The patterns are made up of identical shaded and identical unshaded squares.
- Find the total number of squares in Pattern 6.
- Find the number of unshaded squares in Pattern 6.
- Which Pattern Number has a total of 49 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 6
= (6 + 2)
2 = 8
2
= 8 x 8
= 64
(b)
Number of unshaded squares
= 64 - 4
= 60
(c)
(Pattern Number + 2)
2 = 49
(Pattern Number + 2)
2 = 7 x 7
(Pattern Number + 2)
2 = 7
2 Pattern Number + 2 = 7
Pattern Number = 7 - 2
Pattern Number = 5
Pattern Number that has a total of 49 squares = 5
Answer(s): (a) 64; (b) 60; (c) 5