### Year 6

### Autumn Transition Therapy

**Can recall and use multiplication and division **

**facts for all the times tables**

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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