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

    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?

    1. ANot well — a community shares thinking and takes turns, so three voices went unheard
    2. BPerfectly — the answer was right, and that is all that matters
    3. CNot well — the talker should have stayed silent too
    4. DPerfectly — silent members were being respectful
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    What skills and knowledge do you bring to a group that help the group be successful?

    ✏️ Mathematical Justification & Response
  2. 3 OPEN RESPONSE

    Write THREE community agreements you would propose for our class — at least one for working together and one for working alone — and for each, say what it protects.

    ✏️ Mathematical Justification & Response
  3. 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
  4. 5 OPEN RESPONSE

    A classmate says: 'Math class would be better with no group work — thinking is private.' Using this lesson, write a respectful critique of that IDEA.

    ✏️ Mathematical Justification & Response
  5. 6 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
📐 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