6.AT.7 Lesson 6-14-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.14 Small Group · Group 2

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

The Distributive Property · Distributive Property · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is the distributive property?
1The number outside the parentheses gets "shared" with every term inside — 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. Each bundle has a ticket ($15) and a snack ($5). For 3 bundles I can write 3(15 + 5).
  2. Way 1: add inside first. 15 + 5 = 20, then 3 × 20 = 60.
  3. Way 2: distribute the 3 to each part. 3 × 15 + 3 × 5.
  4. That is 45 + 15 = 60.
  5. Both ways give $60, so 3(15 + 5) = 3 × 15 + 3 × 5.
3Second Model — Try it together — then prove it
  1. Let's expand 2(8 + 3). Where does the 2 go?
  2. We multiply the 2 by each term: 2 × 8 + 2 × 3.
  3. That is 16 + 6 = 22. So 2(8 + 3) = 22.
  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
  • The Distributive Property (La propiedad distributiva) — Multiply a factor by every term inside parentheses.
  • Distributive Property (Propiedad distributiva) — Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.
  • Factor (Factor) — A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
  • Expand (Desarrollar) — To multiply out the parentheses in an expression.
  • Equivalent (Equivalente) — Expressions that always have the same value.
  • Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
5Watch out
  • The most common mistake in The Distributive Property is multiplying the outside factor by only the FIRST term inside the parentheses and forgetting the second — for example, writing 3(x + 4) = 3x + 4 instead of 3x + 12. Before you submit, check: did the outside number reach BOTH terms inside the parentheses?
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Which expression is NOT equivalent to 6x + 12?

    1. A6(x + 12)
    2. B6(x + 2)
    3. C2(3x + 6)
    4. D3(2x + 4)
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Factor 12x + 18 using the GCF.

    1. A6(2x + 3)
    2. B2(6x + 9)
    3. C12(x + 18)
    4. D6(2x + 18)
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Factor 24a + 16 completely, using the GCF.

    1. A8(3a + 2)
    2. B4(6a + 4)
    3. C8(3a + 8)
    4. D16(a + 1)
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Factor 12x + 18 using the GCF.
    2. 2A classmate at our table answered:2(6x + 9)

    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 Common Mistake

    1. 1Expression:5(3x + 2)
    2. 2Distribute:5 × 3x + 2
    3. 3Simplify:15x + 2

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Distributive Error

    1. 1Expression:5(2x + 4)
    2. 2Distribute:5 × 2x + 4
    3. 3Simplify:10x + 4

    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
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