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

10.3 · Part II

Second Practice Form · Independent Application and Spiral Review

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

    (Lesson 10.1) A planter is 4 feet long and 2 feet wide. What is its area?

    1. A8 square feet
    2. B6 square feet
    3. C12 square feet
    4. D2 square feet
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    (Lesson 10.1) That same planter is 4 feet long, 2 feet wide, and needs soil 1 foot deep. How much soil does the gardener need?

    1. A8 cubic feet
    2. B7 cubic feet
    3. C8 square feet
    4. D4 cubic feet
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Why is finding a pattern MORE powerful than just solving the three-disc puzzle by hand?

    1. AThe pattern predicts the answer for towers you have never played, like five or six discs
    2. BThe pattern lets you skip the rules of the puzzle
    3. CPatterns make the discs move by themselves
    4. DA pattern proves the puzzle is impossible
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Why is finding a pattern MORE powerful than just solving the three-disc puzzle by hand?

    1. AThe pattern predicts the answer for towers you have never played, like five or six discs
    2. BThe pattern lets you skip the rules of the puzzle
    3. CPatterns make the discs move by themselves
    4. DA pattern proves the puzzle is impossible
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

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

    1. A7 moves
    2. B3 moves
    3. C6 moves
    4. D9 moves
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

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

    1. APlacing a larger disc on top of a smaller disc
    2. BMoving one disc at a time
    3. CMoving the top disc from a stack
    4. DPlacing a smaller disc on top of a larger disc
    ✏️ Workspace & Solution Steps
  7. 7 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 8 OPEN RESPONSE

    How can you ORGANIZE the information about discs and moves to help you see patterns?

    ✏️ Mathematical Justification & Response
  2. 9 OPEN RESPONSE

    The summary says playing with math lets us think differently by looking for patterns AND by imagining ways to visualize a problem. Describe how you used BOTH of those with the Tower of Hanoi.

    ✏️ 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