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