# Cluster 2: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information
Number: MAFS.7.EE.2
Title: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (Major Cluster)
Type: Cluster
Subject: Mathematics
Domain-Subdomain: Expressions & Equations

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.7.EE.2.AP.3a
Solve real-world, multi-step problems using positive and negative rational numbers (whole numbers, fractions and decimals).
MAFS.7.EE.2.AP.4a
Set up equations with one variable based on real-world problems.
MAFS.7.EE.2.AP.4b
Solve equations with one variable based on real-world problems.

## Related Resources

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

## Assessments

Sample 3 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 4 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 2 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 1 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

## Educational Games

Timed Algebra Quiz:

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

Algebra Four:

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

## Formative Assessments

Recycled Inequalities:

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

Type: Formative Assessment

Solve Equations:

Students are asked to solve two multistep equations involving rational numbers.

Type: Formative Assessment

Write, Solve and Graph an Inequality:

Students are asked to write, solve, and graph a two-step inequality.

Type: Formative Assessment

Write and Solve an Equation:

Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario.

Type: Formative Assessment

Squares:

Students are asked to write and solve an equation of the form p(x + q) = r in the context of a problem about the perimeter of a square.

Type: Formative Assessment

Students are asked to solve a two-step inequality.

Type: Formative Assessment

Algebra or Arithmetic?:

Students are asked to compare an arithmetic solution to an algebraic solution of a word problem.

Type: Formative Assessment

Using Estimation:

Students are asked to assess the reasonableness of answers using estimation strategies.

Type: Formative Assessment

Alexa’s Account:

Students are asked to assess the reasonableness of an answer using mental computation and estimation strategies.

Type: Formative Assessment

Gas Station Equations:

Students are asked to solve a multi-step problem involving percent.

Type: Formative Assessment

Reeling in Expressions:

Students are asked to solve a multi-step problem involving rational numbers.

Type: Formative Assessment

Discount and Tax:

Students are asked to solve a multi-step problem involving percent.

Type: Formative Assessment

## Lesson Plans

Just Right Goldilocks’ Café: Temperature & Turbidity:

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

Just Right Goldilocks’ Café: Turbidity:

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

Just Right Goldilocks’ Café: Temperature:

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

Gather Data For Distribution by Programming an App:

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

Data Sets Represented in Computers:

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

Scout Robot: Mass, Density, Volume, Weight:

In this MEA, students must select which material to use in the development of an advanced military scout robot. Students must analyze data about each material’s individual properties that would make it a valid choice for military or police service. Students must complete calculations to determine material density as well as the overall mass and weight of the robot. This lesson focuses on the characteristic properties of density, unit conversion, and differentiating between mass and weight.

Type: Lesson Plan

Radioactive Dating: Half-Life & Geologic Time:

In this Model Eliciting Activity (MEA), students must use their knowledge of radioactive dating and geologic time to select an effective elemental isotope to be used to date three rare specimens. This decision requires an understanding of the concept of a half-life and the benefits and limitations of radiometric dating. Students must complete mathematical calculations involving equations and operations with fractions and percentages. Students completing this MEA must develop two essays that respond in a professional manner to a client in the scientific industry.

Type: Lesson Plan

How Fast Can One Travel on a Bicycle?:

Students investigate how the pedal and rear wheel gears affect the speed of a bicycle. A GeoGebra sketch is included that allows a simulation of the turning of the pedal and the rear wheel. A key goal is to provide an experience for the students to apply and integrate the key concepts in seventh grade mathematics in a familiar context.

Type: Lesson Plan

3-D Printers: Cost Effective for the Quality?:

Students will compare the cost of pre-made solar car kits to cars made from a 3-D printer. In the second part of the activity, students will research other available 3-D printers and determine what attributes are important to consider. There is also an optional solar panel car race for day 3.

