Lesson 3: Math is PlayfulMPP.7

I can…

I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.

Key words

• puzzle — A problem to play with. It has rules and a goal.
• pattern — Something that repeats or changes by a rule.
• pattern rule — The rule that tells how to get the next number.
• predict — Say what will happen before it happens.
• organize — Put facts in a table so patterns are easy to see.

Steps

1. Before moving anything, I describe what the solved puzzle will look like: the discs in the same order — smallest on top to largest on bottom — but on a different rod.
2. Then I play the small cases: a one-disc tower takes 1 move, and a two-disc tower takes 3 moves.
3. A three-disc tower takes at least 7 moves. Small cases are how mathematicians play.

Try it

Use the pattern rule to predict how many steps a six-disc tower needs.

Check your answer

Check with your guided notes.

Sentence starter

I know ___ because ___.

Goal: I can describe a puzzle strategy using the words pattern, rule, and predict.