Description

What our Unit Rate Problems lesson plan includes

Lesson Objectives and Overview: Unit Rate Problems teaches students how to understand and solve unit rate problems in mathematics. At the end of the lesson, students will be able to solve unit rate problems including those related to unit pricing, constant speed, and others. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional adjustment to the lesson activity is to the increase the number of problems for the activity. If you would like to include a quiz or test, you can use the activity problems. For an additional activity, you could distribute grocery store flyers to your students and have them compare prices between different stores. Finally, you could have your students review the MPGs of several cars and determine cost for trips to different cities based on the price of fuel.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

UNIT RATE PROBLEMS LESSON PLAN CONTENT PAGES

Ratio Review

The Unit Rate Problems lesson plan includes four content pages. Ratios compare values. They describe how much of one thing there is compared to another thing. We can show ratios in three different ways. First, we can use a colon to separate the values. Second, we can use the word “to”. Third, we can represent it as a fraction.

Let’s look at these three ways using an example. The lesson shows a diagram of four squares, three of which are green and one of which is blue. We can show this example’s ratio in each of the three ways mentioned earlier: we can use a colon to separate the values (3:1), use the word “to” (3 to 1), and represent it as a fraction (3/1).

We can also scale ratios higher. Using the same example, we can scale the ratio 3:1 up to 6:2. This is the same as creating an equivalent fraction. Even though the numbers are higher, the ratios are equal.

It’s important to understand ratios, because they show up in everyday life. For example, maybe a person making cookies needs 3 cups of flour to make 5 dozen cookies. The ratio of flour to cookies is 3 cups to 5 dozen, or 3:5. However, what if they want to make 15 dozen cookies instead? To triple the number of cookies, they also need to triple the amount of flour, so the ratio stays the same. 3 cups/5 dozen = 9 cups/15 dozen. They need 9 cups of flour to make 15 dozen cookies.

Solving Unit Rate Problems – Example Problems

To solve unit rate problems, the first step is understanding ratios. The lesson includes a few example unit rate problems to show the different kinds of unit rate problems that students might encounter. These examples questions include:

• A 12 oz box of cereal costs $1.99, but a 16 oz box costs $2.59. What is the better value?
• A painting’s size is 6 x 9 feet (length and width), you have a piece of poster paper 12 inches wide. What length must it be for you to accurately redraw the painting?
• On vacation, your mom drove 200 miles in 4.5 hours. What was her average speed or rate per hour?
• Three cases of soda cost $10. About how much would 1 case of soda cost?
• A worker can mow three lawns in about seven hours. About how many lawns could he mow in 40 hours?

These questions include real-world problems that we can solve by understanding the use of ratios and how to find unit rates.

Another Example Problem: Shirts on Sale

Next, the lesson walks through another example problem. Let’s imagine that you are at a store and have to decide whether to purchase one item for a certain price or possibly save money by purchasing more of the same item for a higher price. You can use ratios to figure out whether or not you can save money by buying more of that item.

As a specific example, let’s say that the cost of a T-shirt with an image of a musical group on the front is $12.99 per shirt. However, the shirts are on sale and you can buy 3 for $29.97. If you only want one shirt, you can buy the single shirt for $12.99. However, the sale may interest you. To decide if it’s worth it, you can find the rate for 1 shirt if you buy 3 on sale. How much would you save if you purchased 3 shirts on sale versus 3 shirts at the regular price?

To figure this out, you can set up two ratios (called a proportion) to determine the unit rate (x) or cost of 1 shirt: 3 shirts/$29.97 = 1 shirt/x dollars. Next, cross-multiply: 3x = 1 x $29.97 or 3x = $29.97. Finally, solve by dividing the $29.97 by 3 which equals $9.99. Therefore, x = $9.99. The cost of one shirt at the sale price is $9.99, so you would save $3.00 per shirt buying them on sale. However, before buying them just because they’re on sale, make sure to ask yourself if you actually need two more shirts!

Two More Example Unit Rate Problems

The lesson closes with two more examples. When reading through these problems, take note of the different set-ups for the ratios and proportions in each problem. The same units may be written across from each other or atop one another.

Let’s look at example 1: A worker can mow 3 lawns in about 7 hours. The worker wants to determine how many lawns he can mow in a full week or 40 hours. At the same rate, how many lawns could he mow in one week?

For this problem, the equation for the solution is 3 x 40 = 7x or 7x = 120. To solve, divide the 120 by 7 to get 17.14 (x = 17.14). Therefore, at the same rate, the worker can mow about 17 lawns per week or 17 lawns every 40 hours.

Finally, let’s look at example 2: A drive to the beach is 350 miles, and it will take about 6 hours to get there in a car. My family will then drive to the mountains which are about 200 miles from the beach. At the same rate, about how many hours will it take to drive from the beach to the mountains?

For this problem, the equation for the solution is 350x = 6 x 200 or 350x = 1200. To solve, divide 1200 by 350 to get 3.42 (x = 3.42). Therefore, at the same rate, the drive to the mountains will take almost three and a half hours.

The lesson concludes with a reminder of some important information about unit rates. The unit rate is the value of one of something. For example, miles per hour (or mph) is a unit rate—miles per hour describes the number of miles traveled in one hour.

When setting up ratios and proportions, writing the words the numbers stand for or using currency symbols for money is an easy way to keep track of the different parts of the unit rate. Understanding how to determine unit rates makes solving unit rate problems in everyday life easy!

UNIT RATE PROBLEMS LESSON PLAN WORKSHEETS

The Unit Rate Problems lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

CREATING PROBLEMS ACTIVITY WORKSHEET

Students will work with a partner to complete the activity worksheet. Each pair will create five different unit rate word problems to be solved by another pair of students. Their word problems should include a variety of scenarios and questions. Once complete, they will exchange their problems with another pair of students. They will also solve the problems created by the other pair. Finally, they will meet and check their answers.

WORD PROBLEMS PRACTICE WORKSHEET

For the practice worksheet, students will solve 10 word problems by finding each unit rate or the total, rounding their answers if necessary. Then, they will solve five additional word problems.

UNIT RATE HOMEWORK ASSIGNMENT

The homework assignment asks students to first compare the amount per price of an item at two different stores and determine which is a better deal and how much someone would save with that deal. Next, they will read two word problems and solve four problems related to each.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.