VALENCE PRIMARY SCHOOL MENTAL MATHS PROGRESSION … · 1 Valence Primary School Mental Maths...
Transcript of VALENCE PRIMARY SCHOOL MENTAL MATHS PROGRESSION … · 1 Valence Primary School Mental Maths...
1
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
2
Valence Primary School Mental Maths Progression Document 2015
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
3
Valence Primary School Mental Maths Progression Document 2015
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
4
Valence Primary School Mental Maths Progression Document 2015
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)
Term Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally
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)
5
Valence Primary School Mental Maths Progression Document 2015
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)
6
Valence Primary School Mental Maths Progression Document 2015
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)
Jigsaw Numbers Step 1: find the missing piece to 10 (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
7
Valence Primary School Mental Maths Progression Document 2015
Year 2 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)
Term Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally
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)
Jigsaw Numbers Step 1: find the missing piece to 10 (Big Maths)
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)
8
Valence Primary School Mental Maths Progression Document 2015
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
9
Valence Primary School Mental Maths Progression Document 2015
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
10
Valence Primary School Mental Maths Progression Document 2015
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
11
Valence Primary School Mental Maths Progression Document 2015
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
12
Valence Primary School Mental Maths Progression Document 2015
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
13
Valence Primary School Mental Maths Progression Document 2015
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.
14
Valence Primary School Mental Maths Progression Document 2015
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
15
Valence Primary School Mental Maths Progression Document 2015
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
16
Valence Primary School Mental Maths Progression Document 2015
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
17
Valence Primary School Mental Maths Progression Document 2015
Year 4 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 4 Autumn
Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally
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
18
Valence Primary School Mental Maths Progression Document 2015
Yr 4 Spring
Reading Numbers Step 6 : Read 3d numbers Big Maths
Squiggleworth Step 4: Partition 2 decimal place 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
Valence Primary School Mental Maths Progression Document 2015
Yr 4 Summer
Reading Numbers step 6: Read 3d numbers Big Maths
Squiggleworth Step 4: Partition 2 decimal
place numbers Big Maths
Core Numbers step 7: Understand 2dp 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
Valence Primary School Mental Maths Progression Document 2015
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
Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally
Reading Numbers steps 7,8,9: read 6, 5, 4digit numbers Big Maths
Squiggleworth Step 4: Partition 2 decimal place 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
Multiplication step 14: Solve any 1d x 2d Big Maths
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
21
Valence Primary School Mental Maths Progression Document 2015
Year 5 Spring
Reading Numbers steps 10, 11: Read 9, 8, 7digit numbers; Read numbers with decimal places Big Maths
Squiggleworth Step 4: Partition 2 decimal place numbers Big Maths
Core Numbers step 7: Understand 2dp numbers Big Maths
Count Fourways: -2s; -5s Big Maths
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
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
Multiplying and Dividing by 10: Step 4: multiply and divide decimals by 100 Big Maths
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
22
Valence Primary School Mental Maths Progression Document 2015
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
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
Count in decimal fractions and decimals, understanding the place value of each digit FN p 24-36
Count in fractions and recognise equivalents
Multiplying and Dividing by 10: Step 5: multiply and divide decimals by 1000 Big Maths
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
Multiplication step 16: Solve any 2d x 2d Big Maths
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
Valence Primary School Mental Maths Progression Document 2015
Year 6 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 6 Autumn/ Spring/ Summer
Rapid Recall and Counting Mental Strategies Children should be able to Calculate Mentally
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
24
Valence Primary School Mental Maths Progression Document 2015
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.