Act One: Check out the video slide show. What questions do you have?
Suggested Question: How many different ways can I stack Jack? That is, how many different color arrangements are there? If I wanted to take a picture of every possible arrangement how many pictures would I need to take?
Act Two: What information would be useful here? Can you use a problem solving stategy such as “solve a simplier version of the problem” or “create an organized list?” Click here to see all of Jack’s pieces. Can you model the possibilities with colored pencils or strips of paper?
You can see a short video on determining permutations at this Khan Academy’s link. You might consider using the video after students have had their own opportunity to grapple with the number of arrangements for creating Jack. The video could be helpful for “cementing” the permutation formula, but only after kids have had ample opportunity to develop the formula on their own through the context of the Stacking Jack problem.
Act Three: StackingJack-solution-act1.pdf
CCSS: 7.SP.8 , HSS-CP.B.9
Sequel: I forgot that five of the six colored parts can be flipped over to make many more unique Stacked Jacks. Factoring this is in and using all parts, how many unique Stacked Jacks can you create?
Thanks to Newton South High School’s Math Department Head, Steven Rattendi, for helping us solve this Sequel.