August 2017
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Month August 2017

Playing with Jim Propp’s essay on Arthur Engel

Jim Propp’s August 2017 blog post is absolutely terrific:

Prof. Engel’s Marvelously Improbably Machines

Even though we are visiting my parents in Omaha, I couldn’t resist having the boys watch the video in the essay and then play with the challenge problem.

Here’s what they thought after watching the video – the nice thing is that they were able to understand the problem Propp was discussing [also, I shot these videos with my phone, so they probably don’t have quote the quality or stability of our usual math videos]:

Next I had them play the game that Propp explained in his video. The idea here was to make sure that they understood how the [amazing!] solution to the problem shown in the video:

Next we tried the challenge problem from the essay. I almost didn’t do this part of the project, but I’m glad I did. It turned out that there were a few ideas in the Propp’s video that the boys thought they understood but there was a bit more explanation required. Once they got past those small stumbling blocks, they were able to solve the problem.

I’m really excited to dive a little deeper into the method of solving probability problems that Propp explains in his essay. What makes me the most excited is that the method came from someone thinking about how to explain probability to kids.

The last video shows that understanding Engel’s method does take a little time. Once kids get the general idea, though, I think they’ll find that applying to a wide variety of problems is pretty easy. It is amazing how such a simple method can made fairly complex probability problems accessible to kids.

Talking through the birthday problem with kids

Today is my birthday – I figured there was no better way to celebrate than to talk through the birthday problem with the boys.

We’ve talked about it before – here’s what they remembered:

Now . . . how to we tackle this problem? Getting started proved to be a little difficult:

Now that we figured out how to approach the problem, we dove into the calculations. This step also proved to be challenging, but eventually they were able to see how the calculation worked.

Finally we wrote a little [ bug filled ] program on Mathematica and played around with the results.

It is always fun to share a famous problem with the boys.

Talking a bit more about my son’s probability problem

Yesterday we did a fun project on a probability problem / game my son was working on. The game involves rolling three 10-sided dice and adding up the numbers. Repeat the process until you’ve seen one of the sums 40 times. Yesterday 15 was the winner:

img_2432

Here’s yesterday’s project:

A probability and stats problem with dice my younger son was working on today

I wrote a short program on Mathematica to play my son’s game 1,000,000 times. I was interested to see how each of the boys would interpret the results.

Here’s what my older son had to say:

Here’s what my younger son had to say:

It is interesting to hear what kids have to say about the various probabilities and distributions. The results of the 1,000,000 simulations are probably pretty surprising. This problem that my son made up is actually a pretty fun problem to explore with kids.

A probability and stats problem with dice my younger son was working on today

When I got up this morning my younger son was playing some sort of dice game in the kitchen. An hour later he was still rolling dice so I finally asked him what he was doing:

It turns out what he was actually trying to was find the first sum that would appear 40 times, but I only understood that later.

This seemed like an easy activity to turn into a project, so we got started by having him explain what he was doing:

Next we turned to Mathematica to play around a little bit with the problem. I had to explain some terms first (and sorry I had part of the screen out of view for a bit). After explaining those terms we looked at the distribution of the sums:

Finally we wrapped up by taking a very deep dive into the distribution of the sum of three 10 sided dice. The kids were able to understand the probability of getting a 3 or a 30, and then we talked about a few of the other probabilities that Mathematica was showing us.

Later in the morning my son finished his game. 15 was the first roll to appear 40 times.

It was really fun to base a project on a math problem that my son came up with on his own.

Going through an AMC 10 geometry problem

The kids got back from an overnight camp yesterday and were a little tired. I figured the energy would be a little low and wanted to pick a problem that would would be instructive as well as challenging. This problem that my older son adn I talked about last week seemed like a good fit:

Screen Shot 2017-08-12 at 10.11.32 AM

 Since my older son had already going through the problem, I tried to ask my younger son most of the questions in this project and my older son come in when my younger son was stuck.

One small note – I’m writing this post at my son’s archery club and I have to have the sound off for the videos (I forgot my headphones) so the descriptions of the videos is going to be a little lighter than usual.

