Division Leicestershire Numeracy Team 2003 1 Division

Leicestershire Numeracy Team 2003 1division

Division


The problems with division

Try these:

186

20224


What is division?

How would you illustrate this division to a child? What would you draw and what

language would you use?

12 3 = 4


12 3 = 4

Sharing

There are three children and 12 cakes. How many can they each have, if I share them out equally?

(Sharing 12 things equally into 3 piles. How many in each)

Skills in Early Division


12 3 = 4Grouping

There are 12 cakes. How many children can have three each?

(How many threes are there is 12?)

Skills in Early Division


Language and division

Since the sign represents both the sharing and grouping aspects of division, encourage the children to read this as ‘divided by’ rather than ‘shared by’.


6000 1000 =

Would you group or share for this calculation?


Introducing division

In Year 2 children are encouraged to understand the operation of division as:

• sharing equally

• grouping or repeated subtraction e.g. How many tens are in 60?


18 3 =


Sharing

• Supports an understanding of halving and the 1 to 1 correspondence between objects.

• Requires little knowledge or skill beyond counting.

• Becomes more difficult to visualise as the divisor increases.

• Is inefficient.


18 3 =

0 3 6 9 12 15 18

Division and number lines


Modelling division on beadstrings

20 4 =


20 4 =


20 4 =


20 4 =


20 4 =


Key Stage 1 - Calculations• Encourage children to use jottings, as well, to check answers to

calculations that have been reached by mental methods

Q29

1 2c 2b 2a 3 All

4% 4% 12% 27% 61% 31%


Grouping

• Links to counting in equal steps on a number line.

• Requires knowledge of subtraction facts (repeated subtraction) and addition facts (counting up).

• Is more efficient than sharing as the divisor increases.

• Provides a firmer basis on which to build children’s understanding of division.


Introducing divisionIn Year 3 and 4 children also need to know that:

• dividing a whole number by 1 leaves the number unchanged: e.g. 12 1 =12

• 16 2 does not equal 2 16

• division reverses multiplication (the inverse) – this allows them to solve division calculations by using multiplication strategies (18 3 by counting the hops of 3 to 18)

•there will be remainders for some division calculations (to be expressed as whole-number remainders).


How many eights in 48?


Continuing division

In Year 4 children need to begin to :

• relate division and fractions

• use a written method for division (chunking).


23the divisor

the number to be divided


2 3the divisor



2 3the divisor



Teaching chunking - partitioning72 5

Partition 72 in to a convenient multiple of 5 + the rest

72 = 50 + 22

Divide each part

50 ÷ 5 = 1022 ÷ 5 = 4 rem 2

Recombine the parts

Answer: 14 remainder 2


72 ÷ 5 =

Grouping - How many 5’s are there in 72?

Adding groups of 5

Teaching chunking - number line

40 45 50 55 60 65 70 72 0 5 10 15 20 25 30 35

5 x 10 or

10 groups of 55 x 4 or

4 groups of 5


Teaching chunking - vertical

72 5 = 72

50 (5 x 10)

22

20 (5 x 4)

2


5 x 1 = 5

5 x 2 = 10

5 x 5 = 25

5 x 10 = 50


Using calculators for repeated subtraction

The constant function

To calculate 72 5 using repeated subtraction

Press 5 - - = then press 72


Teaching chunking - larger numbers

7 x 1 = 7

7 x 2 = 14

7 x 5 = 35

7 x 10 = 70

256 7 = 256 210 (7 x 30) 46 42 (7 x 6) 4

256 7256 = 210 + 46

210 ÷ 7 = 30 46 ÷ 7 = 6 remainder 4

or



Continuing division

In Year 5 and 6 children also need to understand:

• that a number cannot be divided by zero

• how a quotient can be expressed as a fraction and as a decimal fraction

• how to interpret the display when dividing with a calculator.


185 people go to the school concert.

They pay £1.35 each.

How much ticket money is collected?

Programmes cost 15p each.

Selling programmes raises £12.30

How many programmes are sold?

Show your method you may get a

mark.

£



Solve these word problems

To make a box pieces of wood 135mm long have to be cut from a 2.5m length. How many lengths of wood can be cut?

Train fares cost £14.50. I have £52. How many people can I take on the journey?

Documents

Division Leicestershire Numeracy Team 2003 1 Division