6.AT.7 Lesson 6-14-group1 🟡 Group 1 · Support & Scaffolding
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6.14 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the distributive property?
1The number outside the parentheses gets "shared" with every term inside.
  • The distributive property means you can multiply a number by everything inside the parentheses, one piece at a time: a(b + c) = ab + ac. 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. 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.
3Mathematical 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.
4Watch 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
    2(x + 5)
    4(3 + 7)
    ✏️ Scratchpad / Reasoning
  2. 2 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
  2. 4 MULTIPLE CHOICE

    Expand 4(5 − 2) using the distributive property.

    1. A12
    2. B20 − 2
    3. C9
    4. D22
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Expand 3(x + 4) using the distributive property.

    1. A3x + 12
    2. B3x + 4
    3. Cx + 12
    4. D7x
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    When using the distributive property with a(b + c), you must multiply 'a' by:

    1. ABoth b and c
    2. BOnly b
    3. COnly c
    4. Db + c first, then multiply
    ✏️ Workspace & Solution Steps
🗣️ 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
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