MPP.3 Lesson 1-1-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.1 Small Group · Group 2

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

doer of math · math story · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — We are all doers of math
1Everyone uses math daily. We do it differently, and sharing how we do it makes all of us better at it — 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 estimate the Ferris wheel
  1. The Ferris wheel has 20 cars, and about 4 people fit in each car. About how many people can ride at one time?
  2. I count the cars: 20. Then I estimate how many riders fit in one car: about 4.
  3. I do not count every person — an estimate is a reasoned answer that is close enough to be useful.
  4. 20 × 4 = 80, so I would say “about 80 people.”
3Second Model — Try it together — then prove it
  1. 5 = 70 + 8.5.
  2. 5 = 78 + 0.5.
  3. 5 = 80 − 1.5.
  4. Every one of those is the same number wearing different clothes. Find two more.
  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
  • doer of math (persona que hace matemáticas) — Anyone who uses mathematical thinking — which is everyone, every day.
  • math story (historia matemática) — Your own history with mathematics — what you have done, felt, and learned so far.
  • strength (fortaleza) — Something you already do well and can share with others.
  • decompose (descomponer) — To break a number into parts that add, subtract, multiply, or divide back to it.
  • estimate (estimar) — A reasoned answer that is close enough to be useful, without counting every one.
5Watch out
  • Believing that 'doing math' only counts when it happens on paper in a classroom.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Use mental math to complete each Ferris wheel estimate.

    SituationEstimateAnswer
    20 cars, each holding about 4 riders
    About 80 riders each turn, 6 turns in an hour
    About 480 riders each hour, for 2 hours
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each number to a correct decomposition.

    1. 78.5
    2. 78.5 using multiplication
    3. 480
    4. 12.5
    • A70 + 8 + 0.5
    • B(7 × 10) + (8 × 1) + (5 × 0.1)
    • C6 × 80
    • D12 + 0.5
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Estimating 23 × 4, Sam rounds 23 to 20. Nia instead splits it: 23 × 4 = (20 × 4) + (3 × 4). Which comparison is accurate?

    1. ASam's is faster but loses 12 riders; Nia's takes one more step and lands exactly on 92
    2. BBoth give exactly 92, so there is no difference between them
    3. CNia's is an estimate too, because she broke the number apart
    4. DSam's is the only real estimate, so Nia's method does not count
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    The operator removes 3 cars for repairs, so the 23-car wheel now runs 20 cars, and adds a fifth seat to every car. Without multiplying it out, what happens to the number of riders in one turn?

    1. AIt goes up — losing 3 cars costs about 12 riders, but a fifth seat in 20 cars adds 20
    2. BIt stays the same — one change up and one change down cancel out
    3. CIt goes down — removing cars always matters more than adding seats
    4. DThere is no way to tell without doing the multiplication
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    At the same fair, a food stand sells about 38 drinks an hour and is open 7 hours. Estimate the drinks sold in a day, using a strategy of your choice. Then describe a DIFFERENT strategy a classmate could reasonably use, and say what each one is better for.

    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    Ask a classmate about their math story. What is one way their story is DIFFERENT from yours?

    ✏️ 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