Solving Word Problems using Block Modelling  Solving Word Problems using Algebra 
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:
Rectangles 
Pattern 
Total dots 
1 
10 
10 
2 
10 + 7 
17 
3 
10 + 14 
24 
4 
10 + 21 
31 
5 
10 + 28 
38 
6 
10 + 35 
45 
7 
10 + 42 
52 
8 
10 + 49 
59 
9 
10 + 56 
66 
10 
10 + 63 
73 
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:
Layers 
Pattern 
Total dots 
1 
3 
3 
2 
3 + 3 
6 
3 
3 + 3 + 4 
10 
4 
3 + 3 + 4 + 5 
15 
5 
3 + 3 + 4 + 5 + 6 
21 
6 
3 + 3 + 4 + 5 + 6 + 7 
28 
7 
3 + 3 + 4 + 5 + 6 + 7 + 8 
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
I 
1 
7 
13 
19 
25 
II 
2 
8 
14 
20 
26 
III 
3 
9 
15 
21 
27 
IV 
4 
10 
16 
22 

V 
5 
11 
17 
23 

VI 
6 
12 
18 
24 
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.
Number of squares 
1 
2 
3 
4 
5 
6 
7 
8 
Number of triangles 
4 
6 
8 
10 

Number of matchsticks 
12 
19 
26 
33 
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)
Number of squares 
1 
2 
3 
4 
5 
6 
7 
8 
Number of triangles 
4 
6 
8 
10 
12 
14 
16 
18 
Number of matchsticks 
12 
19 
26 
33 
40 
47 
54 
61 
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 exschoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?
Solution;
A 
B 
C 
D 
E 
F 
G 

A 

B 
● 

C 
● 
● 

D 
● 
● 
● 

E 
● 
● 
● 
● 

F 
● 
● 
● 
● 
● 

G 
● 
● 
● 
● 
● 
● 

HS 
6 
5 
4 
3 
2 
1 
Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes
The following video shows more examples of using problem solving strategies and models.Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with stepbystep explanations.
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