VALENCE PRIMARY SCHOOL MENTAL MATHS PROGRESSION … · 1 Valence Primary School Mental Maths...

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Valence Primary School Mental Maths Progression Document 2015

VALENCE PRIMARY SCHOOL

MENTAL MATHS PROGRESSION DOCUMENT ‘The ability to calculate in your head is an important part of mathematics. It is also an essential part of coping with society’s demands and

managing everyday events.’ The National Numeracy Strategy

This draft document has been drawn up by looking at the New National Curriculum together with the National Numeracy Strategy -‘Teaching

Mental Calculation Strategies’ and ‘Progression in Mental Calculation Skills’, as well as Big Maths.

6 Key points when planning and teaching mathematics:

Every day is a mental mathematics day

Hands-on learning is important

Seeing mathematics through models and images supports learning

Talking mathematics clarifies and refines thinking

Make mathematics interesting

Learning from mistakes should build children’s confidence

What we have to do as teachers:

Commit regular time to teaching mental calculation strategies

Provide practice time

Introduce practical approaches and jottings with models and images children can use to carry out calculations as they secure mental

strategies

Engage children in discussion when they explain their methods and strategies to teacher/peers

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Reception (Please note that if a child is able to do the first steps in CLIC, you can move them up to the next step)

Term Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally

Autumn Saying numbers: Count to 10 Actual Counting: Count 3 objects Learn it: Step one 1+1=2; 2+2 = 4

Spring Saying Numbers: Count to 10 Reading Numbers: to 10 Core Numbers: Understand numbers to 10 Counting Skills: Know when to count Actual counting: Step 2,3,4,5: count 4 objects; count 5 objects; count 6 objects; count 10 objects Counting On: Count on and count back in ones Learn it: Step 2: 3+3 = 6 ; 4+4 = 8; 5+5 =10

It’s Nothing New: Step 1: Double 1 digit numbers Halving: Step 1: Find half of 3, 5, 7 and 9

Addition: Step One: know when to add some more Step 2: Know to find the total Subtraction: Step 1: Know when to take some away Step 2: Know to take some away and then count how many are left Division: Step 1: Know how to give out objects fairly

Summer Saying Numbers: Step 2: Count to 20 Reading Numbers: Step 2: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 Core Numbers: Understand numbers to 10 Actual Counting: Count 20 objects Counting On: Steps 2,3,4,5: Count on & back 2; Count on & back 3; Count on or back 4; count on or back 5 Counting Multiples: Step 1: I can count in 10s

It’s Nothing New: Pim the Alien Step 1: Swap objects It’s Nothing New: Step 1: Double 1 digit numbers Halving: Step 1: Find half of 3, 5, 7 and 9

Addition: Steps 3,4,5: Add the right amount Add the right amount and can count how many altogether Add number of objects to 10 Subtraction: Steps 3,4,5: Take away the right amount Take away the right amount and count how many are left Take away objects to 10

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Learn its: Step 3: 2+3=5; 2+1=3; say multiples 1-10; say multiples 1-5 X10: 10,20,30,40,50,60,70,80,90,100

Multiplication: Steps 1,2: Set out groups of toys when playing Find the total amount of toys Division: Steps 2,3,4,5 Count how many each person was given Share an even number of objects between 2 people Halve an even number of objects Share 6,9,12 or 15 objects between 3 people

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Year 1 end of year Mental Calculation expectations: (Please note that if a child is able to do the recommended steps in CLIC, you can

move them up to the next step)


Yr 1 Autumn

Saying Numbers: Steps 3 and 4: Count from 60 to 69; count to 100 Big Maths

Reading Numbers: Steps 3, 4: 10,20,30,40,50,60,70,80,90,100; Read two digit numbers Big Maths

Core Numbers : Step 1: understand numbers to 10 Big Maths

Count from 1 and from any other number forwards and backwards in 1’s 2’s 5’s and 10’s (Big Maths Counting Multiples Steps 1,2,3) FN: p 18 & 22; NS pg 28

Distinguish between ordinal and cardinal numbers How to remember: "Cardinal is Counting"

How to remember: "Ordinal says what Order things are in". FN: p 27, 32, 36

Learn its Step 4: Know by heart all number bonds to 10; Multiples 1-5; (Big Maths)

Re-order numbers in a calculation e.g.

2 + 8 to 8+2 noticing that this does does not change the answer NS: p 31, Big Maths Pim the Alien Step 1

Identifying near doubles,

using doubles already

known i.e. 8 + 7 is

7 + 7 +1 or 8 + 8 – 1 NS: p 43 & 60, Big Maths Doubling with Pim Step 1.

