# MAFS.7.RP.1.3Archived Standard

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
General Information
Subject Area: Mathematics
Domain-Subdomain: Ratios & Proportional Relationships
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. (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.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Units may be the same or different across the two quantities.
• Calculator :

yes

• Context :

allowable

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question:

Nicole bought a meal in a town that has no sales tax. She tips 20%.

Select all meals Nicole could buy for less than or equal to \$15.

• Difficulty: N/A
• Type: MS: Multiselect

• Test Item #: Sample Item 2
• Question: James pays \$120.00 for golf clubs that are on sale for 20% off at Golf Pros. At Nine Iron, the same clubs cost \$8.00 less than they cost at Golf Pros. They are on sale for 13% off.

What is the original cost of the clubs at Nine Iron?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

Ads Galore makes posters with standard dimensions of  inches by 11 inches as shown.

Both the length and width of the poster may vary by , according to Ads Galore's regulations.

What is the smallest acceptable area of one poster, rounded to the nearest thousandth of a square inch?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## Educational Games

Estimator Four:

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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

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

Tiffany‘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

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

Estimating: Counting Trees:

This lesson unit is intended to help you assess how well students are able to:

• Solve simple problems involving ratio and direct proportion.
• Choose an appropriate sampling method.
• Collect discrete data and record them using a frequency table.

Includes worksheets and student work examples, including specific feedback and analysis of misconceptions

Type: Formative Assessment

## Lesson Plans

Netting 4 Bugs:

This is a STEM challenge in which students design and create a net to collect macroinvertebrates in simulated streams. Then students analyze the quality of their nets by the amount of macroinvertebrates they are able to collect. After testing, they will redesign to improve their nets. The final test will be done by evaluating a simulated stream's water quality. Students will conduct a simulated bioassessment of a stream by sampling macroinvertebrates and evaluating a stream's water quality using a pollution tolerance index. They learn about the human impact on waterways and the importance of using aquatic macroinvertebrates to monitor water quality.

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

STEM-Water Filtration:

This is a STEM-Engineering Design Challenge lesson. Students will go through the process of creating a water filtration system using their knowledge of the impact that humans have on the Earth and percent change.

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

Prom Preparations:

Students will make decisions concerning features of their prom. Students will perform operations with percent and decimals to solve real-world problems involving money.

Type: Lesson Plan

Summer Camp Fun:

In this problem, students will work in groups to rank summer camps. They must first calculate the discounted price of each camp by applying a discount percentage. Then they must calculate the number of weeks they can attend each camp based on the discounted price and predetermined budget. There are 5 students going to the camp. Students will be given a data set to help them develop a procedure for ranking the camps. In their teams, they will write a letter giving their procedures and explanation of the strategy they used. Students will practice adding, subtracting, multiplying and dividing numbers to the thousands and will work with percentage discounts. Rubrics are included to help evaluate student work.

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

Developing a Sense of Scale:

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who use inappropriate additive strategies in scaling problems, which have a multiplicative structure, rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems and see multiplication as making numbers bigger, and division as making numbers smaller.

Type: Lesson Plan

Increasing and Decreasing Quantities by a Percent:

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

• translating between percents
• decimals and fractions
• representing percent increase and decrease as multiplication
• recognizing the relationship between increases and decreases

Type: Lesson Plan

Family Restaurant:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best choice on purchasing cooking ingredients for a family who runs a restaurant 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

Students will learn how to calculate markup, markdown, percent increase and percent decrease. Through the use of sales "ad" inserts in newspapers and store flyers, students will understand how these concepts apply to them in real-world situations.

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

Pop-A-Tag: Buying Clothes at a Thrift Shop:

Students will participate in a simulation where they purchase clothing items and determine the total cost of their purchases, including tax and any discounts offered.

Offered as a cooperative group activity, they will simulate being the customer and the sales person. The activity can be modified for independent work, however, the move toward real-world problem solving and Mathematical Practices suggest that it be an activity involving discussion and collaboration between students.

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

Increasing and Decreasing Quantities by a Percent:

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

• Translating between percents, decimals, and fractions.
• Representing percent increase and decrease as multiplication.
• Recognizing the relationship between increases and decreases.

Type: Lesson Plan

Savvy Shopping:

This is the second part of a lesson on this standard. You can find the first part under Markup and Make Money. In Savvy Shopping students will go shopping at a store of their peer 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

Scientific calculations from a distant planet:

Students will act as mathematicians and scientists as they use models, observations and space science concepts to perform calculations and draw inferences regarding a fictional solar system with three planets in circular orbits around a sun. Among the calculations are estimates of the size of the home planet (using a method more than 2000 years old) and the relative distances of the planets from their sun.

