Struggling through a challenging AMC 10 problem

This problem gave my son some difficulty yesterday – it is problem #19 from the 2011 AMC 10a

AMC10.jpg

Last night we talked through the problem. The talk took a while, but I was happy to have him slowly see the path to the solution. Here’s his initial look at the problem:

Next we looked at the equation y^2 - x^2 = 141. Solving this equation in integers is a nice lesson in factoring. Unfortunately by working a bit too quickly he goes down a wrong fork for a little bit.

In the last video we found that the original population of the town might have been 484, and it might have changed to 634 and then once more to 784. We had to check if 784 was a perfect square.

Finally, we needed to compute the approximate value (as a percent) of 300 / 484. The final step in this problem is a great exercise in estimating.

So, a really challenging problem, but also a great problem to learn from. We went through it one more time this morning just to make sure that some of the lessons had sunk in.

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Sharing Kelsey Houston-Edwards’s philosophy of math video with kids

Kelsey Houston-Edwards is making a series of math videos and the first two are outstanding. We looked at the first one last week:

Sharing Kelsey Houston-Edward’s video with kids

This week’s video is about philosophy and math. A deep subject, for sure, but one which the kids thought was interesting. Here’s the video (and the twitter link so you know when the new videos appear!):

Here’s my older son’s reaction and a few things he thought were interesting:

and here’s what caught my younger son’s eye:

It is so great to see someone doing such an incredible math outreach program. I’m so excited about this video series!

Revisiting our Zometool Snowman

When we first moved into our house we did a couple of fun and large Zometool projects because we didn’t have any furniture 🙂

This week I saw a fun tweet from Eli Lubroff that reminded me of one of those projects:

https://twitter.com/eluberoff/status/801541820979167232

Here’s a part of that old project 🙂

Snowman

Today we revisited that old snowman and had the boys talk about each of the Archimedean solids in the shape. This is a fun project – not just because the shapes themselves are cool – but you get a nice opportunity to talk about counting and symmetry. You’ll see in the videos that my older son is a bit more comfortable with the idea, but my younger son seems to catch on by the 3rd video.

Here’s a link to all of the Archimedean solids on Wikipedia:

The Archimedean Solid page on Wikipedia

And here’s our project:

First the bottom of the snowman – the Truncated Icosidodecahedron

Next was the Rhombicosidodecahedron

Next was the Icosidodecahedron

Finally the Archimedean Solid Snowman 🙂 Two years later and he still fits!

Definitely one of my all time favorites and a really fun way to discuss counting and symmetry!

Fun with rotopo

Saw this neat tweet from Jim Propp yesterday:

After playing the game for a just a few minutes I knew that my kids would love it.

Here’s each of their reaction to seeing and playing the game.

My younger son first:

My older son next:

So, definitely a fun little game for kids. They need to be fairly fluent with the arrow keys on the keyboard, but that’s really all that’s required. Definitely some fun puzzles to solve!

Our Raspberry Pi adventure

I happened to see the Raspberry Pi set below at a store earlier in the week:

Screen Shot 2016-11-24 at 3.14.58 PM copy.jpg

 Today I showed it to the kids and we played with it for a bit. Here’s their initial reaction:

 

There wasn’t much to assemble which was nice. We did have some trouble connecting it to my laptop, so we switched to connecting it to our TV. Here’s what the boys had to say after we got it running:

Finally, the kids discovered a few of the games that came loaded on the computer. This squirrel one made them laugh. From start to finish was about an hour – and at least 20 minutes of that was trying and failing to get connected to the laptop.

We’ve only scratched the surface of what was in the kit. I’m excited to have the boys play around with the computer a bit more. It has Mathematica (yay!) and some software for introductory programming like Scratch. Hopefully there will be many more projects to come.

Why I love watching my kids learn math

Had a great night with the boys tonight. My older son was working on some old AMC 10 problems and we talked through one that stumped him for his movie:

It was #15 from the 2013 AMC 10a:

 

AMC10.jpg

Next I spent some time with my younger son. He’s been studying the basics of lines using Art of Problem Solving’s Introduction to Algebra book plus a little bit of Khan Academy (when I’ve been traveling for work). I asked him what he’d learned so far and loved his response. It was a great reminder of the joy of learning new math ideas for the first time: