The patterns are made up of identical shaded and identical unshaded squares.
- Find the total number of squares in Pattern 4.
- Find the number of unshaded squares in Pattern 4.
- Which Pattern Number has a total of 100 squares?
(a)
Total number of squares:
Pattern 1 = 9 = 3
2 = (1 + 2)2
Pattern 2 = 16 = 4
2 = (2 + 2)
2 Pattern 3 = 25 = 5
2 = (3 + 2)
2 Formula:
Total number of squares = (Pattern Number + 2)
2 Total number of squares in Pattern 4
= (4 + 2)
2 = 6
2
= 6 x 6
= 36
(b)
Number of unshaded squares
= 36 - 4
= 32
(c)
(Pattern Number + 2)
2 = 100
(Pattern Number + 2)
2 = 10 x 10
(Pattern Number + 2)
2 = 10
2 Pattern Number + 2 = 10
Pattern Number = 10 - 2
Pattern Number = 8
Pattern Number that has a total of 100 squares = 8
Answer(s): (a) 36; (b) 32; (c) 8