Find half of 3,5,7,9 (big Maths Halving with Pim Step 1)

Jigsaw Numbers : Step 1 Find the missing piece to 10 (Big Maths)

Add or subtract a single digit to or from a single digit without crossing 10 i.e. 4 + 5 = ; 8 -3 (Big Maths Addition and Subtraction Step 5)

Add or subtract a single digit to or from 10

Multiplication Steps 3&4: Set out groups of blocks when playing; find the total amount of blocks (Big Maths)

Division Step 5: Share 6,9,12 or 15 objects between 3 peoples (Big Maths)

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Y1 Spring Saying Numbers Step 4: count to 100 (Big Maths)

Reading Numbers Step 5: 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1000. (Big Maths)

Core Numbers Step 1: Understand numbers to 10(Big Maths)

Counting Mulitples Step 2: Count in 5s (Big maths)

Learn its Step 5: Adding on 2: ; 4+2=6; 5+2=7; 6+2=8; 7+2=9; 9+2=11; Adding on 3: 4+3=7; 5+3=8; 6+3=9 (Big Maths)

Know by heart all number bonds to 20 in 3 forms…. 6+8 = 14 ; 14-8 = 6; 14-6 = 8 FN: p 48 - 55

Doubling and Halving Step 2: Double 2 digit multiples of 10; Half of 30, 50, 70 and 90 (Big Maths)

Begin to bridge through 10, and later 20, when adding a single digit number NS: p 36

Jigsaw Numbers Step 1: find the missing piece to 10 (Big Maths)

Use known number facts and place value to add or subtract pairs of single-digit numbers e.g. 4 + 5; 8-3

Add 9 to single-digit numbers by adding 10 and then subtracting 1 e.g 9 + 4 to 10+4 = 14-1 = 13 NS: p 40

Use patterns of similar calculations i.e. 9+1=10; 9+2=11; 9+3=12

Addition Steps 6,7,8,9: Read a number sentence; arrange a number sentence; solve a number sentence; solve addition on a number line (Big Maths)

Subtraction Steps 6,7,8,9: read a subtraction number sentence; arrange a subtraction number sentence; solve a subtraction number sentence; solve subtraction on a number line (Big Maths)

Multiplication Step 4: Find the total amount of blocks (Big Maths)

Division Step 6: Share 6,9, 12 or 15 objects into 3 (Big Maths)

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Y1 Summer

Saying Numbers: Step 5: Count past 100 (Big Maths)

Reading Numbers: Step 5: Reading 3 digit multiples of 100 (Big maths)

Squiggleworth Step 1: Partition a 2 digit number (Big Maths)

Core numbers Step 2: Understand numbers to 20 (Big Maths)

Counting Multiples: Step 3: Count in 2s (Big Maths)

Count Fourways: 1s, 10s, 2s, 5s (big Maths)

Learn Its: Step 6: 6 + 6=12; 7+&=14; 8+8=16; 9+9=18; Say multiples 1to 5; Say multiples 1-10; x2 tables.

Recall doubles of all numbers to at least twenty and corresponding halves

Begin to recognise two-digit multiples of 2,5,10 FN: p 100

Know odd and even numbers

FN: p 98

Pim the Alien : Step 1: Swap objects (Big Maths)

Doubling and Halving: Steps 2 and 1: Double 2 digit multiples of 10; know half of 30, 50, 70, 90 (big Maths)


Fact Families: Step 1: Know the fact families for 1 digit + 1 digit facts. (big Maths)

Begin to partition to add numbers close to a multiple of 10 e.g 5 + 9 = 5 + 10 – 1 (using a number line)

FL: p 32 & 36

Bridging through numbers other than 10 e.g. 1 week = 7 days ‘It is half past seven. What time was it 3 hours ago?’

Partition small numbers e.g. 8+3 = 8 + 2 + 1

Addition: Steps 10, 11, 12: Add 1 to a number up to 20; Add 2 or 3 to a number up to 20; Add a 1digit number to 20.BM

Subtraction: Steps 10, 11, 12: take 1 from a number to 20, take 2 or 3 from a number to 20; take a 1 digit number from a number to 20. BM

Multiplication: Draw out groups of dots; find the total amount of dots. BM

Division Steps 7,8,9,10,11: Share 8, 12, 16 or 20 objects between 4 people.; share 8, 12, 16 or 20 objects into 4; share equally to solve division problems; make groups of 2,5, 10; find how many altogether by counting each group.BM

Add or subtract a single-digit to or from a ‘teens’ number e.g. 13 + 5 , 17-3

Doubles of all numbers to 20 e.g. 7 + 7 , double 9

Add or subtract 10 to any 2 digit number i.e. 32 + 10 = 42, recognising patterns and the digit that changes

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Y2 Autumn

Reading Numbers Step 5: 100,200, 300, 400, 500, 600, 700, 800, 900, 1 000 (Big Maths)

Squiggleworth step 1: partition a 2digit number Big Maths.

