MPP.3 Lesson 1-6-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.6 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • Problem solving is not one lightning bolt — it is a process you can name, practice, and share. And when the process stalls, getting stuck is part of doing math, not a sign you can't. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
3Mathematical 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.
4Watch 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

    You read a problem and have no idea where to start. According to this lesson, what does that mean?

    1. AYou are doing math — getting stuck is part of the process, and there are strategies to try
    2. BYou are not a math person
    3. CThe problem is broken and should be skipped
    4. DYou should wait silently until someone gives you the answer
    ✏️ Workspace & Solution Steps
  2. 2 DRAG SORT

    Sort each behavior by its effect on our math community.

    Target Categories: Builds our community Hurts our community
    • Asking a partner to explain their strategy
    • Comparing two different approaches to the same problem
    • Saying 'I disagree, because...' with a reason
    • Making sure every group member gets to talk
    • One student doing all the talking
    • Calling an answer 'wrong' with no reason
    • Keeping your strategy secret so you finish first
    • Laughing when someone makes a mistake
  3. 3 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    A bicycle rack holds 8 bikes, and each bike has 2 wheels. How many wheels are on the rack?

    1. A16
    2. B10
    3. C4
    4. D82
    ✏️ Workspace & Solution Steps
  2. 5 MULTIPLE CHOICE

    Another bicycle rack has 6 times as many wheels as the rack with 16 wheels. About how many wheels does it have?

    1. AAbout 96
    2. BAbout 22
    3. CAbout 66
    4. DAbout 616
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    Name TWO strategies from this lesson you can try when you get stuck on a problem.

    💬 Sentence Starter: When I get stuck I can ___ .<br>I can also ___ .
    ✏️ 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
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It