Year 6 Teaching Sequence summer 9 – Multiplication and division (five days)
Prerequisites:
 Know by heart all multiplication and division facts for the 2 to 10 times tables
 Double quickly any two-digit number e.g. 78, 7.8. 0.78, and derive the corresponding halves (see oral and mental
starter bank 9)
 Double multiples of 10 to 1000 e.g. double 360, and derive the corresponding halves (see oral and mental starter bank
9)
 Use knowledge of place value and multiplication facts to work out multiplication and division involving decimals (e.g. 0.8
× 7, 4.8 ÷ 6) (see spring teaching sequence 3)
 Multiply two-digit numbers by single-digit numbers by partitioning, e.g. 4.7 × 6 = (4 × 6) + (0.7 × 6) (see spring
teaching sequence 3)
 Approximate first when multiplying and dividing (see spring teaching sequence 4 and summer oral and mental starter
bank 9)
 Use the grid method to multiply three-digit numbers by two-digit numbers including those with one decimal place (see
spring teaching sequence 4)
Overview of progression:
Children use known multiplication facts to derive others, e.g. doubling the 8 times table to get the 16 times table or adding
the 10 and 7 times table to give the 17 times table. They use the strategy of halving and doubling to multiply even numbers
by multiples of five, e.g. 48 × 35. The grid method of multiplication is used to multiply three-digit numbers with two decimal
places by single-digit numbers, estimation is encouraged. Children begin to divide by decimal numbers, e.g. 35 ÷ 2.5, by
doubling the divisor and doubling the answer. Quotients are expressed as vulgar and decimal fractions e.g. 23 ÷ 4 = 5 ¾, or
5.75.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9 – Sum – 5days
Note that lots of the sessions in this sequence involve lots of playing with numbers, halving and doubling and using known
facts to derive new ones. This should improve children’s flexibility and confidence with multiplication, division and place
value and this is perhaps more important than whether they remember the strategies which emerge or not.
Note that the decimal point is not taken out of calculations and then replaced at the end as children can be confused about
where to put it. Instead the place value of each digit is maintained throughout the calculation.
Watch out for children who make place value errors when multiplying by numbers with two decimal places. Encourage them
to estimate as their estimate can help them to realise that an answers is wrong.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9 – Sum – 5days
Objectives:
 Use factors to multiply e.g. multiply by 8 by multiplying by 4 then doubling
 Use number facts to generate new multiplication facts, e.g. develop the 24× table by multiplying the 6× table by 4
 Develop the 17× table by adding the 10 and 7× tables
 Multiply by halving one number and doubling the other, e.g. calculate 35 × 16, by calculating 70 × 8
 Approximate first
 Use the grid method to multiply three-digit numbers by single-digit numbers including two decimal places, e.g. 4.92 × 3
 Give an answer to division as a vulgar fraction, e.g. 90 ÷ 7 = 12 6/7
 Give an answer to division as a decimal fraction, e.g. 61 ÷ 4 = 15.25
 Use written methods to divide numbers including decimals
 Explain methods and reasoning orally
Whole class
Group activities
Paired/indiv practice
Today we’re going to learn our 16 times table!
Launch the ITP Number dials and choose multiples of 8.
Use to recite multiplication facts for the eight times
table clicking on the multiples to reveal them each time.
How could we use this times table to find multiplication
facts for the 16 times table? Agree that you could
double each number. Recite the 16 times table slowly
pointing to the corresponding multiples of eight as you do
so.
How could we find the 24 times table? Draw out that
they could double multiples of 12 if they know them,
triple multiples of 8, or quadruple multiples of 4. Which
way would you prefer? Use the times table chosen by the
majority, write it as list of vertical multiplications on the
board, and next to it work together to write the 24
times table. Do you think we will have an odd number in
this times table? Why not?
Group of 4-5 children
How could we find the 15 times table?
Discuss how they could triple the 5
times table, but they could also add
numbers in the 10 and 5 times tables.
Ask chn to choose their preferred way
to find the 15 times table.
How could we find the 17 times table?
Ask chn to work in pairs to write the
multiplication facts for the 17 times
table. How many odd numbers do you
think you will have? Why?
Harder: Chn choose a way to derive the
19 times table and the 21 times table.
Chn work in pairs to derive the 14
times table, the 18 times table
and a times table of their own
choice.
Easier: Chn derive the 12 times
table and the 30 times table.
Harder: Chn derive the 32 times
table, the 3.5 times table and a
times table of their own choice.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Resources
 ITP Number
dials
Y6 Maths TS9 – Sum – 5days
Write 35 × 16 on the board. We could work this out by
finding 10 lots of 35 and 6 lots of 35, and then adding
the two products together. But there is a special way of
multiplying multiples of 5 by even numbers such as 16
which can be quite useful. If we multiplied 35 by 8
instead of 16, what could you say about the answer?
