far.

They should recognise and describelinear number sequences, includingthose involving fractions and decimals,and find the term-to-term rule.

They should recognise and describelinear number sequences (for example,3, 3 , 4, 4 ...), including thoseinvolving fractions and decimals, andfind the term-to-term rule in words (for example, add 1).

Example questions

Write 453 002 in words, and vice versa

12

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Notes

8


9

Count forwards orbackwards in steps ofpowers of 10 for anygiven number up to 1 000 000

Count out loud, forwards andbackwards following the sequence10, 100, 1000… from differentstarting points

Starting at 10², children count in powers of 10

Interpret negativenumbers in context,count forwards andbackwards with positiveand negative wholenumbers, includingthrough zero

Build on the counting skills identifiedpreviously to include bridging zerointo negative numbers

Using different starting points, countforwards and using multiples such as6, 7, 9, 25 and 1000 bridging zero

Read and interpret negative numberson a variety of scales

Starting from 54, count in multiples of 9forwards and backwards

Progression shown through starting the countfrom a number that is not a multiple of the stepsize

Starting from 55, count in steps of 9 forwardsand backwards

Present scales both vertically and horizontally

Round any number up to1 000 000 to the nearest10, 100, 1000. 10000, 100000

Using any number up to six digits, beable to round to one or more of thefive criteria, 10, 100, 1000, 10000,100 000

Think of the number 78 456, round it to therange of criteria specified on the left

Is 78 456 nearer to 70 000 or 80 000? Explain how you know

Read Roman numeralsto 1000 (M) andrecognise years writtenin Roman numerals

Ensure children can match Romannumerals to numbers

CXII in Roman numerals represents whichnumber?


Notes

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11


ADDITION AND SUBTRACTION

Add and subtract wholenumbers with morethan 4 digits, includingusing formal writtenmethods (columnaraddition andsubtraction)

Teaching to be in line with schoolCalculation Policy

Methods:• Expanded columnar

• Column

Progression shown through:

Start point

THTU ± THTU (bridging 10 and 100)

End point

THTU.t h ± THTU.t h (with multiple bridging)

Pupils practise using the formal writtenmethods of columnar addition andsubtraction with increasingly largenumbers to aid fluency (seeMathematics Appendix 1).

They practise mental calculations withincreasingly large numbers to aidfluency (for example, 12 462 - 2300 = 10 162).Expanded columnar

Column


Notes

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13

Add and subtractnumbers mentally withincreasingly largenumbers

Children need to be secure with theskills of bridging, partitioning, doublingand know their number bonds andpairs up to ten to add and subtractmentally

Building on the skills introduced inYear 4, children add and subtractmentally THTU ± U, THTU ± T,THTU ± H, TU ± TU and HTU ±TU,increasing the complexity through theintroduction of further bridging

1236 + 4, 1236 + 40, 1236 + 400, 36 + 57

1236 + 7, 1236 + 70, 1236 + 700, 136 + 57


Notes

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15

CONTINUOUS OBJECTIVES – AUTUMN 1

Solve number problemsand practical problemsthat relate to all of theabove (number andplace value)

Be able to answer word andreasoning problems linked to placevalue

Emma has used these digit cards to make thenumber 367.98

How many numbers with two decimal placescan you make that round to 600?

If you made the number that is seven tenthsless than Emma’s, which new digit card wouldyou need?

What is the smallest number with two decimalplaces that you can make?

If you also had a zero digit card, how would thischange your answer?

Convince me that the number half way between12.2 and 40.6 is 26.4

Find the numbers that could fit the followingclues:

• Less than 100 and prime

• Not a multiple of 5 but a multiple of 3

• Not odd but a square number

• Tens digit is double the hundredths digit


Notes

16


Be able to use known facts in orderto explore others. Includecommutativity and inverse and otherrelationships between numbers:

• 42 x 8 is also 84 x 4 because oneside of the multiplication is halved,the other side is doubled

Starting with 42 x 8 = 336:

• 42 x 8 = 336 (and 336 = 42 x 8,336 = 8 x 42)

• Understanding the inverserelationship between multiplicationand division leads to equivalentstatements, such as 42 = 336 ÷ 8

• Knowing division is notcommutative, so 8 ≠ 42 ÷ 336

Are these statements true?

• If 32 x 8 = 256 then 256 ÷ 8 = 32

• If 32 x 8 = 256 then 256 ÷ 32 = 8

• If 32 x 8 = 256 then 8 ÷ 256 = 32

• If 32 x 8 = 256 then 320 x 80 = 2560

17


18

Notes


19

Use rounding to checkanswers to calculationsand determine, in thecontext of a problem,levels of accuracy

Working with numbers up to THTU.t hdigits, ensure that children haveopportunities to:

• Estimate the answer

• Evidence the skill of addition and/orsubtraction

• Prove the inverse using the skill ofaddition and/or subtraction

• Practice calculation skill includingunits of measure (km, m, cm, mm,kg, g, l, cl, ml, hours, minutes andseconds)

• Solve missing box questionsincluding those where missing boxrepresents a digit or represents anumber

• Solve problems including those withmore than one step

• Solve open-ended investigations

Following the calculation sequence:

• Estimate 1245.85 + 1123.36

• Calculate 1245.85 + 1123.36

• Prove 2369.21 – 1123.36 = 1245.85

• Calculate 2369.21m – 1123.36m

• 2369.21cm - = 1245.85cm

• I have 1245.85 litres of water in onecontainer and 1123.36 litres in anothercontainer, how much do I have altogether? I pour out 450 litres, how much is now left?

• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that isodd/even etc.

Solve addition andsubtraction multi-stepproblems in contexts,deciding whichoperations and methodsto use and why


Notes

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21


DOMAIN 1 – NUMBER


MULTIPLICATION AND DIVISION


Identify multiples andfactors, including findingall factor pairs of anumber, and commonfactors of two numbers

Know and use thevocabulary of primenumbers, prime factorsand composite (non-prime) numbers

What does this mean? Notes and guidance(non-statutory)

Example questions

From a two-digit number, childrencan identify all factor pairs

For all multiplication tables up to 12 x12, children can identify multiples

When given a pair of two-digitnumbers, children can identify allfactors that are common to bothnumbers

List all the factor pairs of 24

Write all the two-digit multiples of 11

What are the common factors for the numbers24 and 32?

