# Standard 3: Use percentages and proportional reasoning to solve problems.

General Information
Number: MA.7.AR.3
Title: Use percentages and proportional reasoning to solve problems.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.7.AR.3.AP.1
Solve simple percentage problems in real-world contexts.
MA.7.AR.3.AP.2
Solve simple ratio problems in real-world contexts.
MA.7.AR.3.AP.3
Use tools to solve real-world problems involving conversion of units in the same measurement system.

## Related Resources

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

## Educational Game

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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

Tiffanyâ€˜s Tax:

Students are asked to calculate the amount of sales tax and total price, given prices of individual items to purchase.

Type: Formative Assessment

Notebooks to Trees:

Students are asked to find the approximate number of trees that are saved by using recycled paper.

Type: Formative Assessment

Fishy Formulas:

Students are asked to choose and justify the unit to be used in a formula and are asked to choose and explain the unit used in the answer.

Type: Formative Assessment

Students must find proportionally equivalent values given a set of rational number quantities.

Type: Formative Assessment

Gasoline Prices:

Students are given gasoline prices from a year ago and today and are asked to calculate the percent change.

Type: Formative Assessment

Finding Fees:

Students are asked to complete a multi-step percent problem.

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

What happened to my money? Part 2:

In this lesson, students will extend their understanding of percentages to problem solve with taxes, in context, while exploring how taxes impact local communities.

Type: Lesson Plan

A Florida Vacation:

Students will calculate sales tax to plan a family vacation budget. Through collaborative learning activities and discussions, students will understand the concept of sales tax as a civic responsibility and recognize the importance of considering sales tax in their financial planning to contribute to their community’s public service and infrastructure in this integrated lesson plan.

Type: Lesson Plan

Percent of Change and the House of Representatives Lesson 3 of 3:

Students will analyze the 2020 United States Census to study how the population changes the number of representatives in each state. They will compare the highest populated and least populated states based on the data in this integrated lesson plan.

Type: Lesson Plan

Percent of Change and the House of Representatives Lesson 2 of 3:

Students will use ratios to explore the percent of a state's population that is represented by each of its designated seats in the U.S. House of Representatives.  They will analyze the 2020 United States Census to study how the population changes the number of representatives from each state. Students will compare the highest populated and least populated states based on the data in this integrated lesson plan.

Type: Lesson Plan

Who's in the House? Part 3:

Students will use percentages and states' apportionment of representatives in the House to determine how much funding should be allocated to each state, in this integrated lesson plan.

Type: Lesson Plan

Who's in the House? Part 2:

Use data from U.S. Census Bureau that shows Apportionment Population, Resident Population, and Overseas Population for 2020 & 2010 Census to create and compare ratios in this integrated lesson plan.

Type: Lesson Plan

Budgeting and Decision-Making: Integrating Math and Civics:

This lesson will help students understand the concept of percentages within the context of government budgets. Students will explore how percentages are used to allocate funds in government budgets and how they can be effectively communicated using graphs. The lesson will involve collaborative learning, discussions, and problem-solving to foster critical thinking and application of math concepts in a civics context.

Type: Lesson Plan

Legislative Representation Lesson 3:

This lesson uses percentages and ratios to calculate percent increase in the number of female U.S. Senators from 1989-2025.  Students will use two different methods to calculate these percent increases, one focusing on percentages and one focusing on ratios.  They will be asked to choose which is the more efficient method of calculation and explain their reasoning.

Type: Lesson Plan

WHOâ€™S IN THE HOUSE? PART 1:

Students will use ratios to discuss and examine the relationship between a Census, state populations, and apportionment of representatives in the House of Representatives, in this integrated lesson plan.

Type: Lesson Plan

Which Services can we Afford? Part 2 of 3:

In this lesson, students will be presented with the same scenario as lesson 1. Now there are additional taxes revenues that came in due to new developments in the area. The budget has a 12.5% increase but due to the new developments, there are allocation constraints to the budget. After dispersing their new funds students will compare their results with their original analysis. This is lesson 2 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

Which Services can we Afford? Part 3 of 3:

In this lesson, students will peer review their assignments from lessons 1 and 2 to compare their solutions and determine the validity of the classmate’s process according to the provided rubric. This is lesson 3 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

Which Services can we Afford? Part 1of 3:

In this lesson, students will be re-introduced to ratios and percentages and explain how we use them for budgeting and taxes. Students will get information on tax income funds and use the information to allocate funds for providing the different services in a community (Police, Fire, Schools, Hospitals, Roads, etc.) This is lesson 1 of 3 in a mini-unit integrating civics and math.

