Maths – The strategies we use in school

Calculation

The 4 strands of Maths

• Number

• Shape, Space and Measures

• Data Handling

• Using and Applying Maths

Using and Applying Maths occurs in all 3 other strands, as well as in other lessons, such as Science.

Number

We are going to focus solely number.

• The four operations (+, -, x and ÷)

We are going to talk you through methods we teach children to use to add, subtract, multiply and divide and how build on each stage.

The Four Operations

• The four operations in calculations are grouped into

Adding and Multiplying – where the answer gets bigger

Subtracting and dividing – where the answer gets smaller

Early YearsCounting

• Count reliably to 20 • Count backwards from 10

Number Recognition

• Recognise numbers to 20• Order numbers to 20

Calculation• One more and one less than a given number• Add and subtract two single digit numbers practically

Number Lines

We use number lines in all four operations.

We start with numbered lines like this one –

0 1 2 3 4 5 6 7 8 9 10

Adding

We then move on to using number lines and counting up in ones.

14 + 5 = 19

+1 +1 +1 +1 +1

14 19

Partitioning

Next we learn to partition – splitting the number into tens and units – to add.

What is 72 + 14?T U70 210 4 70+10= 80

2+4= 6 80+6=86

Adding by Partitioning

Now we can add by partitioning –

86 + 57 =

+50 +4 +3

86 136 140 143

Adding by Partitioning

Or by rounding then adjusting, taking it to the nearest 10 and then subtracting

754 + 96 (rounding and adjusting)

+100

-4 754 850 854

Column Addition

Finally, we move on to adding in columns, using place value.

HTU ThHTU 597 7648+ 475 and + 1486 12 160 9134 900 1 1 1

1072

MultiplyingNow we use the number line for repeated

addition.4 x 5 is the same as 5 + 5 + 5 + 5 = 20I have four 5p coins, how much is that?

+5 +5 +5 +5 0 5p 10p 15p 20p

The Grid Method

We can partition to multiply using a grid, like this, this looks more complicated than it actually is –

72 x 38 = 70 2

30 2100 60

8 560 16

Column Method for multiplication

4346

x 8

48

320

2400

32000 

34768

Subtracting

We begin by ‘taking away’, ‘counting back’ and seeing ‘how many left.’

We have 6 teddies in the shop. We sold 2. How many teddies are left?

Subtracting (number lines)

We can use a number line to count back.

22 – 7 =

-5 -2

15 20 22

Subtracting (number lines)

In Key Stage 2, we count UP the number line to find the difference.

What is the difference between 34 and 72?

+30 +8

34 64 72

Subtracting with ‘exchanging’

5 13 1

6 4 6 7

- 2 6 8 4

3 7 8 3

Th H T U

Dividing

Division starts with practical sharing of objects again -

If I share my 9 sweets between 3 people, how many do they each get?

Division with number lines

Number lines are also used to count up in division.

A baker bakes 24 buns. She puts 6 in every box. How many boxes can she fill?

x1 x2 x3 x4

0 6 12 18 24

Division with remainders

Finally, we can jump in groups and record remainders on the number line.

What is 42 divided by 4? 10 groups (Remainders)

x10 +1 +1

0 40 41 42

SATs KS1• Typical questions:

Key Stage 2 SATs• Key Stage 2 SATS are held in May.

• These are statutory, externally marked tests.

• The children sit three papers: Paper A - non-calculator paper Paper B - calculator paper Mental arithmetic paper

• The paper assesses children working between level 3 and level 5. Children will receive a test mark and a teacher assessment.

A minority of children will be entered for the level 6 test.

Key Stage 2 SATsSample Questions:

Key Stage 2 SATsSample Questions:

Extra support for NumeracyExtra support for Numeracy

• EYS and KS1 – Numicon

Key Stage 2

• Booster programme• Linked to numeracy lessons• Targeted at children who, with support, will reach level 4

• Sessions run three times a week for 30 minutes

Year 4

Mental/Oral Starter Activities

Cracking Times Tables•Is a scheme designed to support high standards in mathematics•Is a consistent approach to learning and testing tables across the school•Is based on a series of levels that the children work through at their own pace•Is motivating to children. They receive certificates for each level achieved