Type: Lesson Plan

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

Type: Lesson Plan

Stock Market MEA:

Students will calculate percents and ratios to determine which stock would be the best to invest into. They will be provided a selection of stocks and their cost, growth potential, risk and expert analysis. After developing a procedure for choosing the best stock, they will present their findings orally to the class, describing the analysis that they conducted during their procedure.

Type: Lesson Plan

The Human Population Growth Rate:

Just how quickly is the world's human population growing? In the US and other developed countries, the current growth rate is slow compared to some developing countries where it is speeding up. There are factors that slowed down this growth rate and there are similar factors that actually speed it up. Discussing and explaining the factors that determine the fluctuation in growth rate.

The US population growth between 1950 - 2000 is 7.5 times slower than that of India. In 1950 the US had a population of 80 million which increased every ten years with 1 million.

Type: Lesson Plan

Makeover, Home Edition Part II:

This is the second part of the Unit Lesson, "Makeover, Home Edition". This lesson will continue focusing on unit prices, but also incorporates area and volume as well. Part I (Makeover, Home Edition #48705) is based on creating backyard dimensions for fencing. Part III (Makeover, Home Edition #49025) will deal with creating a scale drawing of this backyard. Part IV (Makeover, Home Edition Final #49090) focuses on inserting a window and painting walls inside the house.

Type: Lesson Plan

Water Troubles:

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water.  Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water.  They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials.  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

The Most Beneficial Bank:

In this Model Eliciting Activity, 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

Best Day Care Center in the Neighborhood:

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the best day care center in the neighborhood for the residents of Dream Living Housing Community. 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

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

Shopping & Dining with Proportions:

In this lesson, students will take an imaginary trip to a retail store and enjoy dinner with their friends while using proportions to calculate sales tax, tips and discounts.

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

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

Disappearing Frogs: Percentage and Environment:

Students must explore and assess the implications various human and environmental factors are having on the yellow-legged frog population in California. Then, they must choose one avenue to attempt to help save these animals. Some options will work quickly, while others will take time to implement. However, the ones that take longer to implement are generally more likely to be effective for a longer period of time. Students will use knowledge of percentages to calculate population size and will complete research to explore the affects of human impact on the environment and the process of adaptation through natural and artificial selection.

Type: Lesson Plan

Markup and Make Money:

In this lesson students will create their own 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 on this standard with the following lesson, Savvy Shopping, Resource ID 48879, allowing students to shop in their peer's store to calculate discount and tax.

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

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

## 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

The Science and Math Behind Sour Fizzy Candy:

Master candymaker Wes Raley describes the process and science behind making sour fizzy candy.

Type: Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

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

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

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.

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.

Sand Under the Swing Set:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

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.

Cooking with the Whole Cup:

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

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.

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.

Lifting a Lion:

"Students will work in groups to solve a real-world problem presented by the book: How Do You Lift A Lion? Using a toy lion and a lever, students will discover how much work is needed to raise the toy lion. They will use proportions to determine the force needed to lift a real lion" from TI World Math.

SeaWorld Snack Shop - SeaWorld Classroom Activity:

In this problem-solving activity, challenges students to take on the role of a Food Services Manager placing orders for a snack shop at Sea World. To solve the problem they will use data and proportional reasoning to make predictions and communicate findings.

## Teaching Ideas

A Penny Saved is a Penny at 4.7% Earned:

There are lots of ways to receive income, and lots of ways to spend it. In this EconomicsMinute teaching idea, students will develop two budgets, or plans, to help them decide how to allocate their income.

Type: Teaching Idea

Statistics and Shopping:

This lesson is designed to develop students' understanding of taking percentages related to multiple markdowns and sale prices when shopping. This lesson provides links to discussions and activities related to the topic as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Teaching Idea

## Tutorials

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship.

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions.

Type: Tutorial

Percent Word Problem:

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

Type: Tutorial

Using the Proportion Method to Solve Percent Problems:

This site explicitly outlines the steps for using the proportion method to solve three different kinds of percent problems. It also includes sample problems for practice determining the part, the whole or the percent.

Type: Tutorial

## Unit/Lesson Sequence

Percents: What's the Use?:

This activity focuses on the use of percents in situations involving discounts and taxes. The students are assigned an interview to discover the use of percents in various careers. Working in pairs and using shopping catalogues, they will further their knowledge of percents by calculating discounts and taxes. To access their knowledge of percents, there is a writing activity and an assignment to create a menu with questions and an answer key.

Type: Unit/Lesson Sequence

## Virtual Manipulative

Mixtures:

In this online activity, students apply their understanding of proportional relationships by adding circles, either colored or not, to two different piles then combine the piles to produce a required percentage of colored circles. Students can play in four modes: exploration, unknown part, unknown whole, or unknown percent. This activity also includes supplemental materials in tabs above the applet, 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

## STEM Lessons - Model Eliciting Activity

Best Day Care Center in the Neighborhood:

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the best day care center in the neighborhood for the residents of Dream Living Housing Community. 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.

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.

Disappearing Frogs: Percentage and Environment:

Students must explore and assess the implications various human and environmental factors are having on the yellow-legged frog population in California. Then, they must choose one avenue to attempt to help save these animals. Some options will work quickly, while others will take time to implement. However, the ones that take longer to implement are generally more likely to be effective for a longer period of time. Students will use knowledge of percentages to calculate population size and will complete research to explore the affects of human impact on the environment and the process of adaptation through natural and artificial selection.

Family Restaurant:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best choice on purchasing cooking ingredients for a family who runs a restaurant 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.

Prom Preparations:

Students will make decisions concerning features of their prom. Students will perform operations with percent and decimals to solve real-world problems involving money.

Stock Market MEA:

Students will calculate percents and ratios to determine which stock would be the best to invest into. They will be provided a selection of stocks and their cost, growth potential, risk and expert analysis. After developing a procedure for choosing the best stock, they will present their findings orally to the class, describing the analysis that they conducted during their procedure.

Summer Camp Fun:

In this problem, students will work in groups to rank summer camps. They must first calculate the discounted price of each camp by applying a discount percentage. Then they must calculate the number of weeks they can attend each camp based on the discounted price and predetermined budget. There are 5 students going to the camp. Students will be given a data set to help them develop a procedure for ranking the camps. In their teams, they will write a letter giving their procedures and explanation of the strategy they used. Students will practice adding, subtracting, multiplying and dividing numbers to the thousands and will work with percentage discounts. Rubrics are included to help evaluate student work.

The Human Population Growth Rate:

Just how quickly is the world's human population growing? In the US and other developed countries, the current growth rate is slow compared to some developing countries where it is speeding up. There are factors that slowed down this growth rate and there are similar factors that actually speed it up. Discussing and explaining the factors that determine the fluctuation in growth rate.

The US population growth between 1950 - 2000 is 7.5 times slower than that of India. In 1950 the US had a population of 80 million which increased every ten years with 1 million.

The Most Beneficial Bank:

In this Model Eliciting Activity, 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.

Water Troubles:

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water.  Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water.  They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials.  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.

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.

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.

## MFAS Formative Assessments

Finding Fees:

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

Gasoline Prices:

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

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

Tiffany‘s Tax:

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

## Original Student Tutorials Mathematics - Grades 6-8

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.

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.

Simple Interest:

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

Taxes, Fees, and Commission:

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

The Percent Times: Percent Increase and Decrease:

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

Working With Proportions:

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

## Student Resources

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

## 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 Games

Estimator Four:

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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

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/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

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

Type: Perspectives Video: Professional/Enthusiast

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.

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.

Sand Under the Swing Set:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

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.

Cooking with the Whole Cup:

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

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.

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

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship.

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions.

Type: Tutorial

Percent Word Problem:

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

Type: Tutorial

Using the Proportion Method to Solve Percent Problems:

This site explicitly outlines the steps for using the proportion method to solve three different kinds of percent problems. It also includes sample problems for practice determining the part, the whole or the percent.

Type: Tutorial

## Virtual Manipulative

Mixtures:

In this online activity, students apply their understanding of proportional relationships by adding circles, either colored or not, to two different piles then combine the piles to produce a required percentage of colored circles. Students can play in four modes: exploration, unknown part, unknown whole, or unknown percent. This activity also includes supplemental materials in tabs above the applet, 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 benchmark.

## Perspectives Video: Professional/Enthusiast

Ratios and Proportions in Mixing Ceramic Glazes:

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

Type: Perspectives Video: Professional/Enthusiast

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.

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.

Sand Under the Swing Set:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

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.

Cooking with the Whole Cup:

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

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.

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.