Cluster 2: Reason about and solve one-variable equations and inequalities. (Major Cluster)Archived

In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. 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: Educational Game

In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. 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: Educational Game

Students are given three inequalities and asked to determine if any numbers from a given set are solutions.

Type: Formative Assessment

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

Students are asked to solve a real-world problem by writing and solving an equation.

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 explain what it means for a number to be a solution of an inequality.

Type: Formative Assessment

Students are asked to explain what it means for a number to be a solution of an equation.

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 given three equations and asked to determine if any numbers from a given set are solutions.

Type: Formative Assessment

This is lesson 3 of 3 in the Goldilocks’ Café Just Right unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” temperature and turbidity level. Students will use both the temperature probe and turbidity sensor and code using ScratchX during their investigation.

Type: Lesson Plan

This is lesson 2 of 3 in the Just Right Goldilocks’ Café unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” level of turbidity. Students will use turbidity sensors and code using ScratchX during their investigation.

Type: Lesson Plan

This is lesson 1 of 3 in the Just Right Goldilocks’ Café unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” temperature. Students will use temperature probes and code using ScratchX during their investigation.

Type: Lesson Plan

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

This lesson is a culminating lesson in the Florida Landforms & Water Unit that gives students the ability to use their knowledge of water and potential weather hazards that affect different Florida landforms. This lesson allows students to create a computer program that demonstrates a flood hazard and how to monitor it.

Type: Lesson Plan

This is the introductory lesson in a 4-lesson unit of study about different bodies of water, their characteristics, and how to translate natural language into computer language.

Type: Lesson Plan

Students will explore the excretory system through a variety of activities that include an inquiry lab, a reading excerpt, an engineering design challenge, and creating an infomercial. Students will build a simulated kidney and explore what factors improve the filtering ability. Students will analyze the data and formulate findings.

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

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 learn to write equations for given real world problems. They will eventually write their own problem, write the equation, then solve it.

Type: Lesson Plan

Students will use dried white and black beans to solve one-step addition and subtraction equations to realize the Addition Property of Equality and Subtraction Property of Equality through the use of inverse operations (zero pairs).

Type: Lesson Plan

In this lesson, students learn about solving one- and two-step equations as well as how to use an equation to model information from a word problem. Students will play Lowest Wins, a game played with normal playing cards that challenges students to set up equations from the cards they have been dealt that will give them the lowest solution possible.

Type: Lesson Plan

This lesson explores using substitution to solve one-step equations. Each real world problems involves discussion and students are expected to support their solutions.

Type: Lesson Plan

This lesson challenges student to develop and solve equations for mathematical and real world situations. Students will be encouraged to use the work backwards strategy using inverse operations to find a solution.

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

In this lesson students will solve one-step equations using mental math and guess-and-check. Students will use number cubes to generate random numbers to test as solutions to the equations.

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

In this introductory lesson, students will learn how to write inequalities to represent situations through guided practice, cooperative learning and comparing the solutions of inequalities to that of equations.

Type: Lesson Plan

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

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation. 

Click here to open Part 1

Type: Original Student Tutorial

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

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

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

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.

Type: Problem-Solving Task

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

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

Students are asked to write and solve an equation in one variable to answer a real world question.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

Students are asked to write and graph two inequalities described in context: one discrete and one continuous.

Type: Problem-Solving Task

Students are asked to solve an inequality in order to answer a real-world question.

Type: Problem-Solving Task

Students are asked to write an equation with one variable in order to find the distance walked.

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

In this activity, the student teacher role is reversed using the "jigsaw activity." This is where there is an original group, and they are separated into different groups. They are then given a particular case, and solve it as a group until they understand it enough to be able to go back to their original group and teach their case to the rest of the students. Each student coming from a different group, they will all have the opportunity to do some teaching.

Type: Teaching Idea

"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

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

Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.

Type: Tutorial

In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.

Type: Tutorial

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

Type: Tutorial

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

Type: Tutorial

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation. 

Type: Tutorial

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

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

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 (or "plugging in").

Type: Tutorial

This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.

Type: Tutorial

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

Type: Virtual Manipulative