# Standard 1: Generate equivalent algebraic expressions.

General Information
Number: MA.8.AR.1
Title: Generate equivalent algebraic expressions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.8.AR.1.AP.1
Use the properties of integer exponents and product/quotient of powers with like bases to produce equivalent algebraic expressions limited to positive exponents and monomial bases.
MA.8.AR.1.AP.2
Use the distributive property to multiply a monomial by a linear expression.
MA.8.AR.1.AP.3
Rewrite the sum of two linear algebraic expressions having a common whole number monomial factor as the common factor multiplied by the sum of two linear algebraic expressions.

## Related Resources

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

## Formative Assessment

Factored Forms:

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

Type: Formative Assessment

## Lesson Plans

Pythagorean Perspective:

This lesson serves as an introductory lesson on the Pythagorean Theorem and its converse. It has a hands-on discovery component. This lesson includes worksheets that are practical for individual or cooperative learning strategies. The worksheets contain prior knowledge exercises, practice exercises and a summative assignment.

Type: Lesson Plan

For a given circle m and point A in a coordinate plane, students will be able to show whether this given point A lies on the circumference of the given circle m using the Pythagorean Theorem. Subsequently, this can be used to prove that an airplane lies within or outside the radar's range with a given radius of detection.

Type: Lesson Plan

Geometree Thievery:

This geometry lesson focuses on partitioning a segment on a coordinate grid in a non-traditional and interesting format. Students will complete a series of problems to determine which farmers are telling the truth about their harvested "Geometrees."

Type: Lesson Plan

Triangles: To B or not to B?:

Students will explore triangle inequalities that exist between side lengths with physical models of segments. They will determine when a triangle can/cannot be created with given side lengths and a range of lengths that can create a triangle.

Type: Lesson Plan

Operating with Exponents!:

Students will participate in a gallery walk in which they observe patterns in algebraic expressions. Students will apply the properties of integer exponents to simplify expressions.

Type: Lesson Plan

Stand Up for Negative Exponents:

This low-tech lesson will have students stand up holding different exponent cards. This will help them write and justify an equivalent expression and see the pattern for expressions with the same base and descending exponents. What happens as you change from 2 to the fourth power to 2 to the third power; 2 to the second power; and so forth? This is an introductory lesson to two of the properties of exponents: and

Type: Lesson Plan

Math Is Exponentially Fun!:

The students will informally learn the rules for exponents: product of powers, powers of powers, zero and negative exponents. The activities provide the teacher with a progression of steps that help lead students to determine results without knowing the rules formally. The closing activity is hands-on to help reinforce all rules.

Type: Lesson Plan

Exponential Chips:

In this lesson students will learn the properties of integer exponents and how to apply them to multiplication and division. Students will have the opportunity to work with concrete manipulatives to create an understanding of these properties and then apply them abstractly. The students will also develop the understanding of the value of any integer with a zero exponent.

Type: Lesson Plan

## Perspectives Video: Teaching Idea

Multiplying Polynomials:

Unlock an effective teaching strategy for teaching multiplying polynomials in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Ants versus humans:

This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass. The solution below converts the mass of humans into grams; however, we could just as easily converted the mass of ants into kilograms. Students are unable to go directly to a calculator without taking into account all of the considerations mentioned above. Even after converting units and decimals to scientific notation, students should be encouraged to use the structure of scientific notation to regroup the products by extending the properties of operations and then use the properties of exponents to more fluently perform the calculations involved rather than rely heavily on a calculator.

The Sign of Solutions:

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Extending the Definitions of Exponents, Variation 1:

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.

## Tutorials

Factor a Linear Expression by Taking a Common Factor:

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

Type: Tutorial

Exponents with Negative Bases:

In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.

Type: Tutorial

## Student Resources

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

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

The Sign of Solutions:

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Extending the Definitions of Exponents, Variation 1:

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.

## Tutorials

Factor a Linear Expression by Taking a Common Factor:

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

Type: Tutorial

Exponents with Negative Bases:

In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.

Type: Tutorial

## Parent Resources

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

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Ants versus humans:

This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass. The solution below converts the mass of humans into grams; however, we could just as easily converted the mass of ants into kilograms. Students are unable to go directly to a calculator without taking into account all of the considerations mentioned above. Even after converting units and decimals to scientific notation, students should be encouraged to use the structure of scientific notation to regroup the products by extending the properties of operations and then use the properties of exponents to more fluently perform the calculations involved rather than rely heavily on a calculator.