A prime number is a number that canbe divided evenly only by 1 or itselfand it must be a whole numbergreater than one

A composite (or non-prime) numberis a whole number that can bedivided evenly by numbers other than1 and itself

Prime factorisation is finding whichprime numbers multiply together tomake the original number

Circle the prime numbers in this list:

12, 3, 21, 23, 30

From a given set of numbers, identify which are prime and which are composite

Find the prime factors of 12

(2 x 2 x 3)

Pupils practise and extend their useof the formal written methods of shortmultiplication and short division (seeMathematics Appendix 1). They applyall the multiplication tables andrelated division facts frequently,commit them to memory and usethem confidently to make largercalculations.They use and understand the termsfactor, multiple and prime, square andcube numbers.Pupils interpret non-integer answersto division by expressing results indifferent ways according to thecontext, including with remainders, asfractions, as decimals or by rounding(for example, 98 ÷ 4 = 9 = 24 r 2= 24 = 24.5 ≈ 25).Pupils use multiplication and divisionas inverses to support theintroduction of ratio in year 6, forexample, by multiplying and dividingby powers of 10 in scale drawings orby multiplying and dividing by powersof a 1000 in converting between unitssuch as kilometres and metres.

12

84


22

Notes


23

Multiply numbers up to4 digits by a one- ortwo-digit number usinga formal written

method, including longmultiplication for two-digit numbers


Methods for X:

• Partitioning (grid)

• Short

• Long


HTU x U

THTU x U

TU x TU

Distributivity can be expressed as a(b + c) = ab + ac.

They understand the terms factor,multiple and prime, square and cubenumbers and use them to constructequivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10).

Pupils use and explain the equals signto indicate equivalence, including inmissing number problems (for example,13 + 24 = 12 + 25; 33 = 5 x ).

Short

Long

Partitioning (grid)

Establish whether anumber up to 100 isprime and recall primenumbers up to 19

Recall prime numbers up to 19 andderive prime numbers between 20and 100

Find all the prime numbers between 35 and 49


Notes

24


25

Multiply and dividenumbers mentallydrawing upon knownfacts

Using knowledge of multiplicationtables to 12 x 12, children can recalland derive associated facts

Include chanting of multiplicationtables both consecutively and non-consecutively

Explore commutativity ofmultiplication

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

Recall of facts such as 6 x 8, 12 x 7, 40 ÷ 5

Knowing that 0.8 x 7 is the same as 7 x 0.8 and that multiplication (without brackets) can be done in any order

If 7 x 0.8 = 5.6, what are the related divisionfacts?

Using x and ÷, 7, 0.8 and 5.6, write down somenumber sentences

Sam multiplies two numbers together and getsthe answer 3.6, what could his two numbersbe?

15 x 12 = 15 x 3 doubled and doubled again


26

Notes


27

Divide numbers up to 4digits by a one-digitnumber using theformal written methodof short division andinterpret remaindersappropriately for thecontext


Methods for ÷:

• Short


HTU ÷ U

THTU ÷ U

Expressing any remainders first usingthe notation ‘r’ moving onto expressionas a fraction then as a decimal

To find a decimal remainder, use theskills of converting a fraction to adecimal, consolidating the linksbetween fractions and decimals

Short

or 1441.67correct to 2 decimal places

Multiply and dividewhole numbers andthose involving decimalsby 10, 100 and 1000

Use knowledge of place valuecolumns when multiplying anddividing by 10, 100 and 1000 (i.e. when moving from right to left,each place value column is ten timesbigger and vice versa)

x 1000 = 28 300

5432 ÷ = 54.32

50.05 x 10 =


Notes

28


Recognise and usesquare numbers andcube numbers, and thenotation for squared (2)and cubed (3)

A square number is formed bymultiplying a digit by itself

A cube number is formed by multiplyinga digit by itself three times

Ensure the correct notation is used andapplied when teaching the objectivesfor area and volume in Spring 1

What is 7 squared?

55 is a square number, true or false?

From the following numbers, which are squared,which are cubed which fit neither criteria?

49, 13, 56, 81, 125, 343, 8, 104

29


30

Notes


31


FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES)

Compare and orderfractions whosedenominators are allmultiples of the samenumber

Building on the work on fractionfamilies in Year 4, children can ordera set of fractions where thedenominators are all multiples of thesame number

Start by using images to show howfractions, where denominators aremultiples of the same number, can be compared

When comparing fractions it is easierwhen the denominators are the same(that is, by finding a commondenominator)

Convert fractions using the skills ofmultiplication and the knowledge offraction families, so that they havethe same denominator and then beable to compare and order them

Identify, name and writeequivalent fractions of a given fraction,represented visually,including tenths andhundredths

Equivalent fractions have the samevalue even though they may lookdifferent because when you multiplyor divide both the numerator anddenominator by the same number,the fraction keeps its value

When given a fraction, children canderive other fractions that areequivalent to it using the skills ofmultiplication and division and theknowledge of fraction families

Pupils should be taught throughoutthat percentages, decimals andfractions are different ways ofexpressing proportions.

They extend their knowledge offractions to thousandths and connectto decimals and measures.

Pupils connect equivalent fractions >1 that simplify to integers with divisionand other fractions > 1 to division withremainders, using the number line andother models, and hence move fromthese to improper and mixed fractions.

Pupils connect multiplication by afraction to using fractions as operators(fractions of), and to division, buildingon work from previous years. Thisrelates to scaling by simple fractions,including fractions > 1.

Pupils practise adding and subtractingfractions to become fluent through avariety of increasingly complexproblems. They extend theirunderstanding of adding andsubtracting fractions to calculationsthat exceed 1 as a mixed number.

Order this set of fractions, , ,

Use a fraction board to help initially and thenprogress into converting all fractions intotwelfths

Find two fractions that are equivalent to

23

56

912

38


Notes

32


Recognise mixednumbers and improperfractions and convertfrom one form to theother and writemathematicalstatements > 1 as amixed number [ for example, + == 1 ]

A proper fraction has a numeratorsmaller than the denominator

An improper fraction has a numerator larger than (or equal to)the denominator

Mixed numbers can also be calledmixed fractions. A mixed fraction is awhole number and a proper fractioncombined

Children can convert mixed fractionsto improper fractions and vice versa

From a selection of mixed fractionsand improper fractions, children canuse the skills of conversion to placethem in ascending and descendingorder

Pupils continue to practise countingforwards and backwards in simplefractions.

Pupils continue to develop theirunderstanding of fractions as numbers,measures and operators by findingfractions of numbers and quantities.

Pupils extend counting from year 4,using decimals and fractions includingbridging zero, for example on a numberline.

Pupils say, read and write decimalfractions and related tenths,hundredths and thousandthsaccurately and are confident inchecking the reasonableness of theiranswers to problems.

They mentally add and subtract tenths,and one-digit whole numbers andtenths.

They practise adding and subtractingdecimals, including a mix of wholenumbers and decimals, decimals withdifferent numbers of decimal places,and complements of 1 (for example,0.83 + 0.17 = 1).

Convert 2 to an improper fraction

Order this set of fractions from smallest to

largest , 2 , , ,

Use the skill of converting all fractions intotwelfths

+

33

25

45

65

15

23

38

56

912

1512

83

Add and subtractfractions with the samedenominator anddenominators that aremultiples of the samenumber

Use denominators up to 10, ensure accurate notation used and calculations extend beyond one whole

When given fractions wheredenominators are different butmultiples of the same number,children can use skills of conversionso that the fractions have the samedenominator and then are able toadd and subtract

56

56

_1512

912

+56

23

_1512

23


34

Notes


35

Multiply proper fractionsand mixed numbers bywhole numbers,supported by materialsand diagrams

Using images to support, children can multiply proper fractions by wholenumbers

Using images to support, children can multiply mixed numbers by wholenumbers

2 x = = 1

2 x 1 = 2

Pupils should go beyond themeasurement and money models ofdecimals, for example, by solvingpuzzles involving decimals.

Pupils should make connectionsbetween percentages, fractions anddecimals (for example, 100%represents a whole quantity and 1% is , 50% is , 25% is ) andrelate this to finding ‘fractions of’.

34

64

24

14

24

1100

50100

25100

Read and write decimalnumbers as fractions[for example, 0.71 = ]

For any decimal number up to threedecimal places but less than 1,children can express it as a fractionwith a denominator of 10 and/or 100and/or 1000

Express each of these numbers as a fraction:

0.8, 0.85, 0.85771100

Recognise and usethousandths and relatethem to tenths,hundredths and decimalequivalents

Build on the knowledge of place value columns to include tenths andhundredths

Reinforce the relationship betweenthe place value columns i.e. is tentimes bigger than , is ten timesbigger than

Link equivalent fractions to comparefractions. For example the knowledgethat = and to find decimalequivalents

Express as a decimal

Express 0.54 as a fraction

= = = 0.9

110

1100

11001

1000

110

2511000

910

90100

9001000

10100


Notes

36


Round decimals withtwo decimal places tothe nearest wholenumber and to onedecimal place

When rounding to the nearest wholenumber, children understand that thevalue of the tenth digit will determinewhether they round up or down

When rounding to one decimal place,children understand that the value ofthe hundredth digit will determinewhether they round up or down

Round 15.47 to the nearest whole number

Round 15.47 to one decimal place

Read, write, order andcompare numbers withup to three decimalplaces

Be able to recognise and recordnumbers in words and figures

Order consecutive and non-consecutive numbers inascending and descending order with particular focus on presentingsets of numbers that have a mix ofone, two and three decimal places

Repeat this with units of measure and money

Be able to talk about the relative size of numbers, a number biggerthan, less than, in between

When presented with number linesplace random numbers between twodemarcations on a number line,working with numbers up to threedecimal places

Three hundred and six point four seven nine

Write this number in figures and then in words

Order this set of numbers

54.673, 504.67, 54.67, 54.679, 54.03,54.003

From a set of numbers with up to three decimalplaces, use the inequality symbols (< > ≤ ≥ )to compare

From a number line with a start number of 54.3and an end number of 54.5, place the number54.38

37


38

Notes


39

Recognise the per centsymbol (%) andunderstand that percent relates to ‘numberof parts per hundred’,and write percentagesas a fraction withdenominator 100, andas a decimal

Per cent means per 100

Children understand the relationshipbetween percentages, fractions anddecimals

When making these connections,children work with fractions with adenominator of 100 and convertthese to decimals with up twodecimal places

Express the shaded area as a fraction and/ordecimal and/or percentage

Express 23% as both a fraction and a decimal

Express 0.57 as both a fraction and apercentage

Express as both a decimal and a percentage310


Notes

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41

CONTINUOUS OBJECTIVES – AUTUMN 2









Fill in the missing numbers:

0.6 x = 60

÷ 1000 = 1.6

6.03 x = 603


Notes

42


43

Be able to use known facts in order to explore others. Includecommutativity and inverse and otherrelationships between numbers:



• 42 x 8 = 336 (and 336 = 42 x 8,336 = 8 x 42)









• If 32 x 8 = 256 then 256 ÷ 8 = 32

• If 32 x 8 = 256 then 256 ÷ 32 = 8

• If 32 x 8 = 256 then 8 ÷ 256 = 32

• If 32 x 8 = 256 then 320 x 80 = 2560


44

Notes


45


Solve addition andsubtraction multi-stepproblems in contexts,deciding whichoperations andmethods to use andwhy

Solve problemsinvolving number up tothree decimal places

Working with numbers up to THTU.t hdigits, ensure that children haveopportunities to:


• Evidence the skill of multiplicationand division

• Prove the inverse using the skill ofmultiplications and division






• Estimate 1245.85 + 1123.36

• Calculate 1245.85 + 1123.36

• Prove 2369.21 – 1123.36 = 1245.85

• Calculate 2369.21m – 1123.36m

• 2369.21cm - = 1245.85cm

• I have 1245.85 litres of water in onecontainer and 1123.36 litres in anothercontainer, how much do I have altogether? I pour out 450 litres, how much is now left?

• Using the digit cards 1 to 9, make thesmallest/biggest answer, an answer that is amultiple of 5 etc.