Core Numbers: Step 2: Understand numbers to 20 (Big Maths)

Counting Multiples Step 3: count in 2s (Big Maths)

Count Fourways Steps 3: count in 100s/200s/500s/2500s. (Big Maths)

Learn its: Step 7: 3+8; 3 +9; 4+7; 4+8; 4+9; 10x table (Big Maths)

Pim the Alien Step 1: Swap objects (Big Maths)

Adding with Pim Step 1: Add tens (BM)

Doubling and Halving Steps 3 and 2: Double 2 digit numbers; Half of 30, 50, 70, 90; half of 300, 500, 700, 900 (BM)


Fact Families Step 2: turn 1d +1d facts into multiples of 10. (BM)

Reorder numbers when adding e.g. 2 + 36 = 36 +2 ; 5 + 7 + 5 = 5+5+7 NS: p 31

Addition: Steps 13,14, 15: Add 1 to a 2d number; add 10 to a 2d tens number; add 10 to any 2d number (BM)

Add or subtract a single-digit to or from any two-digit including crossing 10 e.g. 5 + 8; 12- 7

Subtraction Steps 13,14,15: I can take 10 from a multiple of 10; take 10 from a 2d number; take a multiple of 10 from a multiple of 10 (Big Maths)

Add or subtract a single-digit to or from 10 e.g. 60 +5 , 80 – 7

Multiplication Steps 7 and 8: Write out repeated addition; Solve repeated addition (BM)

Division: Step 12: Find how many altogether by counting in 2s, 5s or 10s (Big Maths)

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Y2 Spring Reading Numbers Step 6: Read 3digit numbers Big Maths

Squiggleworth Step 1: partition 2d numbers Big Maths

Core Numbers Step 2: Understand Numbers to 20 Big Maths

Count in steps of 2, 3, 5, and 10 from any given number FN: p 20, 28 & 33; Big Maths Core Numbers Step 3

Count Fourways: 50s, 500s, 5000s Big Maths

Learn Its schedule 8: 8+9 = 17; 8+7=15; 6+7=13; 5+6=11; 5+4=9; x5 Tables.

Count in fractions up to 10, using ½ and 2/4 equivalence

Know by heart all number bonds that total 20 FN: p 48 - 55

Know by heart all addition and subtraction facts for each number up to 20 FN: p 48 - 55

Pim the Alien Step 1: Swap

objects Big Maths

Adding with Pim Step 2:

Add hundreds Big Maths

Doubling and Halving:

Double 2d numbers; half

of 30 ; 50 ; 70; 90; half of

300, 500, 700 and 900 Big

Maths

Using near doubles e.g. 13

+ 14 is double 14 and

subtract 1 or double 13

and add 1

NS: p 43

Understand halving as the

inverse of doubling

NS: p 60

Find 10 more and less than

numbers to 100 Jigsaw

Numbers Step 2 Big Maths

Fact Families Step 2:

Turn 1d +1d facts into

multiples of 10: Use

patterns of similar

calculations, e.g. 12 + 7 =

19, 120 + 70 = 190 Big

Maths

Addition Steps 16,17, 18

and 19 Big Maths : Add

or subtract a single digit

number to or from a two-

digit number including

crossing the tens

boundary, 23 + 5, 57 – 3 ,

then 28 + 5 , 57 – 7

Find what must be added

to any two-digit multiple

of 10 to make 100

e.g. 70 + □ = 100

Steps 16,17,18, 19 Big

Maths :Add or subtract a

multiple of 10 to or from

any two-digit number

when the difference is

less than 10 e.g. 78 – 71

or 52 – 48

Multiplication Step 8:

Solve repeated addition

Big Maths

Division Steps 13,14,15:

Arrange a division

number sentence; solve a

division number sentence

with objects, solve

division, using objects

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Find the difference by

calculating from the

smaller to the larger

number

Add 3 small numbers by

putting the largest number

first and / or finding a pair

totalling 10 i.e. 2+6+9

becomes (8+2) + 3 =

FN: p 48; NS: p 31

Respond to questions such

as ‘Tell me three numbers

that add to 20?’

