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

Lesson 10.310.3 · Part II

Apply Day · Set BSecond 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.

Remember10.3 · Part II

Algorithmic Thinking & Recursive Patterns

  1. Deconstruct complex multi-step problems into smaller, repeatable sub-tasks
  2. Trace patterns from simple cases to formulate general mathematical rules
  3. Verify algorithmic rules across edge cases and increasing problem sizes

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

  1. 1Complete 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 work
    Final answer:
  2. 2Complete each step, then write the final answer.
    DiscsMoves
    663
    7?

    A 6-disc tower takes 63 moves. How many moves does a 7-disc tower take?

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

    A pattern uses the rule “double, then add 1.” The 4th number is 95. What is the 1st number?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    SquaresToothpicks
    14
    27
    310
    6?
    Look from each row to the next row.

    Toothpicks make a row of squares. 1 square uses 4 toothpicks. 2 squares use 7. 3 squares use 10. How many toothpicks do 6 squares use?

    Show your work
    Final answer:
  5. 5Complete 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:
  6. 6Circle the letter of the best answer. Show how you know.

    A five-disc tower takes 31 steps. Using the pattern rule, how many steps would a SIX-disc tower take?

    1. A32 steps
    2. B36 steps
    3. C62 steps
    4. D63 steps
    Show your work
  7. 7Circle the letter of the best answer. Show how you know.

    What is the fewest number of moves needed to solve a three-disc Tower of Hanoi puzzle?

    1. A3 moves
    2. B6 moves
    3. C7 moves
    4. D9 moves
    Show your work
  8. 8Circle the letter of the best answer. Show how you know.

    Which move is against the rules of the Tower of Hanoi?

    1. AMoving one disc at a time
    2. BMoving the top disc from a stack
    3. CPlacing a larger disc on top of a smaller disc
    4. DPlacing a smaller disc on top of a larger disc
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    What will the solved puzzle look like?

    1. AThe discs in the same order — smallest on top to largest on bottom — but on a different rod
    2. BThe discs in reverse order, largest on top
    3. CThe discs spread out with one disc on each rod
    4. DThe discs back on the starting rod in any order
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help