**Number:**MA.7.AR.3

**Title:**Use percentages and proportional reasoning to solve problems.

**Type:**Standard

**Subject:**Mathematics (B.E.S.T.)

**Grade:**7

**Strand:**Algebraic Reasoning

## Related Benchmarks

## Related Access Points

## Access Points

## Related Resources

## Educational Game

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiasts

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## Student Resources

## Original Student Tutorials

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

## 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

## Perspectives Video: Professional/Enthusiasts

<p>Get fired up as you learn more about ceramic glaze recipes and mathematical units.</p>

Type: Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

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

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

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

## Tutorials

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

## Parent Resources

## Perspectives Video: Professional/Enthusiasts

<p>Get fired up as you learn more about ceramic glaze recipes and mathematical units.</p>

Type: Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

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

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

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