6.AT.7 Lesson 6-8-part2 Apply Day · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.8 · Part II

Second Practice Form · Independent Application and Spiral Review

Properties of Operations · Commutative Property

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.8 · Part II
1Properties of Operations
2The Structural Procedure
  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)?
  1. 1 MULTIPLE CHOICE

    Which property of operations is shown by the equation (7 + 4) + 6 = 7 + (4 + 6)?

    1. AAssociative Property of Addition
    2. BCommutative Property of Addition
    3. CIdentity Property of Addition
    4. DDistributive Property
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which property is shown? 5 + 13 = 13 + 5

    1. ACommutative Property
    2. BAssociative Property
    3. CIdentity Property
    4. DDistributive Property
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Which property is shown? (6 × 3) × 2 = 6 × (3 × 2)

    1. AAssociative Property
    2. BCommutative Property
    3. CIdentity Property
    4. DDistributive Property
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which property is shown? 47 + 0 = 47

    1. AIdentity Property
    2. BCommutative Property
    3. CAssociative Property
    4. DDistributive Property
    ✏️ Workspace & Solution Steps
📐 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.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It