ALEX Classroom Resource

  

Grade 6 Mathematics Module 4, Topic A: Relationships of the Operations

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 4, Topic A: Relationships of the Operations

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

To begin Module 4, students are introduced to important identities that will be useful in solving equations and developing proficiency with solving problems algebraically. In Topic A, students understand the relationships of operations and use them to generate equivalent expressions (6.EE.A.3). By this time, students have had ample experience with the four operations since they have worked with them from kindergarten through Grade 5 (1.OA.B.3, 3.OA.B.5). The topic opens with the opportunity to clarify those relationships, providing students with the knowledge to build and evaluate identities that are important for solving equations. In this topic, students discover and work with the following identities: w - x + x = w, w + x - x = w, a divided by b times b = a, a times b divided by b = a (when b ≠ 0), and 3x = x + x + x. Students will also discover that if 12 divided x = 4, then 12 - x - x - x - x = 0.

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.
Tags: distributive, equivalent, expressions, operations, properties
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Comments

There are four lessons on this topic.

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  This resource provided by:  
Author: Hannah Bradley
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