Rebecca 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 59?
- How many ice-cream sticks are needed for Figure 59?
- Which figure needs a total of 106 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 59
= 59 + 2
= 61
(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 59 = (59 x 3) + 7= 177 + 7 = 184 (c)(Figure number x 3) + 7 = 106Figure number x 3 = 106 - 7 = 99
Figure number = 99 ÷ 3 = 33
Answer(s): (a) 61; (b) 184; (c) 33