46

Notes


47

Solve problemsinvolving multiplicationand division includingusing their knowledgeof factors and multiples,squares and cubes

Solve problemsinvolving addition,subtraction,multiplication anddivision and a

combination of these,including understandingthe meaning of theequals sign

Working with numbers up HTU x U orTHTU x U (where the answer is a 3or 4–digit number) and HTU ÷ U orTHTU ÷ U, ensure that children haveopportunities to:


• Evidence the skill of addition and/orsubtraction

• Prove the inverse using the skill ofaddition and/or subtraction






• Estimate 214 x 7 =

• Calculate 214 x 7 =

• Prove 1498 ÷ 7 = 214

• Calculate 214 ml x 7 =

• 1498 ÷ = 214

• One full barrel holds 214 litres and there are7 full barrels, how much do I have altogether?I sell 2 barrels, how many litres do I have left?



48

Notes


49

Solve problemsinvolving multiplicationand division, includingscaling by simplefractions and problemsinvolving simple rates.

Solve problems whichrequire knowingpercentage and decimalequivalents of

, , , , andthose fractions with adenominator of amultiple of 10 or 25.

For multiplication and division, refer to‘Following the calculationsequence:’ above

Scaling problems use the skills ofmultiplication and division for scalingup and down

Link to work with measures by using recipes

A recipe for 4 persons that must be scaleddown to show quantities for 1 person usingdivision skills

A recipe for 2, that must be scaled up to feed10 people, using the skills of multiplication

Children use the skills of convertingbetween fractions, decimals andpercentages and apply this in aproblem solving context

When making these connections,children work with fractions with adenominator of 100, 50, 25, 20 and10

Which of the following discounts is the greatestand which is the least:

, 0.25, , 0.3, 35%?

Here is a set of prices. All prices are to increaseby 10%, calculate the new prices

£450, £399, £505

If a television cost £300 and is reduced by10%, what is the new price?

A standard cereal box holds 500g. If you get extra free, how many grams are in the box

now?

There are 40 sweets in a packet. David eatssome and there are now only 60% left. Howmany sweets has he eaten?

12

14

15

25

45

525

14

310


50


25

Spring


52



DOMAIN 2 – MEASUREMENT

NEW OBJECTIVES - SPRING 1


Convert betweendifferent units of metricmeasure (for example,kilometre and metre;centimetre and metre;centimetre andmillimetre; gram andkilogram; litre andmillilitre)


When converting, children will usedecimal notation up to 3 decimalplaces

Understand the explicit link with xand ÷ when converting, and build onthe skills of multiplying and dividingby 10,100 and 1000 (e.g. there are1000m in a km , therefore whenconverting km to m, multiply by 1000)

Include lengths (km, m, cm, mm),mass (kg, g), volume/capacity (l, cl, ml)


Pupils use their knowledge of placevalue and multiplication and division to convert between standard units.

Pupils calculate the perimeter ofrectangles and related compositeshapes, including using the relations of perimeter or area to find unknownlengths. Missing measures questionssuch as these can be expressedalgebraically, for example 4 + 2b = 20for a rectangle of sides 2 cm and b cmand perimeter of 20cm.

Pupils calculate the area from scaledrawings using given measurements.

Pupils use all four operations inproblems involving time and money,including conversions (for example,days to weeks, expressing the answeras weeks and days).

Example questions

Using the full range of units of measure ask questions such as:Convert 3.7km into m

If I was converting g to kg, would I multiply ordivide by 10, 100 or 1000?

True or false? 7539 cl = 7.539 l

53


Notes

54


Understand and useapproximateequivalences betweenmetric units andcommon imperial unitssuch as inches, poundsand pints

Know which measures are imperialand which are metric

Know common abbreviations forunits

Use approximate equivalentsintroducing ≈ sign meaningapproximately equal to

Length:Inches compared to centimetresusing1″ ≈ 2.5cmMiles compared to kilometre using1 mile ≈ 1.5km

Other commonly used equivalents for length include:1cm = 2.5 inches1km ≈ mile400m = mile8km = 5 miles

Mass: Pounds compared to kilograms using 2.2lb ≈ 1kg

Volume/Capacity:Pints compared to litres using 2.2 pints ≈1litre

Answer questions such as:

Approximately how many pints in 8 litres?

5″ = cm (approximately)

If I run 5 miles, approximately how many km isthis?

55

5814


56

Notes


57

Measure and calculatethe perimeter ofcomposite rectilinearshapes in centimetresand metres

A composite shape is made up oftwo or more geometric shapes

To find its area, it must be broken upinto smaller shapes

A rectilinear shape is one with rightangles at all its vertices

Calculate the perimeter of shapes bymeasuring the sides accurately witha ruler and /or calculating anyunknown or missing lengths

Calculate the perimeter of this shape


58

Notes


59

Calculate and comparethe area of rectangles(including squares), andincluding

using standard units,square centimetres(cm2) and squaremetres (m2) andestimate the area ofirregular shapes

Building in the work on arrays in year4, children understand that for a

rectangle with length = a and width

= b ,

area = ( a x b ) units ²

Progression to be shownthrough:

Starting with rectangles that aredemarcated into square centimetres

Build up to rectangles where lengthsof sides are given

Finish with rectangles that require anaccurate measurement of sides andthen use of formula to find the area

Use knowledge of the area of arectangle to make estimates ofareas of irregular shapes

Calculate the area of this rectangle which hasbeen drawn on cm² paper

I have a rectangle with a length of 13cm and awidth of 6cm, calculate the area

This is a scale diagram of a swimming poolwith length of 15m and a width of 3m. What isthe area of the swimming pool?

Draw some rectangles with a perimeter of20cm and then calculate their areas.

Use a ruler to measure and then estimate thearea of this shape in cm²


Notes

60


Estimate volume [forexample, using 1 cm3

blocks to build cuboids(including cubes)] andcapacity [for example,using water]

Volume is a measure of the spacetaken up by something that is eithera liquid or a solid

Capacity is the amount that a givencontainer can hold

Units of measure are:

Volume of liquid is measured in litres(l), centilitres(cl), and millilitres (ml)

Capacity is measured in litres (l),centilitres (cl) and millilitres (ml)

Volume of a solid is measured incubic metres (m³) or cubiccentimetres (cm³)

The capacity of this measuring cylinder is300ml. the volume of liquid in the jug is 150ml.

Show similar images with a variety of scales,including partially demarcated scales whereestimates must be made

Using cm³ build a cuboid with a volume of24cm³

Each edge of this cube measures 5cm.

What is the volume of the cube?

