The patterns are made up of identical shaded and identical unshaded squares.
- Find the total number of squares in Pattern 5.
- Find the number of unshaded squares in Pattern 5.
- Which Pattern Number has a total of 64 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 5
= (5 + 2)
2 = 7
2
= 7 x 7
= 49
(b)
Number of unshaded squares
= 49 - 4
= 45
(c)
(Pattern Number + 2)
2 = 64
(Pattern Number + 2)
2 = 8 x 8
(Pattern Number + 2)
2 = 8
2 Pattern Number + 2 = 8
Pattern Number = 8 - 2
Pattern Number = 6
Pattern Number that has a total of 64 squares = 6
Answer(s): (a) 49; (b) 45; (c) 6