Type: Lesson Plan

HOORAH!! Pizza For Lunch:

The principal of Central Middle School is thinking of adding pizza to the lunch menu on Mondays and Fridays but needs help deciding the costs per slice and what students think is important about the pizza. After the students' initial decision about the pizza the principal remembers that there is a delivery charge.The students must revisit their decision and do additional calculations to see if their original process still works.

Type: Lesson Plan

Steps to Solving Equations:

This lesson unit is intended to help you assess how well students are able to form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help you identify and assist students who have difficulties in using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

Type: Lesson Plan

Percent of Change:

Students will investigate percent of change in real-world situations and will differentiate between an increase or a decrease. The students will use a formula to find the percent of change.

Type: Lesson Plan

Car Shopping:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best decision on purchasing official vehicles for school district considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Type: Lesson Plan

In Whose Best Interest is Interest?:

The students will explore real world examples of interest rates. Students will explore loan rates, CD rates and compare benefits of different rates versus different terms of loans. Students will use the formula for simple interest.

Type: Lesson Plan

It's All About Properties of Equality:

Students will apply properties of equality to solve multi-step equations with one variable. Students will complete a gallery walk as formative assessment, to determine students' understanding of properties of operations and equality when applied to equations. Equations increase in difficulty as the lesson progresses. Students complete an error analysis toward the end of the lesson. This lesson includes a powerpoint presentation.

Type: Lesson Plan

Pricing The Twelve Days of Christmas:

Students will discover how much the items in the classic song, "The Twelve Days of Christmas," would cost in the current year; and then they will update the list for modern times.

Type: Lesson Plan

Say Cheese!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase.

Type: Lesson Plan

Understanding Equations Using Perimeter:

This is an introductory lesson in writing and solving equations in the form p(x + q) = r using the perimeter of rectangles.

Type: Lesson Plan

Along for the Ride!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase.

Type: Lesson Plan

Travel Troubles:

This activity engages the students into time scheduling, budgeting, and decision making to maximize time efficiency.

Type: Lesson Plan

Batteries Included:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from E-Z Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase.

Type: Lesson Plan

Where in the world?:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

Type: Lesson Plan

Math in Mishaps:

Students will explore how percents, proportions, and solving for unknowns are used in important jobs. This interactive activity will open their minds and address the question, "When is this ever used in real life?"

Type: Lesson Plan

Which Food Should I Feed My Cat?:

The students will convert fractions into decimals and determine with multiplication the amount of food per serving for their assigned cat. Using this amount, they will calculate (division of decimals) the number of servings and the price per serving of cat food. Student will work with three types of food and enter the data into the chart. Finally, the students will analyze the data to determine the most cost-effective food.

Type: Lesson Plan

Pennies and Post-its:

Students will look at balancing linear equations using pennies as constants and Post-its as the coefficient of the linear term.

Type: Lesson Plan

Here's a tip!:

Students will solve problems involving sales tax and tips; students will apply the properties of operations with numbers in decimal, percent and fraction form. Students will convert between numbers in any form as appropriate.

Type: Lesson Plan

Uncle Henry's Dilemma:

Uncle Henry's Dilemma is a problem solving lesson to determine the global location for the reading of Uncle Henry's will. The students will interpret data sets which include temperature, rainfall, air pollution, travel cost, flight times and health issues to rank five global locations for Uncle Henry's relatives to travel to for the reading of his will. This is an engaging, fun-filled MEA lesson with twists and turns throughout. Students will learn how this procedure of selecting locations can be applied to everyday decisions by the government, a business, a family, or individuals.

Type: Lesson Plan

Bargain Town, USA:

In this lesson, students will participate in a simulated real-world exploration of the relationship between fractions, decimals, and percents, by converting number forms and calculating discounted prices.

Type: Lesson Plan

Let's Go Shopping: Calculating Percents:

In this lesson, students will participate in a simulated shopping experience where they choose items they would like to purchase from local sale advertisements. The students will be able to apply the percent formula and the percent of change formula to real world financial situations. Students will learn how to calculate percent discounts, their percent of savings, and tax. The students will analyze, compare, draw conclusions and explain in writing why specific types of discounts are the most advantageous given specific situations.

