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

1.6 Small Group · Group 2

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

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 FILL TABLE

    Use the bicycle rack problem to complete the table.

    QuestionThinkingAnswer
    Wheels on a rack of 8 bikes
    Wheels on the bigger rack (6 times as many)
    Bikes on the bigger rack
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each stuck moment to the strategy that gets you unstuck.

    1. My strategy is not making progress
    2. I don't understand the problem
    3. My answer looks unreasonable
    4. My partner got a different answer
    • ATry a different entry point
    • BRestate it in your own words
    • CCheck it against an estimate
    • DCompare steps and find where they differ
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Priya tries to answer 'how many bikes fit 96 wheels?' by drawing every single wheel. After two minutes she has 30 wheels drawn and is losing track. By this lesson's process, what should she do?

    1. ANotice the strategy is not making progress and shift — her drawing already shows every 2 wheels is a bike, so compute 96 ÷ 2
    2. BKeep drawing: quitting a strategy means the strategy failed
    3. CErase everything and start guessing numbers
    4. DDecide the problem is unsolvable and move on
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    You are working on your own and get stuck. Which move follows BOTH parts of our working-alone agreements?

    1. ATry a get-unstuck strategy first, then quietly ask for help without interrupting classmates unnecessarily
    2. BImmediately call across the room to a friend
    3. CSit silently for the rest of class without seeking help
    4. DTake a classmate's paper to see their work
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Write your own 'times as many' problem about our school that a classmate could solve, and build in the trap from this lesson (a reader might add instead of multiply). Then give the correct answer AND the trap answer, with a sentence telling them apart.

    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    A classmate claims: 'Group work slows me down — I solve faster alone.' Using the rack problem, write a respectful response that names ONE specific mathematical thing a partner caught or contributed that solo work would likely miss.

    ✏️ 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