Session 2, Part D: Counting Stairs

Session 2, Part D:
Counting Stairs (60 minutes)

Problem D1

Here is a problem in which you can use patterns to make predictions.

Count the number of blocks in each of the following staircases. Then use the Interactive Activity to devise as many general methods as you can for predicting the number of blocks in any staircase. If you come up with a rule for predicting the number of blocks, explain why the rule works. If you used a variable in your rule, explain the meaning of the variable.
Note 10

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. If you prefer, you can view the low-tech version of this acivity, which doesn't require the Flash plug-in.


Problem D2
If someone tells you how many blocks there are in staircase n, describe how you could use that to find the number of blocks in staircase n + 1. Note 11

What is the difference between staircase n and staircase n + 1? Close Tip


Problem D3
Suppose there are 37,401 blocks in the 273rd staircase. How many blocks are there in the 275th?

Use what you learned in Problem D2. Close Tip


Problem D4
How many blocks are there in the 100th staircase?

As in Part A, try to do this problem by using prediction rather than just by extending the table. Close Tip

Problem D5

Look at the following geometric solution for the third staircase. Imagine the rectangle made for the nth staircase. Write a rule to determine the number of blocks in the nth staircase.

Blocks image

Next > Part E: Summing Up

Session 2: Index | Notes | Solutions | Video