Division 6
Dividing using decimal points
Objectives

Use efficient ‘chunking’ to divide numbers greater than 100 by
single-digit numbers including those which leave a remainder

Divide numbers with one decimal place by multiplying by 10
before division, then dividing by 10 afterwards, e.g. work out 78.6
÷ 3 by finding 786 ÷ 3, then dividing by 10

Divide numbers with two decimal places by multiplying by 100
before division, then dividing by 100 afterwards, e.g. work out 7.86
÷ 3 by finding 786 ÷ 3, then dividing by 100
For this unit you will need:
calculators
Watch out for pupils who:

do not know their multiplication facts and so can’t make use of
them to solve divisions;

repeatedly subtract 10 jumps of the divisor rather than first
working out whether there are more than 10, 20, 30... or 100 lots
of the divisor;

try to partition numbers into 100s, 10s and 1s to divide (as they
would for multiplication), rather than into a multiple of 10/100 of
the divisor and the rest, e.g. partition 375 into 300, 70 and 5 to
divide by 5 rather than into 350 and 25;

do not know the common equivalents between fractions and
decimals.
HSNP © Hamilton 2014
Keeping up Term 3
Division 6
Session 1
Objective: Use efficient ‘chunking’ to divide numbers greater than 100 by
single-digit numbers including those which leave a remainder
Teacher input with whole class



Write 637 ÷ 5 on the board. Approximately how many 5s do you think
might be in 637? More than 10? More than 50? More than 100? More
than 200? Agree that there are between 100 and 200 5s in 637, and
that this is a useful estimate as it helps us to subtract our first number
when using ‘chunking’. Work through the steps together:
100 + 20 +7, r2 127 r 2 or 127.4
5 ) 637
─ 500
137
─ 100
37
─ 35
2
Remind pupils of the stages in using this written method:
1. Look for a multiple of 100 of 5 in the 637, i.e. 500. Subtract 500
(leaving 137). Write 100 at the top to record how many 5s are in 500.
2. Look for how many lots of ten 5s there are in 137, e.g. 20 x 5 = 100.
Subtract 100 and write 20 at the top to record how many 5s are in 100.
3. Work out how many 5s are in 37 (7). Write 7 at the top.
4. Subtract 35 to find the remainder, 2. Find this as a fraction of the
divisor (2/5), and record as decimal if known (0.4).
Repeat the process with 813 ÷ 7, agreeing the answer as 1161/7.
Individual practice
 Pupils work out 668 ÷ 6, 436 ÷ 3, 672 ÷ 5, 626 ÷ 3, 759 ÷ 7, expressing
the remainder as fractions to decimals where they can. Encourage
pupils to list multiples of 10 of the divisor, e.g. 30, 60, 90, 120… lots of
the divisor, so that they subtract large numbers, rather than
repeatedly subtracting 10 lots of the divisor. They check one using
multiplication, remembering to add on the remainder at the end.
HSNP © Hamilton 2014
Keeping up Term 3
Division 6
Session 2
Objective: Divide numbers with one decimal place by multiplying by 10
before division, then dividing by 10 afterwards, e.g. work out 78.6 ÷ 3 by
finding 786 ÷ 3, then dividing by 10
Teacher input with whole class
 Ask half the class to work out 37.2 ÷ 3 and the other half to work out
372 ÷ 3, both using calculators. Discuss the two answers. Draw out
that the answer to the first division is a tenth of the answer to the
second.
 Ask all pupils to use efficient chunking to work out 524 ÷ 4.
(100x4=400, 30x40, 1x4=4 so answer = 131)
 What might be the answer to 52.4 ÷ 4? Use a calculator to check
pupil’s suggestions. If we round 52.4 to the nearest whole and then
divide by 4 what would the answer be? So our answer of 13.1 makes
sense.
 Write 36.8 ÷ 4 on the board. Ask pupils to round 36.8 to the nearest
whole and discuss in pairs how many 4s would be in that number. Take
feedback and agree that there would be between nine and ten 4s in
37. Ask pupils to use efficient chunking to work out 368 ÷ 4, and then
divide the answer by 10, checking that the answer makes sense given
their estimate.
Paired pupil work
 Write the following divisions on the board:
142 ÷ 3, 14.2 ÷ 3
486 ÷ 6, 48.6 ÷ 6
375 ÷ 5, 37.5 ÷ 5
176 ÷ 8, 17.6 ÷ 8
423 ÷ 3, 42.3 ÷ 3
576 ÷ 4, 57.6 ÷ 4
 Pupils work out the answers to the first divisions in each pair and use
these to answer the second divisions in each pair.
 They each choose one of the second divisions to check using grid
multiplication.
HSNP © Hamilton 2014
Keeping up Term 3
Division 6
Session 3
Objective: Divide numbers with two decimal places by multiplying by 100
before division, then dividing by 100 afterwards, e.g. work out 7.86 ÷ 3 by
finding 786 ÷ 3, then dividing by 100
Teacher input with whole class
 Say that a piece of wood measuring 4.86m is to be divided into 3 equal
lengths. Discuss how we might find the length of each piece. Draw out
converting the length to centimetres, dividing 486 by 3, then
converting back to metres. Ask pupils to do this. Discuss how the
answer to 4.86 ÷ 3 is a hundredth of the answer to 486 ÷ 3.
 Repeat the process with 5.24m ÷ 4, agreeing the answer as 1.31m.
 Ask pupils to work in pairs to find 117 ÷ 3, 11.7 ÷ 3 and 1.17 ÷ 3.
 Take feedback on how they did this. Round 11.7 to 12 to see that the
answer to 11.7 should be just under 4, and discuss how 1 point
something divided by 3 must be less than 1.
Paired pupil work
 Pupils use efficient chunking to work out the first division in each
group of three, then agree what the answers to the next two in each
group should be.
348 ÷ 4, 34.8 ÷ 4, 3.48 ÷ 4
632 ÷ 4, 63.2 ÷ 4, 6.43 ÷ 4
237 ÷ 3, 23.7 ÷ 3, 2.37 ÷ 3
645 ÷ 3, 64.5 ÷ 3, 6.45 ÷ 3
435 ÷ 5, 43.5 ÷ 5, 4.35 ÷ 5
372 ÷ 6, 37.2 ÷ 6, 3.72 ÷ 6
732 ÷ 6, 73.2 ÷ 6, 7.32 ÷ 6
Teacher input with whole class
 Ask pupils to work out 870 ÷ 10 and compare the answer with 435 ÷ 5.
Agree that they are the same and so another way to divide 435 by 5,
would be to double both numbers, then work out 870 ÷ 10 which is
easy!
HSNP © Hamilton 2014
Keeping Up Term 3