Joshua made patterns using squares and matchsticks and recorded the pattern in the table shown.
| Figure number |
Number of squares |
Number of matchsticks |
| 1 |
3 |
10 |
| 2 |
4 |
13 |
| 3 |
5 |
16 |
| 4 |
6 |
19 |
- How many squares are needed for Figure 18?
- How many matchsticks are needed for Figure 18?
- Which figure needs a total of 127 matchsticks?
(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 18
= 18 + 2
= 20
(b) Pattern for the number for number of matchsticks Figure 1: (1 x 3) + 7 = 10 matchsticks Figure 2: (2 x 3) + 7 = 13 matchsticks Figure 3: (3 x 3) + 7 = 16 matchsticks Figure 4: (4 x 3) + 7 = 19 matchsticks Formula:Number of matchsticks = (Figure number x 3) + 7 Number of matchsticks in Figure 18 = (18 x 3) + 7= 54 + 7 = 61 (c)(Figure number x 3) + 7 = 127Figure number x 3 = 127 - 7 = 120
Figure number = 120 ÷ 3 = 40
Answer(s): (a) 20; (b) 61; (c) 40
