6.AT.7 Lesson 6-8-part2 Apply Day · Practice
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6.8 · Part II

Application Practice for Today's Problem

Properties of Operations · Commutative Property

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.8 · Part II
1Properties of Operations
2Strategy Model — step by step
  1. Commutative Property: Order does not change sum or product
  2. Associative Property: Grouping does not change sum or product
  3. Identity Property: a + 0 = a; a · 1 = a
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

    Which property lets you rearrange 8 × 5 to 5 × 8?

    1. ACommutative Property
    2. BAssociative Property
    3. CIdentity Property
    4. DDistributive Property
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    Explain why the commutative property works for addition and multiplication but NOT for subtraction and division. Give a specific number example for each operation to prove your point.

    💬 Sentence Starter: Addition: ___ + ___ = ___ + ___ = ___ (works). Subtraction: ___ − ___ ≠ ___ − ___ because ___. Multiplication: ___ × ___ = ___ × ___ = ___ (works). Division: ___ ÷ ___ ≠ ___ ÷ ___ because ___.
    ✏️ Mathematical Justification & Response
📐 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