Progression
Tuesday 11th February 2014
Counting
Developing counting skills.
Knowing the number names in order.
Synchronising saying words and pointing or moving
objects.
Keeping track of objects counted.
Recognising that the number associated with the last
object touched is the total number of objects.
Recognising small numbers of objects without
counting them.
Counting
Developing counting skills.. continued
counting things you cannot move or touch or see,
or objects that move around.
counting objects of different sizes.
recognising that if a group of objects already
counted is re-arranged then the number of them
stays the same.
recognising that if objects are added or removed the
number changes.
• This focuses on the development of
children’s awareness, understanding and
use of the language of number.
Addition
These are a selection of mental strategies:
Mental recall of number bonds
6 + 4 = 10
+ 3 = 10
25 + 75 = 100
19 +
= 20
Use near doubles
6 + 7 = double 6 + 1 = 13
+
MENTAL
MATHS
Addition using partitioning and recombining
34 + 45 = (30 + 40) + (4 + 5) = 79
Counting on or back in repeated steps of 1, 10, 100, 1000
86 + 57 = 143 (by counting on in tens and then in ones)
460 - 300 = 160 (by counting back in hundreds)
Add the nearest multiple of 10, 100 and 1000 and adjust
24 + 19 = 24 + 20 – 1 = 43
458 + 71 = 458 + 70 + 1 = 529
Use the relationship between addition and subtraction
36 + 19 = 55
19 + 36 = 55
55 – 19 = 36
55 – 36 = 19
Addition
Practical
How can I record?
Draw simple pictures and talk about it…
Record ideas in a number sentence….
Addition
Addition
Addition
Addition
Reordering to start with the largest number.
Number line
Addition
Number line
Addition
Addition
Partitioning
Addition
These are introduced when the children have a sound
grasp of place value & of the whole addition process.
Addition
Standard Method Column addition….
364
+ 54
418
1
£.
14.62
+ 1.87
56.49
1
238.612
1051.05
+ 81.069
1370.731
1 1 11
Subtraction
-
These are a selection of mental strategies:
Mental recall of addition and subtraction facts
4 = 10 – 6
20 - 17 = 3
10 -
□=2
□ - 8 = 11
Find a small difference by counting up
82 – 79 = 3
MENTAL
MATHS
Counting on or back in repeated steps of 1, 10, 100, 1000
86 - 52 = 34 (by counting back in tens and then in ones)
460 - 300 = 160 (by counting back in hundreds)
Subtract the nearest multiple of 10, 100 and 1000 and adjust
24 - 19 = 24 - 20 + 1 = 5
458 - 71 = 458 - 70 - 1 = 387
Use the relationship between addition and subtraction
36 + 19 = 55
19 + 36 = 55
55 – 19 = 36
55 – 36 = 19
Subtraction
5
Subtraction
Subtraction
Number line
Subtraction
Subtraction
Subtraction
Subtraction
Partitioning
74 – 27
74 – 20 = 54
54 – 7 = 47
27 = 20+7
Subtraction
Subtraction
Subtraction
New Facts from known ones
3+4=7
Place Value
Inverse
13+14 = 27
30+40=70
0.3+0.4 = 0.7
30+4=34
4+3=7
7-3=4
7-4=3
Near facts
Equivalent
4+4=8
3+3=6
2+5=7
1+6= 7
Multiplication
These are a selection of mental strategies:
x
Doubling and halving
Applying the knowledge of doubles and halves to known facts.
MENTAL
Using multiplication facts
Year 2 ~ 2x, 5x, 10x
Year 3 ~ 2x, 3x, 4x, 5x, 6x, 8x, 10x
Year 4 ~ Calculate all multiplication facts up to 12 x 12
Year 5 ~ Quickly recall all facts up to 12 x 12.
MATHS
Using and applying multiplication facts
Use tables knowledge to derive other facts.
e.g. If I know 3 x 7 = 21, what else do I know?
