Look at the pattern.
- Find the total number of squares in Pattern 12.
- How many shaded squares will there be in Pattern 28?
(a)
Pattern for the number of squares
Pattern 1: 1 square
Pattern 2: 1 + 2 = 3 squares
Pattern 3: 1 + 2 + 3 = 6 squares
Formula:
Sum of numbers
= 1 + 2 + 3 + 4 + 5 + . . . + last digit
= last digit x (last digit + 1) ÷ 2
Formula:
Total number of squares = Sum of all numbers up to Pattern number
Total number of squares in Pattern 12
= 1 + 2 + 3 + ... + 12
= 12 x 13 ÷ 2
= 78
(b)
Pattern 1: 0
Pattern 2: 0 + 1 = 1 shaded square
Pattern 3: 0 + 1 + 2 = 3 shaded squares
Total number of shaded squares = Sum of all numbers up to (Pattern number - 1)
Number of shaded squares in Pattern 28
= 1 + 2 + 3 + ... + 27
= 27 x 28 ÷ 2
= 378
Answer(s): (a) 78; (b) 378
