6.AT.7 Lesson 6-14-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.14 Small Group · Group 1

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

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Light Cue 1: Expand 3(x + 4) for the stage-light controller.

    1. A3x + 12
    2. B3x + 4
    3. Cx + 12
    4. D3x + 7
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Expression:4(n + 3)
    2. 2Distribute:4 × n + 3
    3. 3Simplify:4n + 3

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 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
  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
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