Standard 1: Apply previous understanding of arithmetic expressions to algebraic expressions.

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Type: Formative Assessment

Students are asked to write equivalent expressions using the Distributive Property.

Type: Formative Assessment

Students are asked to determine if pairs of expressions are equivalent and to justify their responses.

Type: Formative Assessment

Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.

Type: Formative Assessment

Students are asked to generate and justify an expression equivalent to a given one using the properties of operations.

Type: Formative Assessment

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Type: Formative Assessment

Students are asked to write expressions equivalent to a given one by using the Associative and Commutative Properties.

Type: Formative Assessment

Students are asked to evaluate formulas for given values of the variables.

Type: Formative Assessment

Students are asked to use variables to write expressions that represent quantities described in context.

Type: Formative Assessment

Students are asked to interpret the significance of a variable and its possible values when given a variable expression in a real-world context.

Type: Formative Assessment

Students are asked to write and explain a real-world situation to accompany an algebraic expression.

Type: Formative Assessment

Students are asked to identify key parts of algebraic expressions.

Type: Formative Assessment

Students are asked to write a numerical expression using exponents.

Type: Formative Assessment

Students are asked to evaluate numerical expressions with exponents.

Type: Formative Assessment

Students are given an inequality to graph and asked to list sample solutions.

Type: Formative Assessment

Students are given an inequality to graph and asked to select sample solutions.

Type: Formative Assessment

Students are given a context from which to write an inequality statement.

Type: Formative Assessment

Students are given a context from which to write an inequality statement.

Type: Formative Assessment

Students are asked to write expressions that record operations with numbers and variables.

Type: Formative Assessment

Students will analyze a Scratch program and compare its computerized algorithm to the mathematical order of operations, in this lesson plan.

Type: Lesson Plan

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Type: Lesson Plan

Students will design a color-by-expression picture in order to practice evaluating algebraic expressions including substitution and order of operations.

Type: Lesson Plan

This lesson will focus on how to write, translate, and interpret an algebraic expression. Students will be able to identify the parts of an algebraic expression and the meaning of those parts.

Type: Lesson Plan

Students will write and graph inequalities that represent real-world constraints involving whole numbers, negative numbers, and/or rational numbers. The distinction between continuous and discrete variables is made.

Type: Lesson Plan

Students are introduced to simple inequalities and their graphs as they write inequalities to represent real-world constraints.

Type: Lesson Plan

In this lesson, students use small round candies and equation mats to explore the equivalency of pairs of expressions. Then they show pairs of expressions are equivalent using properties of operations. For those that are not equivalent, they provide a counterexample.

Type: Lesson Plan

Students will use a balance scale graphic organizer to solve for the unknown (variable) in addition and subtraction equations with one variable.

Type: Lesson Plan

This lesson provides a hands-on activity where students can apply solving one-step multiplication and division equations to a real-world problem. The lesson focuses on the relationship between distance, rate, and time. The students will also represent data on graphs and draw conclusions and make interpretations based on the graphs.

Type: Lesson Plan

In this lesson, students will build upon their arithmetic experiences with the distributive property to equate algebraic expressions through a series of questions related to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for moving the concrete learner to the abstract level and the use of matching cards.
This is an introductory lesson that only includes producing equivalent expressions such as 3(2 + x) = 6 + 3x.

Type: Lesson Plan

In this lesson, students will examine and experience collecting like terms through an analogy to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for transitioning a concrete experience to the abstract level and a card-matching activity.

Type: Lesson Plan

The students will use square tiles or cubes to explore the meaning of "squared" and "cubed" numbers. They will model squared and cubed numbers to build a strong foundation for working with exponents. The students will learn the connections between area and volume models and the related positive exponents. This is an introductory lesson.

Type: Lesson Plan

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help you to identify and support students who have difficulty in recognizing the order of algebraic operations, recognizing equivalent expressions and understanding the distributive laws of multiplication and division over addition (expansion of parentheses).

Type: Lesson Plan

Meaning of Exponents... Students will write and simplify numerical and algebraic expressions with natural number exponents. Bases are limited to positive integers.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

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.

Type: Lesson Plan

In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two-day lesson.

Type: Lesson Plan

In this lesson, students will use the properties of operations to generate and identify equivalent algebraic expressions. Students will apply their prior knowledge of the distributive property and combining like terms to create equivalent algebraic expressions. The hands-on memory "match" game will engage students and support student understanding of algebraic thinking.

Type: Lesson Plan

This lesson focuses on using appropriate mathematical language when reading or writing expressions, with students applying this knowledge to translate written phrases into algebraic expressions and vice versa. Students will analyze word problems for key words and write the representative expressions.

Type: Lesson Plan

This lesson will show the student how to use the distributive property to express a sum of two whole numbers 1-100.

