Talking primes using Dirk Brockmann’s “Prime Time” explorable

I’ve been a huge fan of Dirk Brockmann’s explorable math activities since I first learned about them. The full list is here:

Dirk Brockmann’s Explorables

Today’s project was inspired by the “Prime Time” program – direct link here:

Dirk Brockmann’s Prime Time Explorable

I started the project today by asking my son to tell me some things he knew about primes. He gave the definition of a prime numbers, explained how we know that there are infinitely many primes, and talked about twin primes, though he apologized for not knowing how to prove that there were infinitely many twin primes:

Next I showed him the polynomial n^2 + n + 41 and we talked about this equation producing a lot of primes.

Now we went to the “prime time” explorable and my son talked about what he saw in the first two examples -> the Ulam spiral and the Sack spiral.

Finally we looked at the last two patterns -> the Klauber triangle and the Witch’s spiral.

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Exploring machine learning with a 7th grader using Tensorflow’s Playground

Yesterday we did a project exploring machine learning using the site teachyourmachine.com.

Using teachyourmachine.com to let kids explore machine learning

My younger son was interested in doing another project on machine learning today, so we revisited an old idea and went to the Tensorflow Playground:

Tensorflow’s machine learning “Playground”

We started the project today with a short explanation of classification problems and then saw how the algorithm on the Tensorflow website solved a relatively simple classification problem:

Next we studied a slightly simpler classification problem that is the second example on the Tensorflow site:

The third example on the site looks very easy, but it got pretty interesting when we added some noise:

Finally, we looked at the most difficult classification problem on the Tensorflow Playground site -> the spiral. Even the most complicated program we could build still struggled with the classification problem here:

This is either our 3rd or 4th project using the Tensorflow Playground site. I think it is a great way to help kids see some of the basic concepts and ideas in machine learning.

Using TeachYourMachine.com to let kids explore machine learning

Last week attended a lecture by Gil Strang. He had selected a few topics from his new book about machine learning and linear algebra and the lecture was absolutely terrific.

At the end of the lecture he showed two websites that allow anyone to explore machine learning. One – the Tensorflow Plaground – site we’ve played with before:

Sharing basic machine learning ideas with kids

The other site was new to me, though -> teachyourmachine.com

If I understood correctly from the lecture, the website was actually a student project from the linear algebra and machine learning course that Strang taught last year. It is a really great site for exploring some basic ideas in machine learning.

For today’s project I explained the site to each of my sons individually, and then had them play a bit.

Here’s how I introduced the site to my younger son:

Here are his thoughts after playing with the program:

Here’s how I introduced the program to my older son:

Here are his thoughts after playing with the program for a bit:

Sharing Jez Swanson’s amazing Fourier transformation program with kids

I saw an incredible tweet from Jez Swanson yesterday:

The program makes the ideas behind Fourier transformations accessible to kids and I decided to share the program with the boys this morning. So, I had each of them play around with it on their own for about 10 to 15 min. Here’s what they thought was interesting. (sorry for all of the sniffing – I’ve got a cold that’s been kicking my butt for the last few days):

(1) My older son who is in 9th grade:

(2) My younger son who is in 7th grade – it is really fun to hear how a younger kid describes advanced mathematical ideas:

I think Swanson’s program is a great program to share with kids – feels like at minimum it would be fantastic to share with kids learning trig.

A fun discussion about prime numbers with kids inspired by an Evelyn Lamb joke!

Yesterday I saw this tweet from Evelyn Lamb:

It inspired me to do a project on prime numbers with the boys. So, I grabbed my copy of Martin Weissman’s An Illustrated Theory of Numbers and looked for a few ideas:

We began by talking about why there are an infinite number of primes:

Next we moved on to taking about arithmetic sequences of prime numbers. There are a lot of neat results about these sequences, though as far as I can tell, they have proofs way beyond what kids could grasp. So instead of trying to go through proofs, we just played around and tried to find some sequences.

I also asked the boys how we could write a computer program to find more and they had some nice ideas:

Next we played with the computer programs. Sorry that this video ran a bit long. As a challenge for kids – why couldn’t we find any 4 term sequences with a difference of 16?

Finally, we looked at Evelyn Lamb’s joke to see if we could understand it!

It is definitely fun to be able to share some elementary ideas in number theory with kids!

Sharing Craig Kaplan’s isohedral tiling program with kids

I saw an amazing tweet from Craig Kaplan this week:

Ever since seeing it I’ve been excited to share the program with the boys and hear what they had to say. Today was that day 🙂

So, this morning I asked the boys to take 15 to 20 min each to play with the program and pick 3 tiling patterns that they found interesting. Here’s what they had to say about what they found.

My older son went first. The main idea that caught his eye was the surprise of distorted versions of the original shapes continuing to tile the plane:

My younger son went second. I’m not sure if it was the main idea, but definitely one idea that caught his attention is that a skeleton of the original tiling pattern seemed to stay in the tiling pattern no matter how the original shapes were distorted:

Definitely a neat program for kids to play around with and a really fun way for kids to experience a bit of computer math!

The puzzles (and everything else!) from Nervous System will blow your mind

Yesterday Nervous System in Somerville, MA had an open house and I was lucky to have a few hours free while the boys were at their karate black belt tests. Visiting their shop was absolutely incredible:

Definitely check out their website and their twitter feeds. I follow Jessica Rosenkrantz – @nervous_jessica. Here’s the link to their website:

The Nervous System website

At the open house I bought two new puzzles. The boys had seen one previously at Christmas, too. For our project today I’d already wanted something on the easy to talk about / less heavy math side because of the black belt tests yesterday, so talking about the new puzzles was perfect.

We started with the geode puzzle – one of the fun things we talked about was how the boys thought the computer generated the geode shape:

After the introduction to the puzzles, we moved on to talking about the challenge of putting the puzzle together. Favorite line – “once you get started, it gets pretty hard.” Yep!

Next I showed them the latest creation from Nervous Systems – an “infinity puzzle” inspired by the Mobius strip!

I was incredibly lucky to be able to buy one of the infinity puzzles yesterday. So, for the last part of today’s project we did an unboxing:

If you know kids who like puzzles – or you like puzzles! – all I can say is the Nervous System puzzles are absolutely incredible.

3 hours after we finished the project this morning, my younger son had returned to the Geode puzzle: