Spaldwick Number strategies

A step by step guide to helping your child with their maths at

home by using the same methods taught to them at school.

- x = ÷+

Add

ADDITION

How many more make…?

Make

How much more is…?

The sum of…Total

++

+ ++

++

Step 1: Learn numbers up to 10 and 20.

1 3425

6 7 89 10

13121114

18171615

19 20

Step 2: Adding up to 20

• eg. 7 + 4

• Put the biggest number in your head (7), add on (4) using unifix cubes, your fingers, pictures or any other apparatus.

Step 3: Know your number bonds to 10 and 20.

1 + 9 = 102 + 8 = 103 + 7 = 104 + 6 = 105 + 5 = 10

11 + 9 = 20

12 + 8 = 20

13 + 7 = 20

14 + 6 = 20

15 + 5 = 20

16 + 4 = 20

17 + 3 = 20

18 + 2 = 20

19 + 1 = 20

For example:

Step 4: Using a number line.From the biggest number ‘add on’ the smallest number in unit

steps. • Eg. 7 + 6 = 13

0 7

+1 +1 +1 +1+1

135 10 2015

+1

Step 5: Number line addition by adding on tens and units.

• Starting with the biggest number in the sum, add on in ‘chunks’ of tens and units.

• Eg. 21 + 34 = 55

34 44 54 55

+10 +10+1

Step 6: Partitioning.Split the numbers up into tens (T) and units (U). This is the first step to using column

addition.• For example: 36 + 45 =

30 + 40 = 70 6 + 5 = 11 70 + 11 = 81

81

Step 7: Column Addition

• For example: 35 + 27 = 62

T U 3 5 2 7 6 2 1

This method then expands to more complex sums such as those involving hundreds (H) and thousands (TH) or decimals in tenths (t) and hundredths (h).

The ‘1’ in 12 has a value of ten so is carried over to the tens column to be added at the end.

Take away

SUBTRACTIONHow many less is… than…?

How much

fewer?

minus

How many are left over?

leave --

- --

--

Find the difference between…

Step 1: Learn numbers up to 10 and 20.

1 3425

6 7 89 10

13121114

18171615

19 20

Step 2: Subtraction by drawing pictures, using apparatus or

using fingers.

•Eg. 8 – 5 = 3

Step 3: Subtraction using a number line.

• Put the biggest number on the right and subtract in single unit steps.

• If understand number bonds, jump to the nearest ten.

• Eg. 14 – 8 = 6

14

-1-1 -1 -1 -1 -1 -1 -1

6

Step 4: Subtracting TU and TU on a number line.

• Using a number line put large number on the right then partition second number and jump back that number of steps, starting with tens then the units. *Children need experience of oral counting and 100 square knowledge of counting back in tens eg. 91, 81, 71, 61 etc*

• Eg. 55 – 12 = 43

43 44 45 55

-10-1-1

Step 5: Finding the difference between two numbers

• Eg. 14 - 8

Step 6: ‘Finding the difference’ between two numbers on a

number line.• Biggest number on the right, smallest number on the left. Count on from the smallest number to the nearest ten, then add on in tens, then add on the rest of the units. Then count up the ‘jumps’.

23 48

Eg. 48 – 23 =

+ 7

+ 10+ 8

10 + 7 + 8 = 2525

Step 6: Column subtraction

• Eg. 47 – 29 = 18

T U

4 7

2 9

1 8

3 1 Sum is ‘exchanged’ so that 47 is turned into 30 + 17 because 7 – 9 is not possible.

Lots of

MULTIPLICATIONtimes

Multiple of

arrays

Repeated addition

Groups ofxx

x xx

xx

Multiply by

Step 1: Using apparatus, pictures and toys to put into

groups of a number.• Eg. Sort these people into groups of 3. How many

groups are there? How many people are there altogether?

5 groups 15 people altogether

Step 2: Repeated addition on a number line.

• Eg. 5 x 3 = 15.• Starting from zero, add on 5 lots of 3.

+ 3 + 3+ 3 + 3+ 3

0 3 6 9 12 15

Step 3: As arrays

3 x 5 = 155 x 3 = 15

Step 4: Learn your times tables up to 10

Step 5: Learn that when you x 10, you make all the digits once to the left and

have a zero at a ‘place holder’ if needed.

• Eg. 32 x 10 = 320

• H T U

3 2

3 2 0(x 10) H T U . t

3 . 2

3 2(x 10)

You do not just add a zero because once you start multiplying decimals by 10, adding a zero would not make the number ten times bigger.

Step 6: TU x U Grid Multiplication

• Partition (or split up) the two digit number to make the sum more manageable and x by the smallest number.

• Eg. 45 x 3= 225

x40

5

5

200

25

225

If your child knows that 4 x 5 = 20 then they just need to x the answer by 10 to get 40 x 5.

Step 7: Standard Short Method

• Eg. 32 x 23

• STEP 1:

3 2

x 2 3

Multiply 32 by 3, starting with the units column.

3 x 2 = 6

3 x 30 = 909 6

Step 7: Standard Short Method continued…• STEP 2: 3 2x 2 3 9 6

Now multiply 20 by 32

20 x 2 = 40

20 x 30 = 600

600 + 40 = 640

Finish the sum off by adding the totals together using column addition.

6 4 0

STEP 3: 3 2x 2 3 9 6 6 4 0 7 3 6

share

DIVISION

divide

Divided by

Divided into

Share equally xx

x xx

xx

Equal groups of

Step 1: Sharing out toys, cubes and any other apparatus.

Step 2: Repeated subtraction on a number line.

• 15 ÷ 3 = 5

- 3 - 3- 3 - 3- 3

3 6 9 12 150

Step 3: A grouping/sets

15 ÷ 3 = 5

Step 4: Recognising division facts as the inverse of multiplication facts

(times tables)

• 4 x 5 = 20 so 20 ÷ 5 = 4

• 6 x 7 = 42 so 42 ÷ 7 = 6

• 8 x 9 = 72 so 72 ÷ 9 = 8

Step 5: Extended number line division.

42120

- 30- 1210 lots4 lots

3 x table facts

1 x 3 = 3

2 x 3 = 6

4 x 3 = 12

10 x 3 = 30

Eg. 42 ÷ 3 = 14

Count up the ‘lots’ of 3 you have taken away.

Step 6: Column Division

42 - 30 (10 lots) 12 12 (4 lots) 0

3 x table facts

1 x 3 = 3

2 x 3 = 6

4 x 3 = 12

10 x 3 = 30

Eg. 42 ÷ 3 = 14

Step 7: Long DivisionEg. 345 ÷ 25 STEP 1: 1 5 3 4 5

15 won’t divide into 3, so look at the next digit and divide 34 by 15.

2 x 15 = 30

Write the 2 above the 4. Then take 30 away from 34 to find the remainder.

STEP 2: 21 5 3 4 5

Step 7: Long Division Continued

• STEP 3: 2 15 3 4 5 3 0 4 5

“Bring down” the 5 next to the 4, ready to divide 15 into 45.

3 x 15 = 45

Write the 3 above the 5. There are no more numbers to bring down, so the final answer is 23

STEP 4: 2 3 15 3 4 5 3 0 4 5