Year 5 Teaching Sequence 4 - Multiplying and dividing two- and three-digit numbers by single-digit numbers (five
days)
Prerequisites:
 Know by heart multiplication facts for 2, 3, 4, 5, 6, 9 and 10 times tables, and learn corresponding division facts (see
Year 4 Summer teaching sequence 3 and oral and mental starter banks 3 and 4)
 Use the grid method to multiply two-digit numbers by single digits. Use chunking on the ENL to divide two-digit
numbers by single digits, including those leaving a remainder (see Year 4 Summer teaching sequence 9)
Overview of progression:
Children revise using the grid method to multiply two-digit and single-digit numbers together, and then use this to multiply
three-digit numbers by single-digit numbers. Further practice is given, and they are asked to use their experience to
approximate first. They are also asked to spot calculations that are easy to do mentally and where the grid method would be
less efficient. Children revise using chunking on the empty number line (ENL) to divide two-digit numbers by single-digit
numbers including those leaving a remainder, approximating first, and then move on to divide three-digit numbers by singledigit numbers (answers less than 30). They are encouraged to spot the occasional division where quartering (sharing) might
be more efficient than chunking (grouping) and also shown how to check division using multiplication. Word problems are
given and children are asked to round up or down after their calculations in order to answer the problems.
Note that some children might find it helpful to list multiplication facts for multiples of ten of the divisor (e.g. 10, 20, 30
lots of 6 when dividing by 6) and this will become more helpful in later terms when the answers increase to beyond 30.
Note that children need to understand that both the grid method and chunking on the ENL are both structured recordings
to support what is essentially mental calculation.
Watch out for children who are not fluent in multiplying by multiples of ten.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS4 – Aut – 5days
Objectives:
 Approximate first
 Multiply multiples of 100 to 900 by a single digit, e.g. 700 x 4 = 4 x 700 = 4 x 7 x 100 = 2800
 Use the grid method to multiply three-digit numbers by single-digit numbers
 Use chunking on the ENL to divide two- and three-digit numbers by single-digit numbers, including those leaving a remainder
 Decide whether to group or share (including halving and quartering) to solve division
 Decide whether to round up or down after division
Whole class
Group activities
Paired/indiv practice
Resources
How did we show how we worked out 34 × 3
using brackets? And how did we use the grid
method to show this last year?
Ask chn to revise using the grid method to
work out 45 × 5, 76 × 3 and 58 × 6.
Write 134 × 3 on the board. Discuss with your
partner how you might work this out. Take
feedback and draw out that the same
partitioning strategy can be used. Show how
the grid method can be used to record the
steps:
×
100 30
4
Group of 4-5 children
Write the following multiplications on
the flipchart, and explain that four of
them are correct and four are wrong.
225 × 6 = 1236
523 × 4 = 2092
446 × 5 = 2230
524 × 3 = 872
330 × 8 = 2424
625 × 4 = 2500
712 × 9 = 6408
254 × 5 = 10270
Ask chn to discuss which ones might be
wrong and why, for example looking at
units’ digits and approximations.
Easier: Include more examples of
multiplying by 2, 3, 4 and 5.
Harder: Include more examples of
multiplying by 6, 8 and 9.
Chn practise using the gird
method to support multiplying
three-digit numbers by singledigit numbers (see Activity sheet
in resources).
Easier: Use a slightly easier
activity sheet giving easier
products to add together in the
first instance (see resources).
Harder: Ask chn to work through
every other one, and make up
their own three-digit numbers to
multiply by single digits.
 Activity sheets
(see resources)
3
300
90
12
402
What if it were 234 × 3? Work in pairs to use
the grid method to show this on your
whiteboards.
Repeat with 145 × 5, 276 × 3 and 158 × 6.
Repeat with 345 × 5. What happens now?
Discuss how the product of 300 and 5 makes a
four-digit number, i.e. 1500. Repeat with 576 ×
3 and 358 × 6.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS4 – Aut – 5days
Whole class
Group activities
Write the following multiplications on the board:
6 x 376, 319 x 5, 3 x 482, 407 × 4
Which of these do you think will have the biggest
answer? To the nearest hundred, what will the answer
be? How do you know? Will it be more or less than
1800? Which will have the smallest answer? To the
nearest hundred, what will the answer be? Will it be
more or less than 1500? Write approximations for the
other two on your whiteboards. Would you use the
grid method for all of these? How would you work out
407 × 4? Watch out for multiplications that can be
done mentally without using a written method! Work
out all four answers, and point out that with
multiplication, approximations are often further away
from the exact answer than for approximations made
for subtractions and additions for example.
Write the following multiplications on the board:
610 × 4, 7 x 289, 3 x 783, 6 x 551
Write the calculations in order on your whiteboards
with your approximations at the side.
Take feedback. Discuss how 551 is roughly half way
between 500 and 600, so the answer will be roughly
half way between 3000 and 4000, i.e. around 3500.
Would you use the grid method for all four
calculations? How might you record your steps when
working out 610 × 4? Discuss writing 2400 + 40 =
2440, and also the option of using brackets:
610 × 4 = (600 × 4) + ( 10 × 4)
= 2400 + 40
= 2440
Group of 4-5 children
Write the following
multiplications and answers (in
the wrong order) and ask chn to
match them up.
