3H · Develop strategies
Different routes
Summary exercise · Different routes
How many ways can you find?
Before you open a question, try it yourself.
Write down all the possible ways you can think of to calculate it. Then open the tile to check the answer and compare your routes with ours.
You may find a good route that is not listed — that counts too.
6 × 8 — check your routes
Answer: 48
Start from 5
5 × 8 + 1 × 8 = 40 + 8
5 × 8 + 1 × 8 = 40 + 8
Double
3 × 8, then double = 24 × 2
3 × 8, then double = 24 × 2
Start from 10
10 × 6 − 2 × 6 = 60 − 12
10 × 6 − 2 × 6 = 60 − 12
7 × 8 — check your routes
Answer: 56
Start from 5
5 × 8 + 2 × 8 = 40 + 16
5 × 8 + 2 × 8 = 40 + 16
Start from 10
10 × 8 − 3 × 8 = 80 − 24
10 × 8 − 3 × 8 = 80 − 24
Double
7 × 4, then double = 28 × 2
7 × 4, then double = 28 × 2
8 × 9 — check your routes
Answer: 72
Start from 10
10 × 9 − 2 × 9 = 90 − 18
10 × 9 − 2 × 9 = 90 − 18
9s: 10 − 1
8 × 10 − 8 = 80 − 8
8 × 10 − 8 = 80 − 8
Double
4 × 9, then double = 36 × 2
4 × 9, then double = 36 × 2
6 × 7 — check your routes
Answer: 42
Start from 5
5 × 7 + 1 × 7 = 35 + 7
5 × 7 + 1 × 7 = 35 + 7
Double
3 × 7, then double = 21 × 2
3 × 7, then double = 21 × 2
Start from 10
10 × 6 − 3 × 6 = 60 − 18
10 × 6 − 3 × 6 = 60 − 18
7 × 9 — check your routes
Answer: 63
Start from 10
10 × 9 − 3 × 9 = 90 − 27
10 × 9 − 3 × 9 = 90 − 27
9s: 10 − 1
7 × 10 − 7 = 70 − 7
7 × 10 − 7 = 70 − 7
Start from 5
5 × 9 + 2 × 9 = 45 + 18
5 × 9 + 2 × 9 = 45 + 18
8 × 8 — check your routes
Answer: 64
Start from 10
10 × 8 − 2 × 8 = 80 − 16
10 × 8 − 2 × 8 = 80 − 16
Double
4 × 8, then double = 32 × 2
4 × 8, then double = 32 × 2
Start from 5
5 × 8 + 3 × 8 = 40 + 24
5 × 8 + 3 × 8 = 40 + 24
6 × 9 — check your routes
Answer: 54
Double
3 × 9, then double = 27 × 2
3 × 9, then double = 27 × 2
9s: 10 − 1
6 × 10 − 6 = 60 − 6
6 × 10 − 6 = 60 − 6
Start from 5
5 × 9 + 1 × 9 = 45 + 9
5 × 9 + 1 × 9 = 45 + 9
7 × 7 — check your routes
Answer: 49
Start from 5
5 × 7 + 2 × 7 = 35 + 14
5 × 7 + 2 × 7 = 35 + 14
Start from 10
10 × 7 − 3 × 7 = 70 − 21
10 × 7 − 3 × 7 = 70 − 21
9 × 9 — check your routes
Answer: 81
9s: 10 − 1
10 × 9 − 9 = 90 − 9
10 × 9 − 9 = 90 − 9
Start from 5
5 × 9 + 4 × 9 = 45 + 36
5 × 9 + 4 × 9 = 45 + 36
Factor route
3 × 3 × 9 = 27 × 3
3 × 3 × 9 = 27 × 3
6 × 6 — check your routes
Answer: 36
Double
3 × 6, then double = 18 × 2
3 × 6, then double = 18 × 2
Start from 5
5 × 6 + 1 × 6 = 30 + 6
5 × 6 + 1 × 6 = 30 + 6
11 × 7 — check your routes
Answer: 77
Build from 10
10 × 7 + 1 × 7 = 70 + 7
10 × 7 + 1 × 7 = 70 + 7
Turn it around
7 × 11 = 77
7 × 11 = 77
11 × 9 — check your routes
Answer: 99
Build from 10
10 × 9 + 1 × 9 = 90 + 9
10 × 9 + 1 × 9 = 90 + 9
Turn it around
9 × 11 = 99
9 × 11 = 99
11 × 12 — check your routes
Answer: 132
Build from 10
10 × 12 + 1 × 12 = 120 + 12
10 × 12 + 1 × 12 = 120 + 12
Turn it around
12 × 10 + 12 = 120 + 12
12 × 10 + 12 = 120 + 12
Double
11 × 6, then double = 66 × 2
11 × 6, then double = 66 × 2
12 × 7 — check your routes
Answer: 84
Build from 10
10 × 7 + 2 × 7 = 70 + 14
10 × 7 + 2 × 7 = 70 + 14
Double
6 × 7, then double = 42 × 2
6 × 7, then double = 42 × 2
Triple
4 × 7, then triple = 28 × 3
4 × 7, then triple = 28 × 3
12 × 8 — check your routes
Answer: 96
Build from 10
10 × 8 + 2 × 8 = 80 + 16
10 × 8 + 2 × 8 = 80 + 16
Double
6 × 8, then double = 48 × 2
6 × 8, then double = 48 × 2
Triple
4 × 8, then triple = 32 × 3
4 × 8, then triple = 32 × 3
12 × 12 — check your routes
Answer: 144
Build from 10
10 × 12 + 2 × 12 = 120 + 24
10 × 12 + 2 × 12 = 120 + 24
Double
6 × 12, then double = 72 × 2
6 × 12, then double = 72 × 2
Triple
4 × 12, then triple = 48 × 3
4 × 12, then triple = 48 × 3
The answer is fixed. The route is your choice.
The colours help you spot the same type of route appearing in different calculations.
You can stop here.
Repeat this strategy as often as you need before moving on.
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