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 
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
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.
Question 1: Approximate your average speed given some information
Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row.
Question 3: You are hanging three pictures in the wall of your home that is 16 feet wide. The width of your pictures are 2, 3 and 4 feet. You want space between your pictures to be the same and the space to the left and right to be 6 inches more than between the pictures. How would you place the pictures?
The following are some other examples of problem solving strategies.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.