Type: Lesson Plan

Gummy vs. Gum (Number Pattern):

"In this lesson, students use gummy bears and sticks of gum to discover a number pattern and write an equation that describes it. This lesson should be conducted after students have worked with patterns and one- and two-step equations." from the Beacon Learning Center.

Type: Lesson Plan

Inequal-tile-ies:

In this lesson, students will work with Algebra Tiles to solve inequalities. This lesson builds upon student experience with solving equalities, as well as identifying inequalities and representing them on the number line. This lesson is an introduction to solving inequalities. (This lesson addresses part a of the standard)

Type: Lesson Plan

Understanding Decimals:

These games and activities help students investigate the relationship between fractions and decimals, focusing on equivalence.

Type: Lesson Plan

## Original Student Tutorials

Professor E. Qual Part 2: Two-Step Equations & Rational Numbers:

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.

Type: Original Student Tutorial

Professor E. Qual Part 1: 2 Step Equations:

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.

Type: Original Student Tutorial

Balancing the Machine:

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

Type: Original Student Tutorial

## Perspectives Video: Experts

Improving Hurricane Scales:

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

Type: Perspectives Video: Expert

Water Flow Modeling for Archeology Research:

Submerge yourself in math as a hydrogeologist describes calculations used to investigate water flow questions related to ancient shell rings.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Idea

Programming Mathematics: Algebra, Matrices, and Variables to control Open-source Hardware:

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

Type: Perspectives Video: Teaching Idea

Smiles:

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.

Maximizing Area: Gold Rush:

Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work. At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually. In a whole-class discussion students compare and evaluate the different methods they used. Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen. Finally, students reflect on their work.

Anna in D.C.:

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.

Discounted Books:

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Shrinking:

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Sports Equipment Set:

The student is asked to write and solve an inequality to match the context.

Gotham City Taxis:

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Log Ride:

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

## Teaching Ideas

Students Collaborate to Solve Compound Inequalities:

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

Translating Word Problems into Equations:

This site shows students how to translate word problems into equations. It gives seven steps, from reading the problem carefully to checking the solution, to creating equations. The lesson moves on to a few simple exercises in which a natural language sentence is translated to an algebraic equation. It then moves on to more elaborate word problems which require students to identify the important data and follows the given seven steps to create and solve the equation. The more complex questions draw on student understanding of geometric formulae. There are six questions at the end for students to test their new knowledge of how to create and solve equations.

Type: Teaching Idea

True, False, and Open Sentences:

"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

## Tutorials

Solving Percentage Problems with Linear Equations:

Many real world problems involve involve percentages. This lecture shows how algebra is used in solving problems of percent change and profit-and-loss.

Type: Tutorial

Solve a consecutive integer problem algebraically:

Students will learn how to solve a consecutive integer problem. Checking the solution will be left to the student.

Type: Tutorial

Age word problem:

This tuptorial shows students how to set up and solve an age word problem. The tutorial also shows how tp check your work using substitution.

Type: Tutorial

Age word problem :

Students will learn how to set up and solve an age word problem.

Type: Tutorial

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

Basic Linear Equation Word Problem:

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, you will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Combining Like Terms Introduction:

This video teaches about combining like terms in linear equations.

Type: Tutorial

Multiplying and dividing inequalities :

Students will solve the inequality and graph the solution.

Type: Tutorial

Percent Word Problem Example 1:

We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

How to evaluate an expression using substitution:

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

Solving One-Step Equations Using Multiplication and Division:

This tutorial will help you to solve one-step equations using multiplication and division. For practice, take the quiz after the lesson!

Type: Tutorial

Solving Two-Step Equations:

This short video uses both an equation and a visual model to explain why the same steps must be used on both sides of the equation when solving for the value of a variable.

