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

10.3 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each move: legal or against the rules?

    Target Categories: Legal move Against the rules
    • Move the top disc of any stack
    • Place a small disc on a bigger disc
    • Move exactly one disc at a time
    • Move two discs at once
    • Place a big disc on a smaller disc
    • Pull a disc out from the middle of a stack
  2. 2 FILL TABLE

    Use the doubling pattern to complete the table of fewest moves.

    DiscsPattern: double the previous, add 1Fewest moves
    3
    4
    6
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
  2. 4 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
  3. 5 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
  4. 6 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
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 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