6.AT.7 Lesson 6-6-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.6 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Equivalent Expressions · Equivalent · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — When are two expressions equivalent?
1Equivalent expressions give the same answer for every value of the variable.
  • Two expressions are equivalent when they always give the same value, no matter what number you put in for the variable. They can look different but mean the same thing. 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
  1. Producer A wrote 3x + 2x + 10 and Producer B wrote 5x + 10. Are they equivalent?
  2. I test x = 4. For A: 3(4) + 2(4) + 10 = 12 + 8 + 10 = 30.
  3. For B: 5(4) + 10 = 20 + 10 = 30.
  4. Both give 30, and 3x + 2x is just 5x, so they are equivalent.
3Mathematical Word Bank
  • Equivalent Expressions (Expresiones equivalentes) — Expressions that look different but have the same value for every allowed variable value.
  • Equivalent (Equivalente) — Expressions that always have the same value.
  • Simplify (Simplificar) — To rewrite an expression in a shorter form that is still equal to the original.
  • 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.
  • Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
4Watch out
  • A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms — writing 3x + 2x as 5x² instead of 5x. Remember: 3x means 3 groups of x and 2x means 2 more groups of x, so you add the coefficients (3 + 2 = 5) and keep the variable's power the same (x¹, not x²).
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Producer A wrote 2(x + 3) for a beat's cost. Which expression is equivalent?

    1. A2x + 6
    2. B2x + 3
    3. Cx + 6
    4. D2x + 5
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A track stacks 3x and then one more x. Which expression is equivalent to 3x + x?

    1. A4x
    2. B3x²
    3. C4
    4. D3x
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Producer B flipped a formula to 5 + 2x. Which expression is equivalent?

    1. A2x + 5
    2. B7x
    3. C10x
    4. D5x + 2
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Distributive Mistake

    1. 1Expression:3(x + 4)
    2. 2Distribute:Multiply the 3 by the first term only: 3 · x + 4
    3. 3Result:3(x + 4) = 3x + 4

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Combining Mistake

    1. 1Expression:7x + 3 + 2x
    2. 2Combine:Combine every number you see: 7x + 2x + 3 = 9x + 3, then add the 9 and 3 too
    3. 3Result:7x + 3 + 2x = 12x

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Level 2 Extension — The False Remix

    1. 1Expression:2x + 6
    2. 2Claim:2x and 6 are like terms, so combine them
    3. 3Result:2x + 6 = 8x

    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
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