MPP.3 Lesson 1-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.1 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which set shows FIVE different correct decompositions of 78.5?

    1. A70 + 8.5, 78 + 0.5, 80 − 1.5, 39.25 × 2, 157 ÷ 2
    2. B70 + 8.5, 78 + 5, 80 − 1.5, 39.25 × 2, 157 ÷ 2
    3. C70 + 8.5, 78 + 0.5, 80 + 1.5, 39.25 × 2, 157 ÷ 2
    4. D70 + 8.5, 78 + 0.5, 80 − 1.5, 39.25 × 3, 157 ÷ 2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A wheel has 23 cars holding about 4 riders each. Dev rounds 23 to 20 and says “about 80.” Priya rounds to 25 and says “about 100.” The operator needs to know whether one full turn can clear a line of 95 people. Whose estimate is more useful here, and why?

    1. APriya's — a bigger estimate is always the safer one to plan with
    2. BNeither — only the exact answer 92 can be used for a decision
    3. CDev's — it is below the exact 92, so it will not promise the operator more room than the wheel has
    4. DBoth equally — they are both estimates of the same quantity
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Claim: “If you round BOTH numbers up before multiplying, your estimate can never come out below the exact answer.” For counts like cars and riders, is this claim always, sometimes, or never true?

    1. ASometimes — it depends which number you round first
    2. BSometimes — it fails when the two numbers are close together
    3. CNever — rounding up changes the answer unpredictably
    4. DAlways — each factor got bigger, so the product cannot get smaller
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which decomposition of 78.5 uses multiplication correctly?

    1. A39 × 2
    2. B39.25 × 2
    3. C39.25 × 3
    4. D78.5 × 2
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A wheel has 23 cars holding about 4 riders each. Dev rounds 23 to 20 and says “about 80.” Priya rounds to 25 and says “about 100.” The operator needs to know whether one full turn can clear a line of 95 people. Whose estimate is more useful here, and why?
    2. 2A classmate at our table answered:Neither — only the exact answer 92 can be used for a decision

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    The wheel has 23 cars holding about 4 riders each. Write an estimate that is deliberately a little LOW, and say how you made it low on purpose. Then say when a low estimate would be the responsible one to give.

    ✏️ 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