1. Reasoning
about
Numbers

2. that division is the inverse of multiplication.
Today we will be learning:
to solve mathematical puzzles
that subtraction is the inverse of addition
that division is the inverse of multiplication.

3. We are going to practise solving some number problems.
Mental Activity
We are going to practise solving some number problems.
I bought two packets of crisps which cost 25p each. How much did they cost altogether?
50p

4. How much change did I have from 70p?
I had 12 conkers, James gave me 11 more and I lost 9. How many did I have left? 14

5. I had 4 packets of 5 sweets. I ate 6 sweets. How many did I have left?
I bought some sweets for 15p and a pencil for 16p. How much change from 50p did I get?
19p
I had 4 packets of 5 sweets. I ate 6 sweets. How many did I have left? 14

6. I had 20 marbles. I lost half of them and gave 5 to my friend
I had 20 marbles. I lost half of them and gave 5 to my friend. How many did I have left? 5
I bought two bars of chocolate costing 31p each and an apple costing 17p. How much did I spend?
79p

7. Today we are going to solve mathematical problems.
Main Activity
Today we are going to solve mathematical problems. ?
I am thinking of a number.
I halve it. My answer is 6.
What is my number?

8. Today we are going to solve mathematical problems.
Main Activity
Today we are going to solve mathematical problems.
I am thinking of a number. 12
I halve it. My answer is 6.
What is my number?

9. I am thinking of another number.
I add 2.
I double the answer.
I get a total of 10.
What is my number? ?

10. ? I add 2. How can we do this? I double the answer.
We need to work backwards.
I get a total of 10.
What is my number? ?
Half of 10 = 5 10  2 = 5
5 – 2 = 3
So the mystery number is

11. 3 I add 2. How can we do this? I double the answer.
We need to work backwards.
I get a total of 10.
What is my number? 3
Half of 10 = 5 10  2 = 5
5 – 2 = 3
So the mystery number is

12. Top Tip
Halving (division) and doubling (multiplication) are inverse operations.
Inverse means opposite.
What does “inverse” mean?

13. -  + x Here are the signs for the four number operations.
Which number operations are related?
What is the inverse of addition?
Subtraction.

14. Group Work Solve one-step number problems.
Work in pairs. Make up one-step number puzzles for your partner to solve.
Work in pairs. Make up two-step number puzzles for your partner to solve.