61


62

Notes


63










0.6 x = 60

÷ 1000 = 1.6

6.03 x = 603

CONTINUOUS OBJECTIVES – SPRING 1


Notes

64





• 42 x 8 = 336 (and 336 = 42 x 8,336 = 8 x 42)









• If 32 x 8 = 256 then 256 ÷ 8 = 32

• If 32 x 8 = 256 then 256 ÷ 32 = 8

• If 32 x 8 = 256 then 8 ÷ 256 = 32

• If 32 x 8 = 256 then 320 x 80 = 2560

65


66

Notes


67




Working with numbers up to THTU.tht, ensure that children haveopportunities to:









• Estimate 1245.85 + 1123.36

• Calculate 1245.85 + 1123.36

• Prove 2369.21 – 1123.36 = 1245.85

• Calculate 2369.21m – 1123.36m

• 2369.21cm - = 1245.85cm

• I have 1245.85 litres of water in onecontainer and 1123.36 litres in anothercontainer, how much do I have altogether? Ipour out 450 litres, how much is now left?



68

Notes


69


Solve problemsinvolving addition,subtraction,multiplication anddivision and acombination of these,including understandingthe meaning of theequals sign







• Solve problems including those with more than one step





• Prove 1498 ÷ 7 = 214


• 1498 ÷ = 214




70

Notes


71









Use the skills of converting betweenfractions, decimals and percentagesand apply this in a problem solvingcontext

When making these connections,children work with fractions with adenominator of 100, 50, 25, 20, 10, 5and 2


, 0.25, , 0.3, 35%?


£450, £399, £505



now?


12

14

15

25

45

525

14

310


72

Notes


73

Solve problemsinvolving convertingbetween units of time

Be able to convert:

• hours to minutes

• minutes to seconds

• years to months

• weeks to days

and vice versa, applying this skill when solving problems

Give problems that include mixedunits and that specify how an answeris expressed so that a conversion isrequired

3.5 years = months = days

3 runners ran a marathon and their times wererecorded as such:

Runner A = 4 hours 12 minutes 3 seconds

Runner B = 254 minutes 25 seconds

Runner C = 17 200 seconds

Place the runners in order of fastest to slowest

Use all four operationsto solve problemsinvolving measure [forexample, length, mass,volume, money] usingdecimal notation,including scaling.

For problem solving all four operationsrefer to ‘Following the calculationsequence:’ above

Scaling problems involve changing thequantities for groups of different size.Scaling down to decrease quantitiesand scale up to increase quantities

Include decimal notation in measures

Here is the recipe to make 25 cookies. If youneed to make 100 cookies, calculate the newquantities you would need

Here is another recipe but I only need of it.Calculate the new quantities

13


Notes

74



DOMAIN 3 – GEOMETRY

NEW OBJECTIVES – SPRING 2

PROPERTIES OF SHAPES


Identify 3-D shapes,including cubes andother cuboids, from 2-Drepresentations


Name a 3-D shape and describe itsproperties based on a 2-Drepresentation

Include shapes such as cube, cuboid,pyramids, prisms, spheres

Name this shape and describe its properties

Include number and shapes of the faces andnumber of edges and vertices


Pupils become accurate in drawinglines with a ruler to the nearestmillimetre, and measuring with aprotractor. They use conventionalmarkings for parallel lines and rightangles.

Pupils use the term diagonal and makeconjectures about the angles formedbetween sides, and between diagonalsand parallel sides, and other propertiesof quadrilaterals, for example usingdynamic geometry ICT tools.

Pupils use angle sum facts and otherproperties to make deductions aboutmissing angles and relate these tomissing number problems.

Example questions

75

Know angles aremeasured in degrees:estimate and compareacute, obtuse and reflexangles

When given a set of angles, childrencan classify as acute, obtuse or reflex

Using knowledge that a right angle =90° and that a full turn = 360°,children can estimate the size of anangle to a reasonable degree ofaccuracy Name each angle and estimate its size in

degrees

Draw given angles, andmeasure them indegrees (°)

Using a ruler and protractor, childrencan draw angles with a good degreeof accuracy

Draw and label the following angles:

an acute angle measuring 55°

an obtuse angle measuring 130°

a reflex angle measuring 280°


76

Notes


77

Identify:-angles at a point and onewhole turn (total 360°)

angles at a point on astraight line and a turn(total 180°)

-other multiples of 90°

Children understand the relationshipbetween a right angle, a straightangle and a whole turn and theassociated measurements in degrees

Answer questions such as:

If I face west and then turn clockwise through3 right angles, what direction am I facing now?

If I complete 4.5 turns, how many right angleshave I turned through?

Use the properties ofrectangles to deducerelated facts and findmissing lengths andangles

Know that the interior angles of arectangle comprise of 4 right anglesand add to 360°

Know that parallel sides in arectangle are equal in length

Know that the perimeter of arectangle is calculated by adding thelength of all 4 sides or by using theformula perimeter = 2 ( a + b )units

Know that the area of a rectangle iscalculated by multiplying the lengthby the width and can use theformula, area = ( a x b ) units²

Distinguish betweenregular and irregularpolygons based onreasoning about equalsides and angles

A polygon is a 2-dimensional shapemade up of straight lines

If all the angles and sides are equal it is regular, otherwise it is irregular

Polygons include shapes such astriangles, quadrilaterals, pentagons,hexagons, heptagons and octagons

When reasoning about shapesinclude reference to regular /irregular, number and properties ofsides, number and size of angles

What is the size of angle c?

What is the length of b?

If the area is 32cm², what is the length of a?

What is the perimeter of the rectangle?

Name these polygons and describe theirproperties

8cm

cb

a

12


Notes

78


NEW OBJECTIVES – SPRING 2

POSITION AND DIRECTION

identify, describe andrepresent the position of a shape following areflection or translation,using the appropriatelanguage, and know that the shape has notchanged.

When a shape is reflected, it ends up facing the opposite direction,appearing to be reflected as in amirror. The movement is a ‘flip’

With the mirror line vertical orhorizontal, children can reflect agiven shape accurately

This should include examples wherethe shape touches the mirror line aswell as examples where it does not

When a shape is translated, it moves from one place to another.The movement is a ‘slide’

Every point of the shape must movethe same distance in the samedirection

Translation will be described usingthe vocabulary of left, right, up anddown

Reflect these shapes in the given mirror line

Translate this shape by moving it down 4 and 2to the left

79

Pupils recognise and use reflectionand translation in a variety of diagrams,including continuing to use a 2-D gridand coordinates in the first quadrant.Reflection should be in lines that areparallel to the axes.


