6.AT.7 Lesson 6-8-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.8 Small Group · Group 1

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

Properties of Operations · Commutative Property · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What are the properties of operations?
1Changing the order or the grouping of numbers being added or multiplied does not change the answer.
  • Properties are math rules that are always true. The Commutative Property lets you change the order. The Associative Property lets you change the grouping (the parentheses). 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. I have 3 guitarists, 5 drummers, and 2 keyboard players.
  2. I can add them as 3 + 5 + 2, which gives 10.
  3. The Commutative Property says order does not matter: 5 + 3 + 2 also gives 10.
  4. The Associative Property says grouping does not matter: (3 + 5) + 2 = 3 + (5 + 2), both equal 10.
3Mathematical Word Bank
  • Properties of Operations (Propiedades de las operaciones) — Rules that let you reorder or regroup numbers without changing an expression's value.
  • Commutative Property (Propiedad conmutativa) — You can change the order and get the same answer.
  • Associative Property (Propiedad asociativa) — You can change the grouping and get the same answer.
  • Identity Property (Propiedad de identidad) — Adding 0 or multiplying by 1 keeps the same value.
  • Property (Propiedad) — A rule that is always true in math.
  • Distributive Property (Propiedad distributiva) — Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.
4Watch out
  • A common mistake in Properties of Operations is applying the commutative property where it does not belong, or confusing it with the associative property. Students often assume 15 − 8 = 8 − 15 (it does not: 7 ≠ −7 — commutative only works for addition and multiplication), or they see parentheses move and call it "associative" even when the numbers inside just swapped places, like (2 + 3) + 4 = (3 + 2) + 4 (that is commutative — the order inside the parentheses changed, not the grouping). Before you label a property, ask: did only the order change (commutative), did only the grouping change (associative), or was a 0 or 1 involved (identity)?
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Track 2 on the playlist plays 5(7 + 2) = 5 × 7 + 5 × 2. Which property is this?

    1. ADistributive Property
    2. BCommutative Property
    3. CAssociative Property
    4. DIdentity Property
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Track 3 plays (7 + 3) + 5 = 7 + (3 + 5). Only the parentheses moved. Which property is this?

    1. AAssociative Property
    2. BCommutative Property
    3. CDistributive Property
    4. DIdentity Property
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Track 4 plays 1 × y = y. Which property is this?

    1. AIdentity Property
    2. BDistributive Property
    3. CCommutative Property
    4. DAssociative Property
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Statement:4 + 0 = 4
    2. 2Student's label:This shows the Commutative Property.
    3. 3Reasoning:The numbers 4 and 0 switched places, so it must be commutative.

    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 — Catch the Mislabeled Track

    1. 1Track:3(a + b) = 3a + 3b
    2. 2Student's label:This shows the Associative Property.
    3. 3Reasoning:There are parentheses, so the grouping must have changed.

    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 Property Error

    1. 1Statement:15 − 8 = 8 − 15
    2. 2Student's claim:This shows the Commutative Property of Subtraction.
    3. 3Reasoning:I switched the order, so it must be commutative.

    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