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
Which statement best shows what this lesson means by 'math is playful'?
Check your answer
We play with math by imagining possible solutions and looking for patterns that help us think logically about puzzles
The summary names both moves: imagining different ways to visualize the problem, and looking for patterns or relationships that help us think logically.
Sentence starter
I know ___ because ___.
Goal: I can describe a puzzle strategy using the words pattern, rule, and predict.