Year 6 Teaching Sequence 3 - Written methods for multiplication and division (five days)
Prerequisites:
 Use the grid method to multiply two-digit numbers by two-digit numbers and three-digit numbers by single-digit
numbers (see Year 5 Summer teaching sequence 4)
 Use chunking on the ENL to divide three-digit numbers by single-digit numbers, including those leaving a remainder
(see Year 5 Summer teaching sequence 4)
 Revise all multiplication and division facts for the 2 to 10 times tables (see oral and mental starter banks 2 and 3)
 Approximate first when multiplying and dividing (see oral and mental starter bank 3)
Overview of progression:
Children revise multiplying two-digit numbers by two-digit numbers and three-digit numbers by single-digit numbers, and
dividing three-digit numbers by single-digit numbers, approximating first. They move on to multiply four-digit numbers by
single-digit numbers and extend dividing three-digit numbers by single-digit numbers to include those with larger answers
than in Year 5. Given word problems, they decide whether to round answers up or down after division. Children use the
relationship between multiplication and division to find missing numbers.
Note that in Hamilton sequences the ENL is used to record the steps in chunking in Years 4 and 5. This is the first time
that the vertical layout has been introduced. Children are given the choice of which to use throughout Year 6.
Note that the most efficient chunking when recording using the vertical layout looks very similar to traditional long division
on paper, but the process is easier to understand.
Watch out for children who learn to use the grid method by just multiplying all the parts together but who don't
understand why, particularly when multiplying two-digit numbers together. Encourage them to see what is worked out on
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days
each row, so in 45 × 23 for example, the first row is 45 × 20, worked out in two stages, and the second row is 45 × 3, again
worked out in two stages, and the two rows are added together.
Watch out for children who repeatedly draw jumps of 10 lots of the divisor when chunking, rather than biggest multiple of
ten that they can, e.g. they draw six lots of jumps of 30, rather than one big jump of 180 when dividing 188 by 3. This will
become very inefficient when the calculations need 7, 8 or 9 such jumps. Encourage them to write a list of multiples of ten
of the divisor (e.g. 30, 60, 90, 120, 150, 180…).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days
Objectives:
 Multiply pairs of multiples of 10, e.g. 30 x 40, or of 10 and 100, e.g. 600 x 40
 Approximate first before calculating
 Revise using the grid method to multiply three-digit numbers by single-digit numbers and to multiply two-digit numbers by
two-digit numbers
 Use the grid method to multiply four-digit numbers by single-digit numbers
 Revise using chunking on the ENL to divide three-digit numbers by single-digit numbers, including those leaving a remainder
 Decide whether to round up or down after division
Whole class
Group activities
Paired/indiv practice
Resources
Write 7 x 426 on the board and ask chn to
discuss in pairs an estimate for the answer.
Take feedback, drawing out different
strategies. If we round 426 to 400 and find
seven lots of 400, this would give an estimate
of 2800. Will the true answer be more or less
than this? If we round up, 500 multiplied by 7
is 3500, and the true answer will be about a
quarter of the way towards this number.
Sketch an ENL to show 2800 and 3500. So
perhaps the true answer might be closer to
3000 than 2800. Ask chn to use the grid
method to find the answer, and then compare
it with their estimates.
×
400
20
6
Group of 4-5 children
Prepare a flipchart with workings out
for grid multiplications 6 x 683, 723 ×
8 and 37 × 23, using Post-its™ to cover
the numbers being multiplied together,
e.g.
□
□
□
×
Ask chn to work in pairs to
discuss estimates. They record
their estimates and then use the
grid method to find the true
answers (see resources).
Easier: Slightly easier activity
sheet (digits 6, 7, 8 and 9 used
less frequently as these are likely
to be times tables chn are not so
secure with).
Harder: Chn choose five and make
an estimate for each. Challenge
them to complete them accurately
in five minutes. Then challenge
them to come up with a two-digit
by two-digit multiplication with an
answer as close to 3500 as they
can, neither number can be a
multiple of ten.
 Activity sheets
(see resources)
7
2800
140
42
2982
Explain that with multiplication, our estimates
are not as accurate when estimating the
□
3600
480
18
4098
Ask chn to discuss in pairs what
numbers might be hidden. Could the
left-hand single-digit numbers be 5?
Why not? Look at the 18. What other
numbers can’t it be? What numbers
could it be? Agree 2, 9, 3 and 6. Do any
of these fit with the products, 3600
and 480? What numbers have a product
of 36 and 48?
Repeat for 723 × 8 and 37 × 23.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days
answers to subtractions and addition. This is
because the effect of multiplication is to
magnify the effects of rounding.
Repeat with 738 × 6. 700 multiplied by 6 is
4200, 800 × 6 is 4800; the true answer is
likely to be about a third of the way between
the two, so about 4400. Use the grid method
to find out.
