Hythe Primary
School Maths
Strategies
Mental and written
strategies taught for:
* addition
* subtraction
* multiplication
* division
Hythe Primary Maths Strategies
Addition
Stage 1
Concrete apparatus and lots of talk eg two bears went for a walk and met
two more bears. How many bears are there now?
Stories involving number, concrete objects used to represent.
I can count out two groups of objects, and put them together to count all
of them.
Stage 2
Representing concrete apparatus with symbols eg dots, in books. Use of the
+ and = signs.
I can count two sets of objects.
Stage 3
Counting on from biggest number/using number line. Counting on in groups
of ten.
7 + 3 = 10
1
2
3
4
5
6
“Start at 7 and count on 3”
“Put 7 in your head and count on 3.”
I can count on using a number line.
Hythe Primary Maths Strategies
2
7
8
9
10
Stage 4
Partition and recombine.
14 + 7 = 21
10
4
14
7
10
+
4
23 =
20
37
3
Because 14 is 10 and 4, plus the 7...= 21
30
7
I can partition and recombine two digit and one/two digit numbers.
Stage 5
Unstructured number line
16 + 12 =
+10
+2
16
26
28
Stage 6
Column addition, followed by condensed version.
16
12
28
16
38
10
245
367
10
100
54
11
245
367
612
612
Stage 7
Addition of decimals, using partition addition, followed by columns.
1.2 + 3.4 = 4.6
1
0.2
3
1
12.3
3.8
16.1
0.4
1 + 3 = 4 and 0.4 + 0.2 = 0.6
Hythe Primary Maths Strategies
3
Subtraction
Stage 1
Counting backwards/1 less.
Using concrete objects or visual alongside number rhymes and chanting.
There were 7 in a bed and 1 rolled over. How many were left?
Problems should:
Begin with numbers to 5, and then to 10 etc.
Always be in context.
Can I count backwards by finding 1 less from 5, from 10?
Vocabulary:
Number names
Less, fewer, how many are left? Count back, take away
Stage 2
Using concrete objects/human modelling
Used in conjunction with multi-sensory activities e.g. singing, to take away
one child / object at a time.
Begin with numbers 1 - 5, 1 – 10.
Example problem
There were 5 children on the bus, 1 got off. How many children were left
on the bus?
Can I take 1 number away from a number up to 5?
Stage 3
Removing practical objects.
Using concrete objects to solve real life problems and take away more than
one.
Example problem
Jack has 5 sweets, he eats 3. How many are left?
I have 10p and buy a toy for 7p. How much money do I have left?
5–3=2
Can I take away a number from another?
Hythe Primary Maths Strategies
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Stage 4
I can show subtraction using pictures.
Using pictures or symbols to take away.
Example problem
Tony had 6 sweets, Alice took 2 away. How many does Tony have left?
Stage 5
Subtraction through jumping back on a number line.
Using a structured number line and jumping backwards from 10.
I have 10 apples on a plate. I eat 3. What must I do to find out how many I
have left?
1 2
3
4
5
6
7
8
9
10
Stage 6
Subtracting by finding the difference
Finding the difference is introduced through the introduction to larger
numbers. IMPORTANT TRANSITIONARY STAGE
I have 57 marbles and I give 6 to my friend. How many have I got left?
Progress to: Subtraction by finding the difference on an unstructured
number line. An unstructured number line is used to jump on without concrete apparatus. The children count to the nearest 10, then multiple of 10
then unit.
Stage 7
Column subtraction.
For children who have mastered use of a number line.
1
1 24
15
09
Hythe Primary Maths Strategies
5
Multiplication
Stage 1
Chanting in 2s and 10s.
2, 4, 6, 8....
10, 20, 30, ....
Stage 2
Making patterns of twos and counting them. Linking to groups and pattern.
Using number grid placing counters on to spot number patterns. Eg odd
even for two times table.
Stage 3
Arranging random groups of concrete materials into arrays. Repeated addition.
3 6
2
3x2=6
4
or
6
2x3=6
Hythe Primary Maths Strategies
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Stage 4
Using number line in head to add groups of numbers on. Number stories.
3
6
9
12 etc
Stage 5
Knowing times table facts off by heart.
Includes using known facts to find other facts.
Eg 2 x 3 = 6, so 2 x 6 must = 12
Stage 6
Partitioning a two by one digit number.
14 x 3 =
10 x 3 = 30
4 x 3 = 12
Total = 42
Stage 7
Grid method
14 x 25 =
X
10
4
20
200
80
= 280
5
50
20
= 70
= 350
Hythe Primary Maths Strategies
7
Division
Stage 1
Number stories, concrete apparatus. Sharing out concrete materials.
4 /2 =
Stage 2
Sharing dots out on paper into groups.
12 / 3 = 4
Stage 3
On a number line, using repeated addition.
+3
+3
+3
+3
1
3
6
Hythe Primary Maths Strategies
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12
8
12/3 = 4
Stage 4
Numberline, repeated addition in groups eg gps of 10, 5 or 2
27 / 5 = 5 r 2
2x
2x
1x
2 left over (remainder)
0
10
20
25
27
Stage 5
Chunking, repeated addition in columns.
27
2 x 5 = 10 (10)
2 x 5 = 10 (20)
1 x 5 = 5 (25)
Difference between 25 and 27 = 2.....So, 27 / 5 = 5 r 2
Stage 6
Chunking, (repeated subtraction.)
27 /5 = 5 r 2
27
20 (4 x 5)
7
5 (1 x 5)
2
Stage 7
‘Bus stop’ method is only taught if children are completely happy with
chunking.
Hythe Primary Maths Strategies
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