MPP.3 Lesson 10-6-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.6 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

math biography · reflect · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Your math story, one year later
1We are all doers of math and use math in our daily lives. Our math stories continue to grow and evolve as we grow and advance — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me reread my September work
  1. In September I estimated the Ferris wheel: 20 cars with about 4 riders each is 20 × 4 = 80 riders — 'about 80.'
  2. Now I can go further with this year's math: at 6 turns an hour, that wheel moves about 80 × 6 = 480 riders per hour.
  3. Same wheel, same me — but my toolbox grew. That difference IS my math story.
3Second Model — Try it together — then prove it
  1. In September we decomposed 78.5 as 70 + 8.5 and 80 − 1.5.
  2. This year we learned new ways to say the same number: 78.5 = 157 ÷ 2.
  3. And with percents: 50% of 157 = 78.5.
  4. Find one more way to write 78.5 using something you learned this year.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • math biography (biografía matemática) — The story of your relationship with math — and how it has changed over time.
  • reflect (reflexionar) — To look back at what you did, felt, and learned, and think about what it means.
  • growth (crecimiento) — The change between what you could do before and what you can do now.
  • confidence (confianza) — Trusting yourself to try a problem, even when the first attempt might fail.
  • community (comunidad) — The people and places around you — where math shows up outside the classroom.
5Watch out
  • Treating your math story as finished — writing the same answers you wrote in Lesson 1-1 instead of looking for what actually changed. The story grows and evolves; a retrospective that copies September has missed the point.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Answer each quick problem with this year's skills — the same numbers you met in Lesson 1-1.

    Problem from this yearThinkingAnswer
    50% of 157
    10% of 480
    Riders per hour: 80 per turn × 6 turns
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each September estimate to the refined result your math produces now.

    1. 20 cars × about 4 riders each
    2. 80 riders × 6 turns each hour
    3. 78.5 written by place value
    4. 480 riders per hour for 3 hours
    • AAbout 80 riders per turn
    • B480 riders each hour
    • C(7 × 10) + (8 × 1) + (5 × 0.1)
    • D1,440 riders
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Which set shows THREE correct ways to write 78.5 using skills from this year?

    1. A157 ÷ 2, 50% of 157, 78½
    2. B157 ÷ 2, 50% of 157, 78¼
    3. C156 ÷ 2, 50% of 157, 78½
    4. D157 ÷ 2, 25% of 157, 78½
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    Ask a classmate about their math story. How has your classmate's math story changed since the beginning of the year?

    ✏️ Mathematical Justification & Response
  2. 5 OPEN RESPONSE

    In what areas are you more confident about math now? What are your strengths in math?

    ✏️ Mathematical Justification & Response
  3. 6 OPEN RESPONSE

    How have your math thinking HABITS changed from the beginning of the year to now? (Not what you know — how you think.)

    ✏️ Mathematical Justification & Response
✍️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It