30 x 7 = 210, 300 x 7 = 2100, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc
Multiplying by 10 or 100
Knowing the effect of multiplying by 10 (shift in the digits one place to the left).
Knowing the effect of multiplying by 100 (shift in the digits two places to the left).
Partitioning
23 x 4 = (20 x 4) + (3 x 4)
= 80 + 12
= 102
Use of factors
8 x 12 = 8 x 4 x 3
Multiplication
Children are introduced to multiplication by counting on and
back in equal steps of ones, twos, fives and tens.
Working practically or drawing a picture helps children to visualise
the problem.
4x2
Multiplication
 First recognize that multiplication is repeated addition.
No of lots
3
how many per group
x
5
total
=
15
 Is the same as 3 lots of 5 or 5 + 5 +5 = 15
 Use pictorial cues to represent a x sum.
 Encourage them to write the sum:

5
+
5
+
5
=
15
Multiplication
Children use arrays to model a multiplication calculation.
3x5
5x3
Using repeated
addition
0
1
2
3
4
5
6
7 8
9
10 11 12 13 14 15
Multiplication
Dots or tally marks are often drawn in groups.
This shows 3 groups of 6.
3x6
Children can count on in equal steps using an empty number line.
This shows 4 jumps of 4.
Multiplication
Multiplication
Multiplication
Grid method of multiplication
38 x 72
X
70
2
30
2100
60
8
560
16
2160
+ 576
2736
1
Multiplication
1692
Multiplication
Division
These are a selection of mental strategies:
Doubling and halving
Knowing that halving is dividing by 2
and doubling is multiplying by 2
÷
MENTAL
Deriving and recalling division facts
Recall corresponding division facts linked to tables knowledge.
Know 5 x 6 = 30 so ? ÷ 5 = 6
MATHS
Using and applying division facts
Children should be able to utilise their tables knowledge to derive other facts.
e.g. If I know 3 x 7 = 21, what else do I know?
21÷ 7 = 3, 21 ÷ 3 = 7, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc
Dividing by 10 or 100
Knowing the effect of dividing by 10 (shift in the digits one place to the right).
Knowing the effect of dividing by 100 (shift in the digits two place to the right).
Use related facts
Given that 1.4 x 1.1 = 1.54
What is 1.54 ÷ 1.4, or 1.54 ÷ 1.1?
Division
Sharing is a skill children come to school with.
‘One for me one for you’ is repeated subtraction.
Working practically or drawing a picture
helps children to visualise the problem.
12 ÷ 2 = 6
Division
Children progress to removing ‘groups’ of a number.
There are 12 sweets and each party bag needs three sweets.
How many party bags can be made?
In this example children put ‘groups of three sweets’ into the party
bags until they have no sweets left.
Division
Division
Children can count on in equal steps using an empty number line
to work out how many groups of there are.
This shows you need 4 jumps
of 7 to reach 28.
Children begin to jump in
‘chunks’ of the number they are
dividing by, in this example
‘chunks of 4’ are used. A jump
of 10 groups of 4 takes you to
40. Then you need another 5
groups of 4 to reach 60, leaving
a remainder of 3.
Answer is 16 tables.
Division
Short Division
22
6
1
1
132
Division
Short Division with remainders and decimals.
WOW!!
After all that you deserve a cuppa!
When your child can do all of this, they will
learn even more FUN Maths.
A Numberless World
If all the numbers in the world were rubbed out, removed, taken away:
I wouldn’t know how old I was,
I wouldn’t know the time of day,
I wouldn’t know which bus to catch,
I wouldn’t know the number of goals I’d scored.
I wouldn’t know how many scoops of ice-cream I had,
I wouldn’t know the page on my reading book,
I wouldn’t know how tall I was,
I wouldn’t know how much I weighted.
I wouldn’t know how many sides there are in a hexagon,
I wouldn’t know how many days are in the month,
I wouldn’t be able to work my calculator.
And I wouldn’t be able to play hide-and-seek!
But I would know
As far as my mum was concerned,
I was still her NUMBER ONE!
Ian Souter