MPP.7 Lesson 10-3-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.3 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

puzzle · pattern · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Playing with math means playing with patterns
1We play with math by using our imagination and by looking for patterns or relationships that help us think logically — a pattern can tell us the answer to a puzzle we have not even played yet.
  • The objective is to move the whole stack of discs to another rod. The rules: move only one disc at a time, move only the top disc from a stack, and never place a larger disc on top of a smaller disc. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me imagine the solution first
  1. Before moving anything, I describe what the solved puzzle will look like: the discs in the same order — smallest on top to largest on bottom — but on a different rod.
  2. Then I play the small cases: a one-disc tower takes 1 move, and a two-disc tower takes 3 moves.
  3. A three-disc tower takes at least 7 moves. Small cases are how mathematicians play.
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

    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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 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. 5 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
  3. 6 OPEN RESPONSE

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

    💬 Sentence Starter: I can organize the information in a ___ .<br>That helps because ___ .
    ✏️ 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