Standard 1 : Use properties of operations to generate equivalent expressions. (Major Cluster) (Archived)



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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information

Number: MAFS.7.EE.1
Title: Use properties of operations to generate equivalent expressions. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 7
Domain-Subdomain: Expressions & Equations

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.7.EE.1.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MAFS.7.EE.1.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.7.EE.1.AP.1a: Add and subtract linear expressions that include like terms.
MAFS.7.EE.1.AP.1b: Factor and expand linear expressions.
MAFS.7.EE.1.AP.2a: Combine like terms in an expression.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorial

Name Description
Math Soup: Creating Equivalent Expressions by Combining Like Terms :

Learn how to combine like terms to create equivalent expressions in this cooking-themed, interactive tutorial.

Formative Assessments

Name Description
Equivalent Perimeters:

Students are asked to solve a geometric problem by simplifying an algebraic expression.

Rectangle Expressions:

Students are given equivalent expressions with rational coefficients and asked to explain what each expression represents within the context of the problem.

Explain Equivalent Expressions:

Students are given equivalent expressions with rational coefficients and asked to explain what each expression represents within the context of a problem.

Equivalent Rational Expressions:

Students are given a polynomial with rational coefficients and asked to identify equivalent expressions from a given list.

Factored Forms:

Students are given two expressions and asked to rewrite each in factored form using the fewest number of terms.

Identify Equivalent Multistep Expressions:

Students are given an expression and are asked to identify expressions equivalent to it.

Lesson Plans

Name Description
Gather Data For Distribution by Programming an App:

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Best Chicken Franchise for Me:

In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Using Positive and Negative Numbers in Context: This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures:
  • starting temperature + change in temperature = final temperature
  • final temperature – change in temperature = starting temperature
  • final temperature – starting temperature = change in temperature
Steps to Solving Equations:

This lesson unit is intended to help you assess how well students are able to form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help you identify and assist students who have difficulties in using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

Total Recall:

Using the notion of a broken robot, this lesson provides opportunities for students to apply different strategies and properties to expand, add, subtract, or multiply to determine equivalent expressions. The students will analyze their procedures and answers.

Equivalent Expressions?:

This lesson helps build the student's ability to see relationships and meanings of algebraic expressions. Students utilize prior knowledge of properties to identify equivalent expressions. Percent problems are not utilized in this lesson.

The Distributive Property:

Introductory lesson on the distributive property using word problems as context for area models.

Problem-Solving Tasks

Name Description
Equivalent Expressions?:

Students are asked to determine if two expressions are equivalent and explain their reasoning.

Miles to Kilometers:

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Tutorials

Name Description
Factor a Linear Expression by Taking a Common Factor:

This video demonstrates how to factor a linear expression by taking a common factor.

Combining Like Terms Introduction:

This introductory video teaches about combining like terms in linear equations.

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Unit/Lesson Sequence

Name Description
Variables and Patterns of Change: Translating Words Into Symbols; Linear Equations: Lesson Plan 1: Miles of Tiles - The Pool Border Problem, students will recognize patterns and represent situations using algebraic notation and variables. Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives, students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution. Students work in teams of four. Site includes a Topic Overview, Lesson Plans, Student Work, Teaching Strategies, Resources, and a video of Workshop 1; Part 1.


Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorial

Title Description
Math Soup: Creating Equivalent Expressions by Combining Like Terms :

Learn how to combine like terms to create equivalent expressions in this cooking-themed, interactive tutorial.

Problem-Solving Tasks

Title Description
Equivalent Expressions?:

Students are asked to determine if two expressions are equivalent and explain their reasoning.

Miles to Kilometers:

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Tutorials

Title Description
Factor a Linear Expression by Taking a Common Factor:

This video demonstrates how to factor a linear expression by taking a common factor.

Combining Like Terms Introduction:

This introductory video teaches about combining like terms in linear equations.

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Tasks

Title Description
Equivalent Expressions?:

Students are asked to determine if two expressions are equivalent and explain their reasoning.

Miles to Kilometers:

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Tutorial

Title Description
Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.