Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.7

Lesson 10.310.3 Small Group · Group 2

Group 2 · Set BSecond challenge form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions, explain why the method works, and use it on a problem I have not seen before.

Remember10.3 Small Group · Group 2

A pattern rule can predict forward and be undone backward, and it works because each new disc doubles the old moves, plus one. A pattern rule also works backward. Undo each step of the rule to find the input.

Words: puzzle (rompecabezas)pattern (patrón)pattern rule (regla del patrón)predict (predecir)organize (organizar)

  1. 1Complete each step, then write the final answer.

    A 5-disc tower takes 31 steps. Use the pattern rule to find the steps for a 6-disc tower.

    Show your work
    Final answer:
  2. 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 work
    Final answer:
  3. 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 work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Use the rule “double, then add 1.” A 10-disc tower takes 1,023 moves. What is the smallest tower that takes more than 5,000 moves?

    Show your work
    Final answer:

Explain your thinkingWill a tower ever take an even number of moves? Use the rule “double, then add 1” to prove your answer.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help