Draw out that it would be half as big. What if we
multiplied 70 by 16? Draw out that the answer would be
twice as big as the answer to 35 × 16. What if we
multiplied 70 by 8? Agree that the answer would be the
same as to 35 × 16. We get the same answer! So if we
halve one number and double the other, this can make
the multiplication quicker to work out. Why do you think
this works well when multiplying multiples of 5 by even
numbers? Draw out that multiples of 5 are easy to
double, and even numbers will give a whole answer when
halved.
Write 14 × 75 on the board. Work with a partner to use
our halving and doubling method to find the answer.
Which number are you going to halve? Show chn 14 × 75
on a calculator to show that the answer is the same.
Write 72 × 25 on the board. 72 is a much bigger number,
but our halving and doubling method can still be helpful.
If we halve 72 and double 50, we get 36 × 50. But we can
halve and double again and get 18 × 100 which is really
easy! So if we are multiplying by 25, it can be helpful to
double and halve twice.
Write 75 × 24 on the board. We can keep halving and
doubling until we get to a multiplication we like!
75 × 24
= 150 × 12
=300 × 6
Group of 4-5 children
Show chn a rectangle on squared paper
measuring 35 across and 16 down. How
could we find the area of this
rectangle? Fold the rectangle in half
horizontally, and cut it into two.
Rearrange the two halves of the
rectangle to make a 70 by 8 rectangle.
What are the measurements of this
new rectangle? Has the area changed?
No, so 16 × 35 = 8 × 70.
Ask chn to work in pairs to make a
rectangle measuring 28 by 35, and then
to use this to make other rectangles
with the same area, recording the
measurements of each.
Easier: Chn make a 16 by 25 rectangle.
Harder: Chn’s rectangles could include
those with sides, which are not whole
numbers.
Chn use halving and doubling to
work out the following:
18 × 85, 55 × 24, 75 × 32, 65 × 48,
75 × 48 and 75 × 56.
Easier: Chn use halving and
doubling to work out 12 × 25, 16 ×
25, 18 × 25, 24 × 25, 12 × 35 and
24 × 35.
Harder: Chn use halving and
doubling to work out 65 × 48, 75 ×
48 and 75 × 56. They then discuss
whether the strategy of halving
and doubling is useful or not, to
solve the following: 75 × 44, 75 ×
32 and 75 × 42. They discuss and
then write what sorts of numbers
lend themselves to this strategy.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Squared paper
Y6 Maths TS9 – Sum – 5days
Repeat with 65 × 24:
65 × 24
= 130 × 12
= 260 × 6
= 520 × 3
We can work 520 × 3 out easily in our heads!
Write 4.92 × 3 on the board. What do you think the
answer will be approximately? Draw out rounding 4.92 to
5 and then multiplying by 3. Will the true answer be more
than 15 or less than 15? Why? We can use the grid
method to help us to find the exact answer.
Work together to complete the grid. How can we work
out 3 lots of 0.9? What are 3 lots of 9? 3 times 0.9 will
be one tenth of this.
×
4
0.9
0.02
3
12
2.7
0.06
14.76
Ask chn to work in pairs to work out 4.23 × 6. Before you
start, what do you think the answer will be
approximately? Will the true answer be more or less
than this? Afterwards take feedback and ask chn to
explain how they worked out each part, particularly 6
lots of 0.2 and 6 lots of 0.03. Six lots of three
hundredths gives eighteen hundredths, how do we write
this?
Group of 4-5 children
Write 4.28 × 5 on the flipchart. We
could use the grid method to work this
out, but can you think of another way?
Draw out using the strategy of doubling
and halving as in the previous session:
4.28 × 5 is the same as = 2.14 × 10
Now it’s easy!
What if it was 4.28 × 25? Talk to your
partner about how you might find the
answer. Draw out that 4.28 × 25 is the
same as 2.14 × 50 which is the same as
1.07 × 100
It looked like a multiplication where you
would go and find a calculator but
actually it turned out to be one you
would work out mentally! If the whole
part of the number, and the number of
hundredths are divisible by four,
meaning they can be halved twice quite
easily, then multiplying by 25 is easy.
Ask chn also to multiply 8.56, 4.36 and
12.64 by 25 using the same method.
Easier: Chn multiply the same numbers
by 5, not 25.
Chn work in pairs to solve the
following:
4.21 × 5, 6.42 × 3, 5.32 × 4,
3.64 × 5, 4.84 × 6, 5.46 × 3, and
then at least three of their own
similar multiplications.
Ask them to round each number
to the nearest whole to find an
approximate answer.
Easier: Chn work in pairs to
multiply three-digit numbers with
one decimal place by single-digit
numbers:
42.1 × 5, 64.2 × 3, 53.2 × 4,
36.4 × 2, 48.4 × 6, 54.6 × 5.
Ask them to round each number
to the nearest whole to help them
to find an approximate answer.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9 – Sum – 5days
Write 28 ÷ 3.5 on the board. Talk to your partner about
how we could work this out. Draw out that we could count
up in steps of 3.5, or record these on an empty number
line to help.
Draw a line from 0 to 28 and record steps of 3.5 and
conclude that there are eight 3.5s in 28. How many 7s
are in 28? How does that compare with how many 3.5s
are in 28? Discuss how there are twice as many 3.5s in
28 as 7s as each step is half the size.
Write 63 ÷ 4.5 on the board. Ask chn to discuss with
their partner how they could find the answer. Take
feedback, agree that there are seven 9s in 63, and so
there must be 14 4.5s, twice as many as each step is half
the size. How many 2.25s do you think might be in 63?
Why? Use a calculator to check.
Write 22 ÷ 4 on the board. How many 4s are in 18? There
are two left over, this is half of a group of 4, so if we
want an exact answer, there are 5 and a half groups of 4
in 18. Record 22 ÷ 4 = 5½. How else can we write this?
Agree that it can be written as 5.5
Group of 4-5 children
When we were multiplying certain
numbers together, we found it helpful
to halve one and double the other. Does
this work with division? Let’s try with
28 ÷ 3.5. We could double 3.5 and halve
14, so we get 14 ÷ 7. Mm, we’d get an
answer of two, this is much too small.
Why is that? Talk to your partner.
Draw out that the steps are bigger, and
the number being divided is smaller so
this gives a much smaller answer. Has
anyone got any other ideas? Try
doubling both numbers. This seems to
work, why? Discuss that as the steps
are twice as big, the number being
divided needs to be twice as big as well
to give the same answer.
Try and see if doubling both numbers
works with 63 ÷ 4.5 and 30 ÷ 2.5. How
could we check our answers? Encourage
chn to use multiplication to check.
Easier: Try smaller numbers to begin
with e.g. 10 ÷ 2.5 and 7 ÷ 3.5 where chn
may more readily see that the answer
seems reasonable/unreasonable when
doubling both/doubling and halving.
Group of 4-5 children
Display the following word problems:
Mr Baker has 50 buns left. He puts
them in packs of 8. How many packs can
he fill?
Ask chn to work in pairs to solve
the following:
45 ÷ 2.5, 24 ÷ 1.5, 33 ÷ 1.5,
40 ÷ 2.5, 35 ÷ 3.5, 49 ÷ 3.5,
27 ÷ 4.5, 81 ÷ 4.5 and 54 ÷ 4.5.
Easier: Chn may feel more
confident to draw jumps of
multiples of 0.5.
Harder: Also challenge chn to
work out;
45 ÷ 1.25, 40 ÷ 2.25 and 49 ÷ 1.75.
Ask chn to work out the following
divisions giving their answers as
vulgar fractions and also as
decimal fraction where the
conversion is easy to do:
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9 – Sum – 5days
Draw a number line from 0 to 22. Draw five jumps of 4 to
20. Draw another jump of 4, overshooting 22. If we had
another jump of four that would get us to 22, but we
only need half of that jump to get us to 20.
Imagine if you had 22 donuts to share between four
people. How many would they get each? They would give
five each, and there are two left over, which could be
cut in half, so that they get another half each.
If £22 was to be shared between four children, how
much would they get each? Discuss how we could halve
and halve again to find that each child would get £5.50
each.
Write 25 ÷ 3. How many threes are in 25? There is 1 left
over, this is a third of a group of 3, so the exact answer
if 8 1/3. What if it was 26 divided by 3?
Write 27 ÷ 4. How many 4s in 27? How much left over?
What fraction of four is this? How can we write the
answer? Draw out that the exact answer can be written
as 6¾, or 6.75.
Repeat with 50 ÷ 6 and agree the answer as 8 and 2/6.
We could also write this as 8 and a third or 8 point three
recurring.
Mrs Holes is organising a barbeque. She
needs to buy 50 buns. They come in
packs of 8. How many packs does she
need to buy?
Mrs Merttens has eight children. She
gives them £50 to share between them.
How much will they get each?
A length of 50cm ribbon is cut into
eight equal strips. How long is each
strip?
50 sandwiches are shared equally
between eight hungry children. How
many can they have each?
Ask chn to read each word problem and
discuss the calculation needed. Agree
that every problem requires the
calculations 50 ÷ 8, but discuss how the
answer to each is needed in a slightly
different way, rounded up, rounded
down, as a fraction, as a decimal.
Harder: Ask chn to come up with other
number stories which need the answers
in different forms.
33 ÷ 4, 21 ÷ 5, 29 ÷ 5, 28 ÷ 6,
28 ÷ 3, 38 ÷ 3, 45 ÷ 10, 53 ÷ 10,
47 ÷ 7, and 58 ÷ 8. They then
choose two numbers between 50
and 100 to divide by 4, 5 and 8.
Easier: Chn choose four numbers
between 20 and 30 to divide, by
3, 4 and 5.
Harder: Encourage chn to express
the fractions in their simplest
form, e.g. 28 ÷ 6 = 4 2/3.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9 – Sum – 5days