Work out 1 + □ + 5 = 17

FN: p48

Use the relationship

between addition and

subtraction i.e. 8 + 7 = 15

therefore 15 – 8 = 7 and 15

– 7=8

NS: p 26

(with remainders) Big

Maths

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Y2 Summer

Reading Numbers Step 6: Read 3digit numbers

Big Maths

Squiggleworth Step 1: Partition a 2digit number

Big Maths

Core Numbers Step 3: Understand 2digit

numbers Big Maths

Counting Multiples Step 4: Count in 3s Big Maths

Count Fourways: 20s, 200s, 2000s , 1/4s Big Maths

Counting Along Step 1: Count along when numbers are written in Big Maths

Learn Its Schedule 9: 7+9=16; 6+9=15; 5+9=14; 5+8=13; 5+7= 12; 6+8=14 ; x2 Tables

Know by heart doubles of all numbers to 20

Know by heart all halves of numbers to 20

Know by heart all multiplication facts for 2, 5 and 10 tables FN: p 100

Know division facts for multiples of 2,5 10 FN: p 126

Know by heart all bonds of multiples of 10 up to 100 e.g. 30 + 70

FN: p 51

Pim the Alien Step 1: Swap

objects Big Maths

Adding with Pim step 3:

Add thousands Big Maths

Doubling Step 3: Double

2d numbers Big Maths

Halving step 3; know half

of 300, 500, 700 and 900

Big Maths

Jigsaw numbers step 3:

Find the missing piece to

100. Big Maths

Multiply whole numbers

by 10 Big Maths

Divide multiples of 10 by

10 Big Maths

Understand place value to

multiply and divide by 10,

moving digits to right to

multiply by 10 and to the

left to divide by 10 i.e. 17 x

10 = 170 ,

30 ÷ 10 = 3 FN: p32 & 36; NS: p 63

Use knowledge of number

facts and place value to

multiply and divide 2,5 and

10

Additions Steps 20,

21,22,23,24 Big Maths:

solve any 2d +1d ; add

any 2d tens number to

another; add a 2d tens

number to a 2d number;

add 2d number to a 2d

number Big Maths

Subtraction steps 20-27

Big Maths: Spot the next

multiple of 10; count to

the next multiple of 10;

know the gap to the next

multiple of 10; know the

1d gap from a multiple of

10; know the total gap

across a multiple of 10;

take a multiple of 10

from any 2d number; find

the 2 gaps in a 2d – 2d

question; solve any 2d –

2d .

Multiplication step 9:

Solve any 1d x 1d

Division steps 16 and 17:

use tables facts to find a

division fact; use tables

facts to find a division

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NS: p 52

Bridging through numbers

other than 10 e.g. 1 year =

12 months; 10.30 to

10.45

Partition additions into 10s

and units and then

recombine mentally with 2

digit numbers that total

less than 100 i.e. 24 + 12 =

20 + 10 + 4 + 2

30 + 6 = 36 FN: p32 & 36; NS: p 34

Partitioning bridging

through multiples of 10

6 + 7 = 6+4+3 23 – 9 = 23 – 3 – 6 NS: p 36

Use know number facts

and place value to add or

subtract pairs of numbers

NS: p 26 Add or subtract 9, 19, 11 or 21

by rounding and compensating

i.e.

37 + 9 = 37 + 10 – 1 = 46 NS: p 40

fact (with remainders) Big

Maths

Column Methods :

Addition and Subtraction

step 1 Big Maths

Doubles of all numbers to

at least 20. Double any

multiple of 5 up to at

least 50 e.g. double 35

Halve any multiple of 10

up to 100 e.g. halve 50

Mental addition and subtraction of two two-digit numbers, totalling less than 100

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Year 3 end of year Mental Calculation expectations: (Please note that if a child is able to do the recommended steps in CLIC, you can move

them up to the next step)

Year 3 Autumn

Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally

Reading Numbers Step 6: Read 3digit numbers Big Maths

Order numbers and compare to 1000 FN: p 37

Squiggleworth Step 2: partition a 3d number. Big Maths

Core Numbers Step 3: Understand 2d numbers Big Maths

Count in multiples of 2 (Step 4 Big Maths) ,3,4,5,8 and 10 forwards and backwards

Count Fourways Big Maths: 20s, 200s, 2000s, 1/4s

Count in 50s and 100s Know 10 or 100 more than numbers to 1000 FN: p 41

Learn Its schedule 10: Big Maths

Adding with Pim Step 3: Add thousands Big Maths

Find a difference by calculating from the smaller to the larger number e.g. 82-47 = 15

Reorder numbers in a calculation e.g. 12-7-2 = 12-2-5

Add three or four small numbers by putting the largest number first and /or finding pairs totalling 10

