6.AT.7 Lesson 6-15-group2 🟣 Group 2 · Challenge & Extension
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6.15 Small Group · Group 2

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

Simplify Algebraic Expressions · Like Terms · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we simplify by combining like terms?
1Only combine terms that have the same variable part; numbers without a variable combine with each other — 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
  1. The rooms need microphones and stands: (4 + 2 + 6) microphones and (3 + 5 + 1) stands.
  2. Microphones are like items, so I add: 4 + 2 + 6 = 12 microphones.
  3. Stands are like items, so I add: 3 + 5 + 1 = 9 stands.
  4. In algebra this is the same as 4m + 2m + 6m + 3s + 5s + 1s = 12m + 9s.
3Second Model — Try it together — then prove it
  1. Let's simplify 5x + 3x. Are these like terms?
  2. Yes, both have x, so we add the numbers in front: 5 + 3 = 8.
  3. So 5x + 3x = 8x.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Simplify Algebraic Expressions (Simplificar expresiones algebraicas) — Rewrite an expression in a shorter equivalent form by combining like terms and using properties.
  • Like Terms (Términos semejantes) — Terms with the same letter raised to the same power, like 2x and 5x.
  • Combine (Combinar) — To add or subtract terms with the same letter into one.
  • Simplify (Simplificar) — To rewrite an expression in a shorter form that is still equal to the original.
  • Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
  • Term (Término) — A single number, variable, or product of them, separated by + or − signs.
5Watch out
  • A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms — for example, simplifying 6x + 4 + 2x as 12x by adding all three numbers (6 + 4 + 2 = 12) instead of recognizing that 4 has no variable and cannot combine with 6x and 2x. The correct simplified expression is 8x + 4 (combine 6x + 2x = 8x, and let the 4 stay on its own). Before you submit, check that every term you combined has the exact same variable part.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Simplify each expression by combining like terms.

    ExpressionLike Terms CombinedSimplified
    3a + 5a + 2
    6x + 4 + 2x + 7
    10m − 3m + 5
    4y + 3 + y + 9
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each expression to its simplified form.

    1. 8x + 3x + 1
    2. 5a − 2a + 7
    3. 4n + n + 6
    4. 12y − 5y
    5. 3m + 8 + 4m + 2
    6. 9p + 1 − 3p
    • A11x + 1
    • B3a + 7
    • C5n + 6
    • D7y
    • E7m + 10
    • F6p + 1
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Simplify the track: 4a + 2 + a.

    1. A5a + 2
    2. B7a
    3. C5a²+ 2
    4. D6a
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Clean up this channel: 7y − 3y.

    1. A4y
    2. B10y
    3. C4
    4. D21y
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Simplify the mix: 6m + 4 + 3m.

    1. A9m + 4
    2. B13m
    3. C9m + 4m
    4. D10m
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — Crossed Channels on the Board

    1. 1Track:3x + 5
    2. 2Combine:Add the 3 and the 5
    3. 3Simplify:8x

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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