Type: Tutorial

Linear Equations in One Variable:

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

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

Solving Equations with One Variable :

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

Type: Tutorial

## Unit/Lesson Sequences

Drawing to Scale: Designing a Garden:

In this lesson (or series of lessons), students interpret and use scale drawings to plan a garden layout. Students start by producing their own layout and then work together to refine their garden design. The activity requires that students use short rules (rulers), meter rules (meter sticks), string, protractors, scissors, glue, card, plain paper, graph paper, and colored pencils. Students work individually for 20 minutes, engage in a 100-minute lesson (or two 50-minute lessons), and complete a 10-minute follow up lesson or homework.

Type: Unit/Lesson Sequence

Variables and Patterns of Change: Translating Words Into Symbols; Linear Equations:

Lesson Plan 1: Miles of Tiles - The Pool Border Problem, students will recognize patterns and represent situations using algebraic notation and variables. Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives, students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution. Students work in teams of four. Site includes a Topic Overview, Lesson Plans, Student Work, Teaching Strategies, Resources, and a video of Workshop 1; Part 1.

Type: Unit/Lesson Sequence

## Video/Audio/Animations

Solving Motion Problems with Linear Equations:

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Type: Video/Audio/Animation

Solving Problems with Linear Equations:

How do we create linear equations to solve real-world problems? The video explains the process.

Type: Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

## Virtual Manipulative

Linear Function Machine:

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. 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

## Student Resources

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

## Original Student Tutorials

Professor E. Qual Part 2: Two-Step Equations & Rational Numbers:

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.

Type: Original Student Tutorial

Professor E. Qual Part 1: 2 Step Equations:

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.

Type: Original Student Tutorial

Balancing the Machine:

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

Type: Original Student Tutorial

## Educational Games

Timed Algebra Quiz:

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

Algebra Four:

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

Smiles:

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.

Anna in D.C.:

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.

Discounted Books:

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Shrinking:

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Sports Equipment Set:

The student is asked to write and solve an inequality to match the context.

Gotham City Taxis:

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Log Ride:

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

## Tutorials

Solving Percentage Problems with Linear Equations:

Many real world problems involve involve percentages. This lecture shows how algebra is used in solving problems of percent change and profit-and-loss.

Type: Tutorial

Solve a consecutive integer problem algebraically:

Students will learn how to solve a consecutive integer problem. Checking the solution will be left to the student.

Type: Tutorial

Age word problem:

This tuptorial shows students how to set up and solve an age word problem. The tutorial also shows how tp check your work using substitution.

Type: Tutorial

Age word problem :

Students will learn how to set up and solve an age word problem.

Type: Tutorial

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

Basic Linear Equation Word Problem:

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, you will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Combining Like Terms Introduction:

This video teaches about combining like terms in linear equations.

Type: Tutorial

Multiplying and dividing inequalities :

Students will solve the inequality and graph the solution.

Type: Tutorial

Percent Word Problem Example 1:

We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

How to evaluate an expression using substitution:

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

Solving One-Step Equations Using Multiplication and Division:

This tutorial will help you to solve one-step equations using multiplication and division. For practice, take the quiz after the lesson!

Type: Tutorial

Solving Two-Step Equations:

This short video uses both an equation and a visual model to explain why the same steps must be used on both sides of the equation when solving for the value of a variable.

Type: Tutorial

Linear Equations in One Variable:

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

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

Solving Equations with One Variable :

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

Type: Tutorial

## Video/Audio/Animations

Solving Motion Problems with Linear Equations:

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Type: Video/Audio/Animation

Solving Problems with Linear Equations:

How do we create linear equations to solve real-world problems? The video explains the process.

Type: Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

## Virtual Manipulative

Linear Function Machine:

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. 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

## Parent Resources

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

Smiles:

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.

Anna in D.C.:

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.

Discounted Books:

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Shrinking:

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Sports Equipment Set:

The student is asked to write and solve an inequality to match the context.

Gotham City Taxis:

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Log Ride:

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

## Tutorial

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

## Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation