*Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.*

**Subject Area:**Mathematics

**Grade:**7

**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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**

Units may be the same or different across the two quantities.**Calculator :**yes

**Context :**allowable

**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

## Related Access Points

## Related Resources

## Assessments

## Educational Games

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## Unit/Lesson Sequence

## Virtual Manipulatives

## STEM Lessons - Model Eliciting Activity

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.

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.

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.

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.

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.

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.

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 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.

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

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.

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

## Student Resources

## Educational Games

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

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

## Educational Software / Tool

This manipulative is a versatile online savings calculator that calculates both simple and compounding interest. This free online calculator calculates and graphs accrued interest and total savings balance. The calculator allows for a variety of variables including interest rates, initial investment, time, compounded interest, and whether there are regular deposits made.

Type: Educational Software / Tool

## 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!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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?

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

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

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Type: Problem-Solving Task

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

## Tutorials

This video demonstrates how to write a decimal as a percent.

Type: Tutorial

This video demonstrtates a visual model of a percent greater than 100.

Type: Tutorial

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 Manipulatives

This virtual manipulative allows the student to enter any two of the three quantities involved in percentage computation: the whole, a part and the percent. This manipulative can also be used for the discussions of relations among fractions, decimals, ratios and percentages.

Type: Virtual Manipulative

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

## Educational Software / Tool

This manipulative is a versatile online savings calculator that calculates both simple and compounding interest. This free online calculator calculates and graphs accrued interest and total savings balance. The calculator allows for a variety of variables including interest rates, initial investment, time, compounded interest, and whether there are regular deposits made.

Type: Educational Software / Tool

## 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!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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?

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

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

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.

Type: Problem-Solving Task

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

## Teaching Idea

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

## Virtual Manipulative

This virtual manipulative allows the student to enter any two of the three quantities involved in percentage computation: the whole, a part and the percent. This manipulative can also be used for the discussions of relations among fractions, decimals, ratios and percentages.

Type: Virtual Manipulative