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

6.14 Small Group · Group 2

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

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 FILL TABLE

    Use the distributive property to expand each expression.

    Factored FormExpanded Form
    3(2x + 5)
    7(a − 4)
    2(3m + 8)
    5(6 − y)
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each factored form to its expanded form.

    1. 2(x + 9)
    2. 5(3n − 2)
    3. 4(a + 6)
    4. 3(7 − y)
    5. 6(2m + 1)
    6. 8(x − 3)
    • A2x + 18
    • B15n − 10
    • C4a + 24
    • D21 − 3y
    • E12m + 6
    • F8x − 24
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Light Cue 2: Expand 5(2 + n) to set two spotlight banks.

    1. A10 + 5n
    2. B10 + n
    3. C7 + 5n
    4. D10 + 5
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Light Cue 3: Expand 4(a + 2) for the back-row beam.

    1. A4a + 8
    2. B4a + 2
    3. Ca + 8
    4. D4a + 6
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Expand 6(n + 3) using the distributive property.

    1. A6n + 18
    2. B6n + 3
    3. Cn + 18
    4. D6n + 9
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — The Spotlight Only Hit One Term

    1. 1Light cue:3(x + 4)
    2. 2Distribute:3 × x + 4
    3. 3Simplify:3x + 4

    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