Math Problem Solving Strategies

The following are some examples of problem solving strategies.

Explore it//Act it/Try it (EAT) method (Basic)

Explore it//Act it/Try it (EAT) method (Intermediate)

Explore it//Act it/Try it (EAT) method (Advanced)

Finding a Pattern (Basic)

Finding a Pattern (Intermediate)

Finding a Pattern (Advanced)

Find A Pattern (Intermediate)

In this lesson, we will look at some intermediate examples of Find a Pattern method of problem solving strategy.

Example:

The figure shows a series of rectangles where each rectangle is bounded by 10 dots

a) How many dots are required for 7 rectangles?

b) If the figure has 73 dots, how many rectangles would there be?

Solution:

a) The number of dots required for 7 rectangles is 52.

b) If the figure has 73 dots, there would be 10 rectangles.

Example:

Each triangle in the figure below has 3 dots. Study the pattern and find the number of dots for 7 layers of triangles.

Solution:

The number of dots for 7 layers of triangles is 36.

Example:

The table below shows numbers placed into groups I, II, III, IV, V and VI. In which groups would the following numbers belong?
a) 25
b) 46
c) 269

Solution:

The pattern is: The remainder when the number is divided by 6 determines the group.

a) 25 ÷ 6 = 4 remainder 1 (Group I)
b) 46 ÷ 6 = 7 remainder 4 (Group IV)
c) 269 ÷ 6 = 44 remainder 5 (Group V)

Example:

The following figures were formed using matchsticks.

a) Based on the above series of figures, complete the table below.

b) How many triangles are there if the figure in the series has 9 squares?
c) How many matchsticks would be used in the figure in the series with 11 squares?

Solution:

a)

b) The pattern is +2 for each additional square.
18 + 2 = 20

If the figure in the series has 9 squares, there would be 20 triangles.

c) The pattern is + 7 for each additional square
61 + (3 x 7) = 82

If the figure in the series has 11 squares, there would be 82 matchsticks

Example:

Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?

Solution;

Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes

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