Answers – Learning Session One - Strategies for solving problems
Some methods are:
1. Lamb & Turkey
Answer: There are 6 turkeys and 9 lambs.
Guess and improve:
turkeys
lambs
legs
2
13
4 + 52=56
10
5
20+20=40
6
9
12+36=48
Comment
Too many
Too few
Systematic
Start with all lambs which gives 15 x 4 = 60. Change lambs to turkeys till you reach 48 legs. This
gives 12 legs which is 6 turkeys; 15 – 6 = 9 lambs.
Use Algebra
x = number of turkeys, y = number of lambs
2x + 4y = 48 and x + y = 15. Solve simultaneously.
Use imaging or draw a diagram
2. Cory & Scarlett
Answer: Scarlett is 24 when Cory is 48
Guess & improve
Start with a guess
Cory
Scarlett
Comment
32+12=44 8+12=20 They have to be older
32+14=46 8+14=22
32+15=47
Can’t be an odd number added
32+16=48 8+16=24
Use insight
Cory is 24 when Scarlett is born so he is twice her age when he is 48 and Scarlett is 24.
3. Boxed In
Answer:
=6
=8
=7
=4
Look for a pattern
3 circles and 1 triangle = 18, 3 circles and 1 square = 20
So 1 square = 1 triangle + 2
2 squares + 2 triangles = 28 1 square + 1 triangle = 14
2 triangles + 2 = 14
So 1 triangle + 1 = 7 1 triangle must equal 6.
The remaining shapes can be found by substitution.
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4. Loose Change
Answer: 22 different ways
Systematic
$1
50 ₵
20₵
1
1
1
1
4
1
3
1
1
2
1
1
1
1
1
2
1
3
1
4
1
5
1
6
1
2
3
4
5
6
7
8
9
10₵
1
2
8
4
6
11
9
7
5
3
1
17
14
12
10
8
6
4
2
18
Number of coins
4
5
6
9
7
8
13
12
11
10
9
8
18
16
15
14
13
12
11
10
9
18
5. Basketball Champ
Answer: 15 different games
Systematic
Starting a tree diagram shows a pattern. Every team can play 5 other teams which gives 6 x 5 = 30
but team A playing team B is the same as team B playing team A so the answer is half of 30.
Draw a diagram
Label teams A, B, C, D, E, F, join with lines and count the lines.
B
C
D
A
E
F
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6. Cube Cuts
Answer: 24 cubes
Draw a diagram
4 cubed is 64 so each side of the cube is a square with side = 4
The cubes on the edges are painted on 2 or 3 sides so the only cubes painted on 1 side are the 4
cubes in the centre. 6 sides with 4 cubes gives 24 cubes.
7. One Straight Cut
Answer: A corner must be cut off so that the hypotenuses of the right angled triangles are equal
Draw a diagram
After one or two guesses it usually becomes apparent that the cut cannot be parallel to one of the
sides. The properties of an equilateral triangle can lead to the correct answer.
8. Sharing Space
Answer: 1600 metres by 1000 metres
Work backwards (Can be simplified by scaling down to 2 by 3)
1000
400
600
1000
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9. Work of Art
Answer: 40 minutes or two-thirds of an hour
Draw a diagram
One and a half walls take one hour; three walls take two hours so one wall takes two-thirds of an
hour.
Reasoning
Dad paints 1 wall in 2 hours, Harvey paints 2 walls in 2 hours so together they paint 3 walls in 2
hours. This means they paint 1 wall in two-thirds of an hour.
10. Coins Around
Answer: 6 coins
Use materials ($2 coins or identical cut-out circles)
If coins are used the question arises “Is it true for all coins?”
List everything you know about circles and draw a diagram
The triangle forms the basis of a hexagon using the radii of the circles.
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