Type: Lesson Plan

This lesson teaches Least Common Multiples.

Type: Lesson Plan

This lesson uses a real-life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Type: Lesson Plan

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads to solving GCF word problems and using the distributive property to express a sum of two whole numbers.

Type: Lesson Plan

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Type: Lesson Plan

This lesson is designed to help students decode word phrases and then translate them from word form into numerical form. It provides a resource, in the form of a foldable, that can be kept all year and used anytime the students need to decode word phrases.

Type: Lesson Plan

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula. 

Type: Lesson Plan

Students will translate verbal phrases into algebraic expressions. Students are given practice in writing expressions that record operations with numbers and variables. Special attention is given to writing operations in the correct order. Class work and homework worksheets are provided with answer keys for each.

Type: Lesson Plan

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

Type: Lesson Plan

Students will learn how to write inequalities through guided practice, cooperative learning, and comparing the solutions of inequalities to those of equations.

Type: Lesson Plan

Evaluate numerical expressions with fractions using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

This is part 2 of a series on evaluating expressions with whole numbers.

Type: Original Student Tutorial

Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Follow Jamal as he represents algebraic inequalities on a number line while visiting a theme park with his family in this interactive tutorial.

This is part 2 in a two-part series on inequalities. Click HERE to open part 1. 

Type: Original Student Tutorial

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series. 

• Algebraic Expressions Part 1: Addition and Subtraction
• Part 3 (Coming Soon)

Type: Original Student Tutorial

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Use models to solve balance problems on a space station in this interactive, math and science tutorial. 

Type: Original Student Tutorial

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

• MacCoder’s Farm Part 1: Declare Variables
• MacCoder’s Farm Part 2: Condition Statements
• MacCoder's Farm Part 3: IF Statements

Type: Original Student Tutorial

Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

• MacCoder’s Farm Part 1: Declare Variables
• MacCoder's Farm Part 2: Condition Statements
• MacCoder's Farm Part 4: Repeat Loops

Type: Original Student Tutorial

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

• MacCoder's Farm Part 1: Declare Variables
• MacCoder’s Farm Part 3: If Statements
• MacCoder's Farm Part 4: Repeat Loops

Type: Original Student Tutorial

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Follow Jamal as he translates theme park written descriptions into algebraic inequalities in this interactive tutorial.

Type: Original Student Tutorial

Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

There are 10 ways to use algebra to program a binary-counting circuit: fun and more fun.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Unlock an effective teaching strategy for using patterns to help students make generalizations when adding integers in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

If you are having trouble understanding variables, this video might help you see the light.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Type: Problem-Solving Task

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Type: Problem-Solving Task

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Type: Problem-Solving Task

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Type: Problem-Solving Task

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task

This informational text resource is intended to support reading in the content area. The text describes a method for predicting the win-loss record for baseball teams based on runs scored and runs allowed, using the "Pythagorean Expectation" formula invented by Bill James. The text goes on to show the relationship of the prediction formula to the Pythagorean theorem, pointing out a very cool application of the theorem to the world of sports.

Type: Text Resource

This informational text resource is intended to support reading in the content area. Researchers in Australia have found kangaroos to produce more acetate in their flatulence than methane. Cows and goats produce methane-heavy flatulence twenty times more potent than carbon dioxide, adding to the greenhouse gases contributing to global warming. Scientists are trying to use this research on kangaroo farts to discover a way to alter the amount of greenhouse gases in animal flatulence worldwide.

Type: Text Resource

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

Learn how to write basic algebraic expressions.

Type: Tutorial

Learn how to write inequalities to model real-world situations.

Type: Tutorial

Learn how to write simple algebraic expressions.

Type: Tutorial

Learn how to write basic expressions with variables to portray situations described in word problems.

Type: Tutorial

Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.

Type: Tutorial

Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.

Type: Tutorial

Learn how to apply the distributive property to algebraic expressions.

Type: Tutorial

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

Learn how to evaluate an expression with variables using a technique called substitution.

Type: Tutorial

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

Explore how the value of an algebraic expression changes as the value of its variable changes. 

Type: Tutorial

In this example, we have a formula for converting a Celsius temperature to Fahrenheit. 

Type: Tutorial

Students will simplify an expression by combining like terms.  

Type: Tutorial

This tutorial is an explanation on how to combine like terms in algebra. 

Type: Tutorial

This is an introduction to combining like terms in this tutorial.

Type: Tutorial

Students will evaluate expressions using the order of operations.

Type: Tutorial

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

This video will show how to evaluate expressions with exponents using the order of operations.

Type: Tutorial

Examples of evaluating variable expressions

Type: Tutorial

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Type: Tutorial

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

Learn how to apply the distributive property to factor numerical expressions.

Type: Video/Audio/Animation

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative