Back in 2018 Annie Perkins posted this drawing: #MathArt #IslamicArt #mtbos #iteachmath pic.twitter.com/qsBn45DooN — Annie Perkins (@anniek_p) February 24, 2018 We did a project talking about it back then, but I decided to revisit it today with my younger son. First we recreated part of the drawing using our Zometool set, and then I had my son share his thoughts about the shapes – it is always so fun to hear what kids see when they look at shapes: Next I had my son talk about the Zometool shape we made ..read more

With school nearly over for the year I was looking for some ideas to explore with my younger son over the summer.  I thought some introductory trig ideas might be fun since he saw some basic right triangle trig inn his math class at school this year.  The first thing that came to mind for me was a short exploration of what the functions sin(x) and cos(x) look like.  It was fun to hear his ideas about these functions evolve over the course of our discussion this morning.  I started by asking him what he already knew:   After that introduction, I introduced the unit ..read more

I saw a tweet from Amy Hogan this morning that reminded me of an old project: Two thieves steal a necklace w/ 10 rubies and 14 emeralds, fixed in some arbitrary order on a loop of golden string. Show they can cut the necklace in 2 places so when each thief takes one of the resulting pieces, they get ½ the rubies and ½ the emeralds. From @MoMath1 #mathchat — Amy Hogan (@alittlestats) June 6, 2021 The old project is here: Grant Sanderson’s “Fair Division” video shows a great math project for kids And Grant’s video is here: Before we started the project today, I had my son wat ..read more

I saw an interesting tweet from Matt Enlow earlier today and thought it would be fun to have my younger son try out the problem: It doesn't matter how many times we go over it, SO many of my students will still start to solve an inequality like x ≤ (2x+3)/(x+4) by multiplying both sides by x+4. I guess they've been… "well-trained"? — Matt Enlow (@CmonMattTHINK) June 5, 2021 One bit of hesitation I had was that I didn’t know if my son had seen rational functions in school or not, so we started with an overview of the problem just to make sure that he understood it: In the first video ..read more

Last week I did a brief introduction to the Poisson distribution with my younger son. That project is here: https://mikesmathpage.wordpress.com/2021/05/09/introducing-some-basic-ideas-about-the-poisson-distribution-to-my-younger-son/ Today I dove in a little more to see if he could see some of the patterns that emerge in the distribution. We started with a quick review and a look at data from a few simulations I ran: Next we looked at the data from four simulations with an averages of 1, 2, 3, and 4 events expected per year. It was a little hard for him to see the overall pattern, but aft ..read more

For our project today, I though it would be fun to talk about the Poisson distribution. For me it is one of the most interesting and important ideas in probability. This question, for instance, is fascinating -> If a random event happens on average once per time period, what is the probability that it happens twice? I started the introduction with a version of the idea I mentioned above and asked my son for some estimates of what he thought the answer would be: Then we looked at some simulations. Here I’m looking at the idea of a random event that happens on average once per year and cho ..read more

Last week I learned about an really interesting probability problem from Pasquale Cirillo: Today I asked him to think about the problem while I was out and when I got back home he walked me through his solution: The last video shows his general approach – now he calculated the asnwer: To wrap up I showed him how to modify his original argument just a bit to avoid the infinite series calculation. This is a much shorter way to solve the problem, but does require a bit more mathematical sophistication: I really love the problem and think that it is a great one to share with kids. Even if k ..read more

Yesterday my younger son and I talked through this fun problem I learned from Pasquale Cirillo: Our project is here: https://mikesmathpage.wordpress.com/2021/05/01/talking-through-a-neat-introductory-probability-expected-value-problem-from-pasquale-cirillo-with-my-younger-son/ and Cirillo’s discussion of the problem is here: Brain Teasers for Quants, Episode 9: A simple dice game and American options in disguise. https://t.co/CXP3HNv8b3 — Pasquale Cirillo (@DrCirillo) April 26, 2021 Yesterday we did not get to the optimal solution, but rather looked at the strategy of stopping when yo ..read more

This problem was posted by Pasquale Cirillo last week and I thought it would be great to talk through with my son: This is the video where Cirillo talks through the problem if you want to see his full solution: Brain Teasers for Quants, Episode 9: A simple dice game and American options in disguise. https://t.co/CXP3HNv8b3 — Pasquale Cirillo (@DrCirillo) April 26, 2021 I’d asked my son to think about it a bit ahead of us sitting down to talk. Here are some of his ideas: Here we find the expected winnings if we use my son’s first rule – stop in either of the first 2 rounds if you get a ..read more

Yesterday we did a project on this fun problem from Futility Closet: Today we finished the project by talking about the 2nd part of the problem and then having a discussion about why the answers to the two questions were different. Unfortunately there were two camera goofs by me filming this project – forgetting to zoom out in part 1 and running out of memory in part 4 – but if you go through all 4 videos you’ll still get the main idea. Here’s the introduction to the problem and my son’s solution to the 2nd part of the problem. Again, sorry for the poor camera work. Next we went to the com ..read more