6.AT.7 Lesson 6-15-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.15 Small Group · Group 2

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

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

    Simplify 7x + 3x.

    1. A10x
    2. B10x²
    3. C21x
    4. D73x
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Simplify 9n + 4 + 2n.

    1. A11n + 4
    2. B15n
    3. C11n² + 4
    4. D92n + 4
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Simplify the mix: 6m + 4 + 3m.
    2. 2A classmate at our table answered:10m

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Spot the Mistake — Swept-Up Constant

    1. 1Expression:6x + 4 + 2x
    2. 2Combine:Add everything: 6 + 4 + 2 = 12
    3. 3Simplify:12x

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Find the Simplification Error

    1. 1Expression:5x + 3 + 2y + 4x
    2. 2Combine:5x + 2y + 4x + 3
    3. 3Simplify:11xy + 3

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 OPEN RESPONSE

    Three students simplified 4x + 3 + 2x + 5 + x differently. Student A got 7x + 8. Student B got 7x² + 8. Student C got 6x + 9. Who is correct? Explain the mistakes the other two students made.

    ✏️ 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