Stuck? Start here. Read the steps, try the problem, then check your answer.
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 designed to be played with — it has rules, a goal, and room to imagine solutions.
pattern — Something that repeats or changes in a predictable way.
pattern rule — A rule that tells you how to get the next value in a pattern from the one before it.
predict — To say what will happen before it happens, using a pattern or reasoning.
organize — To arrange information — often in a table — so patterns become easier to see.
Steps
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.
Then I play the small cases: a one-disc tower takes 1 move, and a two-disc tower takes 3 moves.
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.