Multiplication course; functions and functionals; playful calculus – Newsletter August 15

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I am Moby Snoodles, and this is my newsletter. I love to hear from you at

Moby Snoodles

WOW – Multiplication! An open online course for parents and teachers

To sign up or for more info, email

Multiplication and division are areas where many kids lose their fight against dreary, rote methods of teaching mathematics. Most children who start to believe they aren’t good at math never recover enough to go into science, technology, or engineering fields. How can you change that for your kids and their friends?

Multiplication real tables

In the first week of the course, we will discuss researcher-developed, parent-tested activities where multiplication is meaningful, beautiful, and fun. In the second week, you will gather your kids and their friends in a casual Math Circle, and then answer a few questions about the experience.

As with most of our courses, we have adapted the activities for all ages from toddlers to adults. Where young ones go on a scavenger hunt for pretty snowflakes and cool truck wheels, older kids build bridges from multiplication to symmetry, spatial transformations, and proportions.

Combinations Model

WOW – Multiplication! is a pilot study for a citizen science project for mathematics education. By actively participating in the course, you help us learn what support parents and teachers need to start informal Math Circles, and how to adapt materials for each learner’s unique needs. We are excited to invite you to contribute to original scientific research!

We are starting the course on Monday, September 9. The course is for parents, teachers, and leaders of math playgroups and Math Circles with children of any age. The goal is to learn deep structures that are the foundation of multiplication – through quick games you can play for years.

You can expect to spend about two hours a week on the course, including reading, forum discussions, and activities with children. There will be optional live meetings online.

If this sounds like a course for you and yours, e-mail

A young girl reinvents functionals

Katie and her adventurous mom are inventing functions, compositions of functions, and even functionals (functions of functions)!

A few days ago I introduced the concept of a function to Katie, and again the credit for the idea goes to Moebius Noodles, this time the book. Since I wanted Katie to right away think that functions are really cool, my first example was: girls can go in and princesses come out.  Katie was in disbelief.  ‘That doesn’t exist,’ she said.  I told her that functions can be real or make believe.

One of the coolest aspects of math is making your own imaginary worlds. Pretend-play leads into mathematical “What if?” inventions:

My three favorites from her were: 1) boys go in and boys come out (the identity function!), 2) goats go in and sheep come out, sheep go in and goats come out, and 3) one function goes in and another one comes out.

Moebius Noodles book page 49

Picture: two pages from the Moebius Noodles book.

Playful explorations inspired by calculus

We are starting to collect young calculus activities, at our Facebook page and at a math ed LinkedIn group we frequent. Our math ed friends have a lot of questions and fears about “calculus for five-year-olds” – and even more inspired ideas! Growth and toy roller-coasters for kids? Joseph Austin writes:

As for “teaching” differential equations to children, I would start with the “exponential growth” equation: y’ = ky. You could teach this with a game based on the “each one teach one” principle, doubling the number at each iteration.

Next, I’d introduce the concept of velocity and acceleration, that is, “speed” and “increasing speed”: “how fast is the car or bicycle or snowball speeding up as it rolls down the hill?” If you do it in reverse, you get Zeno’s paradox!

Tony Cron offers an interactive polygon limit exploration. See a similar idea at Guillermo Batista’s “Intuitive introduction to limits.”

Polygons in a circle

Jeanie Clemmens has another idea about limits.

This is fun, thinking like a five year old and an adult math person at the same time. What if ten children divide one pie equally, then a hundred children, then a thousand divide the same pie equally. Children should see that the size of the pieces gets smaller and smaller approaching zero. Likewise, ten children returning their pieces to the pan, or a hundred, etc. never adds up to more than one pie, i.e. there is a limit both ways.

Share your young calculus ideas at our question and answer hub!

WRAL interview in the Go Ask Mom series

Go Ask Mom

Sarah Hall wrote the story and made a short video clip of us talking about the Moebius Noodles book.

The two authors say collaboration between parents and kids is an important part of the process. They’d love to see math games and activities become a regular part of family life just like bedtime stories or playing catch. In many cases, they’ve heard from parents who say they’re learning right along with their kids as they play the games.


You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything as you wish, as long as you share your creations on the same terms. Please credit

More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA



Talk to you again on August 30th!

Moby Snoodles, aka Dr. Maria Droujkova

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