Students represent problem situations using expressions and then evaluate the expressions for the given values of the variables.Key ConceptsAn algebraic expression can be written to represent a problem situation.To evaluate an algebraic expression, a specific value for each variable is substituted in the expression, and then all the calculations are completed using the order of operations to get a single value.Goals and Learning ObjectivesDevelop fluency in writing expressions to represent situations and in evaluating the expressions for given values.

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Students see how different expressions for percent of increase and percent of decrease problems represent different ways to solve these problems. Students use equivalent algebraic expressions to solve percent problems.Key ConceptsStudents have previously solved percent of increase and percent of decrease problems. In this lesson, they look at how percent problems can be represented by algebraic expressions. Seeing the relationship of these problems to various equivalent algebraic expressions helps students relate different ways of solving problems involving percent of increase or percent of decrease.For example, the sale price of a pair of jeans with original price p and discount of 10% can be represented as p − 0.1p, or just 0.9p. The first expression leads to a way of solving the problem in two steps; the second expression leads to a one-step solution. Similarly, the total price of an item with a cost c dollars and 5% tax can be written as c + 0.05c, or just 1.05c.Goals and Learning ObjectivesSolve percent of increase and percent of decrease problems using equivalent algebraic expressions.

Here is a site that clearly and thoroughly explains many topics related to algebraic expressions. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have been absent or who need additional instruction on this or many other topics.

Visualize a word problem in multiple ways to develop your problem solving skills. This video focuses on converting a problem with fractions into a one-variable equation and alternately modeling it using unit blocks.

Discover the importance of order of operations when solving an expression. This video focuses on implementing PEMDAS and demonstrates the reason we need order of operation by solving a single expression.

Simplify this tricky expression using the order of operations. Expression include negative numbers and exponents. [4:36]

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.

Exponents are near the top of the food chain when it comes to order of operations. See some examples from Sal Khan. [3:34]

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.

Not only will you learn how to multiply and divide rational expressions, but Purplemath shows you what common mistakes are made so you can avoid them.

Use this Purplemath lesson to learn everything you've ever wanted to know about simplifying rational expressions. You'll find great explanations and examples on this page.

An astrobiologist and a physicist explain how mathematics is universally critical to helping understand nature and the cosmos in this video from KAET. In the accompanying classroom activity, students discuss the mathematics in the video, including the use of algebra, and then practice writing, reading, and evaluating algebraic expressions in a class bingo game. [5:45]

Watch network engineer Diana Tootle explain how she uses math in her work in this video from KAET. In the accompanying classroom activity, students watch the video and then complete an activity involving an aspect of math that Ms. Tootle discusses: converting numbers between base 2 and base 10. [4:37]

Simplify expressions with rational numbers using the distributive property of multiplication. This student-generated video focuses on using the distributive property to create equivalent expressions when multiplying by negative numbers and fractions, which can then be simplified.

In this video segment from Cyberchase, Hacker and the CyberSquad race to reach the Good Vibration on staircases that grow at different rates and have steps of varying sizes.

This video will walk you step-by-step through the process of solving one-step linear equations by multiplication and division. [2:39]

Let's practice some two step equations, some of which require merging terms and using the distributive property. [13:50]

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.

Students are introduced to algebraic expressions that use more than one variable and have multiple solutions. They figure out combinations of two items at different costs, with each combination adding up to 100.

Find a quick, concise explanation of simplifying expressions. Examples are given and clearly explained.