Using Beetles and Dance to Broaden Ideas about Math

Currently I’m participating in a slow-paced book study of Malke Rosenfeld’s fascinating book Math on the Move.  In it, Malke illustrates the amazing learning that happens when the body and math come together in both dance and non-dance settings. The book study goes until November 30th, so if it interests, go here.

In the Introduction, Malke writes how her ideas of mathematics have shifted through her work:

I used to think that math was some kind of inaccessible, abstract magic trick, a sort of in-joke that excluded us common folk, these days I appreciate that math is not that at all. The reality is…[math is] a large, expansive, multidimensional, intelligent, sensitive, expressive creature. [p. xiv, Math on the Move]

As I read this gorgeous quote, I was reminded of another book Malke co-authored. A book perfect for some summer time math-ing. A book that debucks the myth that math is all numbers and algorithms. Mathematics is an “large, expansive, multidimensional, intelligent, sensitive, expressive creature.” This week’s magical math book is a way to begin to show children this.

The Book

Socks are like Pants, Cats are like Dogs was written by Gordon Hamilton and Malke Rosenfeld and published in 2016 by Delta Stream Media, an imprint of Natural Math.


Gordon Hamilton is a board game and puzzle designer who founded with the primary objective to get 13 curricular unsolved problems into classrooms worldwide. Malke Rosenfeld  (@mathinyourfeet) is a percussive dance teaching artist and creator of the Math in Your Feet Program.

From the Natural Math website: Our early algebra book Socks are Like Pants, Cats are Like Dogs is filled with a diverse collection of math games, puzzles, and activities exploring the mathematics of choosing, identifying and sorting. Teachers and parents have tested all activities in real classrooms and living rooms. The activities are easy to start and require little preparation.

The bright, simply designed pages are easy to read and immediately invite exploration.  The especially lovely beetle photographs shown below are from the beetle collector Dr. Udo Schmidt.

Page 28, Socks are Like Pants, Cats are like Dogs, Rosenfeld and Hamilton

Variations and adaptions are given for different age groups. The book can be shared with multi-age groups of children and/or with the same child year after year. We suggest a target age of 3-8.

The Math

To outline the math in each activity, the book offers “keyword lists.” But these keywords will feel very different than the multiplication, addition, subtraction, division, fractions words you may be used to.

Here is a list of some of the key words to get a sense of the mathematics in the book: Sorting, categorizing, graph theory, attributes. multiples, grouping, units, patterns, rhythm, Venn diagrams, intersecting sets, shared/non-shared attributes, variables, symmetry, transformation, congruence, equivalence, same, similar, and  different.

What I find refreshing about this book is the amount of noticing it affords. Children are invited to notice connections, similarity and differences throughout all the activities.

The Magic

In the last year, I’ve been really drawn to mathematical learning 3-5 year olds and the important mathematical work preschool teachers do every day (as mentioned in @crskreger’s tweet below).

While I wholeheartedly believe @Erikonmath and @crskreger’s message, most of my work has been with older children and adults. Thus it was important for me to experience part of that work (e.g, Stringing beads) to see the mathematics involved in preschool for myself. Socks are like Pants, Cats are like Dogs outlined a lovely collection of activities to explore this foundational work of choosing, identifying and sorting math.

Beading Patterns

I have to admit, I haven’t strung many beads with children before this book. And so I had yet to experience first hand the math talk that this activity can inspire.

While my two year old was able to string a few beads on the pipe cleaner, he mostly played “hockey” by shooting the beads off the table with the pipe cleaner.  However,as I listened and watched him string beads, I got some insight into his beginning notions of binary situations. As he pulled the beads on and off the pipe cleaner, he would say “on” and “off” . Later that day, I listened as he did the same with light switches in the house and the water from the faucet (“on” and “off”). By sharing the Bead Pattern activity with him, I began to see his sense making in a new light. A mathematical light.

Here are some images from my older children’s beading patterns. Sometimes we ran out of colors (see bottom right, orange was substitute for pink). Sometimes they goofed around and didn’t want to follow the directions in the activity.



But the bead pattern play brought about interesting patterns nonetheless. For example, here is my 8 year old’s creation below. There was symmetry and “opposites” involved. He was careful to reverse bead patterns each each loop (eg., on the bottom black look notice pink-purple-pink on one side becomes purple-pink-purple on the other).



Create Your Own Matching Game

Here’s a slide show (4 scenes) of the matching game cards my children made together. They were incredibly proud and were so happy to play “their game.” They selected the shapes/colors and designs for each pair in the game.



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This is Like That

This activity was something my 5 and 8 year old enjoyed chatting about.  As they shared the book in another room together,  I eavesdropped and listened to them share their ideas. [In this activity, one places the four objects so that when they are connected by the line segment you can justify why “This is like that”]

Page 11, Socks are Like Pants, Cats are like Dogs, Rosenfeld and Hamilton

Beetle Sort

In this activity, my children got to be entomologists and notice similarities and differences among different bug families. This was a big hit in our family.  Even for me, who is not a fan of bugs, I enjoyed categorizing these beautiful beetles with my children.

Page 28, Socks are Like Pants, Cats are like Dogs, Rosenfeld and Hamilton

Throughout the book my children remarked how much fun they were having. Note: They do not say this while they are completing the summer “math” packets sent home by their school. The math is Socks are like Pants, Cats are like Dogs is fun. And it is a different type of math.  Math is a “large, expansive, multidimensional”  subject. If you think you are not a “math person” because you haven’t been successful in the past, perhaps you just haven’t found your math.


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


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