Partition into tens and units and recombine for calculating answers to exceed 100

Understand doubling as inverse of halving

Double 2d numbers Big Maths Step 3

Know half of 300, 500, 700 and 900 Big Maths step 3

Find what must be added to any multiple of 100 to make 1000 e.g. 300 + □ = 1000

Add or subtract any pair of two-digit numbers, with and without crossing a tens boundary or 100 e.g. 33 + 45, 87 – 12 Big Maths Addition step 25, subtraction step 28

Find what must be added to/subtracted from any two-digit number to make the next higher/lower multiple of 10 e.g. 64 + □ = 70 , 56 - □ = 50

Multiplication step 9: Solve any 1d x 1d Big Maths

Division Step 17: use a tables fact to find a division fact (with remainders) Big Maths

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Jigsaw Numbers Step 3: Find the missing piece to 100 Big Maths

Multiply and divide whole numbers by 10 Big Maths

To multiply a number by 10/100, shift its digits one, two places to the left- NS: p 65

To divide a number by 10/100, shift its digits one, two places to the right NS: p 65

Column methods for addition and subtraction: Step 2 Big Maths.

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Year 3 Spring

Reading Numbers step 6: read 3d numbers Big Maths

Squiggleworth step 2: partition a 3d number; then a 4d number Big Maths

Core Numbers step 3: understand 2d numbers Big Maths

Counting multiples step 5: Count in 4s Big Maths

Count Fourways: 1000s

Learn its schedule 11: Big Maths

Count in fractions to 10, also count forwards and backwards in tenths. Recognise equivalents

Know by heart addition and subtraction facts for each number up to 20 Know by heart all sums and differences of multiples of 10 up to 100 FN: p 92-110

Know by heart all doubles of multiples of 5 and 10 up to 100 Know by heart all halves of multiples of 10 up to 100 FN: p 92-110

Bridge through a multiple of ten and adjust – be able to do this with 3 digit numbers e.g. 149 + 32 = 149 +1 +31 150 + 31=181 NS: p 36-37

Add and subtract pairs of 1 and 2 digit numbers FN: p 84

Add and subtract 3 digit numbers and 1 digit, 3 digit and tens, 3 digit and hundreds FN: p 86-88 ; Big Maths

Doubling and Halving Step 4: double 3d multiples of 100; know half of 3,5, 7 and 9 as decimals Big Maths

Jigsaw numbers step 3: find the missing piece to 100 Big Maths

Multiplying whole numbers by 10; dividing multiples of 10 by 10 Big Maths

Recognise and use inverses with + and -, multiplication and division

Addition Steps 26,27 Big Maths: Solve 3d + 2d

Subtractions Step 28: Take away and 2d number from 100 big Maths

Find what must be added to / subtracted from any three digit number to make the next higher/lower multiple of 10 e.g. 647 + □ = 650

Multiplication: step 10 Big Maths Multiply single digit numbers by 10 or 100 e.g. 6 x 100

Division step 17 Big Maths

Addition and subtraction Column methods steps 3 and 4 Big Maths

Divide any multiple of 10 x 10 e.g. 60 ÷ 10

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Partition into ‘5 and a bit when adding 6,7,8 or 9, then recombine

Add or subtract mentally a ‘near multiples of 10’ to or from a two digit number e.g 53 + 71= 53 + 70+1

Use patterns of similar calculations e.g. 15+17=32, therefore 150+170=320

Say or write a subtraction statement corresponding to a given addition statement e.g. 16+13=29, 29-13=16

Year 3 Summer

Reading numbers step 6: Read any 3d number Big Maths

Squiggleworth step 2: partition a 3d number; then a 4d number Big Maths

Core numbers step 4: understand 3d numbers Big Maths

Counting Multiples: Step 6 – count in 8s Big Maths

Count Fourways: 1/10s; 0.1s Big Maths

Learn Its schedule 12 Big Maths

Know by heart all multiplication facts for 2,3, 4,5, 8, 10 up to 12 FN: p 96-97

Know the corresponding division facts for above tables to 12 FN: p 92-110

Pim the Alien Steps 2 and 3: Swap amounts; swap units of measure Big Maths

Adding with Pim step 3: add thousands Big Maths

Doubling step 5: double 3d numbers Big Maths

Halving step 5: halve any 2d number Big Maths

Identify near doubles e.g. 18+16 is double 18 and subtract 2 or double 16 add 2 (HA) , 7 + 6 is double 7 -1 or double 6 add 1 ( LA)

Addition Step 28: solve 3d + 3d Big Maths

Subtraction step 29 : take 100 from any 3d number Big Maths

Subtract any 3 digit number from any three digit number when the difference is less than 10 e.g. 458 – 451

