This is a great activity to introduce linear patterns, building tables from patterns and writing rules. A great exploration to develop the idea of slope, y-intercept, and linear equations.
Powerpoint is 29 slides with 13 different patterns showing pictures of the first 3 steps. Upon clicking it will show the number of cubes in the 4th, 5th, 10th, 100th, and nth step for each pattern.
Two worksheets are included. One has 2 patterns that I use as an introduction with the class. The second worksheet has 8 more for students to work on with Rainbow Centimeter Cubes. I use the powerpoint to discuss their solutions with them.
The directions for the worksheets say, "Create each step of the patterns using rainbow cubes. Decide how many cubes the 4 and 5 steps will take. Then predict how many the 10 and hundredth steps will take. Then write a rule for the total number of cubes in step “n”."