Use the distributive property to write equivalent numerical and algebraic expressions

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How can you represent the area of a diagram using numerical expressions? Students apply their knowledge of area and order of operations to match area diagrams with numerical expressions.

How can you represent the area of a diagram using numerical expressions? Students connect their knowledge of area and equivalent expressions to the commutative and distributive properties for day 2 of this investigation.

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.

Sal finds equivalent expressions by combining like terms and using the distributive property. [1:57]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Apply your critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to get you to recognize patterns and determine a rule.

This animated Math Shorts video explains how the distributive property can help students model and create equivalent expressions. In the accompanying classroom activity, students play a quick game where they identify common factors within an expression and work on a series of problems that expand their understanding of how to apply the distributive property. While the problems begin with whole number expressions, students soon work toward algebraic notation and eventually develop the idea that ax + bx can be rewritten as x(a + b).

Sal shows how to factor the expression 4x+18 into the expression 2(2x+9). [3:28]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Brush up on your math skills relating to equivalent expressions then try some practice problems to test your understanding.

Use this tool to strengthen understanding and computation of numerical expressions and equality using a balance scale.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Students participate in an icebreaker activity, finding a classmate whose card contains an expression equivalent to the expression on their own card. The resulting student pairs will be partners for this unit. Students spend time exploring the digital course. They learn new symbols for multiplication and detect possible errors in evaluating numeric expressions. The class discusses and decides upon norms for math class.Key ConceptsStudents evaluate numerical expressions and identify equivalent expressions. They explore why the order of operations affects calculation results and how to use parentheses to clearly describe the order of the operations.Goals and Learning ObjectivesEvaluate numerical expressions.Understand the reason for the order of operations and how to use parentheses in numerical expressions.Use the basic features of the application.Create and understand the classroom norms.Use mathematical reasoning to justify an answer.PreparationPrint out the Expressions Icebreaker cards. Select the number of pairs of Partner 1 and Partner 2 cards needed for your class. Shuffle the cards before distributing to students.Write on the board or chart paper: Find a classmate whose card has an expression that is equivalent to the expression on your card.Choose a hand signal or phrase for common activities, such as putting technology away and focusing on the teacher.

Learn about the competitive sport of fencing along with the resulting mathematical problems and equivalent expressions that help determine the number of matches played per tournament in this video from the Center for Asian American Media. This resource is part of the Math at the Core: Middle School Collection. [2:23]

An interactive simulation that teaches about equivalent, evaluating, and simplifying expressions through games and exercises building coin expressions. This simulation can either be downloaded or played online and includes handouts, lesson plans, and additional materials.

Find a quick, concise explanation of how to take the words from problems and substitute variables, operations and numbers to create an equivalent expression. Examples are given and clearly explained.

Explains what equivalent equations are and how to find out if two equations are equivalent. The video is accompanied by a downloadable transcript and quiz questions. [7:57]