Strand: EXPRESSIONS AND EQUATIONS (7.EE)

Use properties of operations to generate equivalent expressions (Standards 7.EE.1-2). Solve real-life and mathematical problems using numerical and algebraic expressions and equations (Standards 7.EE.3-4).
This lesson begins with students viewing this UEN-produced video which demonstrates the term additive inverse. The accompanying activity has students play a die game and create an equation equal to 0 as well as a word problem using additive inverse. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Algebra Four
This lesson contains a game activity designed to help students practice solving algebraic equations.
• Anna in D.C.
The purpose of this task is to give students an opportunity to solve a multi-step percentage problem that can be approached in many ways.
• Bookstore Account
The purpose of this task is for students to use algebra and the number line to understand why it makes sense that we sometimes represent debt using negative numbers. If we agree that depositing money in an account adds a positive number to the balance, and buying somethings subtracts a positive number from the balance, then it is natural to represent debt with negative numbers.
• Chapter 1 - Mathematical Foundation (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence.
• Chapter 3 - Mathematical Foundation (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations I.
• Chapter 3 - Student Workbook (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 7 student workbook. It covers Expressions and Equations I.
• Chapter 6 - Mathematical Foundation (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities.
• Chapter 6 - Student Workbook (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It focuses on these topics: Real-world equations and Inequalities.
• Commutative and Associative Equations
This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Discounted Books
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
• Drill Rig
The purpose of this task is to provide a context for multiplying and dividing signed rational numbers, providing a means for understanding why the signs behave the way they do when finding products.
• Equivalent Expressions?
The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.
• Expressions & Equations (7.EE) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 Cluster "Use properties of operations to generate equivalent expressions."
• Finding Patterns to Make Predictions
This activity asks students to identify and contemplate mathematical patterns that we see around us. They are asked to represent them in a table and predict the pattern to the 7th, 9th, and nth terms. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Finding Unknown Angles
In this Math Shorts video from the Utah Education Network students learn to find unknown supplementary, complementary, vertical and adjacent angles. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
• Gotham City Taxis
The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways.
• Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)
In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.
• Grade 7 Math Module 2: Rational Numbers (EngageNY)
In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers.This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation.
• Grade 7 Math Module 3: Expressions and Equations (EngageNY)
This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form. They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms.
• Grade 7 Math Module 4: Percent and Proportional Relationships (EngageNY)
In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 7 Unit 2: Expressions and Equations (Georgia Standards)
The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn how to solve multi- step equations and discuss the difference between equations and expressions. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.
• Guess My Number
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations.
• Linear Inequalities
This online tutorial is designed to help the student to understand the vocabulary of inequalities and then use addition, subtraction, multiplication and division to solve linear inequalities.
• 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.
• Repeating Decimal Rings
In this interactive activity you will explore the patterns that occur when expanding seventh and thirteenth fractions into decimals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Shrinking
Given information about how women's height decreases over time, students must calculate shrinkage amounts for two scenarios.
• Solving Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Linear Equations with Negative Numbers
This video is designed for students to learn a strategy to solve a linear equation that has a negative number as a solution. The classroom activity builds on this knowledge by requiring them to use the strategy to solve a series of equations with both positive and negative coefficients and solutions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Solving Linear Inequalities with Negative Numbers
Students will learn how to solve linear equations that have a negative number solution. They then solve a series of equations with both positive and negative coefficients and solutions in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Sports Equipment Set
The purpose of this task is to present students with a context that can naturally be represented with an inequality and to explore the relationship between the context and the mathematical representation of that context; thus, this is an intended as an instructional task.
• Stained Glass
The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project. The shape of the regions in the stained glass window are left purposefully unspecified, as one component skill of modeling with mathematics (MP4) is for students to make simplifying assumptions themselves.
• Steps to Solving Equations
This lesson unit is intended to help educators assess how well students are able to form and solve linear equations involving factorizing and using the distributive law.
• The Number System (7.NS) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System
• Ticket to Ride
The purpose of this instructional task is to illustrate how different, but equivalent, algebraic expressions can reveal different information about a situation represented by those expressions. This task can be used to motivate working with equivalent expressions, which is an important skill for solving linear equations and interpreting them in contexts. The task also helps lay the foundation for students' understanding of the different forms of linear equations they will encounter in 8th grade.
• Translating Word Problems into Equations
Seven steps are presented on this site showing the student how to translate word problems into a solvable equation.
• Valentine Cards: Exploring Relationships Between Variables
The exchange of Valentine's Day cards between students is the focus of this interactive activity. Students learn a technique to calculate the total number of cards exchanged between classes with differing numbers of students. They then look at a recursive pattern and try to find the math pattern that rules it. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Who is the better batter?
The purpose of this task is to give students a real-world context for comparing fractions where it is natural to convert the fractions to decimals or describe the situation in terms of percents.
• Writing and Using Inequalities video
This video introduces and explains the topic.
• Writing Expressions
This task requires students to write an expression for a sequence of operations.
• Writing, Solving and Graphing Inequalities in One Variable video
This a video introduction and explanation of the topic.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.