CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.
📲Technology Required
⏰TIME
45 minutes
📃SUMMARY
In this lesson students are given definitions of ratio and rate and examples of computing rate and distance. Students complete a short assignment using animals observed outdoors as the data for computing ratio, rate and proportion. An alternative assignment is given for students learning at home or otherwise requiring modification. The lesson concludes with game play.
📚LESSON
Mini-lecture
Begin with this Google slides presentation defining ratio and rate and including examples of rate and distance problems. Students learning at home can read the presentation and do the activities and problems on their own.
OPTIONAL VIDEO
If your students are having difficulty understanding the problems, this video may help.
An example of solving time, rate and distance problems
Compute rate, ratio and proportion
In this short assignment, also linked in the Google slides presentation, using animals observed outdoors as the data for computing ratio, rate and proportion.
Everyone needs to get a partner. You and your partner will go outside and each count as many different species of animals as you can. Do this for exactly 5 minutes. Two of the exact same kind of animal only count as one species.
After 5 minutes is up, find the ratio of your animals compared to your partner’s list of animals.
Next, find the rate. How many animals did you see per minute?
Lastly, your group shall compare your ratio to another group. Are they proportional or non-proportional?
An alternative assignment is given for students learning at home or otherwise unable to work outside with a partner, where students find animals in two slides.
End with a game
Students play AzTech games for 15 minutes to end the lesson. Time-rate-distance problems are included as a bonus question in AzTech: The Story Begins and are required to win the game in AzTech: Meet the Maya.
Assessment
Once students have played the game, you can look in the AzTech teacher reports to see an individual students response. You will need to know your students’ usernames. To see an example of a report, enter the username “ddtester” .
CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.
CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations
⏰Time Required
30-45 minutes
📲Technology Required
Projector and computer required to watch video in class. Alternatively, students can be assigned to watch on computer, phone or tablet at home. Google apps or PowerPoint required for slide presentation.
📃Lesson Summary
Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.
📚Lesson Plan
This lesson plan assumes that your students understand simplifying complex fractions. They should know how to divide a fraction by an integer or by another fraction.
1. Watch video explaining unit rates
2. Solve a problem as a class
Using this Google slides presentation, students solve a problem together as a class. They are reminded the meaning of “reciprocal” and that in dividing one fraction by another, you multiply by the reciprocal of the fraction in the denominator. Additional slides give students instruction and tips on solving rates problems that include complex fractions.
3. Solve a variety of problems involving rates and complex fractions
Assign the problems, have the students give these a try and then correct together as a class.
Select some of the problems to review together and assign the remainder as homework.
Assign the problems for students to complete individually, as either in-class work or homework and grade using the answer key provided.
4. Watch a video of a student applying ratio and proportion
At this point, many students will still need further clarification. In this video, Eva shows how she uses ratio and proportion to reduce a recipe for 4 dozen cookies to one for 2 dozen cookies.
Assessment
Students will be assessed based on performance on the problems provided.
State Standards
Missouri Learning Standard 7.RP.A.1
Minnesota Math Standard 7.2.2.1 – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.
CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
CCSS.Math.Content.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. (Common Core Standards)
📃 Summary
Time-rate-distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time. Because we have found many students struggle with this type of problem, we find it so helpful to have multiple examples through videos, slides, and through a video game. In all of these problems, students solve for distance. Video, game and presentation resources are available in both English and Spanish.
The formula for distance problems is:
distance = rate × time or d = r × t
📲 Technology required
The game AzTech: The Story Begins can be played for free on iOS (iPad and iPhone) and in a web browser on any computer. The game can be installed in an iPad and played off-line by students who do not have reliable Internet access.
⏰ Time required
15-25 minutes – time varies depending upon discussion of questions and length of game play allowed.
📚 Lesson Plan
Watch video introducing students to Time-Rate-Distance problems
Introducing time-rate-distance problems 3:04
This brief video uses number bonds as one means of finding the total number of hours, then multiplies hours by rate to find the total distance. We work step by step through an example to find how far Spanish troops needed to ride to attack the Aztecs.
2. Video or Presentation of time-rate-distance example
How many miles did Grandma drive? 1:24
Teaching Options
Students can watch another video solving for distance. If it takes 2 1/2 days to get to Honduras from Iowa, and Grandma drives 60 miles per hour without stopping, what is the distance from Iowa to Honduras? This video solves the problem step by step, beginning with converting 2.5 days to hours.
3. Video or Presentation of a second time-rate-distance example
How far is Iowa from Texas? 1:19
Teaching Options
Students can watch another video solving for distance. If it takes Grandpa one day to get from Iowa to Texas and he drives 55 miles per hour, what is the distance from Iowa to Texas? This video shows, step by step, how to solve this problem.
Bonus question in level 1 of AzTech: The Story Begins
Play AzTech: The Story Begins. Not only will students have fun and be exposed to educational content on Latin American history, but they will also have to answer mathematics questions to progress. Instruct students to be sure to answer the first bonus question, shown above. Remind them that the icon at the bottom of the screen can be used to pull up a calculator. (There is no arrow on the screen in the game. It is merely shown above for emphasis.) Once students have played the game, you can look in the AzTech teacher reports to see an individual students response. You will need to know your students’ usernames. To see an example of a report, enter the username “ddtester” .
State Standards
Minnesota Math Standard 6.2.3.2 – Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.
Minnesota Math Standard 7.1.2.1 – Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.
Minnesota Math Standard 4.1.1.3 – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.
