Beginning Algebra: Proportions

Lesson: Introduction to Setting Up and Solving Proportions

Essential Questions for students (objectives):

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Can you solve for an unknown using proportions?
Can you apply a proportion to a real-life situation?

Common Core Standard: 7.RP.1-2

Book: If You Hopped Like a Frog
Facts on animals handout
White paper, measuring tapes, rulers, glue sticks

Instructional Format:
Teacher lead instruction, cooperative groups

Vocabulary for a Word Wall:
Proportion, fraction


1) Introduction (20 minutes): Teacher starts the lesson by introducing a basic proportion. For this lesson, I would focus on converting measurements (i.e. miles to feet) and solve for an unknown. Allow students to practice sample problems individually or in pairs. For example 48in/x = 12in/1ft.

2) (10 minutes) Read If You Hopped Like a Frog. Ask the students how the author knows that his assumptions are true? Share with them how he solved the problems illustrated and explained at the end of the story. Work one of the situations the author created by setting up the proportion for them.

3) (6-10 minutes) Have the students check a different problem that is given in the book. Ask them to work with a partner to generate some information that they would need in order to solve the problem. Open the discussion up as a class to address what information is needed. Give any information they request or let them know that it might not be important, then have them solve the proportion to check.

4) (20 minutes) Break students up into groups of four. Each student needs a piece of white paper, a measuring tape, and glue stick. Assign each group an animal from the "facts on animals" sheet (you should have these cut up in advance). Each group will get the facts on the animal and one cut-out of the animal to glue on their own paper. As a group, they need to work together for everyone to create their own page in If You Hopped Like A Frog. They will have to decide how to use the information given, set-up a problem on their paper, solve the problem on their paper, and have each group member ready to explain their own work.

5) (15 minutes) As a class, move to an open area (hallway, courtyard) taking the students' problems and measuring tapes. Each group will present their problem, show how the problem is set-up, how it was solved, and they will need to demonstrate their answer for the group. For example, if they were solving about being able to run as fast as a spider, they would need to mark off 50 yards to show everyone that they would be able to run that far in ONE second. I would ask each group member to do a different part of the presentation so no individual student does all the talking. [tip: assign the parts of the presentation a number, then have the group members number off, that is the role they will have to present]

6) Optional assignment: Have students research animal facts on their own and write and illustrate their own page from the book.

7) Extension: Present students with the Proportion Problems worksheet. All of these problems can be solved using proportions. In groups, they might want to see if they can set-up the proportions (solving may not need to be the focus at this time). After examining the problems, it is important to have a class discussion/brainstorming session on what traits they notice about the word problems that could help distinguish them as proportion problems.

Prior Knowledge/ Possible Warm-up Activities:
Basic Multiplication, one step equation solving

Time needed:
1 hour and 20 minutes

Assessment (Acceptable Evidence):
Students are to create their own page from If You Hopped Like a Frog, showing all calculations. Also, they must present to their peers and show a measurement. 

Attached worksheets or documents:
Facts on Animals
Proportion Problems

Cautionary notes/ misconceptions:
Setting up proportions is much more difficult for students that solving them. I would practice quite a bit at the beginning staying with basic measurement conversions. I wouldn't make it too difficult at the onset, so that the students can delve into the topic with this activity and assignment. Then I would move on to more difficult conversions. It is very important to stress to students that similar parts (units) should be in the same part of the fraction before they do this lesson. However, the lesson is designed to encourage the students to struggle and think about important information as well as if their answer makes sense.

I would caution a teacher to set up groups homogeneously on the creating a page of the book assignment. The hippo and the leopard are the easiest animals to create a problem from the information given.

Optional Assignment: Be careful to explain to students that they need to research more than one piece of information on their animal/insect (that was the point of brainstorming needed information) and they will need to use one piece of related information on themselves. I always warn students that it is not acceptable to say, a deer has large antlers, so if I were a deer, I would have large antlers.

Extension: These problems are from released copies of the Nevada State High School Proficiency Exam. Most students miss these types of problems because they don't recognize them as proportion problems.

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