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Grade: Middle
Subject: Mathematics

#3513. Proportions

Mathematics, level: Middle
Posted Mon Jul 11 14:57:23 PDT 2005 by Marilyn Schmelzle (
Eastgate Middle School, Kansas City, MO, USA
Materials Required: "If You Hopped Like a Frog" by David Schwartz, pencil, paper, worksheet
Activity Time: two 45 minute class periods
Concepts Taught: proportions, fractions

--Schwartz, David. (1999). If you hopped like a frog. New York. Scholastic Press.

The student will be able to perform mathematical operations to create proportional measurements. Missouri Standards Addressed:
-solve problems involving proportions, such as scaling and equivalent ratios

Input (including procedures):
Start the lesson off by reading If You Hopped Like a Frog by David Schwartz. Be sure to read the "Dear Reader" letter at the beginning. Tell the students that Mr. Schwartz was able to figure this out by using math!!!
After reading the book, ask the students if they have any idea how Mr. Schwartz was able to come up with these facts. If the students don't bring up "PROPORTIONS" or setting up fractions, offer that as a suggestion.

Using the first fact that a frog can hop 20 times its body length, demonstrate how to find how far you could hop using your own height.
Point out to the students that the same unit should be in the same place for each fraction. For example, object height in the numerator and hopping distance in the denominator of both fractions.

Guided Practice:
Provide a couple of example proportions for the students to solve such as: 2/ 3 = 7/ x or 4/9 = x/27

Check for Understanding:
Ask students to explain how the solved for x. Check their work while waiting for all students to complete the examples.

Independent Practice:
When the students are finished, give them an animal fact from the book (found at the back of the book) OR have students research some interesting animals facts on their own. With the animal facts, they will need to take their own body measurements with the help of their partners to figure out how far, in feet, inches, miles, etc. they could perform a task by setting up a proportion. Instead of using an item in the book, for example. . ..telephone pole, Statue of Liberty, baseball field, have them suggest another distance that would be equivalent to the figures that they created. Be sure to have almanacs, encyclopedias, and other reference books available for them to search for information. I have attached a record sheet for the students to show their work.

None required

Students could create their own PAGE illustrating their fact and combine all student pages into a class book.


Math Name __________________
If You Hopped Like a Frog Record Sheet Hour ____Date ___________

1. Measure your own height.

in inches: ____________
in centimeters: _________________
in meters: ____________
in feet: ________________

2. State your animal fact:

3. Set up your proportion:

4. Solve your proportion (SHOW ALL WORK):

5. State a new distance or object using your new fact. You may use the encyclopedias, internet, almanacs, etc. to locate a new object for your fact.