314 × 5
2168
271 × 8
1656
428 × 4 1570
624 × 3 4908
792 × 5 4689
818 × 6 1872
521 × 9 3960
What clues can we use? Discuss
the units’ digits and
approximations. Which
multiplications will give an answer
with 0 in the units’ place? Which
multiplication could give an 8 in
the units place? Any others? So
which is which? Why do you think
that? Split the calculations
between the group to check.
Easier: Include more examples of
multiplying by 2, 3, 4 and 5.
Harder: Include more examples
of multiplying by 6, 8 and 9.
Paired/indiv practice
Resources
Chn practise making
approximations before choosing to
use the grid method or a jotting to
support mental calculation when
multiplying three-digit numbers by
single-digit numbers.
Easier: Use the main activity
sheet from yesterday, but also
make approximations.
Harder: Ask chn to work through
every other calculation and then to
come up with their own three-digit
by single-digit multiplications with
approximations of 1200, 1600,
1800, 2000 and 2500.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheets
(see resources)
Y5 Maths TS4 – Aut – 5days
Whole class
Group activities
Paired/indiv practice
Resources
Write 92 ÷ 6 on the board and sketch a line from 0 to
92. How many 6s do you think might be in 92? More
than 10? More than 20? So if there are more than 10,
we can draw one big jump of 10 lots of 6, rather than
lots of little hops of 6.
Draw and label one jump from 0 to 60, also labelling
60. How much is left? And how many 6s are in 32?
Draw a jump to show five lots of 6, also labelling 90.
And how much is left now? Can we get another 6 in
that space? No, so this is our remainder. Label this
section r 2. So how many 6s are in 92? Write 92 ÷ 6 =
15 r 2. Our estimating that there were between 10
and 20 lots of 6 in 92 helped us. Remind chn that this
method of division is called ‘chunking’ as we don’t
count the 6s individually, but find how many 6s are in
larger ‘chunks’ of the number we are dividing.
Write 76 ÷ 3 on the board. How many 3s are in 76?
More than 10? More than 20? More than 30? Record:
10 lots of 3 = 30
20 lots of 3 = 60
30 lots of 3 = 90
Agree that 20 lots of 3 is 60 and 30 lots of 3 is 90
and so the answer is between 20 and 30, probably
about half way between. Draw a large jump of 20 lots
of 3, labelling it and the point where it lands. How
much is left? And how many 3s are in 16? Draw a jump
to show 3 lots of 5 landing on 75, and label the
remainder. So how many 3s are in 76? Record 76 ÷ 3 =
25 r 1. So the answer was roughly half way between
20 and 30.
Group of 4-5 children
Write 92 ÷ 6 on the flipchart. We
drew an empty number line to help
us to find how many 6s are in 92.
We split 92 into ‘chunks’. First we
found how many 6s were in 60, and
then in the remaining 32. Record
this as:
92 ÷ 6
= (60 ÷ 6) + (32 ÷ 6)
= 10 + 5 r 2
= 15 r 2
Ask chn to discuss in pairs how we
could use this method of
recording to show 76 ÷ 3. Take
feedback and repeat with 97 ÷ 4.
How could we check our answer?
Draw out using multiplication, and
show this using brackets:
97 ÷ 4 = 24 r1
(24 × 4) + 1
= (20 × 4) + (4 × 4) + 1
= 80 + 16 + 1
= 97
Ask chn to discuss what chunks
they would split 85 into when
dividing by 3, 4, 5 and 6. Help
them to show this using brackets
to ‘chunk’ the 85 in appropriate
ways.
Chn practise using chunking,
recording their approximations
first, e.g. between 20 and 25 (see
Activity sheet in resources).
Easier: Encourage chn to record
the multiplication facts for
multiples of 10 as for 76 ÷ 3 in the
whole class teaching. Chn’s
estimate might be ‘between 20 and
30’ rather than ‘between ’25 and
30’ at this stage.
Harder: Chn work through every
other example, and then write
their own divisions by 3, 4 and 5
with answers in the following
ranges:
Between 15 and 20, between 20
and 25, between 25 and 30,
between 30 and 35.
 Activity sheet
of chunking
practice (see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS4 – Aut – 5days
Repeat with 97 ÷ 4. Do you think the answer will be
closer to 20 or 30? So the answer is between 20 and
25. Stress how this estimate means that we draw
fewer jumps and the chunking is more efficient.
Easier: Begin with 39 ÷ 3, 43 ÷ 3,
48 ÷ 4, 57 ÷ 4, then discuss how to
split 65 when dividing by 3, 4, 5
and 6.
Write 88 ÷ 4 on the board. Ask chn to discuss in pairs
how they might work this out. Explain that we could
use chunking. Ask chn to draw an ENL on their
whiteboards to show this. Remind chn that chunking
uses the grouping model of division, but we could also
use sharing to solve this division, thinking of sharing
88 between four equal groups rather than thinking of
how many 4s might be in 88. Remind chn of the link
between sharing between 4 and finding a quarter.
