How children learn (and we teach)

the Four Operations

To understand expectations of the new curriculum in mathematics.

To be familiar with methods used for addition and subtraction

To become familiar with methods used for multiplication and division

To clarify progression

Aims

The Hat Game

3

The New Curriculum for mathematics aims to ensure that all pupils:become fluent in the basics of mathematicsreason mathematically can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication

The New Curriculum for mathematics

5

Your feelings of maths

1999+ 2009 312 x 54 1850 ÷ 25 2786 – 1899 178.45 x 13 4782 ÷ 13 2345 + 2346

Consider for a moment…

15 – 5 = 29+11=18 – 16 = 2007 – 1992 =

359 – 211 =

1997 +33 =

6+4+7 =24.6 – 12.4 =

How would you approach these questions?

Little Big Maths ~ Jupiter Class

CLIC ~CountingLearn ‘It’s facts’ (no bonds)‘Its nothing new’ (applying)Calculations (Methods =, + , - ,x , division)

7

We may have been taught different ways at school

387 + 564

ADDITION

Counting on

Number Lines (Progression)

•Numbered lines

•Bead strings

•Partly numbered lines

Counting On

Not crossing tens boundary

e.g. 34 + 23

Jumps of 10s and 1s

Encourage children to become more efficient

•Add 3 in 1 jump

•Add 20 in 1 jump

Crossing tens boundary

e.g. 37 + 25

Jumps of 10s and 1s

Help children become more efficient:

Add 5 in jumps of 3 and 2

(bridging over 10) Add 20 in 1 jump

Counting on

476+973= 476+ 973-------------- 9 (6 + 3) 140 ( 70 + 70) 1300 ( 900 + 400)---------------- 1449

Column addition

476+973=

400 + 70 + 6900 + 70 + 3------------------

1300 + 140 + 9= 1449

We only use these if children are able to manipulate numbers and have a good understand

of place value

Compact (Formal) method New Curriculum

Accurate use of language is key.

7 8 9+ 6 4 2 1 4 3 1 1 1 (These are carried)

SUBTRACTION

Using a numberline for larger numbers ~

using find the difference

74 – 27 = 47

+ 3+ 40

+ 4

27 30 70 74

74 – 27 = 40 + 4 + 3 = 47

368 - 152 216

No ‘borrowing’

Formal written method

932-457

9 3 2 - 4 5 7 4 7 5

Compact Formal method New Curriculum

1218

Multiplication

Slide 2.18

Counting sticks Repeated addition Rapid recall of multiplication tables facts

Games Good as oral / mental starters Using known facts (e.g. doubling)

Arrays

Early Multiplication

Grid method 26 x 7

Moving on with MultiplicationProgression

2 digit x 1 digit 3 digit x 1 digit3 / 4 digit x 2 digit

30

2

10

300

20

20

6

7

140

42

=182

4

32 x 14

120 420

8 28

= 448

3 4 2 x 7 2 3 9 4 2 1

Formal Methods – New curriculum

1 2 4 x 2 6 7 4 4 1 2

2 4 8 0

3 2 2 4

22

Division

Children appear to find sharing (partitive) tasks easier but this becomes inefficient with larger numbers,

e.g. 196 Smarties divided by 6 children – on a one for you, one for me basis this takes a while!!!

We therefore need to help children to move from sharing individual items to groups of items,

e.g. We could do 20 for you, 20 for me etc, we are taking away groups of the divisor from the dividend (CHUNKING).

Dividing - Sharing and grouping

Children’s working

A tent holds 6 children.How many tents are needed to hold 70 children?

48 ÷ 6 =

Number line division

1 x 6 1 x 6 1 x 6 1 x 6 1 x 6 1 x 61 x 61 x 6

0 24 30 36 42 486 12 18

To divide 81 by 3

20 x 3 7 x 3

0 60 81

Remainders

17 ÷ 5 = 3 r 2 or 3 2

5

1050 17

555

15

5

2

200 1715105

r2

126 72

60 10 x 6 12

12 2 x 6 0

Chunking

Slide 2.28

Formal method – short and long division

New curriculum

1 4 2

7 9 8

2 8 r 12

1 5 4 3 2 3 0 0 1 3 2 1 2 0 1 2

Progression chartLearning through play

Helping at home ~ Early years/KS1

Maths help at home ~ KS2

Slide 2.30