Cluster 1: Apply and extend previous understandings of arithmetic to algebraic expressions. (Major Cluster)Archived

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 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 asked to write and evaluate a numerical expression using exponents.

Type: Formative Assessment

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

Type: Formative Assessment

Students are asked to expand and evaluate exponential expressions containing whole number exponents.

Type: Formative Assessment

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Type: Lesson Plan

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

MSP Racing Company is a cutting edge company that wishes to break through and develop the fastest renewable energy vehicle of its kind. In this lesson, students will be divided into teams of three and will be assigned the task of developing a solar-powered race car to be purchased and developed in full scale by MSP Racing. Each group of students will be employees of MSP Racing Company and will have to develop, test, and present their car to the boss (teacher) of the company.

Type: Lesson Plan

Students will design a color-by-expression picture in order for students to practice designing and evaluating algebraic expressions.

Type: Lesson Plan

Students will be introduced to the power of exponents through the parable A Grain of Rice, by Demi. Students analyze the parts of an exponential expression and evaluate the expression using mental math and paper and pencil.

Type: Lesson Plan

In this lesson, students use M&Ms 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

This lesson is designed to assist in teacher facilitation of student understanding related to the concept of translating between verbal and algebraic two-step equations. 

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

Students will use the provided data to calculate distance and total cost. Students will consider this data and other provided criteria to assist a travel agent in determining which airline to choose for a client.

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 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 behind the terms "squared" and "cubed" numbers. They will be able to connect understanding between modeling squared and cubed numbers to build a strong foundation for working with exponents. The students also make connections between area and volume models and exponential forms of numbers using whole number exponents. This is an introductory lesson.

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 whole-number exponents. Bases are limited to positive integers.

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 MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

This lesson uses students' prior knowledge of operational clue words and applies it to translating written phrases into algebraic expressions and vice versa, as well as analyzing word problems for key clue words and writing the representative expression.

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

This lesson teaches students to translate verbal phrases into algebraic expressions. Students are given practice in writing expressions that record operations with numbers and with letters representing numbers. Special attention is given to writing operations in the correct order. A class work and homework worksheet is provided with keys for each.

Type: Lesson Plan

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

Type: Lesson Plan

In this lesson, students will determine the perimeter of a train of polygons, for different regular polygons. The accompanying videos (intended audience is teachers) provide segments of an implementation of the lesson.

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

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

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

Students are asked to explore and then write an expression with an exponent. The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.

Type: Problem-Solving Task

This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

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

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

"Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions.

Type: Teaching Idea

Students will learn that non-zero numbers to the zero power equal one. They will also learn that zero to any positive exponent equals zero.

Type: Tutorial

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

Type: Tutorial

You will discover rules to help you determine the sign of an exponential expression with a base of -1.

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

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

This video demonstrates how to evaluate expressions with whole number exponents.

Type: Tutorial

Learn why a number raised to the zero power equals 1.

Type: Tutorial

Examples of evaluating variable expressions

Type: Tutorial

Evaluating Expressions with Two Variables

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

In this example of evaluating expressions, we're dusting off some geometry. On top of that, it's a word problem. We're seeing how different concepts in math are layered on top of each other to create more interesting and complex problems to solve.

Type: Tutorial

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

Type: Tutorial

Our focus here is understanding that a variable is just a letter or symbol (usually a lower case letter) that can represent different values in an expression. We got this. Just watch.

Type: Tutorial

The distributive property states that the terms of addition or subtraction statements within parentheses may be separately multiplied by a value outside the parentheses. In this tutorial, students will learn the distributive property, which is very helpful with mental math calculations and solving equations.

Type: Tutorial

Take a look at the logic behind the associative and distributive properties of multiplication.

Type: Tutorial

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.

Type: Tutorial

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

This lesson unit helps teachers assess how students perform arithmetic operations, write and evaluate numerical expression s from diagrammatic representations, apply the distributive and commutative properties, and find areas of compound rectangles. The time for the lesson is broken into a 15 minute pre-lesson task, an 80 minute lesson (or two 40 minute lessons), and a 15 minute follow up lesson or homework. Individual students will need a copy of the two tasks, a mini-whiteboard, a pen, and an eraser. Each small group will need cut-up copies of the card sets, a large sheet of poster-sized paper, and a glue stick.

Type: Unit/Lesson Sequence

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

Type: Video/Audio/Animation

This interactive game allows students to review math concepts, including shapes, shape names, addition, multiplication, negative numbers, and equivalent expressions.

Type: Virtual Manipulative

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