• Title of Book: If You Hopped like a Frog
  • Author: David M. Schwartz
  • Publisher: Scholastic Press/1999
  • ISBN: 0-590-09857-8
  • Grade Levels for Recommended Use: 4th -6th grade
  • TEKS:
  • Knowledge and skills:

(11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area.

(A) Estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary;

(B) Perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system;

(2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions.

(C) Use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates;

(3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships.

  • Brief Summary:

The book "If You Hopped like a Frog" by David Schwartz is full of interesting facts that help students visualize and think about proportional reasoning. If you hopped like a frog, he says, you could jump from home plate to first base in a single bound. He also speaks about ants and snakes and other creatures in the same way, and uses proportional reasoning and amazing pictures to help students see what would happen if they too had the same abilities.

  • Materials needed:
  • The book
  • Handouts/ papers
  • Pens/ pencils/ crayons or markers: For drawing
  • Some students might need rulers.
  • Candies
  • 5 paper frogs.
  • Suggested Activity:
  • Reading the book.
  • Handout:
  • Pass the handout to each student (Appendix I).
  • Explain the handout.
  • Put candies in the basket, each candy has number (1-20) on it.
  • Each student takes a candy from the basket and does the question on the handout which has the same number with the candy.
  • Activity – Create a candy clock:
  • Give every student a piece of paper, and then ask them to draw the animals of the questions and calculate the result of the questions. Then, draw the same proportion result on the paper as well.
  • Total time of this activity is 5 minutes.
  • After 5 minutes, ask 5 volunteers to share their questions with the whole class.
  • Each volunteer can get a paper frog as reward.
  • Adapted by Yi-Ju Tien 2012

20 problems from http://mindfull.wordpress.com/2008/02/24/if-you-hopped-like-a-frog-proportional-reasoning/

and the link of her (frogproblems).

  • Appendix I

If you Hopped Like a Frog

Read the story “If You Hopped Like a Frog” by David Schwartz. Then pick your own example below. Create your own “If you could” poster. Be sure to include the following:

  • Pick the number from the basket.
  • Draw the animal(s) from the question number you picked.
  • Calculate your question.
  • Draw your result of "if I could do the same as (animal name), I would be able to do (result)".
  • I will pick 5 volunteers to share their posters with the whole class.

1. A dolphin’s brain is 7 times larger than the human brain (average human brain is 140 mm wide and 167 mm long). Make a visual representation of a human brain and a dolphin brain on paper. / 2. A snake can open its jaws to 5 times its normal size to eat. Show with a visual representation what the jaws would look like if human (you) could do the same thing. Length? / 3. Cockroaches move 50 body-lengths per second. If you moved at the same rate, how fast would you move? / 4. A giraffe’s neck is almost half its total height. If your neck was in the same proportion, how long would it be?
5. The orangutan’s reach (arm span) from finger-tip to finger-tip is 10 times the size of its hand. If you had the same proportions, what would your arms span be? / 6. A moth eats 86,000 times its own body weight in its first 56 days of life. If human babies did the same, how much baby food (in ___ ounce jars) would a 7 pound human baby eat in 56 days? / 7. At birth a kangaroo baby is only a sixtieth the size of its mother in length.
If you were in the same proportion to your mother when you were born, how long would you be? / 8. A pygmy shrew eats its own body weight in food every three hours. How much food would a human (you) with the same characteristic eat in 24 hours?
9. A kiwi bird lays an egg that is three fourths its size. If you had the same characteristics, how big would the egg be? / 10. A flea can jump 100 times its height. If you could do the same thing, how high could you jump? / 11. The scarab beetle can lift 850 times its own weight. If you could do the same thing, how much could you lift? / 12. Cows produce one-eighth of their weight in saliva every day. If you did the same thing, how much saliva would you produce?
13. A red deer’s antlers are as wide as 3/5 of its body length If you had antlers in the same proportion, how wide would they be? / 14. An African elephant’s ears are half of its height. If your ear were in the same proportion, how big would they be? / 15. A baby crocodile grows to be 4000 times its weight at birth. How much would a 7-pound human baby weigh as an adult? / 16. A bee can pull 300 times its weight. If you (125 lb.) could pull a load in this same proportion, how many pounds could you pull?
17. The sperm whale’s head is 1/3 of its body. If your head were in the same proportion, how big would it be? / 18. A polar bear can eat 10 percent of its body weight in 30 minutes. If you could do the same, how much would you eat in 30 minutes? / 19. An octopus’ arms are seven-tenths of its length. If your arms were in the same proportions, how long would they be? / 20. A proboscis monkey’s nose is approximately one-seventh of the monkey’s length. If a human nose were in the same proportion, how long would it be?

You have 5 minutes to solve your questions and finish the drawing. The first 5 volunteers who share their pictures and answers can get secret gifts.