Repeat with 24 x 67. Take feedback. 20 times
70 is 1400. The answer is likely to be more
than this. 25 multiplied by 70 might give a
closer estimate. What are seven 25s? And
seventy 25s? Will the true answer be more or
les than this? So the true answer will be a bit
less than 1750, but more than 1400.
Repeat with 52 × 48. 50 multiplied by 50 is
2500, will the true answer be more or less
than this? It’s not so difficult to say this time!
(You could explain that when we rounded 52
down to 50, we subtracted two lots of 48, and
then when we rounded 48 up to 50 we added
two lots of 50, so the true answer will be a
little more than 2500, but 2500 is probably a
close enough estimate!) Ask chn to use the
grid method to find out.
Write 29 x 51 on the board. Discuss an
estimate with your partner. Take feedback.
Discuss how you could use the grid method to
find the answer, or you could find 30 lots of
51, and then subtract one lot of 51 to find the
answer, recording a few jottings along the way.
Easier: Don’t cover the second number
in the multiplication, i.e. those on the
right of the grid, i.e. 6, 8 and 23.
Remind them that the first top
numbers is a multiple of 100, a multiple
of 10 and the last one a single-digit
number in the first multiplication.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days
Write 3 x 4235 on the board and ask chn to
discuss in pairs how they might find the
answer. Take feedback and discuss how the
grid method could be used, this time with an
extra column. Ask chn to work in pairs to use
the grid method to find the answer.
Write 2137 × 6 on the board. Discuss with
your partner what might be a good estimate
for this product. Take feedback. 2000
multiplied by 6 is 12,000, and if we multiply
the rest of the number by 6, we’re probably
going to get near another 1000, so 13,000
would be a good estimate. Ask chn to use the
grid method to find the true answer.
Repeat with 7 x 6423.
Group of 4-5 children
Write 3 x £4.72 on the flipchart. How
could we use the grid method to find
the answer? What would be a rough
estimate?
Together work through using the grid
methods to find the answer:
×
£4
70p
2p
3
£12
£2.10
6p
£14.16
Ask chn to use the grid method to find
6 x £5.45.
How could we use the grid method to
find 3 x £24.72? Talk to your partner
and sketch the grid on your whiteboard.
Take feedback.
Then demonstrate
×
£20
£4
70p
2p
3
£60
£12
£2.10
6p
£74.16
Ask pairs to make up three of their own
four-digit prices and multiply them by
single-digit numbers. Which was the
easiest? Why? And the most difficult?
Why?
Easier: Keep to three-digit prices and
avoid digits such as 7 and 8 if chn are
unsure of these times tables.
Harder: When thinking of their own
multiplications, say that the answers
must be over £100.
Ask chn to work in pairs to
discuss estimates. They record
their estimates and then use the
grid method to find the true
answers (see resources).
Easier: Slightly easier activity
sheet (digits 6, 7, 8 and 9 used
less frequently as these are likely
to be times tables chn are not so
secure with).
Harder: Chn choose five and make
an estimate for each. Challenge
them to complete them accurately
in five minutes. Then challenge
them to come up with a four-digit
by single-digit multiplication with
an answer as close to 20,000 as
they can, the four-digit number
cannot be a multiple of 10, 100 or
1000.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheets
(see resources)
Y6 Maths TS3 – Aut – 5days
Write 327 ÷ 5 on the board. How many 5s do
you think might be in 327? More than ten?
More than twenty? Record the multiples of 50,
100, 150… 350. So they are more than sixty
lots of five, but fewer than seventy. So our
first chunk can be 300. Ask chn to draw with
ENL jotting to work out the division. Take
feedback, revising any steps they have
forgotten.
Now write the following jottings on the board:
5 lots of 7
60 lots of 7
0
420
r1
455 456
456 ÷ 7 = 65 r 1
-
456
420
-
36
35
(60x7)
Group of 4-5 children
Work in pairs to write a three-digit by
single-digit division with an answer
between 30 and 40. Be prepared to tell
the group how you came up with your
division. Take feedback. Draw out
finding 30 lots and 40 lots of 6 for
example, and then choosing a number
between these two products to divide
by 6. Find another division with a
different divisor with an answer
between 30 and 40. Take feedback
Now think of two divisions with an
answer between 40 and 50.
Easier: Think of a three-digit by singledigit division with an answer of between
10 and 20, then 20 and 30.
Harder: Think of a three-digit by
single-digit division with an answer of
between 70 and 80, then 80 and 90.
Chn practise using both layouts
for chunking for four calculations
and then choose their favourite
to use for others (see resources).
Easier: Slightly easier activity
sheet (digits 6, 7, 8 and 9 used
less frequently as these are likely
to be times tables chn are not so
secure with). Ensure that chn list
multiples of ten of the divisor to
help them with the estimate and
the first chunk.
