ALEX Classroom Resource

  

Commutative and Associative Properties of Addition

  Classroom Resource Information  

Title:

 Commutative and Associative Properties of Addition

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh.math.nf.commprop/commutative-and-associative-properties-of-addition/

Content Source:

 PBS
Type: Audio/Video

Overview:

Generate equivalent expressions using two additive properties. This video focuses on using the associative and commutative properties of addition to combine like terms, simplify expressions, and create equivalent expressions.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
16. Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given contextual or mathematical problems which may be modeled by algebraic expressions, use properties of the operations to produce combined and re-written forms of the expressions that are useful in resolving the problem.
Teacher Vocabulary:
  • Properties of operations
  • Distributive property
  • Inverse property
  • Identity property
  • Commutative property
  • Associative property
  • Equivalent algebraic expressions
Knowledge:
Students know:
  • the properties of operations, including inverse, identity, commutative, associative, and distributive and their appropriate application to be able to generate equivalent algebraic expressions.
Skills:
Students are able to:
  • Accurately use the properties of operations on algebraic expressions to produce equivalent expressions useful in a problem solving context.
Understanding:
Students understand that:
  • The properties of operations used with numerical expressions are valid to use with algebraic expressions and allow for alternate but still equivalent forms of expressions for use in problem solving situations.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.16.1:Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
M.6.16.2: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
M.6.16.3: Combine terms that are alike of a given expression.
M.6.16.4: Recognize the property demonstrated in a given expression.
M.6.16.5: Simplify an expression by dividing by the greatest common factor.
Example: 18x + 6y = 6(3x + y).
M.6.16.6: Determine the greatest common factor in an algebraic expression.

Prior Knowledge Skills:
  • Define parentheses, braces, and brackets.
  • Define numerical expression.
  • Recognize expressions.
  • Apply properties of operations as strategies to add and subtract.
  • Recall properties of operations as strategies to add and subtract.
  • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
  • Define simple expression.
  • Recall simple equations.
  • Recognize properties of addition and multiplication.
  • Recall addition, subtraction, multiplication, division symbols.
  • Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
  • Apply properties of operations as strategies to multiply and divide.
Mathematics
MA2019 (2019)
Grade: 6
17. Determine whether two expressions are equivalent and justify the reasoning.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a contextual or mathematical situation that could be represented algebraically,
  • Explain by reasoning from the context why two expressions must be equivalent.
  • Use properties of operations and equality to verify if two algebraic expressions are equivalent or not.
Teacher Vocabulary:
  • Equivalent
  • Expressions
Knowledge:
Students know:
  • The properties of operations, including inverse, identity, commutative, associative, and distributive and their appropriate application to be able to determine whether two expressions are equivalent.
  • Conventions of order of operations.
Skills:
Students are able to:
  • Accurately use the properties of operations to produce equivalent forms of an algebraic expression when interpreting mathematical and contextual situations.
  • Use mathematical reasoning to communicate the relationships between equivalent algebraic expressions.
Understanding:
Students understand that:
  • Manipulation of expressions via properties of the operations verifies mathematically that two expressions are equivalent.
  • Reasoning about the context from which expressions arise allows for interpretation and meaning to be placed on each of the expressions and their equivalence.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.17.1: Define equivalent expressions.
M.6.17.2: Recognize equivalent expressions.
M.6.17.3: Substitute for the variable to find the value of a given expression.
M.6.17.4: Calculate a numerical expression.
M.6.17.5: Recognize that a variable without a written coefficient is understood to have a coefficient of one. (Ex. x = 1x).

Prior Knowledge Skills:
  • Use comparison symbols.
    Examples: >, =, or < .
  • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
  • Comparison symbols.
    Examples: >, =, and < .
  • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
  • Compare two fractions with the same numerator or the same denominator by reasoning about their size.
  • Recognize that comparisons are valid only when the two fractions refer to the same whole.
  • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • Convert fractions to decimals.
  • Compare two decimals to tenths.
  • Compare whole numbers.
  • Identify comparison symbols.
    Examples: >, <, and = .
Tags: additive, equivalent, expressions, like terms, simplify
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource contains supplemental materials to use with this lesson.

To access the materials click on the link for the supplemental materials in the upper right-hand corner of the webpage titled Support Materials for Teachers. 

  This resource provided by:  
Author: Kristy Lacks
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