Year 6
Autumn Transition Therapy
Can recall and use multiplication and division
facts for all the times tables
This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may
be freely used within the member school.
All opinions and contributions are those of the authors. The contents of this resource are not connected with nor endorsed by any other company, organisation or institution.
PiXL Club Ltd endeavour to trace and contact copyright owners. If there are any inadvertent omissions or errors in the acknowledgements or usage, this is unintended and PiXL will remedy these on written notification.
Commissioned by The PiXL Club Ltd. July 2020
Teacher Notes
q There is not scope within one therapy to cover all the multiplication facts to 12 x 12. However, this therapy is editable so it may be appropriate to change the
numbers or the focus of particular slides to rehearse a particular multiplication table.
q The therapy begins by explaining and modelling the relationship between
multiplication, division and fractions. It is advisable to always rehearse ‘trios’ so this key relationship is emphasised at every opportunity.
q See also the PiXL Times Table app and the Times Table DTT resources for both CPD and pupil resources and sessions.
Pupils should be taught some basic roots and their meanings in
order to help them build a ‘toolkit’ for working out the meaning of
unfamiliar language. This activity helps pupils explore roots within
words and how they shape the meaning of new and familiar
language. Give pupil a root and discuss the meaning. Ask them to
identify other words containing this root and discuss how this
affects the overall meaning of the whole word. How many relevant
words can pupils collect per root?
DE
CO
N
ST
RU
CT
IT
At the root of it
The root ‘multi’
means many or
much. How
does this relate
to the overall
word meaning
of ‘multiply’?
multi
DE
CO
N
ST
RU
CT
IT
Knowing key multiplication facts to 12 x 12 means related
division and fractions facts can be found. This gives us
plenty of tools to solve mathematical problems.
Which times tables are you
confident with?
Which times tables do you need to
work on?
Multiplication and division are the
inverse of each other. Using one
reverses the effect of the other.
Linking multiplication and division
7 x 2 = 14
14 ÷ 2 = 7 half of 14 = 7
Fractions also link to
division.
!
Linking multiplication and division
This array shows 4 x 3 = 12
This array shows 3 x 4 = 12
Multiplication is commutative. This means
the product is the same whichever way we
perform the calculation.
Linking multiplication and division
12 ÷ 3 = 4
! #of 12 = 4
12 ÷ 4 = 3
! $of 12 = 3
We can also use the array to show the link
with division and fractions.
It is important to be able to recall the multiplication facts instantly. How quick are you?
Let’s use a counting stick to help us recall multiples of 5.
5 10 15 20 25 30 35 40 45 50 55 60
Your turn
Trios
Complete the missing division and fraction facts. Can you find another fact for each box in each trio?
7 x 5 = 35 35 ÷ 7 = 5 ! " of 35 = 7 66 ÷ 5 =
?
?
Use what you know about the multiples of 5 to find the missing numbers and solve the problem.
Your turn
? x 5 = 55
35 ÷ ? = 7
! "of 25 = ?
500 ÷ ? = 100
In PE, 30 pupils are organised into
groups of 5. How many groups
are there?
Now let’s move on to multiples of 6.
Let’s use a counting stick to help us recall the multiples of 6.
Multiples of 6
Use what you know about the multiples of 6 to find the missing numbers and solve the problem.
Your turn
? x 6 = 72
36 ÷ ? =6
! #of 18 = ?
600 ÷ ? = 100
In PE, 30 pupils are organised into
groups of 6. How many groups
are there?
Your turn
Trios
Complete the missing division and fraction facts. Can you find
another fact for each box in each trio?
3 x 6 =
?
?
72 ÷ 6 = ? ?Your turn
Choose a multiplication table you need to practise.
?
? ?
1. Write down a multiplication fact and draw an array to show the link between multiplication,
division and fractions.
2. Sketch two trios for the multiplication table.
Using the inverse to solve problems
Knowing that division is the inverse of multiplication can help us to solve problems. Let’s look at an
example.
x 4
x 7
6
54
3
12
81
63
Talk to your partner.
How would you go about finding the missing numbers?
Using the inverse to solve problems
Solving problems like these involves being systematic.
Start by filling in the cells where you have both numbers for a row and a
column. For example: 4 x 6.
x 4
x 7
6
54
3
12
81
63
This makes 24, so I can fill in this cell. We can also solve 6 x 7 as we know both of the factors.
Using the inverse to solve problems
Now, it becomes trickier as, for the remaining numbers, we have a factor and the multiple, but not two factors as before. The key is finding out the
missing column and row headings. This means we need to use the
inverse.
x 4
x 7
6
54
3
12
81
63
Let’s start with 54.
We will write an equation to help us. I will write down what I know.
24
42
6 x ? = 54 So, 54 ÷ 6 = ?
So, the missing column heading must be 9, as I know that 9 x 6 = 54.
Using the inverse to solve problems
x 4
x 7
6
54
3
12
81
63
24
42
9
Work with a partner to complete
the remaining missing numbers.
Your turn
Can you find the missing numbers in this
multiplication grid? Try to work systematically.
x 3
x 10
8
24
48
7
21
Using the known facts to solve problems
Explain how you would use 12 x 6 = 72 to
work out 17 x 6.
Think about how
you would do
Using the known facts to solve problems
Explain how you would use 12 x 6 = 72 to work out 17 x 6.
Start by focusing on what is the same and what is different about the two equations. I have written them out one above the other
and labelled one, ‘A’ and the other, ‘B’. This helps me when explaining ideas.
A. 12 x 6 = 72
B. 17 x 6 = ?
They are both multiplying by 6 but statement ‘B’ has 5 more lots of 6 than
Using the known facts to solve problems
Explain how you would use 12 x 6 = 72 to work out 17 x 6.
A. 12 x 6 = 72
B. 17 x 6 = ?
I know that 5 x 6 = 30, so the product of statement ‘B’ will be 30 more than the
product of statement ‘A’.
72 + 30 = 102
So, 17 x 6 = 102
Now we have worked this out, we need to explain to actually answer the
Using the known facts to solve problems
Explain how you would use 12 x 6 = 72
to work out 17 x 6.
17 x 6 is 5 more lots of
6 than 12 x 6.
5 x 6 = 30 so
17 x 6 = 72 + 30 = 102
Notice that we haven’t used many words. The mathematical facts help
us to explain concisely.
Conjunctions like ‘so’ or ‘therefore’ are very
Your turn
Explain how you would use 12 x 8 = 96
to work out 18 x 8.
Try to follow the steps and explain concisely
using mathematical statements.
Remember to use
conjunctions to support
your reasoning, e.g. so, therefore, consequently.
Your turn
Which pairs of numbers could be written in
the spaces?
a) ___ x ___ = 72 b) 36 = ___ x ___
Which pairs of numbers could be written in
the spaces?
Your turn
The dimensions of a kitchen tile are 15cm wide and 8cm high. What is the area of one tile?
Explain how you calculated this.
The height of the area to be tiled is 640cm. How many tiles high will the area be if the tiles
are fitted this way around?
15cm
