Description
What our Ratio and Rate Word Problems lesson plan includes
Lesson Objectives and Overview: Ratio and Rate Word Problems focuses on word problems that deal with rate, a ratio that compares two different types of quantities. The lesson uses proportions to solve the word problems, and uses a variety of real- world examples so students will understand that math is relevant to their everyday lives. At the end of the lesson, students will be able to solve real-world, multi-step word problems regarding ratios and unit rates. This lesson is for students in 5th grade and 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 addition to the lesson activity is to have your students also compare cell phone companies for unit rates to determine which company is the better deal. An optional adjustment to the activity is to have your students pick three companies and services to compare of their choice. You could also have your students compare prices of actual items in the classroom such as cost per ounce of cereal and bring in the cereal boxes or noodle bags. Finally, you could have your students write problems using magazine circulars.
Teacher Notes
The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.
RATIO AND RATE WORD PROBLEMS LESSON PLAN CONTENT PAGES
Rate Word Problems
The Ratio and Rate Word Problems lesson plan includes two content pages. Rate are specific types of ratios that compare two different types of quantities. Rates are also ratios that expresses how long it takes to do something, such as traveling a certain distance, packing a certain number of boxes, or creating a scale model. When you use proportions to solve a real-world problem, it is very important to compare the quantities in the same order every time.
Example 1
Let’s look at an example! Miranda runs 4 km in 30 minutes. At that rate, how far could she run in 45 minutes?
The first step is to write a verbal comparison (the two items being compared) and proportion. In this example, you’re comparing kilometers and minutes. When setting up your proportion, you can place the two things you’re comparing in any order. For this example, you can put kilometers in either the numerator or denominator without changing the final outcome.
Next, place the information that corresponds to one another in the first fraction and the extra piece of information in the second fraction. Use a variable (such as x) to represent the unknown quantity you are solving for. Your problem will be set up as: kilometers/minutes = 4/30 = x/45.
The second step is to use cross-products to solve: 4/30 = x/45 becomes 4(45) = 30x, which becomes x = 6. The final step is to write the numeric answer with the correct unit. The answer to this problem is 6 kilometers.
Example 2
Let’s look at another example. In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long. However, a model was used for the beetle that was really only 20 inches long. A 30-inch tall model building was also used in the movie. How tall did the building seem in the movie?
The first step is to write the comparison and proportion: Movie size (ft) / actual size (in) = 50/20 = x/30. Next, use cross-products to solve: 50(30) = 20x becomes x = 75. Finally, write the numeric answer with the unit: 75 feet.
Examples 3 & 4
Let’s look at two more examples. These examples deal with unit rates, which are a type of rate with a denominator of zero. To solve unit rates, you need to divide the numerator by the denominator. Let’s explore this with our examples.
You go to the grocery store and are looking for the best deal on cheese. The first one that you see cost $3.95 for 20 ounces. How much does one ounce cost (what is the unit rate)? To solve, you set up a proportion and solve: 3.95/20 = 0/1957. Therefore, one ounce of the first cheese costs about 20 cents.
You look further around and see another brand of cheese. It is on sale for $4.29 for 24 ounces. How much does one ounce cost (what is the unit rate)? You solve in the same way: 4.29/24 = 0.17875. One ounce of the second cheese costs about 18 cents.
The better deal is the second cheese, because it costs about 2 cents less per ounce!
RATIO AND RATE WORD PROBLEMS LESSON PLAN WORKSHEETS
The Ratio and Rate Word Problems lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.
SERVICES COMPARISON ACTIVITY WORKSHEET
For the activity worksheet, students will research four services (Netflix, Hulu, Amazon Prime, and Local Cable) to determine which service provides the best deal on movies and television shows. They will calculate the unit rate per day for each company. Finally, they will decide which service they would choose based on price and the services offered.
WORD PROBLEMS PRACTICE WORKSHEET
The practice worksheet asks students to solve two ratio and rate word problems. They will show their work.
RATIO AND RATE HOMEWORK ASSIGNMENT
Like the practice worksheet, for the homework assignment, students will solve two ratio and rate word problems. They will show their work.
QUIZ
This lesson also includes a quiz that you can use to test students’ understanding of the lesson material. For the quiz, students will answer a multi-part word problem, making sure to show their work.
Worksheet Answer Keys
This lesson plan includes answer keys for the practice worksheet, the homework assignment, and the quiz. 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.
