About This Chapter
Standard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. (CCSS.Math.Content.7.RP.A.1)
About This Chapter
This chapter presents lessons critical to understanding and applying proportions and ratios to real-life scenarios. Students will learn to define proportions and ratios, solve for missing elements of proportions, and work with unit rates across various units of measurement. This chapter includes lessons on:
- Defining proportionality
- Calculating proportions and ratios
- Finding an unknown in a proportion
- Calculations of unit rates associated with ratios of fractions
Students who have mastered these lessons will correctly identify proportions and understand their relationship to ratios. They will learn to apply concepts of ratios and proportions across a wide variety of real-world scenarios. These lessons help build the foundation for further analysis of units and rates.
How to Use These Lessons in Your Classroom
Here are some ideas for ways to incorporate the lessons in this chapter into your classroom instruction.
Build your own test
Watch the Calculations with Ratios and Proportions video in class, which defines ratios and proportions and provides several examples of each. Assign students the homework of creating a list of 10 things in their daily life which can be represented by ratios. They then must create a word problem which describes the ratio and asks to solve for an unknown in a proportionate ratio. Randomly distribute completed homework among the students the next day and have them complete the tests their classmates created.
Lesson application and assessment
Assign the videos and their associated quizzes in this chapter as homework. Have students measure the distance from their home to work using an online mapping service and measure how long it takes to get to school in the morning. Have each student identify their mode and rate of travel at the start of class. Ensure students understand that they must represent distance or time as improper fractions if they exceed a whole.
Analyzing weekly activities
Have students keep a daily journal with approximate amount of time they perform a given activity (e.g. school, homework, watching television, playing games, or doing chores). At the end of the week total the sums of time spent in each activity, expressed as a fraction of the week (requiring students to convert minutes and hours to weeks). Have them calculate relationships between activities, such as the ratio of how much homework they do versus how much TV they watch or of how much school they attend over how much they sleep.
1. Proportion: Definition, Application & Examples
When we want to compare one ratio, or fraction, to another equivalent ratio, it's a proportion. Learn all about proportions and practice solving proportion problems in this lesson.
2. Calculations with Ratios and Proportions
Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.
3. How to Find an Unknown in a Proportion
Artists, engineers, athletes, and accountants all use proportions in their daily lives, and setting them up is really quite easy, once you know the rules. In this lesson, you'll learn how to solve proportions when there is an unknown value and work on some practice problems.
4. Calculating Unit Rates Associated with Ratios of Fractions
This lesson demonstrates a few different ways to calculate unit rates. We use them to solve problem such as how many beats per minute, or how many miles per hour. To master this lesson, you must understand how ratios and fractions will help to find the unit rate based off of a higher ratio of values.
Earning College Credit
Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Common Core Math Grade 7 - Ratios & Proportional Relationships: Standards course