 Activity sheets
(see resources)
(5x7)
1
65
456 ÷7 = 65 r 1
Two chn have worked out 456 divided by 7.
These are their jottings. Look at each and
discuss with your partner what you think they
have done. Draw out that the first layout looks
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days
familiar, and that the second is not. Why has
the second child written 420? And then 60x7
in brackets? What have they done then? How
does this relate to the number line jotting?
Draw out that the child has subtracted 420
from 456 to find how much is left on the
number line.
Ask chn to work in pairs to use both layouts to
work out 327 ÷ 6, and then 445 ÷ 8.
These are two layouts of just different ways
of recording the steps in chunking, which did
you prefer?
Display the following problem:
An apple picker has picked 153 apples. They
are to be packed into trays of four apples.
How many full trays can be packed?
Ask chn to discuss it in pairs. What calculation
needs to be worked out? 153 ÷ 4 Work it out
on your whiteboards.
153
- 120 (30 x 4)
33
– 32 (8 x 4)
1
So what’s the answer to the problem? 38 r 1
Discuss how only 38 trays will be filled, and so
for this word problem we round the answer
down.
Display the following problem:
A primary school needs 145 apples for their
healthy snack times this week. How many
Group of 4-5 children
We divided 153 by 4 and got an answer
of 38 r 1. How could we check that this
is correct? Draw out using
multiplication. What multiplication
would we need to do? Together work
out 4 x 38:
= (4 x 30) + (4 x 8)
= 120 + 32
= 152
But this is 152 not 153? Discuss how we
need to add the remainder of 1 on, and
so would get 153.
Ask chn to work in pairs to do and then
check the following:
260 ÷ 6 = 43 r 2
382 ÷ 7 = 56 r 2
345 ÷ 9 = 37 r 3
389 ÷ 8 = 48 r 5
Chn work through problems,
finding solutions and deciding
whether answers to the required
calculations need rounding up or
down (see resources).
Easier: Slightly easier activity
sheet (with easier calculations).
Harder: Ask chn to write ‘up’ or
‘down’ by the side of each
problem, and choose four to work
out, plus the last one. Then set
them the following challenge: A
long distance walker is attempting
to walk round the coast of
Britain, a total of 9471 miles. He
will walk for eight hours per day.
He walks at three miles per hour.
How many hours would it take?
How many days? Weeks? Months?
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheets
of word
problems (see
resources)
Y6 Maths TS3 – Aut – 5days
packs need to be ordered?
Ask chn to discuss it in pairs, work out the
necessary calculation (145 ÷ 4), then to answer
the problem. Take feedback. Did you need to
round up or down this time? (Up)
Write □ ÷ 6 = 87 on the board. Discuss with
your partner how we could find the missing
number. Take feedback; draw out multiplying
87 by 6 to find the number that was initially
divided. Ask chn to find this product and then
use chunking to check that the division does
indeed work.
522 ÷ 6
522
– 480 (80 x 6)
42
– 42 (7 x 6)
So the answer is indeed 87.
Repeat with □ × 7 = 48.
Write □ × 8 = 416 on the board. Discuss with
your partner how we could find the missing
number. Take feedback; draw out dividing 416
by 8 to find what number was multiplied by 8.
Ask chn to work out the division and then to
multiply to check that this does work.
Repeat with □ × 7 = 392.
Easier: Check:
137 ÷ 6 = 23 r 5
96 ÷ 7 = 23 r 5
113 ÷ 4 = 28 r 3
172 ÷ 8 = 22 r 4
Group of 4-5 children
Show chn 25 × 25 using the ITP Multi
Grid:
If I increase the first 25 by one, and
decrease the second 25 by one, to make
the multiplication 26 multiplied by 24,
do you think I will get the same
answer? Discuss this with your partner.
Write down the product 625 to keep a
record of it. Increase the first 25 to
26 by using the toggle. How much has
been added? Now decrease the second
25 by one. And how much has been
subtracted? What's the new product?
Repeat with 50 × 50 and another pair of
numbers of the chn’s choice.
Ask chn to use the digits 5, 6, 7,
8 and 9 to make four-digit by
single-digit multiplications and
divisions, and two-digit by twodigit and four-digit
multiplications, at least two of
each type of calculation.
Easier: Use digits 4, 5, 6 and 7 to
make three-digit by single-digit
multiplications and divisions, and
two-digit by two-digit
multiplications.
Harder: Challenge chn to find the
greatest and least answer for
each type of calculation.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 ITP Multi Grid
Y6 Maths TS3 – Aut – 5days
Easier: Use the ITP to show 325 × 5. If
I increase the 5 to 6, how will the
product change? How much will be
added? What if I increase it to 7? How
do you know? What if I change it from
5 to 4? Repeat with similar
multiplications.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS3 – Aut – 5days