80

Notes


81

CONTINUOUS OBJECTIVES – SPRING 2















0.6 x = 60

÷ 1000 = 1.6

6.03 x = 603


Notes

82


83




• 42 x 8 = 336 (and 336 = 42 x 8,336 = 8 x 42)




• If 32 x 8 = 256 then 256 ÷ 8 = 32

• If 32 x 8 = 256 then 256 ÷ 32 = 8

• If 32 x 8 = 256 then 8 ÷ 256 = 32

• If 32 x 8 = 256 then 320 x 80 = 2560


84

Notes


85




Working with numbers up to fourdigits, ensure that children haveopportunities to:


• Evidence the skill of addition and/or subtraction




• Solve problems including those with more than one step



• Estimate 1245.85 + 1123.36

• Calculate 1245.85 + 1123.36

• Prove 2369.21 – 1123.36 = 1245.85

• Calculate 2369.21m – 1123.36m

• 2369.21cm - = 1245.85cm




86

Notes


87














• Prove 1498 ÷ 7 = 214


• 1498 ÷ = 214




Notes

88


89












, 0.25, , 0.3, 35%?


£450, £399, £505



now?


12

14

15

25

45

525

14

310


90

Notes


91


Be able to convert:



• years to months

• weeks to days















13


92


Summer


94


95


DOMAIN 3 – STATISTICS

NEW OBJECTIVES - SUMMER 1


Solve comparison, sumand difference problemsusing informationpresented in a linegraph


A line graph shows information thatis connected in some way (such as achange over time)

Children should be able to read andinterpret information on such graphsin order to answer simple questions


Pupils connect their work oncoordinates and scales to theirinterpretation of time graphs.

They begin to decide whichrepresentations of data are mostappropriate and why.

Example questions

This graph shows the cost of phone calls in thedaytime and in the evening

How much does it cost to make a 9 minute callin the daytime?

How much more does it cost to make a 6minute call in the daytime than in the evening?


Notes

96


How many minutes did Carol take to travel thelast 10 kilometres of the ride?

Use the graph to estimate the distancetravelled in the first 20 minutes of the ride.

Carol says, 'I travelled further in the first hourthen in the second hour'. Explain how the graphshows this.

97

Complete, read andinterpret information in tables, includingtimetables.

Where information is presented in atable, children can read and interpretthe information in order to answersimple questions

This table shows the distances in kilometresbetween five towns.

Use the table to find the distance from Londonto Manchester.

James goes from Newcastle to Birmingham,and then on to Cardiff. How many kilometresdoes he travel?

Carol went on a 40-kilometre cycle ride. This isa graph of how far she had gone at differenttimes.


98

Notes


99

Here is part of a train timetable

How long does the first train from Edinburghtake to travel to Inverness?

Ellen is at Glasgow station at 1.30pm. She wantsto travel to Perth. She catches the next train. Atwhat time will she arrive in Perth?


Notes

100


101

CONTINUOUS OBJECTIVES – SUMMER 1















0.6 x = 60

÷ 1000 = 1.6

6.03 x = 603


102

Notes


103




• 42 x 8 = 336 (and 336 = 42 x 8,336 = 8 x 42)




• If 32 x 8 = 256 then 256 ÷ 8 = 32

• If 32 x 8 = 256 then 256 ÷ 32 = 8

• If 32 x 8 = 256 then 8 ÷ 256 = 32

• If 32 x 8 = 256 then 320 x 80 = 2560


Notes

104


105




Working with numbers up to THTU.tht, ensure that children haveopportunities to:


• Evidence the skill of addition and/or subtraction







• Estimate 1245.85 + 1123.36

• Calculate 1245.85 + 1123.36

• Prove 2369.21 – 1123.36 = 1245.85

• Calculate 2369.21m – 1123.36m

• 2369.21cm - = 1245.85cm




106

Notes


107














• Prove 1498 ÷ 7 = 214


• 1498 ÷ = 214




Notes

108


109












, 0.25, , 0.3, 35%?


£450, £399, £505



now?


12

14

15

25

45

525

14

310


Notes

110


111


Be able to convert:



• years to months

• weeks to days















13


112


51

Basic SkillsAppendix 1


114


SKILLS

Count forward and backwards in steps of powers of 10 for any givennumber up to 1 000 000

Read and write numbers up to 1 000 000 and determine the place value ofeach digit

Recognise the place value in large whole numbers to at least 1 000 000

Compare and order numbers to at least 1 000 000

Partition numbers into place value columns

Partition numbers in different ways

Round any number up to 1 000 000 to the nearest 10, 100, 1000,

10 000 and 100 000

GUIDANCE NOTES

Count out loud, forwards and backwards in powers of 10 following thesequence 10, 100, 1000 etc. from different starting points

(use of visuals will help children to have an understanding of the size of thenumbers)

Use structured apparatus and place value grid to support conceptualunderstanding of place value

What is the value of the 5 digit in these three numbers, 11 025, 125 123,122 510 and 62 258

Play place value games to reinforce this concept (e.g. if I add 200 to thenumber 12 510, which digit would change, what would the new digit be?)

Compare two six-digit numbers, children can say which is the bigger, thesmaller, they also use the < and > signs.

Order consecutive and non-consecutive numbers both forwards andbackwards

Partition six-digit numbers

253 164 = 200 000 + 50 000 + 3 000 + 100 + 60 + 4

Include decimals up to 3 decimal places

253,164 = 200 000 + 50 000 + 3000 + 100 + 60 + 4

and also = 170 000 + 80 000 + 2000 + 1100 + 50 + 14 etc.

Include decimals up to 3 decimal places

562 234 is approximately 562 230 (to the nearest 10), 562 200 (to thenearest 100), 562 000 (to the nearest 1000), 560 000 (to the nearest 10000) and 600 000 (to the nearest 100 000)

YEAR 5 - BASIC SKILLS

115


116

Notes


117

Use rounding to support estimation and calculation

Use knowledge of place value to derive new addition and subtraction facts

Identify multiples and common factors of two or more numbers

Find factor pairs of a two-digit number

Understand the terms multiple, factor, and prime, square and cube numbersand use them to construct equivalent statements

Know and use the vocabulary of prime numbers, prime factors andcomposite (non-prime) numbers.

