I’ve had this blog post kicking around in my mind for a month or so. During that month it has morphed from not quite started to not quite finished. But I’m leaving on a work trip next week and decided to push publish today.

There are so many great math and science ideas that researchers are sharing publicly these days. These ideas have led to dozens of really fun projects that I’ve been able to share with my kids. So, for anyone looking for neat math and science ideas to share with middle school through high school students, I’ve put together a bunch of projects below that were really memorable. All of these projects were inspired by work that experts were sharing publicly – and I’m incredibly grateful that they all took the time to share their ideas.

So, this one is definitely not one of my better written posts, but don’t let my poor writing get in the way of these really fun math and science ideas to share with kids.

**(1) Heather Macbeth’s talk about developable surfaces**

In the winter of 2018 I saw Heather Macbeth – now a math professor at Fordham – give a amazing lecture about developable surfaces at MIT. The mathematical properties of these shapes are incredible all by themselves, but what made the talk especially neat was that Macbeth shared ways to make these shapes on your own! These surfaces are a great way for kids to be surprised by the shapes you can make from simply twisting pieces of paper!

Sharing developable surfaces with kids thanks to a brilliant lecture from Heather Macbeth

**(2) Richard Green’s number theory problem**

Richard Green is a math professor at the University of Colorado. He used to share his ideas on Google+, so unfortunately I’m not sure if his original posts still exists or not, but at least we go through one of his a bit one of his number theory posts in the first video in the project below. We used several of Green’s posts for projects – this one is about a neat question in number theory about representing integers in different bases.

Another great piece of math to share with kids from Richard Green

**(3) Alissa Crans’s JMM Talk**

Alissa Crans is a math professor at Loyola Marymount University and gave a great talk at the Joint Math meetings two years ago. The ideas in Crans’s talk inspired me to share some basic group theory with kids

Sharing an idea from Alissa Crans’s JMM talk with kids

**(4) Sharing the image of the black hole**

The image of the black hole is one of the most exciting scientific achievements that I can remember getting to see! Since doing the project below with my younger son I’ve learned a bit more and been to a few more talks. It feels like the more I learn about the project the more amazed I am that the team was able to accomplish what they did. Actually, at this point I can’t believe that anyone thought it was even possible in the first place – ha!

When the image was published I was able to find ideas about the image shared by three physics professors, Chanda Prescod-Weinstein from the University of New Hampshire, Katie Mack from North Carolina State, and Leo Stein at Ole Miss. There was also a nice Ted talk by Katie Bouman, one of the computer scientists involved in the project who was a post doc at MIT at the time and is now at Caltech.

All of that information inspired me try to share some ideas about the image with my younger son.

Sharing ideas about the plack hole picture with a 7th grader

**(5) Laura DeMarco and Kathryn Lindsey’s folded fractals**

An article in Quanta Magazine introduced me to the absolutely fascinating work of Laura DeMarco and Kathryn Lindsey on folded / folding fractals. DeMarco is a math professor at Northwestern and Lindsey is a professor at Boston College. This topic is probably as far out of reach for kids as the black hole image is (!), but the article gave several neat ways to play around with the ideas. Allie helped us hold one of the shapes in our hand by sewing one of the examples in the article:

We also made a 3d print – it was really fun to share these ideas with the boys:

Sharing Laura DeMarco and Kathryn Lindsey’s 3d folded fractals

**(6) Nassim Taleb’s statistical ideas**

Sharing statistical ideas from Nassim Taleb with the boys has been an absolute joy since explaining the ideas helps me understand them better. Taleb is terrific at explaining the ideas in ways that are easy to understand and then backing up the explanations with deep mathematical explanations if you want to dig deeper.

Explaining some statistical ideas from Nassim Taleb to kids

**(7) Ole Peters ideas about ergodicity and economics**

I’m a gigantic fan of the work that Ole Peters is doing at the London Mathematical Laboratory. That work, I think, is going to cause many people to see financial risk in a totally new light. As with Taleb’s work, I love sharing Peters’s work with my kids since explaining it helps me understand the work better.

An insight from Ole Peters that can help kids see some pitfalls in summary statistics

**(8) Chanda Prescod-Weinstein and Bruce Macintosh sharing a neat idea from astronomy**

This example is one that I felt especially lucky to see – thanks to a retweet from Chanda Prescod-Weinstein – as it shows how concepts from high school math courses are used to solve problems in physics and astronomy. It also shows that ideas in physics that initially might not seem super hard can be pretty tricky.

