Aria made patterns using squares and ice-cream sticks and recorded the pattern in the table shown.
| Figure number |
Number of squares |
Number of ice-cream sticks |
| 1 |
3 |
10 |
| 2 |
4 |
13 |
| 3 |
5 |
16 |
| 4 |
6 |
19 |
- How many squares are needed for Figure 17?
- How many ice-cream sticks are needed for Figure 17?
- Which figure needs a total of 118 ice-cream sticks?
(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 17
= 17 + 2
= 19
(b) Pattern for the number for number of ice-cream sticks Figure 1: (1 x 3) + 7 = 10 ice-cream sticks Figure 2: (2 x 3) + 7 = 13 ice-cream sticks Figure 3: (3 x 3) + 7 = 16 ice-cream sticks Figure 4: (4 x 3) + 7 = 19 ice-cream sticks Formula:Number of ice-cream sticks = (Figure number x 3) + 7 Number of ice-cream sticks in Figure 17 = (17 x 3) + 7= 51 + 7 = 58 (c)(Figure number x 3) + 7 = 118Figure number x 3 = 118 - 7 = 111
Figure number = 111 ÷ 3 = 37
Answer(s): (a) 19; (b) 58; (c) 37