How would you find a quarter of 88? Draw out halving
and halving again to arrive at 22. Ask chn to vote (now
that they have seen both ways) for the way that they
would prefer for this particular division.
Write 64 ÷ 4, 58 ÷ 4, 76 ÷ 4 and 93 ÷ 4 and ask chn
to discuss in pairs how they would solve each, using
grouping (chunking) or sharing (finding a quarter).
Take feedback. It is likely that chn are happy to use
sharing for 64 as both digits are even, both 60 and 4
can be halved twice and give whole number answers.
When dividing two-digit numbers by single-digit
numbers using chunking watch out for the occasional
division where it might be easier and quicker to use
sharing, finding a quarter.
Group of 4-5 children
Write the following division on the
flipchart:
127 ÷ 6, 119 ÷ 4, 123 ÷ 5, 128 ÷ 7
And ask chn to discuss in pairs
which might have the greatest
answer and which might have the
smallest. Take feedback, drawing
out chn’s reasoning, e.g. thirty 4s
are 120 so 119 ÷ 4 will be just
under 30.
Ask chn to then write the
divisions in order from the
smallest answer to the greatest.
Take feedback, again drawing out
chn’s reasoning.
Write the following divisions on
the flipchart:
48 ÷ 4, 96 ÷ 2, 96 ÷ 8, 24 ÷ 8.
Two of these divisions have the
same answer, which two do you
think they are and why? Let chn
discuss this for a while, before
drawing out that the first and last
are the same. Discuss how the 48
is doubled to make 96, and so the
group size is also doubled to keep
Chn have further practice using
chunking, again recording
approximations but also watching
out for the occasional division that
might be easier solved using
quartering.
Easier: Slightly easier Activity
sheet (smaller answers) see
resources).
Harder: Slightly harder Activity
sheet (see resources, also
challenged to make up their own
divisions by 6, 7, 8 and 9 with
answers of between 20 and 30).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheets
of chunking
practice (see
resources)
Y5 Maths TS4 – Aut – 5days
Display the following problem:
A hotel is preparing for a wedding. There are 124
guests who will sit at tables of eight, how many tables
are needed?
Discuss in pairs what calculation is needed to solve
this problem and work together on your whiteboards
to solve it. Take feedback. What calculation did you
do? And what was the numerical answer. And so what
is the answer to the problem? Do we need to round
the answer up or down? What do you think the hotel
will probably do? Discuss how 124 ÷ 8 = 15 r4, and so
16 tables will be needed, rather than 15 as 4 people
would have nowhere to sit. Discuss how the hotel will
probably put out two tables for six rather than just
the number of groups the same.
(96 ÷ 2 will have a much bigger
answer where as 24 ÷ 8 has a
much smaller answer.)
Knowing this, how might you work
out 144 ÷ 8? Agree that you could
work out 72 ÷ 4, or even 36 ÷ 2.
Easier: Ask chn to order the
following calculation: 123 ÷ 3, 123
÷ 4, 123 ÷ 5. Draw out that
dividing by a larger number will
give a smaller answer as each
group is larger, and so there will
be fewer of them. Then order the
calculations as above.
Harder: Ask chn also how they
might work out 248 ÷ 16 by finding
equivalent calculations.
Group of 4-5 children
We divided 126 by 8 and got an
answer of 15 r6. How could we
check that this is correct? Draw
out using multiplication. What
multiplication would we need to
do? Together work out 15 × 8:
= (10 × 8) + (5 × 8)
= 80 + 40
= 120
But this is 120 not 126? Discuss
how we need to add the remainder
of 6 on, and so would get 126.
Ask chn to work in pairs to check
Chn work through problems,
finding solutions and deciding
whether answers to the required
calculations need rounding up or
down (see resources).
Easier: Some chn may need to
sketch diagrams to help them to
understand the problem, but still
encourage them to work out what
calculation is needed.
Harder: Ask chn to write ‘up’ or
‘down’ by the side of each problem,
and choose four to work out. Then
set them the following challenge:
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheet
of word
problems (see
resources)
Y5 Maths TS4 – Aut – 5days
one table of four.
Display the following problem:
A packer for an internet company is gift wrapping
remote control sand buggies. It takes 3m of paper to
wrap each sand buggy. There is 86m of wrap left, how
many buggies can he wrap before he needs to go to
the warehouse to get more paper?
Ask chn to discuss this in pairs, work out the answer
to the calculation and then to the problem. Do you
need to round up or down?
the following:
137 ÷ 6 = 23 r 5
96 ÷ 7 = 23 r 5
113 ÷ 4 = 28 r 3
172 ÷ 8 = 22 r 4
Easier: Check:
87 ÷ 6 = 13 r 4
96 ÷ 7 = 23 r 5
95 ÷ 4 = 22 r 3
92 ÷ 8 = 11 r 2
the wedding cake has four tiers.
The top tier is going to the bride
and groom. The other three are to
be shared between the guests.
The biggest tier is twice the
volume of the next biggest tier,
which has twice the volume of the
next tier. How many pieces do you
think each tier should be cut into
so that all guests get a piece?
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS4 – Aut – 5days