Type: Lesson Plan

Legislative Representation Lesson 2:

Students will calculate the net change in the seats for the U.S. House of Representatives for each state. They will add all the net changes to equal 0, since the total number of seats has remained constant at 435 during this time period. They will then calculate the percent change for each state from the 1960 U.S. Census to the 2020 U.S. Census, in this integrated lesson plan.

Type: Lesson Plan

Understanding Taxation and Civic Obligation:

Students will use their knowledge of percentages to calculate federal income tax and local sales tax. They will explore the obligation of citizens to pay taxes and how taxes fund public services. Students will evaluate different tax models by comparing percentages of income taxed at different income levels.

Type: Lesson Plan

Using Percent Change to Analyze WTO Membership (Part 2):

Students will analyze the change in the World Trade Organization’s membership using ratios to find the percent change while examining the purpose of the World Trade Organization and the United States’ role as a member in this integrated lesson plan.

Type: Lesson Plan

Legislative Representation Lesson 1:

Students will use percentages and ratios to determine the portion of political party affiliation to number of seats of a county commission. Students will discuss the legislative branch of our government and compare it at the local, state and national levels in this integrated lesson plan.

Type: Lesson Plan

Students will work collaboratively to rank civic duties and responsibilities needed to keep a constitutional republic. They will utilize mathematical strategies to convert measurements of time as they calculate costs using the four operations with decimals and create an effective schedule for the ads within a budget in this model eliciting activity.

Type: Lesson Plan

Analyzing Government Spending: Integrating math & civics:

Students will practice their skills in interpreting data and creating graphical representations in this integrated civics lesson. Students will apply graphing skills to analyze government spending data and reflect on the importance of mathematics in communicating complex numerical information visually so the public can better stay informed.

Type: Lesson Plan

Percent of Change and the House of Representatives:

Students will use ratios to explore the percentage of seats in the U.S. House of Representatives for different states.  They will analyze the 2020 United States Census to study how the population changes the number of representatives from each state. Students will compare the highest populated and least populated states based on this data in this integrated lesson plan.

Type: Lesson Plan

Comparing Amendments:

Students will read brief summaries about different amendments ratified throughout history intended to expand civic participation, analyze voter turnout and voting age population data for presidential elections before and after the ratification of each amendment, and use percentages and ratios to rank the amendments in order of most to least effective in expanding civic participation, in this model eliciting activity.

Type: Lesson Plan

A Rocky Debate: How do coastal structures reduce rates of coastal erosion?:

Students will be tasked with analyzing various methods of protecting coasts from erosion. Students will review a dataset with logistics about each type of coastal structure. Students will rank which structures they feel should be utilized to best protect a local beachfront town. The students will write a letter to the local government to persuade them on which structure should be used. Students will be challenged to think critically, analyze information, and work collaboratively in this model eliciting activity.

Type: Lesson Plan

Comparing Amendments:

In this lesson plan, students will analyze voter turnout and voting age population data for past presidential elections to explore how various amendments broadened the opportunity for civic participation in the political process.

Type: Lesson Plan

Build a New School:

Students will calculate, interpret, and use measures of center and spread of different populations to determine in which city in Manatee County new schools should be built. Students will also use percentages to estimate the future population of school-aged children which will be used to determine where new schools should be built.

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: https://www.cpalms.org/cpalms/mea.aspx to learn more about MEAs and how they can transform your classroom.They resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. 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.

Type: Lesson Plan

Election Predictions:

Students will examine poll results from three cities to predict a voting outcome on a local level. They will make inferences about a population based on the poll results and develop a written statement to present their findings to the board of county election commissions. Students will then use the peojected election results to determine the impact of citizens in the community.

Type: Lesson Plan

Budget Committee:

In this MEA, students will take on the role as a member of the Sunshine County Budget Committee. Members will collaborate to determine the optimal sales tax rate, use that rate to calculate how much money can be used for special projects, then decide which special projects to include in the budget proposal. Students will use percentages to problem-solve in context while considering citizen input and constraints on spending.

Type: Lesson Plan

What happened to my money? Part 1:

In this lesson, students will extend their understanding of percentages to problem solve with taxes, in context, while learning about some of the different types of taxes.

Type: Lesson Plan

Guiding Grids: Math inspired self-portraits:

Students will create a proportional self portrait from a photo using a gridded drawing method and learn how a grid system can help accurately enlarge an image in a work of art. Students will use the mathematical concepts of scale, proportion and ratio, to complete their artwork.

Type: Lesson Plan

Real Life Tax, Tip, and Discount!:

Students calculate the tax, tip, and discount in real-world situations.

Type: Lesson Plan

Wolves of Yellowstone - Ecology & Human Impact:

In this MEA, students will decide how many wolves to introduce into Yellowstone National Park's ecosystem. The number of wolves could influence many factors, from the tourism industry to local farming businesses, as well as the populations of other species in the area. Students must choose to introduce the number of wolves they feel will be most beneficial to the preservation of Yellowstone National Park as determined by the mission statement of Yellowstone and the National Park Service.

Type: Lesson Plan

Partition Point For The Queen:

Students will locate a point that partitions a line segment into a given ratio. Students will use a variety of methods; the activities range from informal student definitions and sketches to tasks using number lines and the coordinate plane.

Type: Lesson Plan

Geometree Thievery:

This geometry lesson focuses on partitioning a segment on a coordinate grid in a non-traditional and interesting format. Students will complete a series of problems to determine which farmers are telling the truth about their harvested "Geometrees."

Type: Lesson Plan

Partitioning a Segment:

In this lesson, students find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Type: Lesson Plan

Dilation Transformation:

Students identify dilations, verify that polygons are similar, and use the dilation rule to map dilations. Task cards are provided for independent practice. The PowerPoint also includes detailed illustrations for constructing a dilation using a compass and a straight edge.

Type: Lesson Plan

Partition Me:

Students will learn how to partition a segment. Turn your class into a partitioning party; just BYOGP (Bring your own graph paper).

Type: Lesson Plan

Fast Food Frenzy:

In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages.

Type: Lesson Plan

Lauraâ€™s Babysitting Job:

In this 7th grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

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

Students at a local middle school are interested in attending a basketball tournament in Orlando. There is an entrance fee and hotel costs to consider. Students must calculate the total cost and the cost per student to attend the tournament. Each hotel has different qualities that could influence the students' choice of which hotel is best for their team.

Type: Lesson Plan

Which van is the best buy?:

The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.

Type: Lesson Plan

Family Restaurant:

In this Model Eliciting Activity, MEA, students will use unit rates and scoring systems to analyze and interpret data to recommend the best store from which a family restaurant should purchase its weekly non-frozen food items.

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 learn how to calculate markup, markdown, percent increase, and percent decrease. Using sales "ad" inserts from the internet, newspapers, and store flyers, students will understand how these concepts apply to real-world situations.

Type: Lesson Plan

Car Shopping:

In this Model Eliciting Activity, MEA, students will analyze and interpret data to recommend the best vehicle purchases for a school district. Students will work collaboratively to perform calculations that can be used to make comparisons and create composite scores for each vehicle.

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

Pricing Twelve Days of Celebration:

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

We're Going on Vacation!:

In this Model Eliciting Activity, MEA, students will act as travel agents to plan a vacation package for a family of 5. Students will apply proportional reasoning and multi-step problem-solving skills to design vacation packages that meet specific criteria and stay within a given budget.

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

Savvy Shopping:

This is the second part of the CPalms lesson titled Markup and Make Money. In Savvy Shopping students will shop at their peers' store and buy items. If it is discounted, they will have to calculate the revised price. They will then find the total price including the tax.

Type: Lesson Plan

Have you ever heard students ask the question, "Why do I have to learn this?" This lesson answers that question because it requires the students to apply their knowledge in real world scenarios but does not teach a basic conceptual understanding of percentages. The teacher may use the whole lesson or select specific problems.

Type: Lesson Plan

Stock Market MEA:

In this Model Eliciting Activity, MEA, students will apply their knowledge of percentages and ratios to evaluate various stocks for investment. Students will develop a systematic procedure to recommend the best stock for investment.

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

Are My Values Proportional?:

Students will learn that a proportional relationship can be represented by a table, a graph, or an equation. They will also be able to determine the constant of proportionality from a table, graph, or equation.

Type: Lesson Plan

Installing Tile Floor:

In this Model Eliciting Activity (MEA), students will analyze data related to tiling rooms in a house. Students will calculate the square footage of various rooms, convert measurements to determine the amount of tile needed, and compute both the cost of the tiles and the cost of installation. They will evaluate and compare different flooring options based on cost, quality, and installation factors, and develop a procedure to recommend the best choices.

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

Travel Troubles:

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

Makeover, Home Edition Part III:

This is the third part of the lesson, "Makeover, Home Edition". This lesson is designed to teach students how to put ideas into reality by creating and using scale drawings in the real world. In Part I (#48705) students determined backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into the backyard. In Part III (#49025) students will create a scale drawing of the backyard. Part IV (#49090) will focus on inserting a window and painting walls inside the house.

Type: Lesson Plan

Zany's Joke Shop Dilemma:

In this Model Eliciting Activity, MEA, students will analyze and compare data for various products sold in a joke shop to make recommendations on the best, and worst, products. Students will apply weighted averages, ratios, percentages, and proportions to perform calculations that support their recommendations as well as create graphical representations to help make sense of and compare the data.

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

Water Troubles:

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water.Â  Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water.Â  They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials.Â  Students will utilize measures of center and variation to compare data, assess proportional relationships to make decisions, and perform unit conversions across different measurement systems.

Type: Lesson Plan

Importing Machine Parts:

In this Model Eliciting Activity, MEA, students will analyze various costs and develop a procedure to recommend the best shipping methods for machine parts. They will use mathematical skills such as calculating total costs, comparing rates, and applying percentage discounts and surcharges to determine the most cost-effective shipping options.

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.Â To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

The Most Beneficial Bank:

In this Model Eliciting Activity,Â MEA, students will work in cooperative groups to discuss and come up with a procedure to rank the banks from best to worst by estimating the simple interest and total loan amount.

Type: Lesson Plan

All Around Fences:

In this Model Eliciting Activity, MEA, students will help analyze, compare, and select fencing options for a college’s pool and recreation area. Students will use unit conversions, calculate total costs, and justify their recommendations to develop problem solving and critical thinking skills within a purchasing context.

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

Best Day Care Center in the Neighborhood:

In this Model Eliciting Activity, MEA, students will evaluate and compare daycare centers near a neighborhood. They will develop a scoring system to assess various characteristics of each center and justify their ranking using averages, ratios, and other mathematical calculations.

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

Sugar Scrub:

In the Sugar Scrub MEA students will analyze 5 sugar scrub formulas. In the first part, students are asked to evaluate each formula based on color, scent, and exfoliation. In the second part, students apply their methodology to a cost analysis of the scrubs.

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

Cool Uniforms:

In this Model Eliciting Activity, MEA, students are asked to rank fabrics designated for a new women's volleyball team. Students will use proportional reasoning, percentages, and conversions to analyze and compare fabrics to support their rankings.

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

Orange Juice Conversion:

In this MEA, the students will be able to convert measurements within systems and between systems. They will be able to use problem solving skills to create a process for ranking orange juices for a Bed and Breakfast.

Type: Lesson Plan

Is It Fair?:

In this lesson students will use their understanding of ratios and unit rate to solve problems where they must decide whether various situations are fair.

Type: Lesson Plan

Math in Mishaps:

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

Roll of the Dice and Some Turkey Fun!:

Students will conduct experiments on their own to experience the difference between experimental and theoretical probabilities.

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

Students will go on a virtual "road trip" with a partner. Using the scale on a map, students will calculate the distance traveled, the amount of gas used, and the cost of the gas.

Type: Lesson Plan

A Roll of the Dice:

What are your chances of tossing a particular number on a number cube? Students collect data by experimenting and then converting the data in terms of probability. By the end of the lesson, students should have a basic understanding of simple events.

Type: Lesson Plan

Fastest Route:

In this Model Eliciting Activity, MEA, students will interpret and analyze a scale drawing to provide possible routes from a teacher’s home to the school. Students will consider factors including traffic patterns, construction zones, and wait times to recommend the best route including the total distance, in miles, and estimated delay times.

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

Markup and Make Money:

In this lesson students will create their own imaginary store with at least 15 items to sell. They will begin with a discussion and then learn about markup. They will use their knowledge to calculate prices and create a display for their store. This is the first of 2 lessons (next lesson is Savvy Shopping, Resource ID 48879), which allows students to shop in their peer's store to calculate discount and tax.

Type: Lesson Plan

## Original Student Tutorials

Working With Proportions:

Roll up your sleeves and learn how proportions can be used in everyday life in this interactive tutorial.

Type: Original Student Tutorial

Estimating Tax and Tip:

Follow Hailey and Kenna as they estimate tips and sales tax at the mall, restaurants, and the hair salon in this interactive tutorial.

Type: Original Student Tutorial

Math at the Mall: Markups and Markdowns:

Let's calculate markups and markdowns at the mall and follow Paige and Miriam working in this interactive tutorial.

Type: Original Student Tutorial

Simple Interest:

Calculate simple interest and estimate monthly payments alongside a loan officer named Jordan in this interactive tutorial.

Type: Original Student Tutorial

Taxes, Fees, and Commission:

Explore sales tax, fees, and commission by following a customer service representative named Julian in this interactive tutorial.

Type: Original Student Tutorial

The Percent Times: Percent Increase and Decrease:

Learn to solve percent change problems involving percent increases and decreases in in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

<p>Ceramic glaze recipes are fluid and not set in stone, but can only be formulated consistently with a good understanding of math!</p>

Type: Perspectives Video: Professional/Enthusiast

Coffee Mathematics: Ratios and Total Dissolvable Solids:

Math - the secret ingredient for an excellent cup of coffee!

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Energy and Nutrition:

Calorie-dense foods can power the human body across the ocean? Feel the burn.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

<p>This teacher explains how a 3D-printed quadrat can be used with an M&amp;M sampling lesson to engage students when they explore how to use data from a random sample to draw inferences about a population.</p>

Type: Perspectives Video: Teaching Idea

Archimedes and the King's Crown:

This problem solving task uses the tale of Archimedes and the King of Syracuse's crown to determine the volume and mass of gold and silver.

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.

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.

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as many protein bars as magazines. Each protein bar costs \$0.70 and each magazine costs \$2.50. The sales tax rate on both types of items is 6½%. How many of each item can he buy if he has \$20.00 to spend?

Chess Club:

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Comparing Years:

Students are asked to make comparisons among the Egyptian, Gregorian, and Julian methods of measuring a year.

Finding a 10% Increase:

5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?

Friends Meeting on Bikes:

Using the information provided find out how fast Anya rode her bike.

Music Companies, Variation 2:

This problem has multiple steps. In order to solve the problem it is necessary to compute: the value of the TunesTown shares; the total value of the BeatStreet offer of 20 million shares at \$25 per share; the difference between these two amounts; and the cost per share of each of the extra 2 million shares MusicMind offers to equal to the difference.

Sale!:

Students are asked to determine which sale option results in the largest percent decrease in cost.

Selling Computers:

The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. How many computers must the sales team sell to receive the bonus? Explain your reasoning.

Stock Swaps, Variation 2:

Students are asked to solve a problem using proportional reasoning in a real world context to determine the number of shares needed to complete a stock purchase.

Stock Swaps, Variation 3:

Students are asked to solve a multistep ratio problem in a real-world context.

Tax and Tip:

After eating at your favorite restaurant, you know that the bill before tax is \$52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip?

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

Two-School Dance:

The purpose of this task is to see how well students students understand and reason with ratios.

## Teaching Ideas

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

Calculating Sharks-SeaWorld Classroom Activity:

• Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
• Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
• Given the conversion factor, students will be able to convert from metric to English units.

Type: Teaching Idea

## Tutorials

Percent Word Problem:

Learn how to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

## Student Resources

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

## Original Student Tutorials

Working With Proportions:

Roll up your sleeves and learn how proportions can be used in everyday life in this interactive tutorial.

Type: Original Student Tutorial

Estimating Tax and Tip:

Follow Hailey and Kenna as they estimate tips and sales tax at the mall, restaurants, and the hair salon in this interactive tutorial.

Type: Original Student Tutorial

Math at the Mall: Markups and Markdowns:

Let's calculate markups and markdowns at the mall and follow Paige and Miriam working in this interactive tutorial.

Type: Original Student Tutorial

Simple Interest:

Calculate simple interest and estimate monthly payments alongside a loan officer named Jordan in this interactive tutorial.

Type: Original Student Tutorial

Taxes, Fees, and Commission:

Explore sales tax, fees, and commission by following a customer service representative named Julian in this interactive tutorial.

Type: Original Student Tutorial

The Percent Times: Percent Increase and Decrease:

Learn to solve percent change problems involving percent increases and decreases in in this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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

## Perspectives Video: Professional/Enthusiasts

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

<p>Ceramic glaze recipes are fluid and not set in stone, but can only be formulated consistently with a good understanding of math!</p>

Type: Perspectives Video: Professional/Enthusiast

Archimedes and the King's Crown:

This problem solving task uses the tale of Archimedes and the King of Syracuse's crown to determine the volume and mass of gold and silver.

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.

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.

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Chess Club:

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Comparing Years:

Students are asked to make comparisons among the Egyptian, Gregorian, and Julian methods of measuring a year.

Finding a 10% Increase:

5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?

Friends Meeting on Bikes:

Using the information provided find out how fast Anya rode her bike.

Music Companies, Variation 2:

This problem has multiple steps. In order to solve the problem it is necessary to compute: the value of the TunesTown shares; the total value of the BeatStreet offer of 20 million shares at \$25 per share; the difference between these two amounts; and the cost per share of each of the extra 2 million shares MusicMind offers to equal to the difference.

Sale!:

Students are asked to determine which sale option results in the largest percent decrease in cost.

Selling Computers:

The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. How many computers must the sales team sell to receive the bonus? Explain your reasoning.

Stock Swaps, Variation 2:

Students are asked to solve a problem using proportional reasoning in a real world context to determine the number of shares needed to complete a stock purchase.

Stock Swaps, Variation 3:

Students are asked to solve a multistep ratio problem in a real-world context.

Tax and Tip:

After eating at your favorite restaurant, you know that the bill before tax is \$52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip?

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

Two-School Dance:

The purpose of this task is to see how well students students understand and reason with ratios.

## Tutorials

Percent Word Problem:

Learn how to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

## Parent Resources

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

## Perspectives Video: Professional/Enthusiasts

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

<p>Ceramic glaze recipes are fluid and not set in stone, but can only be formulated consistently with a good understanding of math!</p>

Type: Perspectives Video: Professional/Enthusiast

Archimedes and the King's Crown:

This problem solving task uses the tale of Archimedes and the King of Syracuse's crown to determine the volume and mass of gold and silver.

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.

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.

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as many protein bars as magazines. Each protein bar costs \$0.70 and each magazine costs \$2.50. The sales tax rate on both types of items is 6½%. How many of each item can he buy if he has \$20.00 to spend?

Chess Club:

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Comparing Years:

Students are asked to make comparisons among the Egyptian, Gregorian, and Julian methods of measuring a year.

Finding a 10% Increase:

5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?

Friends Meeting on Bikes:

Using the information provided find out how fast Anya rode her bike.

Music Companies, Variation 2:

This problem has multiple steps. In order to solve the problem it is necessary to compute: the value of the TunesTown shares; the total value of the BeatStreet offer of 20 million shares at \$25 per share; the difference between these two amounts; and the cost per share of each of the extra 2 million shares MusicMind offers to equal to the difference.

Sale!:

Students are asked to determine which sale option results in the largest percent decrease in cost.

Selling Computers:

The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. How many computers must the sales team sell to receive the bonus? Explain your reasoning.

Stock Swaps, Variation 2:

Students are asked to solve a problem using proportional reasoning in a real world context to determine the number of shares needed to complete a stock purchase.

Stock Swaps, Variation 3:

Students are asked to solve a multistep ratio problem in a real-world context.

Tax and Tip:

After eating at your favorite restaurant, you know that the bill before tax is \$52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip?

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

Two-School Dance:

The purpose of this task is to see how well students students understand and reason with ratios.