# Year 2 Teaching Sequence xxx ```Year 3 Teaching Sequence Summer 11 - Multiplication and division (four days)
Prerequisites:
 Know multiplication facts for 2, 3, 4, 5, and 10 times tables, and corresponding division facts (see summer teaching
sequence 10 and oral and mental starter banks 10 and 11)
 Begin to learn multiplication facts for 9 times table (see summer teaching sequence 9 and oral and mental starter
bank 11)
 Double two-digit numbers (see spring teaching sequence 4 and summer oral and mental starter bank 11)
Overview of progression:
Children revise the concept of commutativity (a x b  b x a) and use this to solve multiplication of single-digit numbers
choosing which order will help them to make use of their multiplication facts, or make the counting on easier. They use
grouping to divide numbers by 2, 3, 4, 5, 6, 9 and 10 including those which leave a remainder. The strategy of partitioning to
double is extended to multiply teens numbers by 3 and 5. Children are shown how to partition numbers into a multiple of ten
of the divisor and the remaining part of the number, e.g. partition 36 into 30 and 6 when dividing by 3 to help children make
use of their multiplication facts. They then use ‘chunking’ on the ENL. Number dials are used to help children in partitioning
numbers and links are made between the two images. Divisions do not leave remainders at this stage (’chunking’ leaving
remainders is introduced in Year 4).
Note that the same jottings is used to multiply teens numbers as used in doubling sequences to help children to see that
the same strategy can be used. This multiplying by partitioning and recombining will lay for the foundation for the grid
method in Year 4.
Note that multiplication sentences can be read in two ways; 4 &times; 5 can be read as four fives (4 lots of 5) or alternatively as 4
multiplied by 5, i.e. 4, five times (5 lots of 4). Children need to be aware of the different terminology used (lots of, times,
multiplied by), but more importantly understand that multiplication is commutative and so the answer is the same whichever
way round we write a multiplication. Thus 4 lots of 5 is equivalent to 5 lots of 4. Understanding commutativity helps children
to multiply efficiently because they can choose which times table to use. For example, many children will prefer to treat 5 x
7 as 7 fives.
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS11 – Sum – 4days
Note that the grouping model of division is used in this sequence to relate multiplication and division. There is a more
natural link between grouping and multiplication facts (e.g. four 10s are 40, how many 10s in 40?) than between sharing and
multiplication. For this reason it is important that the &divide; sign is not read as ‘sharing’, which would confuse the two models.
Watch out for children who try to share between groups rather than using grouping, as they will find the larger numbers
too cumbersome to share.
Watch out for children who do not understand the link between multiplication and division, and so cannot use one to solve
the other, particularly in missing number problems.
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS11 – Sum – 4days
Objectives:
 Multiply single-digits by 2, 3, 4, 5, 6, 9 and 10, and divide two-digit numbers by the same
 Begin to use facts to multiply teens numbers by 3 and 5, e.g. 12 &times; 3 = (10 &times; 3) + (2 &times; 3) = 30 + 6 = 36
 Begin to divide two-digit numbers just beyond tables, e.g. 60 &divide; 5, 33 &divide; 3
Whole class
Group activities
Paired/indiv practice
Resources
Write 5 &times; 7 on the board. Explain that this can be read
as ‘five lots of seven’, or ‘five multiplied by seven’ (five,
seven times, i.e. seven lots of five). Which way would you
work this one out? Five lots of seven or seven lots of
five? We haven’t learned our sevens yet so perhaps seven
lots of five might be easier! Draw seven jumps of five
above a 0-50 beaded line and five jumps of seven below
it, to show that they come to the same number.
What divisions could we write to go with these hops?
Record 35 &divide; 5 = 7, reading this as I have 35, how many
5s? Answer 7, and 35 &divide; 7 = 5, I have 35, how many 7s?
Write 4 &times; 6 on the board and ask chn to discuss in pairs
how they would find the answer. Take feedback. Show
four hops of 6 and six hops of 4 on the beaded line. Ask
chn to write the corresponding divisions on their boards.
Group of 4-5 children
Write 3 &times; 4 = 12 in the centre of the
flipchart.
If we know this, what else do we know?
What divisions can we write? Ask chn
up to the flipchart to record these
round the outside. If three 4s are 12,
what do you think six 4s are? So what
are four 6s? What about eight 6s?
Build up a fact web of multiplication and
division facts.
Easier: Begin with 2 &times; 3 = 6.
