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If You Hopped Like A Frog
Author: David M. Schwartz
Illustrator: James Warhola
Publisher: Scholastic Press
Copyright: 1999
ISBN: 0-590-09857-8
Number of Pages: 32
Ohio Standards Alignment: Grades 5–8

Through illustrations as well as text, this book introduces the concepts of ratio and proportion by comparing what humans would be able to do if they had the capabilities of different animals. For example, if you ate like a shrew, you could devour more than 700 hamburgers in a day! The last pages of the book provide all the facts that validate the claims and explain how they translate into human terms. The measurements for each ratio are listed, along with questions that help students calculate the equivalent ratio for their own measurements.

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How to Use This Book
Highlights and Insights
Related ORC Resources
Ohio Standards

 


How to Use This Book

  • The book can be used as an introduction to the concepts of ratio and proportion or as applications for older students.  
  • Students can use the questions at the end of the story as problems that they can calculate using their own body measurements.
  • Students can use the book as a starting point and then find ratios that are not listed (e.g., the distance at which a dog can identify the odor of a certain quantity of material) and then calculate the human body's ability to do the animal task.
  • Teachers or students could, time permitting, make paper models to show one or two of the ratios more concretely than the book illustrations can. The hands-on experience makes the mathematical conclusions more "real" to students.

Highlights and Insights

  • The facts in this book are important as real-world connections.
  • This approach to ratio and proportion would hold the interest of many students. 
  • This topic is important, especially at the 7th grade level, where proportionality has been designated a curriculum focal point by NCTM.

Related ORC Resources

How Many Noses Are in Your Arm?
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ORC# 130
Resource Information
Resource Type: Lessons
Discipline: Mathematics
Grades: Grade 6
Professional Commentary: In this lesson, students view a picture or video of the Statue of Liberty and are asked how long the arm would be if the nose measures 4 feet 6 inches. Given chart paper, string, and rulers, students work in groups to develop their own strategies for finding the solution....
Earth, Moon, and Mars Balloons
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ORC# 4648
Resource Information
Resource Type: Lessons
Discipline: Mathematics
Grades: Grade 6
Professional Commentary: Making a scale model of the solar system is not a novel idea, but this site restricts its consideration to the Earth, Moon, and Mars and explains in more detail than most. Using balloons for the planetary bodies makes the actual construction simple....
Alphabits
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ORC# 119
Resource Information
Resource Type: Lessons
Discipline: Mathematics
Grades: Grade 6
Professional Commentary: Students list questions of a mathematical nature that could be asked about the contents of a box of Alphabits cereal. They decide to investigate the percent of each letter of the alphabet found in a box of Alphabits....
Measuring Up : Lesson 6 - In Your Shadow
View Full RecordAdd to My ORC Collection
ORC# 3957
Resource Information
Resource Type: Lessons
Discipline: Mathematics
Grades: Grades 6–7
Professional Commentary: On a sunny day, students measure their height and the length of their shadow and use proportional reasoning to find the heights of various tall objects by measuring the lengths of the shadows of the objects. A recording sheet, questions for students, assessment options, and ideas for teacher reflection are included....

Ohio Standards

Number, Number Sense and Operations Standard
    Benchmarks (5-7)
    D. Use models and pictures to relate concepts of ratio, proportion and percent.
    I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.
    Grade Level Indicators (5)
    1. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
    Grade Level Indicators (6)
    5. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
    14. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
Measurement Standard
    Benchmarks (5-7)
    B. Convert units of length, area, volume, mass and time within the same measurement system.
    Grade Level Indicators (5)
    5. Make conversions within the same measurement system while performing computations.
    Grade Level Indicators (7)
    2. Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters.
    4. Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.