Maths Planssmartfuse.s3.amazonaws.com/...Maths-Plans-Year-4-final-09-05-14.pdf · The Liverpool Maths team have developed a medium term planning document to support effective implementation

Maths PlansYear 4

SIL�Maths�Plans�Year�4_Layout�1��06/05/2014��13:55��Page�2


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.


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

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 (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

3


4


Autumn


6


7

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…


Notes

8


9

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


Notes

10


11

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


Notes

12



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).

13

Expanded columnar

Column

Column


Notes

14


15

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


Notes

16


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.

17


18

Notes


19


DOMAIN 1 – NUMBER


MULTIPLICATION AND DIVISION


Recall multiplication anddivision facts formultiplication tables upto 12 x 12


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


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.


Notes

20


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

21


22

Notes


23

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


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


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)


Notes

24



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


26

Notes


27

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


Notes

28


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

29

1100

110

1100

110

1100

10100

x 10 = = 110

14

34

12


30

Notes


31

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


Notes

32


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



Can you think a number that would be betweenthese two numbers, that is larger than thisnumber, that is smaller than this number?

33


34

Notes


35

CONTINUOUS OBJECTIVES – AUTUMN 2


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



Convince me that the number half way betwee12 and 40 is 26



6 x = 600

÷ 100 = 6

0.6 x = 60


Notes

36



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



• Evidence the skill of addition and/or subtraction



• Solve missing box questions includingthose where missing box represents adigit or represents a number

• Solve problems including those with more than one step



• Estimate 1245 + 1173

• Calculate 1245 + 1173

• Prove 2368 – 1123 = 1245


• 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?


37


38

Notes


39

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:


• Evidence the skill of multiplicationand division

• Prove the inverse using the skill ofmultiplications and division





• 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.


Notes

40


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

23


42


25

Spring


44



DOMAIN 2 – MEASUREMENT

NEW OBJECTIVES - SPRING 1


Convert betweendifferent units ofmeasure

Measure and calculatethe perimeter of arectilinear figure(including squares) incentimetres and metres


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


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)

45


Notes

46


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


48

Notes


49

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


50

Notes


51


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


Be able to answer word, logic andreasoning problems linked to placevalue


• 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



6 x = 600

÷ 100 = 6

0.6 x = 60

CONTINUOUS OBJECTIVES – SPRING 1


Notes

52



Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations andmethods to use and why






• Solve missing box questionsincluding those where missing box represents a digit orrepresents a number




• Estimate 1245 + 1173

• Calculate 1245 + 1173

• Prove 2368 – 1123 = 1245


• 2368cm - = 1245cm



53


54

Notes


55





• Prove the inverse using the skill of multiplications and division







• Prove 98 ÷ 7 = 14


• 98 ÷ = 14




Notes

56


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



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?



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


58

Notes


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?


Notes

60



DOMAIN 3 – GEOMETRY

NEW OBJECTIVES – SPRING 2

PROPERTIES OF SHAPES


Compare and classifygeometric shapes,including quadrilateralsand triangles, based ontheir properties andsizes


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


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


62

Notes


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


Notes

64


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


66

Notes


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?


Notes

68


CONTINUOUS OBJECTIVES – SPRING 2




• 5 x 8 = 40 (and 40 = 5 x 8, 40 = 8 x 5)






Convince me that the number half way between 12 and 40 is 26



69

6 x = 600

÷ 100 = 6

0.6 x = 60


70

Notes


71


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



• Evidence the skill of additionand/or subtraction

• Prove the inverse using the skill of addition and/or subtraction


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



• 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.


72

Notes


73












• Prove 98 ÷ 7 = 14


• 98 ÷ = 14




Notes

74









of the sweets in my jar is 15, what is the totalnumber of sweets in my jar?





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


76

Notes


77


Building on conversion work, children can now apply these skillswhen solving problems



It took Peter 3.5 hours to run the marathon andMike 200 minutes, who was quicker?


78


Summer


80


81


DOMAIN 3 – STATISTICS

NEW OBJECTIVES - SUMMER 1


Interpret and presentdiscrete and continuousdata using appropriategraphical methods,including bar charts andtime graphs


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)


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


Notes

82


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


84

Notes


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?


Notes

86


CONTINUOUS OBJECTIVES – SUMMER 1




• 5 x 8 = 40 (and 40 = 5 x 8, 40 = 8 x 5)






Convince me that the number half way between12 and 40 is 26



87

6 x = 600

÷ 100 = 6

0.6 x = 60


88

Notes


89


Solve addition andsubtraction two-stepproblems in contexts,deciding whichoperations andmethods to use and why










• Estimate 1245 + 1173

• Calculate 1245 + 1173

• Prove 2368 – 1123 = 1245


• 2368cm - = 1245cm




Notes

90













• Prove 98 ÷ 7 = 14


• 98 ÷ = 14



91


92

Notes


93








of the sweets in my jar is 15, what is the totalnumber of sweets in my jar?





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


Notes

94



Building on conversion work, childrencan now apply these skills whensolving problems



It took Peter 3.5 hours to run the marathon and Mike 200 minutes, who was quicker?

95


96


51

Basic SkillsAppendix 1


98


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


100

Notes


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


Notes

102


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


104

Notes


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


Notes

106


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


108


57

ProgressionAppendix 2


110


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


112

Notes


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


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


Notes

114


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

115


116

Notes


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


Y4


Notes

118


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

14

12

34

71100

25

45

65

15


120

Notes


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


Notes

122


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


124

Notes


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


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


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


Notes

126


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

127


128


129


For more information please contact:

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


Documents

Maths Planssmartfuse.s3.amazonaws.com/...Maths-Plans-Year-4-final-09-05-14.pdf · The Liverpool Maths team have developed a medium term planning document to support effective implementation