Harder: Also include examples such as
30 &times; 4 = 120 (ten times as much).
 Large 0-50
(see
resources)
 0-100
lines (see
resources)
Write 2 &times; 12 on the board. How might you work this out?
Agree that they can double 12 by doubling 10, doubling 2
and then adding 20 and 4 together. Write 3 &times; 12 on the
board. Discuss with your partner how you might work this
out. Take feedback and draw out that chn can use the
same strategy as when they were doubling numbers, but
multiply each part of 12 by 3 this time instead of 2.
Group of 4-5 children
Show chn an apple priced at 13 pence.
Ask chn to make 13p using coins. If I
wanted to buy two apples how much
would it cost? Make another 13p to
show this. You now have two lots of 10p
and two lots of 3p. Use your coins to
Write the following multiplications on
the board:
5 &times; 4, 9 &times; 2, 5 &times; 6, 7 &times; 4, 4 &times; 9, 5 &times; 7,
6 &times; 8, 7 &times; 6
Chn write how they decided to find
the answer to multiplications, so for
example for 5 &times; 6 they write 6 lots of
5 if they choose to count on in 5s or
use their tables facts for 5 rather
than counting on in 6s. Suggest that
they draw jottings or use a 0-100
beaded line (see resources) to help
them with any for which they don’t
yet know the multiplication facts
(particularly multiples of 6).
They write the corresponding
divisions for each multiplication.
Easier: Chn will probably need to use
a 0-100 beaded line to support
counting on more frequently.
Write the following multiplications on
the board for chn to practise:
2 &times; 11, 3 &times; 11, 5 &times; 11
12 &times; 2, 12 &times; 3, 12 &times; 5
2 &times; 13, 3 &times; 13, 5 &times; 13
14 &times; 2, 14 &times; 3, 14 &times; 5,
2 &times; 15, 3 &times; 15, 5 &times; 15
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 ITP
Number
dials
 Apple,
banana and
coins
 Activity
Y3 Maths TS11 – Sum – 4days
Model recording:
&times;3
12
30
&times;3
6
36
Write 5 &times; 12 on the board, and ask chn to work in pairs
to find the answer, recording any jottings on
whiteboards. Repeat with 2 &times; 13, 3 &times; 13 and 5 &times; 13.
show three lots of 13p. Repeat for 4,
then 5 apples. Build up a table on the
flipchart:
1 &times; 13p = 13p
2 &times; 13p = 26p
3 &times; 13p = 39p
4 &times; 13p = 52p
5 &times; 13p = 65p.
Note how the answers are going up by
13p for each item.
Repeat, finding the price of 1, 2, 3, 4
then 5 bananas priced at 15p.
Easier: The apples cost 11p and the
banana 12p.
Harder: Ask chn to continue each table
up to 10 items.
Encourage them to use jottings to
help them.
Easier: Provide chn with partially
completed jottings for the first six
multiplications to help them (see
resources).
Harder: Chn also choose other teens
numbers to multiply by 3 and 5.
sheet of
partial
jottings
(see
resources)
Launch the ITP Number Dial, choose 3 as the multiple
and click to show the outside numbers. How could we use
this dial to help us to work out 13 lots of 3? It only goes
to up to 10 lots of 3. Talk to your partner. Take feedback and draw out that we can split 13 into 10 and 3, find
10 lots of 3 and 3 lots of 3 (both of which we know).
Repeat with 15 &times; 3. Change the dial to multiples of 5 and
repeat with 12 &times; 5, 14 &times; 5 and 15 &times; 5.
Write 3 &times; 15 on the board. Explain that this can be read
as ‘three lots of fifteen’, or ‘three multiplied by fifteen’
(three, fifteen times, i.e. three lots of fifteen). Which
way would you work this one out? Talk to your partner.
Discuss how chn can work out 3 lots of 10, 3 lots of 5 and
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS11 – Sum – 4days
then add the two numbers together, or find 10 lots of 3
and 5 lots of 3 and add the two numbers together. Both
ways are very similar and give the same answer.
Write 23 &divide; 5 on the board. How many fives do you think
there might be in 23? Do you think there will be a
remainder? Why? Launch the ITP Grouping, and choose
23 &divide; 5 as the calculation. Click on 23 to show 23 objects,
and then click on five to show one group. Can we make
another five? Repeat clicking on fives until there are only
three left. What's happened? Click to show the number
sentence. The little ‘r’ stands for remainder, the number
left over.
