Riordan made patterns using squares and toothpicks and recorded the pattern in the table shown.
| Figure number |
Number of squares |
Number of toothpicks |
| 1 |
3 |
10 |
| 2 |
4 |
13 |
| 3 |
5 |
16 |
| 4 |
6 |
19 |
- How many squares are needed for Figure 52?
- How many toothpicks are needed for Figure 52?
- Which figure needs a total of 97 toothpicks?
(a)
Pattern for the number of squares
Figure 1: 1 + 2 = 3 squares
Figure 2: 2 + 2 = 4 squares
Figure 3: 3 + 2 = 5 squares
Figure 4: 4 + 2 = 6 squares
Formula:
Number of squares = Figure number + 2
Number of squares in Figure 52
= 52 + 2
= 54
(b) Pattern for the number for number of toothpicks Figure 1: (1 x 3) + 7 = 10 toothpicks Figure 2: (2 x 3) + 7 = 13 toothpicks Figure 3: (3 x 3) + 7 = 16 toothpicks Figure 4: (4 x 3) + 7 = 19 toothpicks Formula:Number of toothpicks = (Figure number x 3) + 7 Number of toothpicks in Figure 52 = (52 x 3) + 7= 156 + 7 = 163 (c)(Figure number x 3) + 7 = 97Figure number x 3 = 97 - 7 = 90
Figure number = 90 ÷ 3 = 30
Answer(s): (a) 54; (b) 163; (c) 30
