Session 2, Part D:
Counting Stairs

 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. You can use cubes or blocks to construct the stairs. Then 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

 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 3rd staircase. Imagine the rectangle made for the nth staircase. Write a rule to determine the number of blocks in the nth staircase.

Next > Part E: Summing Up

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