MPP.3 Lesson 1-6-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.6 Small Group · Group 2

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

make sense of a problem · representation · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — When we do math, we solve problems
1We make sense of problems, look for patterns, choose representations and tools, make a plan, watch our progress, and shift strategies when needed — together and on our own — 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 work the wheel problem
  1. First I make sense of it: one rack holds 8 bikes, each bike has 2 wheels, so this rack has 8 × 2 = 16 wheels. The other rack has 6 times as many wheels — that is what I don't know yet.
  2. I choose a representation: 6 equal groups of 16. Then I make a plan: multiply.
  3. 16 × 6 = 96, so the other rack has about 96 wheels. I check my progress: 96 is 6 groups of 16, and 16 × 6 = 96, so my answer matches my plan.
3Second Model — Try it together — then prove it
  1. When we do math, sometimes we get stuck. What can we try?
  2. Think of questions to ask a classmate or the teacher. Visualize the problem or draw pictures of it.
  3. Think of problems we have seen like this before. Identify what we don't understand about the problem.
  4. Which of these have you actually used? Which will you try next time?
  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
  • make sense of a problem (comprender un problema) — To figure out what a problem is asking — what you know, and what you don't know yet.
  • representation (representación) — A way of showing a problem — a drawing, table, equation, or model — that helps you see it.
  • strategy (estrategia) — A plan of attack for a problem — and something you can switch when you get stuck.
  • critique (criticar constructivamente) — To examine an idea and say what is convincing or not — about the idea, never about the person.
  • community agreement (acuerdo comunitario) — A rule the whole class agrees to so that everyone can learn together.
5Watch out
  • Treating 'stuck' as a stop sign instead of a signal — waiting silently instead of trying a strategy: asking a question, drawing the problem, or recalling a similar problem.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    For the rack with 6 times as many wheels, Maya computes (8 × 2) × 6 = 96. Jon computes (8 × 6) × 2 = 96. Which statement describes the two strategies fairly?

    1. AOnly Maya's is right, because you must find the wheels before multiplying by 6
    2. BOnly Jon's is right, because bikes come before wheels in the problem
    3. CBoth are valid: Maya scales the wheels, Jon imagines 6 racks of bikes first — the grouping changes, the count does not
    4. DOne of them must have made an error, since they used different orders
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    You are solving a problem and realize your strategy is not making progress. What does the problem-solving process say to do?

    1. AKeep using the same strategy no matter what
    2. BNotice your progress has stalled and shift to a different strategy
    3. CErase everything and decide the problem is impossible
    4. DCopy a classmate's paper
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A third rack has HALF as many wheels as the 96-wheel rack. How many BIKES does it hold, and which plan gets there?

    1. A12 bikes — divide 96 by 6 and then by... something
    2. B24 bikes — halve the wheels (96 ÷ 2 = 48), then 2 wheels per bike gives 48 ÷ 2 = 24
    3. C48 bikes — half of 96 is 48, and that is the answer
    4. D192 bikes — double 96 because each bike has 2 wheels
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    Solve this with your full process, narrating each step: a rack has 16 wheels, and another rack has 6 times as many wheels. If a third rack held HALF as many wheels as the big rack, how many bikes would fit on it?

    ✏️ Mathematical Justification & Response
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A group solves a hard problem, but one student did all the talking while three stayed silent. By this lesson's standards, how did the GROUP do?
    2. 2A classmate at our table answered:Perfectly — the answer was right, and that is all that matters

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 OPEN RESPONSE

    A student answers: 'The second rack has 16 + 6 = 22 wheels.' Explain what they misread, why the wrong answer is SO much smaller than 96, and write the question you would ask to help them find it themselves.

    ✏️ 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