Observe the toothpick pattern below:
(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.
Solution:
(a)The completed table is as follows:
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 7 | 10 | 13 | 16 | 19 |
(b) & (c) The graph of the given table is drawn below:
For pattern number 7 the number of tooth picks is 22 and for pattern number 8 the number of toothpicks is 25
(d)The points on the graph can be joined find out the number of toothpicks for not only patterns 7 and 8, but patterns beyond.
✦ Try This: Observe the toothpick pattern given below:
(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 13 |
(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.
(a) The table can be completed as shown below:
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 3 | 5 | 7 | 9 | 11 | 13 |
(b)The graph of the above table is given below
For pattern number 7 the number of tooth picks is 15 and for pattern number 8 the number of toothpicks is 17
(c) Joining the points helps to find the number of tooth picks for any pattern number.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 15
NCERT Exemplar Class 8 Maths Chapter 12 Problem 78
Observe the toothpick pattern below: (a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms. (b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30. (c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them. (d) Would it make sense to join the points on this graph? Explain.
Summary:
The table with the help of which the graph is plotted in the solution above shows the number of toothpicks used for making different patterns.
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