Math is Playful

MPP.7 · Unit 10 · Lesson 3

Name   Period

Objectives / Objetivos

Content Objective: I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions.

Language Objective: I can describe a puzzle strategy using the words pattern, rule, and predict.

Key Idea / Idea clave

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

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
puzzle
rompecabezas		A problem designed to be played with — it has rules, a goal, and room to imagine solutions.
Un problema diseñado para jugarse: tiene reglas, una meta y espacio para imaginar soluciones.
pattern
patrón		Something that repeats or changes in a predictable way.
Algo que se repite o cambia de una manera predecible.
pattern rule
regla del patrón		A rule that tells you how to get the next value in a pattern from the one before it.
Una regla que te dice cómo obtener el siguiente valor de un patrón a partir del anterior.
predict
predecir		To say what will happen before it happens, using a pattern or reasoning.
Decir lo que va a pasar antes de que pase, usando un patrón o el razonamiento.
organize
organizar		To arrange information — often in a table — so patterns become easier to see.
Ordenar la información, muchas veces en una tabla, para que los patrones sean más fáciles de ver.

Practice Preview / Vista previa de práctica

  1. What is the fewest number of moves needed to solve a three-disc Tower of Hanoi puzzle?
    1. 7 moves
    2. 3 moves
    3. 6 moves
    4. 9 moves
  2. The table shows 1 disc → 1 step, 2 discs → 3 steps, 3 discs → 7 steps. What is the pattern rule for the number of steps when you add one more disc?
    1. Double the number of steps and add 1
    2. Add 2 to the number of steps
    3. Add the number of discs to the steps
    4. Multiply the number of steps by 3
  3. Use the pattern rule to complete the table: how many steps for a four-disc tower?
    1. 15 steps
    2. 14 steps
    3. 9 steps
    4. 28 steps
  4. A five-disc tower takes 31 steps. Using the pattern rule, how many steps would a SIX-disc tower take?
    1. 63 steps
    2. 62 steps
    3. 36 steps
    4. 32 steps

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: