Lesson 10.310.3 · Part II
Start hereWords, worked example, and sentence starters
Learning target I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.
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. |
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 · Part II
Apply Day · Version ASupported practice
Learning target I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.
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1Complete each step, then write the final answer.
Discs Moves 2 3 3 ? Use the rule “double, then add 1.” A 2-disc tower takes 3 moves. How many moves does a 3-disc tower take?
Show your workHint Double 3. Then add 1.
Final answer: -
2Complete each step, then write the final answer.
Towers of 3 and 4 discs take 7 and 15 moves. How many moves does a 5-disc tower take?
Show your workHint Find the rule from 7 to 15. Use it on 15.
Final answer: -
3Complete each step, then write the final answer.
A pattern uses the rule “double, then add 1.” It starts 3, 7. What number comes next?
Show your workHint Use the rule on 7.
Final answer:
Lesson 10.310.3 · Part II
Apply Day · Version BCore practice
Learning target I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.
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1Complete 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 workFinal answer: -
2Complete each step, then write the final answer.
A 10-disc tower takes 1,023 moves. How many moves does an 11-disc tower take?
Show your workFinal answer: -
3Complete each step, then write the final answer.
An 8-disc tower takes 255 moves. How many moves does a 9-disc tower take?
Show your workFinal answer:
Lesson 10.310.3 · Part II
Apply Day · ChallengeExtension
Learning target I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.
-
1Complete each step, then write the final answer.
A 3-disc tower takes 7 moves. Jay says a 6-disc tower takes 7 × 2 = 14 moves, because 6 is double 3. How many moves does a 6-disc tower take?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A pattern uses the rule “double, then add 1.” The 4th number is 79. What is the 1st number?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Each week, Maya doubles her savings and then adds $3. After 3 weeks, she has $53. How much money did she start with?
Show your workFinal answer: