MPP.7 Lesson 10-3-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.3 · Part II

Supported Application · Guided Entry to Today's Problem

puzzle · pattern

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 10.3 · Part II
1Algorithmic Thinking & Recursive Patterns
2Strategy Model — step by step
  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
3Mathematical Word Bank
  • puzzle (rompecabezas) — A problem designed to be played with — it has rules, a goal, and room to imagine solutions.
  • pattern (patrón) — Something that repeats or changes in a predictable way.
  • pattern rule (regla del patrón) — A rule that tells you how to get the next value in a pattern from the one before it.
  • predict (predecir) — To say what will happen before it happens, using a pattern or reasoning.
  • organize (organizar) — To arrange information — often in a table — so patterns become easier to see.
4Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    How many moves does a one-disc tower take? A two-disc tower?

    1. A1 move and 3 moves
    2. B1 move and 2 moves
    3. C2 moves and 4 moves
    4. D1 move and 4 moves
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    The number of discs in a Tower of Hanoi puzzle can vary. What NEVER varies?

    💬 Sentence Starter: The number of ___ never changes.<br>There are always ___ .
    ✏️ Mathematical Justification & Response
  2. 3 OPEN RESPONSE

    What does it mean to be playful with math? Use the Tower of Hanoi as your example.

    💬 Sentence Starter: Being playful with math means ___ .<br>With the Tower of Hanoi, I ___ .
    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
MPP.7 Lesson 10-3-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.3 · Part II

On-Level Application · Standard Rigor

puzzle · pattern

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 10.3 · Part II
1Algorithmic Thinking & Recursive Patterns
2The Structural Procedure
  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
3Mathematical Word Bank
  • puzzle (rompecabezas) — A problem designed to be played with — it has rules, a goal, and room to imagine solutions.
  • pattern (patrón) — Something that repeats or changes in a predictable way.
  • pattern rule (regla del patrón) — A rule that tells you how to get the next value in a pattern from the one before it.
  • predict (predecir) — To say what will happen before it happens, using a pattern or reasoning.
  • organize (organizar) — To arrange information — often in a table — so patterns become easier to see.
4Watch out
  • 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.
  1. 1 MULTIPLE CHOICE

    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. ADouble the number of steps and add 1
    2. BAdd 2 to the number of steps
    3. CAdd the number of discs to the steps
    4. DMultiply the number of steps by 3
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Use the pattern rule to complete the table: how many steps for a four-disc tower?

    1. A15 steps
    2. B14 steps
    3. C9 steps
    4. D28 steps
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    What is the minimum number of steps to solve a FIVE-disc Tower of Hanoi puzzle?

    1. A31 steps
    2. B15 steps
    3. C30 steps
    4. D35 steps
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
MPP.7 Lesson 10-3-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.3 · Part II

Extension &amp; Non-Routine Application

puzzle · pattern

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 10.3 · Part II
1Algorithmic Thinking & Recursive Patterns
2The Structural Procedure
  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
3Mathematical Word Bank
  • puzzle (rompecabezas) — A problem designed to be played with — it has rules, a goal, and room to imagine solutions.
  • pattern (patrón) — Something that repeats or changes in a predictable way.
  • pattern rule (regla del patrón) — A rule that tells you how to get the next value in a pattern from the one before it.
  • predict (predecir) — To say what will happen before it happens, using a pattern or reasoning.
  • organize (organizar) — To arrange information — often in a table — so patterns become easier to see.
4Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

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

    1. A63 steps
    2. B62 steps
    3. C36 steps
    4. D32 steps
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Look at the table a different way: 1 disc → 1, 2 discs → 3, 3 discs → 7, 4 discs → 15, 5 discs → 31. Which describes the relationship between the number of discs and the number of steps?

    1. AThe steps are 1 less than a doubling pattern: 2, 4, 8, 16, 32 each minus 1
    2. BThe steps are the number of discs multiplied by itself
    3. CThe steps are 6 times the number of discs, plus or minus 1
    4. DThe steps are the two previous step counts added together
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    The 15 Puzzle is a sliding puzzle with 15 tiles in a frame 4 tiles high by 4 tiles wide. You arrange the tiles from 1 to 15 by sliding one tile at a time into the open space. Sometimes it is solvable and sometimes it is not. How would you make an argument about whether a particular 15 Puzzle is solvable, using what this lesson taught about being playful?

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It