# MA.7.AR.3.1

Apply previous understanding of percentages and ratios to solve multi-step real-world percent problems.

### Examples

Example: 23% of the junior population are taking an art class this year. What is the ratio of juniors taking an art class to juniors not taking an art class?

Example: The ratio of boys to girls in a class is 3:2. What percentage of the students are boys in the class?

### Clarifications

Clarification 1: Instruction includes discounts, markups, simple interest, tax, tips, fees, percent increase, percent decrease and percent error.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Percent of Change
• Percent Error
• Rate
• Simple Interest

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students solved mathematical and real-world problems involving percentages, ratios, rates and unit rates. Students then solve multi-step real-world percent problems in grade 7 and solve multi-step linear equations of any context in grade 8.
• Instruction includes discounts, markups, simple interest, tax, tips, fees, percent increase, percent decrease and percent error (MTR.7.1).
• Markdown/discount is a percentage taken off of an original price. Instruction includes showing the connection between subtracting the calculated discount or taking the difference between 100% and the discount and multiplying that by the original price.
• For example, if there was a 15% discount on an item that costs \$15.99, students could take 85% of \$15.99 or take 15% of \$15.99 and subtract that value from the original price of \$15.99.
• Markup showcases adding a charge to the initial price. Markups are often shown in retail situations.
• Simple interest refers to money you can earn by initially investing some money (the principal). The percentage of the principal (interest) is added to the principal making your initial investment grow. The formula, $I$ = $P$$r$$t$, represents $I$=interest, $P$=principal, $r$=rate, and $t$=time. When using simple interest, provide the formula as students should not be expected to memorize this.
• Tax, tips and fees are an additional charge added to the initial price. Students can add the calculated tax, tip or fee to the original price or add 1 to the tax, tip or fee to reach the final cost.
• For example, if there was a 6% sales tax on clothing and a t-shirt costs \$7.99. Students can add 100% to the 6% and multiply that value to \$7.99 or students can find 6% of the \$7.99 and add that to the original value of the t-shirt.
• Percent Increase/Percent Decrease asks students to look for a percentage instead of a dollar amount. Students should discover that they can use the formula below to help become more flexible in their thinking.

• Percent Error is a way to express the size of the error (or deviation) between two measurements.
• Use bar models to model percent increase and decrease problems.
• For example, if you are finding percentages that are in multiples of 10%, your bar model may look like the model below.

To showcase the percent increase, you would add additional boxes into the bar model. If you are showcasing a percent decrease, then you would cross out boxes for the decrease (MTR.2.1).
• Use bar models, double number lines, tables or other visual representations to model relationships between percentages and the part and whole amounts (MTR.2.1).
• Double Number Line

• Table

Instruction includes the use of patterns when using a table. In the example above, students can use the idea of 100% being 300 and using this knowledge to find other percentages. 10 is of 100, so students can divide by 10. To find 20%, students can multiply their solution from 10% by 2. The pattern can continue to relate common connections between percentages (MTR.5.1).
• Reinforce how percentages relate to fractions and decimals. Help students write equivalent ratios to represent problems using reasoning about the relationships between the quantities.
• Instruction includes using proportional relationships and multiplicative reasoning to solve problems.

### Common Misconceptions or Errors

• Students may incorrectly place the decimal point when calculating with percentages. If students have discovered the shortcut of moving the decimal point twice, instruction includes understanding of how a percent relates to fractions and decimals. Refer to MA.7.NSO.1.2 to emphasize equivalent forms.
• Students may forget to change the percent amount into decimal form (divide the percent by 100) when setting up an equation (MTR.3.1).
• Students may incorrectly believe all percentages must be between 1 and 100%. To address this misconception, provide examples of percentages below 1% and over 100%.
• Students may incorrectly believe a percent containing a decimal is already in decimal form.
• For example, emphasize that 43.5% is 43.5 out of 100 and dividing by 100 will provide the decimal form.
• In multiple discount problems, students may incorrectly combine the discounts instead of working them sequentially (MTR.5.1).
• For example, 25% off, then 10% off could incorrectly lead to 35% off rather than finding 25% off before calculating the additional 10% off.
• Students may incorrectly invert the part and the whole in the percent problem. To address this misconception, students should use bar models to help visualize and make sense of the problem (MTR.2.1).

### Strategies to Support Tiered Instruction

• Instruction includes the use of estimation to find the approximate solution before calculating the actual result to help with correct placement of the decimal point and reasonableness of the solution.
• Teacher provides opportunities for students to use a 100 frame to review place value for and the connections to decimal, fractional, and percentage forms.
• Teacher provides support for students in dividing by 100 to change percent into decimal form. Teacher supports by providing calculators, manipulatives and base ten blocks to multiply decimals.
• Instruction includes having students take different percentages of the same amount, such as 40% of 80, 4% of 80, 0.4% of 80, 0.04% of 80 and 400% of 80. Students can be given the flexibility to provide the answer as decimal or fraction and compare.
• Teacher provides support for students when solving multi-discount problems and combining the discounts. Instruction might begin with a single step discount problem in a real-world context.
• For example, teacher can include local sale flyers with products that students are interested in buying. Have students explain how to apply the multi-discounts with a comparison of the difference in costs when combining the discounts incorrectly.
• Teacher provides opportunities for students to reason and think about multiple discount problems by providing prompts.
• For example, “if a pair of jeans are 50% off with an additional 50% off, does that mean the jeans are 100% off, or free?” or “what if the jeans are 75% off with an
• additional 50% off, does that mean the jeans are 125% off and the store now owes
• you money to take them?”
• Teacher provides opportunities for students to comprehend the context or situation by engaging in questions (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
• What do you know from the problem?
• What is the problem asking you to find?
• Can you create a visual model to help you understand or see patterns in your problem?
• Teacher provides support when solving multi-discount problems, by providing students with a table to keep track of the information in the problem.
• Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
• First, read the problem with the purpose of answering the question: What is the problem, context, or story about?
• Second, read the problem with the purpose of answering the question: What are we trying to find out?
• Third, read the problem with the purpose of answering the question: What information is important in the problem?
• Teacher encourages the use of bar models to help visualize and make sense of the problem.
• Instruction includes understanding of how a percent relates to fractions and decimals if students have discovered the shortcut of moving the decimal point twice. Refer to MA.7.NSO.1.2 to emphasize equivalent forms.

SurfPro Shop and The Surfer Store both sold surfboards for \$350. In February, SurfPro Shop wanted to increase their profits so they increased the prices of their boards by 15%. When this increase failed to bring in more money, they decreased their price again by 10% in November. To beat their competitor who had increased prices, The Surfer Store decided to decrease their price of surfboards by 10% in March. However, when they started to lose money on the new pricing scheme, they increased the price of surfboards in November by 15%.
• Part A. If no other changes were made after November, which store now has the better price for surfboards?
• Part B. What is the difference between their prices?

### Instructional Items

Instructional Item 1
A college’s intramural soccer team has 30 players, 60% of which are women. After 22 new players joined the team, the percentage of women was reduced to 50%. How many of the new players are women?

Instructional Item 2
Miguel takes out a loan that adds interest each year on the initial amount. What is the interest Miguel will pay on the loan if he borrowed \$5,000 at an annual interest rate of 4.5% for 15 years? (Use the formula $I$ = $P$$r$$t$, where $I$ is the interest, $P$ is the principal or initial investment, $r$ is the interest rate per year, and $t$ is the number of years.)

Instructional Item 3
Massimo lost his mathematics textbook. The school charges a lost book fee of 70% of the original cost of the book. If Massimo received a notice he owed the school \$73.50 for the lost textbook, what was the original cost?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## 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))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.AR.3.AP.1: Solve simple percentage problems in real-world contexts.

## Related Resources

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

## 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

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

Discount and Tax:

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

Type: Formative Assessment

## Lesson Plans

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

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

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

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

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

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

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

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

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

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

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

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/Enthusiast

Coffee Mathematics: Ratios and Total Dissolvable Solids:

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

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

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

Type: Perspectives Video: Teaching Idea

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.

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?

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.

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

## Tutorial

Percent Word Problem:

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

Type: Tutorial

## STEM Lessons - Model Eliciting Activity

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.

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.

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

Discount and Tax:

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

Finding Fees:

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

Gas Station Equations:

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

Gasoline Prices:

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

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.

## Student Resources

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

## Original Student Tutorials

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

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.

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?

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.

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.

## Tutorial

Percent Word Problem:

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

Type: Tutorial

## Parent Resources

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

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.

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?

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.

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?