Activity One

Organising the results in an in/out table may help students to recognise patterns:

Activity Two

Some students may need a calculator to help them, although processing the problems mentally is more efficient.
Realising that the = sign must go in one of the vacant squares is a clue to how the problems can be
solved in an organised way.
For example, question 3 offers three possibilities:
15 = 21  4  40 [This looks unlikely.]
15  21 = 4  40 [More likely, although + and – are the only likely operators.]
15  21  4 = 40 [Using addition signs gives the correct solution.]
Students may enjoy making up their own problems, although this is another case where creating
problems is much easier than solving them.

Answers to Activities

Activity One
+ 5
2 + 5 = 7
4 + 5 = 9
6 + 5 = 11
8 + 5 = 13
10 + 5 = 15

- 8
8 – 8 = 0
12 – 8 = 4
16 – 8 = 8
20 – 8 = 12

x 3
7 x 3 = 21
8 x 3 = 24
9 x 3 = 27
10 x 3 = 30

÷ 5
5 ÷ 5 = 1
10 ÷ 5 = 2
15 ÷ 5 = 3
20 ÷ 5 = 4

Activity Two
1. 6 ÷ 3 = 2 or 6 = 3 x 2
2. 50 = 10 + 10 + 30, 50 – 10 = 10 + 30, or 50 – 10 – 10 = 30
3. 15 + 21 + 4 = 40
4. 24 = 6 x 4 or 24 ÷ 6 = 4
5. 16 + 17 = 3 x 11
6. 10 = 2 x 3 + 4 or 10 + 2 = 3 x 4
7. 12 = 3 x 2 x 2 or 12 ÷ 3 = 2 x 2
8. 40 + 3 + 7 = 50

Activity Three
Answers will vary.