Lesson 10.310.3 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| puzzleSpanish: rompecabezas | A problem designed to be played with — it has rules, a goal, and room to imagine solutions. | Tower of Hanoi: three rods, a stack of discs, and two rules. |
| patternSpanish: patrón | Something that repeats or changes in a predictable way. | Circle, square, triangle, circle, square, triangle … |
| pattern ruleSpanish: regla del patrón | A rule that tells you how to get the next value in a pattern from the one before it. | 1 → 3 → 7 → 15: the rule is “double it and add 1”. |
| predictSpanish: predecir | To say what will happen before it happens, using a pattern or reasoning. | We counted towers of 1, 2 and 3 discs. Reach PAST them: the rule says 5 discs takes 31 steps — before moving one. |
| organizeSpanish: organizar | To arrange information — often in a table — so patterns become easier to see. | Discs 1, 2, 3 in one column and steps 1, 3, 7 in the next. |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Move a 2-disc tower from Rod A to Rod C. Move one disc at a time. Never put a big disc on a small disc. What is the least number of moves?
- Picture the goal first.
- Move the small disc out of the way: small: A → B
- Move the big disc to Rod C: big: A → C
- Put the small disc on top: small: B → C
- A 2-disc tower takes 3 moves. A 1-disc tower takes only 1 move.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Discs: 1, 2, 3. Steps: 1, 3, 7. Find the pattern rule. Use it to find the steps for 4 discs and 5 discs.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
Word bank puzzlepatternpattern rulepredictorganize
Watch outA common mistake
Doubling the previous number of steps but forgetting to add 1 — answering 14 instead of 15 for four discs, or 30 instead of 31 for five.
Lesson 10.310.3 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions — one step at a time, with support.
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1Complete each step, then write the final answer.
Part Moves 2 discs off ? big disc ? 2 discs back ? Three parts solve a 3-disc tower. A 2-disc tower takes 3 moves. To move a 3-disc tower, move the top 2 discs off. Then move the big disc. Then move the 2 discs back on top. How many moves in all?
- 1How many moves does it take to move the top 2 discs off?
- 2How many moves for the big disc?
- 3How many moves to put the 2 discs back on top?
- 4Add the three parts. How many moves in all?
Final answer: -
2Complete each step, then write the final answer.
Part Moves 3 discs off ? big disc ? 3 discs back ? The top 3 discs move off, then back. A 3-disc tower takes 7 moves. Use the same three parts to solve a 4-disc tower. How many moves does it take?
- 1How many moves does it take to move the top 3 discs off?
- 2How many moves for the big disc? For the 3 discs back?
- 3How many moves in all?
- 4Write it with the rule “double, then add 1.”
Final answer: -
3Complete each step, then write the final answer.
A pattern starts at 4. The rule is “double, then add 1.” What is the 3rd number in the pattern?
Show your workHint Use the rule on 4 to get the 2nd number. Then use the rule again.
Final answer: -
4Complete each step, then write the final answer.
Discs Moves 6 63 7 ? A 6-disc tower takes 63 moves. How many moves does a 7-disc tower take?
Show your workHint Use the rule “double, then add 1” on 63.
Final answer: -
5Complete each step, then write the final answer.
Lee solves tower puzzles. A 7-disc tower takes 127 moves. Lee makes 1 move each second. How many seconds does an 8-disc tower take him?
Show your workHint First find the moves for 8 discs. Each move takes 1 second.
Final answer: -
6Complete each step, then write the final answer.
A 4-disc tower takes 15 moves. Sam says a 5-disc tower takes 16 moves, because it has 1 more disc. Is he right? How many moves does it take?
Show your workHint Sam only added 1 move. The rule says to double first.
Final answer:
Explain your thinkingWhy does one new disc double the old moves, then add 1? Talk about moving the small tower off and back.
Sentence starter First I move the small tower off, which takes ___ moves. · The rule is “double, then add 1” because ___.