6.AT.7 Lesson 6-6-part2 Apply Day · Practice
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6.6 · Part II

Application Practice for Today's Problem

Equivalent Expressions · Equivalent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.6 · Part II
1Equivalent Algebraic Expressions
2Strategy Model — step by step
  1. Equivalent expressions produce the same value for any substitution of the variable
  2. Simplify expressions using algebraic properties (Distributive, Commutative, Associative)
  3. Test equivalence by substituting two different test numbers
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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    Simplify: 5n + 2n

    1. A7n
    2. B10n
    3. C7n²
    4. D52n
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    A student says 2x + 3 and 5x are equivalent because both equal 5 when x = 1. Is the student correct? Explain why testing one value is not enough to prove equivalence, and find a value of x where they give different results.

    💬 Sentence Starter: The student is ___ because ___. When x = 1: 2(1) + 3 = ___ and 5(1) = ___. But when x = ___: 2(___) + 3 = ___ and 5(___) = ___. To prove equivalence, expressions must be equal for ___ values of x.
    ✏️ 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
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