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

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

Type: Formative Assessment

Students are asked to solve two equations involving rational numbers.

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

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.

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

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

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.

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

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.

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

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

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

Students will use simple interest to 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.

Type: Lesson Plan

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

Students will discover how much items would cost if they were to give gifts for 12 days. They will learn how to calculate and add sales tax to find a total.

Type: Lesson Plan

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

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

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each decision.

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 processes. 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 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.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Students will explore how percentages, 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

The students will convert fractions into decimals and multiply to determine the amount of food to feed their assigned cat. Using this amount, they will calculate (division of decimals) the number of servings and the price per serving of cat food. Students will work with three brands of food and enter the data into their charts. Finally, the students will analyze the data to determine the most affordable food.

Type: Lesson Plan

Students will use manipulatives (pennies and post-its) to model solving one-variable equations.

Type: Lesson Plan

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 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.

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 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

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.

Type: Lesson Plan

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

Type: Lesson Plan

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 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

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

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

Type: Perspectives Video: Expert

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

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

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.

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 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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

The student is asked to write and solve a two-step inequality to match the context.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

"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

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

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

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

Type: Tutorial

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

Type: Tutorial

The video will solve the inequality and graph the solution.

Type: Tutorial

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

Type: Tutorial

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

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

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

Type: Tutorial

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

Type: Tutorial

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

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

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

Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.

Type: Video/Audio/Animation

The video explains the process of creating linear equations to solve real-world problems. 

Type: Video/Audio/Animation

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

Type: Video/Audio/Animation

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