Here’s the introduction to the problem:

The first idea we talked about was finding the center of the inscribed circle in a right triangle. There are a couple of directions we could have gone here. I thought about discussing the A = s*r formula, but our discussion here ended up deriving a different formula that comes up in a right triangle 2*r = A + B - C.

Next we talked about some special properties about the circumscribed circle in a right triangle. The geometric idea here is that a triangle inscribed in a semi circle is a right triangle.

Finally, now that we’d found both the incenter and circumcenter of the triangle, we talked about how to find the distance between those two points. my younger son got confused by a small arithmetic point.

So despite the low energy, a fun project. I like using the old AMC problems to motive some basic math ideas. It is also fun to see the difference between how the boys react to seeing ideas for the first time vs the 10th time.

Working through three AMC 8 problems

My younger son was working on some problems from the 2004 AMC 8 today. Here’s a link to that contest:

The 2004 AMC 8 on Art of Problem Solving’s site

I love using the old AMC problem to give the kids a little variety in the types of problems they see. Today we talked through three of them.

The first problem we talked about was #12

Problem 12

Here’s what my son had to say about that problem:

The next problem was #18:

Problem 18 copy

Here’s what he had to say about that problem:

 

Finally we talked through problem #22:

Problem 22

Here’s what he had to say about that problem:

Definitely a fun morning. I love the old AMC 8 problems because they are both challenging and accessible. Going over the problems that the boys struggle with always leads to fun discussions.

Sharing Gary Rubinstein’s Perfect Number video with my 6th grader

Saw a neat tweet from Gary Rubinstein earlier in the week:

Our first project with his videos used his “Russian Peasant” multiplication video. That project is here:

Using Gary Rubinstein’s “Russian Peasant” video with kids

Today my older son is away at camp, so I was working with my younger son alone. I asked him to pick another one of Rubinstein’s videos and he picked the one on perfect numbers.

After watching the video I sat down with him to do a project – there was enough in Rubinstein’s video to easily fill three short videos, but we did just one. It was absolutely incredible to see how much my son took out of the perfect number video. There’s a fun and totally unexpected and unplanned connection with the Russian Peasant video at the end, too:

I love it when the projects go this well 🙂

Paige Applegate’s game is for real

I’ve been really excited about the journey’s that ultimate players have been taking lately.  After the World Games I wrote about Anna Nazarov:

Why Anna Nazarov matters to me

Another player whose on-field journey I’ve been following for the last couple of years is Molly Brown’s Paige Applegate. Before writing this post I went back and watched the All-Stars vs. Molly Brown game from 2015 just to remind myself where she was as a player two years ago.

Nothing makes me happier than seeing players work hard and improve. It is hard to think of a player who has come farther that Applegate has in the last two years. If you run into her at a tournament you should ask her about what she’s been doing and listen carefully because you want to follow her formula (bad news, though, it is probably involves lots of hard work and dedication rather than magic beans).

What really impresses me about her play and her journey over the last few years is that it is really, truly hard to find the right balance between (what I think is) her natural “let’s take some risk” style of play and the duties of an elite O-line handler. It takes years of work and the list of players who tried and failed to find that balance is incredibly long. But players who make it out the other side of that journey like Applegate and Jenny Fey are so incredibly fun to watch, and also, for the purposes of this blog, so great to learn from.

So, below are 5 clips of Applegate’s play that caught my eye watching the Molly Brown vs Fury US Open semifinal:

(1) The mix of soft touch passes, great fundamentals, and attacking on Molly Brown’s second goal:

What I love from Applegate here is . . . well, everything.

(i) That soft little pass to Chastain. Handler to handler passes (swings or resets or otherwise) should be easy to catch. Turns on this passes are awful and Applegate (and really all of Molly Brown) did a great job with this skill all game.

(ii) The communication with her hands – we’ll see more examples of this later, too.

(iii) The little forehand fake to move Nazarov to the flick side! The 2nd replay really shows how effective that fake was.

