Measure the pipe cleaner by using the grid below. How many units long is the pipe cleaner?
2a. What is the height of the pipe cleaner in the figure?
2b. The bottom part of the pipe cleaner is called the base. What is the length of he base in the figure?
2c. The area of the figure is the number of squares above the pipe cleaner, but no higher than the tops of the pieces bent upward. What is the area of the figure?
3a. Now straighten the pipe cleaner. Bend it again so that the length of each bent upward is 2. What is the length of the base of the pipe cleaner now?
3b. Place the pipe cleaner on the grid and find the area.
4. Continue straightening and bending the pipe cleaner so that the length of the piece bent upward is one unit larger each time. Record the results in the table below. You may stop when there is no longer enough pipe cleaner to continue.
| Height | Base | Area |
1 |
||
2 |
||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 |
5. Study the base and height columns. What happens to the base when the height increases by 1?
6. Study the base and height columns. What happens to the height when the base increases by 1?
7. Add the numbers in the height column to the corresponding numbers in the base column. What do you notice?
8. Study the height and the base columns in your table. Is there a relationship between the base and the height? Can you find a rule that describes how to obtain the base in your table from the height?
9. Find a rule for calculating the area from the base and the height.
10. Find a rule for calculating the area from the height alone.