What do you think would happen if we had 24 divided by
5? Draw a line from 0 to 24. Draw 4 hops of 5, landing on
20. How much is left? What if we had 25 &divide; 5, how many
would be left then? What would happen? Write the
division on your whiteboards. Discuss how we have an
extra one, and so we can make another group of five.
Repeat with 20 &divide; 6. This is a bit trickier as we don't
know our 6 times table yet, so we carefully count in 6s.
Label 20 on a 0-50 beaded line and draw three hops of
six. Point out the two left over. Record 20 &divide; 6 = 3 r 2.
Write 65 &divide; 5 on the board, and then sketch a line from 0
to 65. We could draw every hop of 5, but we don’t need
to! We can use our tables. Do you think there are more
or fewer than 10 lots of 5 in 65? Why? What are 10 lots
of 5? Where would that get us on the line? How much is
left? And how many 5s are in 15? Draw an ENL to show.
10 lots of 5
0
3 lots of 5
50
Repeat for 70 &divide; 5, 36 &divide; 3 and 42 &divide; 3.
65
Group of 4-5 children
Write the following numbers on the f/c.
21, 25, 13, 26 and 32.
Which of these numbers do you think
would have a remainder of 1 when
divided by 5? Why? Take chn’s
suggestions and test them out by
drawing hops on the 0-50 beaded line.
Which do you think will have a
remainder of 1 when divided by 4?
Ask chn to work in pairs to make up five
of their own divisions that would give a
remainder of 1.
Easier: Give chn cubes and ask them to
find other numbers that will give a
reminder of one when divided into
groups of five.
Harder: Chn think of divisions that will
give a reminder of 2.
Group of 4-5 children
Write the following multiplications on
the flipchart:
&times; 3 = 39
&times; 5 = 60
&times; 3 = 33
&times; 5 = 65
&times; 4 = 44
&times; 3 = 36
&times; 4 = 48
&times; 5 = 70
How can we work these out? Draw out
Write the following divisions on the
board:
32 &divide; 5, 17 &divide; 4, 48 &divide; 5, 33 &divide; 4, 15 &divide; 2,
20 &divide; 3, 15 &divide; 6, 30 &divide; 9.
Suggest that they draw jottings or
use a 0-100 beaded line (see
resources) to help them with any for
which they don’t yet know the
multiplication facts (particularly
multiples of 6 and 9).
Easier: Chn will probably need to use
a 0-100 beaded line to support
counting on more frequently.
 ITP
Grouping
 Large 0-50
(see
resources)
 Cubes
 0-100
lines (see
resources)
Write the following divisions on the
board for chn to practise:
33 &divide; 3, 55 &divide; 5, 39 &divide; 3, 70 &divide; 5, 36 &divide; 3,
60 &divide; 5, 42 &divide; 3, 75 &divide; 5, 44 &divide; 4, 48 &divide; 4
Encourage them to use jottings to
help them. Provide chn with partially
completed jottings for the first four
divisions to help them (see
resources).
Easier: Provide chn with partially
completed jottings on beaded lines
for the first four divisions to help
 ITP
Number
dials
 Activity
sheets of
partial
jottings
(see
resources)
 0-75
lines (see
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS11 – Sum – 4days
Launch the ITP Number dial and put 5 as the centre
number.
Discuss with your partner how we could use this to work
out how many 5s are in 65. Draw out how we can split 65
into 50 and 15 as on the line earlier, and we can see (but
already know!) that there are ten 5s in 50, and three 5s
in the remaining 15. How many 5s are in 75?
Change the central number to 3. How many 3s are in 42?
What can we split 39 into two help us? (30 and 9) How
many 3s in 42? What can we split 42 into to help us? (30
and 12)
that we can find how many 3s are in 39
for example. We could count up in 3s to
do this. It would probably take quite a
long time. Do you think there are more
or fewer than ten 3s in 39? What are
ten 3s? So ten 3s are 30. So what are
eleven 3s? Hold one finger up. Twelve
3s? Hold up another finger. Thirteen
threes. Hold up another finger. We’re
there! So there are thirteen 3s in 39.
Fill in 13. Let’s check. Ten 3s are 30,
and three 3s are 9, 30 and 9 makes 39.
Repeat for at least one more
multiplication, and then ask chn to work
in pairs to solve the remaining
multiplications.
Easier: Use 0-75 beaded lines to help.
them (see resources).
Harder: Chn draw their own jottings.
&copy; Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
resources)
Y3 Maths TS11 – Sum – 4days
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