Double any number to at least 20 e.g. double 18 and corresponding halves , ½ 36 , Double 60 , halve 120

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Recognise multiples of 2,5, 10 up to 1000

Know all pairs of multiples of 100 with a total of 1000 e.g. 800 + 200

Know all pairs of multiples of 5 with a total of 100 i.e. 65 + 35

Rounding to 10 and 100

Use knowledge of number facts and place value to multiply or divide 2,3,4,5.10 and 100

Recognise fractions and pairs of fractions equivalent to one

Calculate with fractions that have same denominator within one whole e.g. 1/7 + 2/7 = 3/7

Say or write a division statement corresponding to a given multiplication statement.

Multiplication step 11: solve 1d x 2d Big Maths

Division steps 18 and 19: combine 2 or more tables facts to solve division with and without remainders Big Maths

Column Methods: Addition steps 4,5,6; Subtraction step 5; Multiplication and division step 1. Big Maths

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Year 4 Autumn


Reading numbers Step 6: Read 3digit numbers Big Maths

Squiggleworth Step 4: Partition 2 decimal place numbers Big Maths

Core Numbers step 5: Understand 4d numbers Big Maths

Count in multiples of 2,3,4,5,6,7,8,9,10,25,100, 1000 from any number FN: p 42; big Maths steps 7,8,9

Count Fourways: 25s, 250s, 2500s Big Maths

Learn Its schedule 13: x6; x7; x9 Big Maths

Adding with Pim Step 3: Adding thousands Big Maths

Double and Halve 2d numbers Big Maths

Jigsaw Numbers step 4: find the missing piece to 1000 Big Maths

Round any number to the nearest 10 or 100 FN: p 43

Use place value to aide calculation FN: p 28

Multiply whole numbers by 100 Big Maths

Divide multiples of 10 by 10 Big Maths

Show use of number facts in mental calculation strategies and be able to talk about them

Find what must be added to any two digit number to make 100 e.g. 37+? =100

Add or subtract any pair of two- digit numbers e.g. 38+85, 92 – 47

Step 28, 29 Big Maths Addition and Subtraction: Find out what must be added to / subtract from any two or three digit number to make the next higher/lower multiple of 100, e.g.

374 + ?=400, 826 - ? =800

Double any whole number from 1-50 e.g. double 36 and find all the corresponding halves e.g. 96 ÷ 2 NS: p 61

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Yr 4 Spring

Reading Numbers Step 6 : Read 3d numbers Big Maths


Core Numbers step 6: Understand 1dp numbers Big Maths

Count Fourways: 0.2s; 0.5s; 0.25s Big Maths

Say 10,100,1000 more or less than a number FN: p 41

Learn Its schedule 14: x 11 tables Big Maths

Adding with Pim step 4: add tenths Big Maths

Doubling and Halving step 4: Double three digit numbers ; double 3d multiples of 100 Big Maths

Jigsaw Numbers step 4: Find the missing piece to 1000 Big Maths

Multiplying and dividing step 2: Multiply and divide whole numbers by 100, giving decimal answers Big Maths

Calculate with increasingly complex numbers e.g 12,462 - 2400 or 2,462+ 600

Bridge through a 100 or 1000 89+67 (67=11+56) 89+11+56=156

Add or subtract 9,19,29,11,21,etc by rounding and compensating

Use knowledge of near doubles, e.g 38+37 NS: p 43-44

Addition and Subtraction step 29 big Maths: solve any 3d +3d; take 100 from any 3d number Big Maths

Subtract any four-digit number from any four digit numbers when the difference is small

e.g. 3641-3628 or 6002 – 5991

Multiply any two-digit number by 10 e.g. 26 x 10

Divide a multiple of 100 by 10 e.g. 600÷10

Double any multiple of 10 to 500 e.g 380x2 and find all corresponding halves e.g. 760 ÷ 2, 130 ÷ 2

Multiply any two-digit multiple of 10 by 2,3,4,5 e.g. 60x4, 80x 3

Column Methods: Addition step 7; Subtraction step 6, Multiplication and division step 2. Big Maths