Establish whether a number up to 100 is prime and recall prime numbers upto 19

Can find the prime factors of a given number

Read and recognise Roman numerals up to 1000

Recognise and use square and cube numbers

Double any number between 1 and 1000 and find all corresponding halves

Before calculating, make reasonable estimates 12 234 + 168 isapproximately 12 200 + 200 = 12 400 etc.

If I know 830 + 170 = 1000, I know:

8 300 + 1 700 = 10 000

83 000 + 17 000 =100 000

0.83 + 0.17 = 1

Consider the numbers 4 and 5. What is the lowest common multiple?

Consider the numbers 18 and 30. What are the common factors?

List all the factor pairs of 24

4 x 25 = 2 x 2 x 25

3 x 270 = 3 x 3 x 9 x 10 = 9² x 10

Know the difference between a prime number and a composite number andidentify prime numbers

What are the prime factors of 18

Match up the Roman numeral CXII with the correct number

Identify the squares of a single digit number

Be able to calculate simple cube numbers

Use partitioning to double 365 so that it becomes double 300 + double 60+ double 5.

Halve 730 by partitioning it into 600, 120 and 10 then halving each andrecombining


Notes

118


Add and subtract mentally with increasingly large numbers to aid fluency

e.g. TthTHTU ± THTU, TthTHTU ± HTU, HTU.t ± HTU.t

Multiply and divide whole numbers including those involving decimals by 10,100 and 1000

Use knowledge of inverse to derive associated multiplication and divisionfacts

Use known facts and knowledge of multiples to derive new facts

Count up and down in tenths, hundredths and thousandths in decimals andfractions including bridging zero

For fractions and decimals derive pairs with complements to 1 and to otherwhole numbers

Identify equivalent fractions

Recognise decimal equivalents of fractions with a denominator of ten, onehundred and one thousand

Read and write decimal numbers with up to 3 decimal places as fractions

Secure the skills of bridging, partitioning, doubling and know their numberpairs up to ten to add and subtract mentally 12 462 ± 2 300 14 756 ± 230 367.6 ± 10.3

Use knowledge of place value columns when multiplying and dividing by 10,100 and 1000, that is, when moving from right to left, each place valuecolumn is ten times bigger and vice versa

If I know 9 × 8 = 72, I know 8 x 9 = 72, 72 ÷ 8 = 9, 72 ÷ 9 = 8

If I know 5 × 9 = 45, I know 5 × 90 = 450 and then 50 x 90 = 4500

Use knowledge that 45 ÷ 9 = 5, to solve 4500 ÷ 9

Count forwards and backwards, from different starting points, consecutivelyand non-consecutively (e.g. , , ) and make connections with thedecimal equivalents during counting (e.g. 0.04, , 0.06 etc.)

Include fraction pairs ( + ) mixed whole number and decimals (3.2 + 4.8) mixed decimal/fraction pairs (0.2 + ) and decimalcomplements of 1 (0.83 + 0.17 = 1)

See the links between fraction families and can say that and areequivalent

Match decimals to fraction equivalents and vice versa ( = 0.03, 0.003 = )

Use knowledge of place value columns to express decimals as fractions

0.3 = , 0.24 = , 0.345 =

119

3100

48

48 8

10

5100

48

1224

31000

3100

241000

310

3451000

3100

4100

5100


120

Notes


121

Read, write order and compare numbers with up to three decimal places

Round decimals with up to two decimal places to the nearest whole numberand to one decimal place

Know percentage and decimal equivalents of , , , , , and thosefractions with a denominator of a multiple of 10 or 25

Use knowledge of complements to 60 and that there are 60 minutes in anhour to convert time durations

Compare two decimals, and say which is the bigger, the smaller, use of the< and > signs

Include decimals with different number of decimal places

Place a set of decimals in ascending order 23.5, 23.35, 23.123, 23.358

18.66 rounded to 19 (nearest whole number) and to 18.7 (rounded to 1decimal place)

Know that 100% represents a whole quantity and 1% is , 50% is 25% is

Convert simple fractions to decimals and then percentages

= = 0.04 = 4%

When given a start and finish time, calculate duration in minutes and hours

Convert 3 hours 25 minutes into minutes, 4.5 hours into minutes, 175minutes into hours and minutes

12

14

15

25

45

1100

5010025

100

14

4100


122


57

ProgressionAppendix 2


124


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 that involveall of the above and with increasingly largepositive 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

Y6

read, write, order and compare numbers up to 10000 000 and determine the value of each digit

round any whole number to a required degree ofaccuracy

use negative numbers in context, and calculateintervals across zero

solve number and practical problems that involve allof the above

PROGRESSION THROUGH THE DOMAINS

NUMBER AND PLACE VALUE

Y5

read, write, order and compare numbers to atleast 1 000 000 and determine the value of eachdigit

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) andrecognise years written in Roman numerals

125


126

Notes


127

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

Y6

solve addition and subtraction multi-step problemsin contexts, deciding which operations andmethods to use and why

perform mental calculations, including with mixedoperations and large numbers

identify common factors, common multiples andprime numbers

use their knowledge of the order of operations tocarry out calculations involving the four operations

solve problems involving addition, subtraction,multiplication and division

use estimation to check answers to calculationsand determine, in the context of a problem, anappropriate degree of accuracy

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-stepproblems in contexts, deciding which operationsand methods to use and why


Notes

128


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

Y6

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal writtenmethod of long multiplication

divide numbers up to 4 digits by a two-digit wholenumber using the formal written method of shortdivision where appropriate, interpreting remaindersaccording to context

divide numbers up to 4 digits by a two-digit wholenumber using the formal written method of longdivision, and interpret remainders as whole numberremainders, fractions, or by rounding, asappropriate for the context

perform mental calculations, including with mixedoperations and large numbers.

identify common factors, common multiples andprime numbers


Y5

identify multiples and factors, including finding allfactor pairs of a number, and common factors oftwo numbers

solve problems involving multiplication anddivision including using their knowledge of factorsand multiples, squares and cubes

know and use the vocabulary of prime numbers,prime factors and composite (non-prime)numbers

establish whether a number up to 100 is primeand recall 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 drawingupon known facts

divide numbers up to 4 digits by a one-digit numberusing the formal written method of short divisionand interpret remainders appropriately for thecontext

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)

