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.
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.
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.
What is the difference between staircase n and staircase n + 1? Close Tip
Suppose there are 37,401 blocks in the 273rd staircase. How many blocks are there in the 275th?