The start of Bruce Macintosh’s twitter thread that inspired our project is here – Macintosh is an astronomy professor at Stamford:

A neat logarithm example for kids thanks to Chanda Prescod-Weinstein and Bruce Macintosh

(9) Laura Taalman’s math and 3d printing work

I don’t even know what to say – Taalman has been such a huge influence on me and has showed me how 3d printing can be used to help students explore math. Here’s just one example:

Rather than a single blog post, here is a link to a all of our projects inspired by Laura Taalman’s work:

All of our blog posts inspired by Laura Taalman

**(10) A neat mathematical game shared by Jordan Ellenberg **

Ellenberg is a math professor at the University of Wisconsin. We’ve used several of the ideas that he’s shared on his blog and in his book How not to be Wrong for projects. We used his post about a neat math game with a quarter circle just yesterday – it was sort of the motivation to get going and write up this collection of projects.

Sharing Jordan Ellenberg’s “Quarter Circle Game” with kids

**(11) Katherine Johnson work at NASA **

Katherine Johnson was a mathematician at NASA, is a Presidential Medal of Freedom winner, and was one of the inspirations for Margot Lee Shetterly’s *Hidden Figures*. After seeing the movie I was interested in finding ways to share some of her work with the boys. Fortunately the NASA technical papers are available online, and I used ideas from one of her papers for two projects with my older son:

An attempt to share some of Katherine Johnson’s math ideas from Hidden Figures with my son

Using an idea from one of Katherine Johnson’s NASA technical papers to introduce polar coordinates

**(12) Federico Ardila’s incredible Numberphile video**

This video featuring Federico Ardila, a math professor at San Francisco State University, completely blew me away:

It is an absolutely amazing video to share with kids, and I’ve used it combined with a Zometool set for several “hands on” math lectures for high school students. I was 47 years old and had a math PhD when I learned that the rows of Pascal’s triangle are hiding in n-dimensional cubes!

Federico Ardila’s “Combinatorics and Higher Dimensions” video is incredible!

**(13) Larry Guth’s “no rectangles” problem**

Larry Guth is a math professor at MIT. I think it was in 2015 when I saw him give a public lecture on what he called the “no rectangles” problem. The idea is to put X’s in boxes in an NxN grid without any 4 of the X’s forming the corners of a rectangle. Solving for the most boxes that can be filled in without forming a rectangle is an incredibly difficult problem in general, but the smaller cases (like filling in boxes in the 3×3 and 4×4 grids) are great to share with kids.

I’ve shared this problem with kids as young as 2nd graders – it is so fun to see kids work through it! The two projects below show my younger son working through the 3×3 and 4×4 cases – you’ll see how this problem brights out lots of different mathematical ideas in kids.

Revisiting Larry Guth’s “no rectangles” problem

Talking through the 4×4 case of Larry Guth’s “no rectangles” problem with my younger son

**(14) Cathy O’Neil work on bias in algorithms**

O’Neil is a PhD mathematician who is doing work outside of academia studying problems created by / exacerbated by computer algorithms. Her book Weapons of Math Destruction is a must read. After seeing her speak at Harvard last year I did a project with the kids showing how even seemingly small biases can have large impacts.

Helping kids understand the math of unfair algorithms inspired by a Cathy O’Neil talk

**(15) Deke Arndt**

Arndt is the head of the Climate Monitoring Branch at NOAA’s National Centers for Environmental Information. He is active on twitter sharing terrific data visualizations that show how temperatures are changing all over the world. This public work he is doing is something that kids can understand and appreciate and I think is a great way for kids to learn about both climate change and also statistics.

Using some temperature graphs from Deke Arndt to talk about probability distributions with kids

**(16) Moon Duchin**

Finally, Moon Duchin is a math professor at Tufts University who has been doing fascinating work studying gerrymandering. She also has led several conferences on math and gerrymandering. One of the really great resources that has come out of Duchin’s work is a set of materials to help k-12 educators talk about gerrymandering with their students. A link to those recoursec is in the blog post below. In that blog post I go through one of the exercises Duchin’s team came up with to help kids understand gerrymandering better.