19


Yr 4 Summer

Reading Numbers step 6: Read 3d numbers Big Maths

Squiggleworth Step 4: Partition 2 decimal

place numbers Big Maths


Count Fourways: 1/5s Big Maths

Learn Its schedule 15: x 12 tables Big Maths

Count up through the next multiple of 10,100 or 1000 e.g. 789,799,809 etc

Reorder numbers in a calculation

Count in fractions and decimal fractions forwards and backwards

Double any two or three digit number

Halve any two or three digit number

Know all multiplication tables up to 12x12

Know all division tables up to multiple 12x12

Know decimal equivalents to ¼, ½ ,¾ and any number tenths and hundredths

Adding with Pim step 4: add tenths Big Maths

Doubling and Halving steps

5 and 6: Double 3d

numbers; halve and 2d and

3d number Big Maths

Jigsaw Numbers step 4: Find the missing piece to 1000 Big Maths

Multiplying and dividing step 2: Multiply and divide whole numbers by 100, giving decimal answers Big Maths

Continue to use the relationship

between addition and

subtraction, multiplication and

division

Use knowledge of multiplication

and division facts to calculate

questions such as 640 divided by

8

Use distributive law to derive

facts such as 39x8=30 x 8 + 9 x 8

Partition to carry out

multiplication 56x7 = (50x7) +

(6x7)

350 + 42= 392

Use closely related facts to carry

out multiplication and division

e.g. 7 x 6 =42, therefore 70 x 6 =420 or 6 x 8 =6 x 4 x 2

Addition: step 30, 31 : solve any 3d + 3d as money Big Maths

Subtraction step 30: solve 3d – 2d Big Maths

Multiplication steps 14; division steps 20-23 Big Maths

Double any multiple of 5 to 100 e.g. 65 x 2

Column Methods: Additon step 8; subtraction step 7; multiplication step 3; Division steps 3,4,5

20


Year 5 end of year Mental Calculation expectations: (Please note that if a child is able to do the recommended steps in CLIC, you can move

them up to the next step)

Year 5 Autumn


Reading Numbers steps 7,8,9: read 6, 5, 4digit numbers Big Maths


• Core Numbers step 7: Understand 2dp numbers Big Maths

Count Fourways: -1s Big Maths

Count forwards and backwards in steps of 10,100,1000 or 10,000 for any given number up to 1,000,000 FN p18-39; NS p 28-29

Recall quickly multiplication and division facts up to 12x12 and use them to multiply and divide pairs of multiples of 10 and 100.FN p43,44 ; NS p52 e.g. 3 x 7 30 x 70, 24 ÷ 4 240 ÷ 40

Identify pairs of factors for 2 digit whole numbers

Recall prime numbers to 19

Know connections between percentages, fractions and decimals NS p69

Adding with Pim step 5: adding hundredths Big Maths

Jigsaw numbers step 5: find the missing decimal piece Big Maths

Multiplying and Dividing by 10: Step 3: multiply and divide decimals by 10 Big Maths

Use estimation in calculating and verbalise

Add and subtract, multiply and divide mentally with increasingly large numbers, practicing speed and fluency FN p 46-67

Use partitioning and place value in calculation NS p34

Add or subtract the nearest multiple of 10, 100 or 1000 then adjust

Add or subtract any pair of 3 digit numbers e.g. 560 + 250, 620 – 380 ; Add or subtract any pair of decimal fractions each with unit or tenths, or each with tenths and hundredths e.g. 5.7 + 2.5, 0.63 – 0.48 FN p46-79; Big Maths steps 31, 32, 33


Division step 24, 25: Big Maths

Find what must be added to a decimal fraction with units and tenths to make the next higher whole number e.g. 4.3 + ? = 5 FN p46-79 FN p46-79

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Year 5 Spring

Reading Numbers steps 10, 11: Read 9, 8, 7digit numbers; Read numbers with decimal places Big Maths



Count Fourways: -2s; -5s Big Maths


Round numbers up to 1,000,000 to the nearest 10,100,1000, 10,000 and 100,000 FN p23

Reorder numbers in a calculation FN p32,39 ; NS p31

Double any number with up to 2 decimal places NS p60

Halve any number with up to 2 decimal places NS p61


Calculate whether a number up to 100 is prime

Identify near doubles and use in strategies to calculate NS p43

Use factors e.g. 15 x 6 10 x 6 = 60 5 x 6 = 30 60 + 30 = 90

Use closely related facts to carry out multiplication and division e.g. 11 x 15 10 x 15 = 150 1 x 15 = 15 150 + 15 = 165

Use doubling and halving NS p60,61

Add or subtract any pair of 3 digit numbers; Add or subtract any pair of decimal fractions each with unit or tenths, or each with tenths and hundredths

e.g. 5.7 + 2.5, 0.63 – 0.48 FN p46-79; Big Maths steps 32, 33,34, 35

Multiplication step 15,16: Solve any 1d x 3d ; 2d x 2d Big Maths

Division step 26, 27: Big Maths

Subtract a four digit number just less than a multiple of 1000 e.g. 5001 – 1997 FN p46-79

