Math is Playful
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 / Término | Definition / 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
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the fewest number of moves needed to solve a three-disc Tower of Hanoi puzzle?
- A 3 moves
- B 6 moves
- C 7 moves
- D 9 moves
Answer:
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?
- A Add 2 to the number of steps
- B Add the number of discs to the steps
- C Multiply the number of steps by 3
- D Double the number of steps and add 1
Answer:
3. Use the pattern rule to complete the table: how many steps for a four-disc tower?
- A 9 steps
- B 14 steps
- C 15 steps
- D 28 steps
Answer:
4. A five-disc tower takes 31 steps. Using the pattern rule, how many steps would a SIX-disc tower take?
- A 32 steps
- B 36 steps
- C 62 steps
- D 63 steps
Answer:
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: