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

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students 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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.  Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students 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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson 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

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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson, students will 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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students 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

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

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

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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students 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

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

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students 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

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Type: Perspectives Video: Professional/Enthusiast

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

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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?

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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?

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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?

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

• 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

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

Type: Tutorial

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

Type: Tutorial