More Math Book Magic from David M. Schwartz

A big thank you and a dozen virtual roses to our 1st guest math book magic seeker.  Jenny Jankowski is a middle school mathematics teacher from the Chicagoland area. I met Jenny a few years back while working on revisions to the elementary math curriculum Everyday Mathematics. It was a pleasure to be part of her team. Her students are lucky to have her!   Now that she’s back in the classroom, I was excited for her to share her experiences using picture books with older students.

Here is the a bit about the Book, the Math, and the Magic from Jenny’s classes.


 I shared “If You Hopped Like a Frog” with my 6th and 7th grade students.


This picture book is written by David M. Schwartz, illustrated by James Warhola, and printed by Scholastic Press. David M. Schwartz is the author of many popular math and science books for children. [Math Book Magic wrote about two of Schwartz’s books here and here. ] Amazon has a suggested age of 7-10, but I used it with older students and they enjoyed it as well.


My 6th and 7th graders had completed units on ratios and proportional reasoning earlier in the school year. We were in the midst of PARCC testing and I only saw each class a few times and so we were doing an additional mini unit on proportional reasoning. I used this book to launch those ideas again. Students tend to naturally think additively and for some it is a struggle to think more multiplicatively when making comparisons. [For more on the difference between additive and multiplicative reasoning, here is a video and here is a lovely resource from the Alberta Regional Consortia.]


While reading, students most strongly reacted to the strength of the ant, the growth of the baby, and all the animals with unusual eating habits such as the pelican, shrew, chameleon, and the snake. They enjoyed the illustrations and were straining to see them. They laughed at the illustration of the snake and the pelican.

image 1
Image from If You Hopped like a Frog

Some students jokingly compared themselves or their friends to the shrew who eats a lot in comparison to its size. In all my classes, I reread the statistics about the baby because students were so shocked and many uttered “Huh?”. It was surprising to them to think about how fast they grow before they are born.

After we read, we shared our favorite parts.  Here is a few things the middle schools shared.

“The spider was my favorite because I really didn’t know spiders were really fast.”

“I found out that shrews can eat a lot which was surprising for me because that’s A LOT OF FOOD.”  

“The ratio comparing growth rate in your first 9 months to the rate before you were born was surprising. I was surprised to find out how you would be taller than a mountain and heavier than millions of elephants.”

“Shrews eat lot like me.”

 “My favorite would have to be the pelican because it was funny.”

Afterwards, I had students do some of the comparisons in the book using their own measurements. It made me realize how using real world comparisons for measurements helped students visualize large numbers and get a stronger understanding of ratios. 

image 2
Student work. This student misread the scale factor as 3 to begin with and then changed to scale factor of 5 later on and ran of time at the end of class to correct the error in her work.


One pair of students were asked to imagine how much food they would eat if they were a shrew. These two particular students chose to imagine what food they would want to eat that large of a quantity of (e.g., seafood, pizza, spaghetti). Personalizing the comparisons shared in the book allowed students to be engaged and interested in the topic of ratios. I liked that David M. Schwartz included the pages in the back.

image 3
Back Pages, If You Hopped like a Frog

As shown above, the back pages dove deeper into the math for each animal and asked readers to apply it to their own measurements. Reading this magical math book reminded me how even middle schoolers enjoy a good picture book and how relating our topic of study to themselves is a great way to hook them.


Thanks so much Jenny for sharing your mathbookmagic! And readers, if you (or someone you know) might want to share some math book magic from your class or a home, we’d love to hear!  See below for how to contact us.

Have a magical math book you’d like share? Please go to the Shared booklist to find out how.  If you’d like to receive these magical math book posts every other Monday, be sure to follow this blog in the side bar of this page.

Thanks and see you in two weeks!  #mathbookmagic





  1. I have used this book frequently with students. Younger students like the pictures. After the first example I challenge them to come up with their ideas for comparisons. If you were as strong as an ant, what would you be able to do? For middle level, students could be challenged to research an animal and create, measure, calculate, and illustrate their own animal/human feats. Assignments like this allow for differentiated learning as student work at their ability level to write new stories. Middle level and high school students will find a whole new interest in creating and solving proportions.


  2. […] It was on Twitter that I first heard about him using this week’s magical math book. I asked if he would be willing to write a guest post, and he graciously agreed. His magical post arrived the day my family was leaving for our first trip to the magical land of Disney.  As if I wasn’t already on cloud nine, I was jumping for joy that my dream of having this blog be a place where math book magic is shared was coming true once again. […]


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s