Multiply any two or three digit number by 10 or 100 e.g. 26 x 10, 79 x 10 FN p 81 – 133 ; NS p 66

Divide a multiple of 100 by 10 by a single digit e.g. 60 x 7 FN p 81 – 133

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Year 5 Summer

Squiggleworth step 5: partition a 3dp number Big Maths

Core Numbers steps 8, 9: Understand 3dp numbers; understand 5, 6, 7 and 8d numbers Big Maths

Count Fourways: -25s Big Maths


Count in decimal fractions and decimals, understanding the place value of each digit FN p 24-36

Count in fractions and recognise equivalents


Work out sixths by halving thirds e.g. 1/6 of 30 1/3 of 30 = 10 10 ÷ 2 = 5 (1/2 of a 1/3)

Use the relationship between addition and subtraction, multiplication and division.

Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times) NS p45

Add or subtract any pair of 3 digit numbers; Add or subtract any pair of decimal fractions each with unit or tenths, or each with tenths and hundredths

e.g. 5.7 + 2.5, 0.63 – 0.48 FN p46-79; Big Maths steps 34, 35,36,37,38


Division step 28-31: Big Maths

Find 50%, 25%, 10% of a small whole number or quantities e.g. 25% of £8 NS p69

Calculate complements of 1 with two decimal numbers to two places

23




Year 6 Autumn/ Spring/ Summer


Core Numbers step 10: understand numbers with different decimal places Big Maths

Be able to order to 10 million FN p36-40

Continue to count regularly, whole numbers, fractions, decimals, negative numbers FN p19-30 ; NS p28-29

Generate linear number sequences including negative and decimal numbers e.g. 1.4; 1.1; 0.8

Know by heart all the squares and square roots of numbers between 12 x 12

Recognise and recall factors of numbers up to 100 and corresponding multiples of 100

Use knowledge of place value and x facts to 10 x 10 to derive related x / ÷ facts e.g. (0.8 x 7 = 5.6) NS p52

Know by heart tests of divisibility for multiples of 2,3,4,5,6,8, 9, 10 and 12

Prime numbers less than 100

Consolidate all strategies from previous years

Use known number facts and place value to add or subtract pairs of three digit multiples of 10 and two digit numbers with two decimal places

Add or subtract the nearest multiple of 10 or 100, 1000 , 10 000, then adjust

Continue to use the relationship between addition and subtraction, multiplication and division

Use factors e.g. 35 x 18 35 x 2 x 3x3 70 x 3 x 3 210 x 3 = 630

Practice mental calculations and ensure an increased speed of complex calculations

Perform mental calculations with mixed operations

Multiply/Divide and two digit number by a single digit e.g. 34 x 6; 68 ÷4 FN p 81-133 ; NS p66

Multiply or divide any whole number by 10 or 100 giving any remainder as a decimal e.g. 47 ÷ 10 = 4.7 1763 ÷ 100 = 17.63

Find squares of multiples of 10 to 100

Find any multiple of 10 % of a whole number or quantity e.g. 70% of £20 NSp69

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Equivalent fractions, decimals and percentages for hundredths e.g. 35% is equivalent to 0.35 or 35/100 NS p69

Use knowledge of place value and number bonds to aide calculation

Use doubling and halving

Use closely related facts to carry out multiplication and division

Work out 17 times table by adding 7 and 10 times facts and other multiplication tables

Use the relationship between multiplication and division e.g. 0.75 x 4 = 3 buy one get one free

Calculate with unit fractions and use the knowledge of this to see inverse. ¼ of a length is 36 so the total length is 36 x 4 = 144

Use knowledge of fractions and decimals to calculate remainders

Partition: Using partitioning and the distributive law to divide tens and ones separately e.g. 94 ÷ 4 = ( 80 +12) ÷ 4 = 20 + 3 = 23

Form an equivalent calculation e.g. to divide by 25, divide by 100 then multiply by 4; to divide by 50, divide by 100 then double NS p63, 66

Double decimals with units and tenths e.g. double 7.6 and find corresponding halves e.g. half of 15.2

Multiply/divide 2 digit decimals e.g. 0.8 x 7; 4.8 ÷ 6 FN p81-133

Simplify fractions by cancelling

Scale up/down using known facts e.g. 3 oranges cost 24p; find the cost of 4 oranges.

VALENCE PRIMARY SCHOOL MENTAL MATHS PROGRESSION … · 1 Valence Primary School Mental Maths...

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Transcript of VALENCE PRIMARY SCHOOL MENTAL MATHS PROGRESSION … · 1 Valence Primary School Mental Maths...