(iv) Then that i/o backhand. That’s a risky pass and needs a lot of work to be game ready. Nazarov also uses it extremely well for Fury.

So many lessons from Applegate in this short clip!

(2) Similar to the clip in (1) but with a harder pass to the break side

Passes like the i/o backhand here are why I said above that it takes years to develop into the kind of player Applegate has become. It takes a lot of experience to learn when this pass is ok and when it just pushing the needle a bit too far.

The same nice soft touch passes and the forehand fake that were on display in the first clip are part of this clip, too:

(3) Fun physical play and great on field leadership

I’m sure that both Payne and Applegate walked off the field after this point thinking “that was fun.” I love the physical play from Applegate to get open and then to stand up after the grab and fire that pass down field to Megan Cousins (who, for the 1000th time just magically appears on the screen down the field standing around wide open . . . )

But watch Applegate raise her hands to slow everything down when Pitcaithly has the disc unmarked. It takes a very special player to throw the switch from “physical battle with Opi” to “time to watch the grass grow” in the space of 5 seconds. Smart play and super on field leadership from Applegate here.

(4) A small thing that I think she could do a little better.

The goal here is nice, but I was wondering why the first cut from Megan Cousins didn’t work out. Because of the way Applegate caught the swing pass, it took one extra beat to transfer the disc to her throwing hand. If she catches this with a (two handed!) claw catch instead, she’ll save a beat and be able to throw the forehand just a little faster.

Also, when the D knows that the quick forehand might be coming, you’ll suddenly have much more room on the backhand side, too, as the defender now has to take one extra step to close down the flick side.

(5) Finishing with a really nice and crafty goal.

I love how Applegate stays engaged with Chastain the whole way through on the cut that eventually scores. They way she uses her body to shield her defender from the disc is also great.

You’ll hear the announcers praising Applegate’s play in nearly all of the clips above. I’m glad that she’s getting recognized – that recognition is 100% deserved.

Also, I am totally serious about pulling her aside to talk to her if you are looking for someone to help improve your own game. After the journey she’s been on the last couple of years, if you are a young handler looking to improve there might not be a better person in the game to learn from.

Using Gary Rubinstein’s “Russian Peasant” video with kids

Saw a neat tweet from Gary Rubinstein yesterday:

This morning I thought it would be fun to look at the “Russian Peasant” multiplication video with the boys. Here’s Rubenstein’s video:

I had the boys watch the video twice and then we talked through an example. My older son went first. He had a fun description of the process: “It is like multiplying, but you aren’t actually multiplying the numbers.”

Next my older son worked through a problem. This problem was the same as the first one but the numbers were reversed. It isn’t at all obvious that the “Russian Peasant” process is commutative when you see it for the first time, so I thought it would be nice to check one example:

Next we moved to discussing why the process produces the correct answer. My older son had a nice idea -> let’s see what happens with powers of 2.

The last video looking at multiplication with a power of 2 gave the kids a glimpse of why the algorithm worked. In this video they looked at an example not involving powers of 2 (24 x 9) and figured out the main idea of the “Russian Peasant” multiplication process:

This was a really great project with the boys. It’ll be fun to work through Rubinstein’s videos over the next few months. I’m grateful that he’s shared the entire collection of ideas.

Playing with Three Sticks

I saw this tweet from Justin Aion at the end of July and immediately ordered the game:

When I returned from a trip to Scotland with some college friends the game was on the dining room table – yes!! Today we played.

In this blog post I’ll show how the game ships and two rounds of play (and we might not be playing exactly right) to show how fun and accessible this game is for kids.

First, the unboxing. The game comes out of the box nearly ready to play.

Here’s our first round of game play. I think we misunderstood one of the rules here, but you’ll still see that the game is pretty easy to play:

Here’s the 2nd round of play. I think we understood the rules better this time, which is good. You’ll also see how this game gets kids talking about both numbers and geometry:

Finally, here’s what the boys thought about the game:

I’m really happy that I saw Justin Aion’s tweet and now have this game in our collection. It is a great game for kids!