129


130

Notes


131

Y4 Y6

solve problems involving addition, subtraction,multiplication and division

use estimation to check answers to calculationsand determine, in the context of a problem, levelsof accuracy


Y5

solve problems involving addition, subtraction,multiplication and division and a combination ofthese, including understanding the meaning of theequals sign

solve problems involving multiplication anddivision, including scaling by simple fractions andproblems involving simple rates


Notes

132


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

Y6

use common factors to simplify fractions; usecommon multiples to express fractions in the samedenomination

compare and order fractions, including fractions >1

add and subtract fractions with differentdenominators and mixed numbers, using theconcept of equivalent fractions

multiply simple pairs of proper fractions, writing theanswer in its simplest form (e.g. × = )

divide proper fractions by whole numbers (e.g. ÷ 2 = )

associate a fraction with division and calculatedecimal fraction equivalents (e.g. 0.375) for asimple fraction (e.g. )

identify the value of each digit to three decimalplaces and multiply and divide numbers by 10, 100and 1000 giving answers up to three decimalplaces

FRACTIONS (INCLUDING DECIMALS Y4 AND PERCENTAGES Y5 AND Y6)

Y5

compare and order fractions whose denominatorsare all multiples of the same number

identify, name and write equivalent fractions of agiven fraction, represented visually, includingtenths and 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 anddiagrams

read and write decimal numbers as fractions (for example 0.71 = )

recognise and use thousandths and relate themto tenths, hundredths and decimal equivalents

round decimals with two decimal places to thenearest whole number and to one decimal place

133

14

12

34

71100

25

45

65

15

14

12

18

13

16

38


134

Notes


135

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

Y6

multiply one-digit numbers with up to two decimalplaces by whole numbers

use written division methods where the answer hasup to two decimal places

solve problems which require answers to berounded to specified degrees of accuracy

recall and use equivalences between simplefractions, decimals and percentages, including indifferent contexts

FRACTIONS (INCLUDING DECIMALS Y4 AND PERCENTAGES Y5 AND Y6)

Y5

read, write, order and compare numbers with upto three decimal places

solve problems involving number up to threedecimal places

recognise the per cent symbol (%) andunderstand that per cent relates to “number ofparts per hundred”, and write percentages as afraction with denominator hundred, and as adecimal

solve problems which require knowing percentageand decimal equivalents of , , , , andthose with a denominator of a multiple of 10 or 25

12

14

15

25

45


Notes

136


Y4 Y6

solve problems involving the relative sizes of twoquantities where missing values can be foundusing integer multiplication and division facts

solve problems involving the calculation ofpercentages [for example, of measures such as15% of 360] and the use of the percentage forcomparison

solve problems involving similar shapes where thescale factor is known or can be found

solve problems involving unequal sharing andgrouping using knowledge of fractions andmultiples

RATIO AND PROPORTION

Y5

137


Notes

138


Y4 Y6

use simple formulae

generate and describe linear number sequences

express missing number problems algebraically

find pairs of numbers that satisfy an equation withtwo unknowns

enumerate possibilities of combinations of twovariables

ALGEBRA

Y5

139


140

Notes


141

Y4

convert between different units of measure (for example, kilometre to metre; hour to minute)

measure and calculate the perimeter of arectilinear figure (including squares) incentimetres and metres

find the area of rectilinear shapes by countingsquares

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

Y6

solve problems involving the calculation andconversion of units of measure, using decimalnotation up to three decimal places whereappropriate

use, read, write and convert between standardunits, converting measurements of length, mass,volume and time from a smaller unit of measure toa larger unit, and vice versa, using decimal notationto up to three decimal places

convert between miles and kilometres

recognise that shapes with the same areas canhave different perimeters and vice versa

recognise when it is possible to use formulae forarea and volume of shapes

calculate the area of parallelograms and triangles

calculate, estimate and compare volume of cubesand cuboids using standard units, including cubiccentimetres (cm3) and cubic metres (m3), andextending to other units [for example, mm3 andkm3 ]

MEASUREMENT

Y5

convert between different units of metricmeasure (e.g. kilometre and metre; centimetreand metre; centimetre and millimetre; gram andkilogram; litre and millilitre)

understand and use approximate equivalencesbetween metric units and imperial units such asinches, pounds and pints

measure and calculate the perimeter ofcomposite rectilinear shapes in centimetres andmetres

calculate and compare the area of squares andrectangles (including squares) and includingusing standard units, square centimetres (cm2)and square metres (m2) and estimate the area ofirregular shapes

estimate volume (e.g. using 1 cm3 blocks tobuild cuboids) and capacity (e.g. using water)

solve problems involving converting betweenunits of time

use all four operations to solve problemsinvolving measure (e.g. length, mass, volume,money) using decimal notation including scaling


142

Notes


143

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 by size

identify lines of symmetry in 2-D shapespresented in different orientations

complete a simple symmetric figure with respectto a specific line of symmetry.

Y6


draw 2-D shapes using given dimensions andangles

recognise, describe and build simple 3-D shapes,including making nets

compare and classify geometric shapes based ontheir properties and sizes and find unknown anglesin any triangles, quadrilaterals, and regularpolygons

illustrate and name parts of circles, includingradius, diameter and circumference and know thatthe diameter is twice the radius

recognise angles where they meet at a point, areon a straight line, or are vertically opposite, and findmissing angles

GEOMETRY

Y5


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 indegrees (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 deducerelated facts and find missing lengths andangles

distinguish between regular and irregularpolygons based on reasoning about equal sidesand angles.

12


144

Notes


145

Y4

Position and direction

describe positions on a 2-D grid as coordinates inthe first quadrant

describe movements between positions astranslations of a given unit to the left/right andup/down

plot specified points and draw sides to complete a given polygon

Y6


describe positions on the full coordinate grid (all four quadrants)

draw and translate simple shapes on thecoordinate plane, and reflect them in the axes

GEOMETRY

Y5


identify, describe and represent the position of ashape following a reflection or translation, usingthe appropriate language, and know that theshape has not changed


Notes

146


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

Y6

interpret and construct pie charts and line graphsand use these to solve problems

calculate and interpret the mean as an average

STATISTICS

Y5

solve comparison, sum and difference problemsusing information presented in a line graph

complete, read and interpret information intables, including timetables.

147


148


149


For more information please contact:

School Improvement LiverpoolE-mail: [email protected] Telephone: 0151 233 3901


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