# Revisiting one of Annie Perkins’s drawings

Back in 2018 Annie Perkins posted this drawing:

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:

# An introdution to sin(x) and cos(x) with my younger son

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.

After that introduction, I introduced the unit circle and asking him to make a guess as to what the graph of y = cos(x) would look like:

In the last video we looked only at the interval 0 to 90 degrees. Here we made a sketch of y = cos(x) and y = sin(x) from 0 to 360 degrees. It was fun to hear what he thought of these graphs as he was drawing them:

The discussion we had today was really fun and even had a few nice surprises. I’m excited to continue this discussion a bit more over the next couple of weeks.

# Revisiting Grant Sanderson’s “fair division” video thanks to an Amy Hogan tweet

I saw a tweet from Amy Hogan this morning that reminded me of an old project:

The old project is here:

And Grant’s video is here:

Before we started the project today, I had my son watch Grant’s video. Here are some of his takeaways:

Now we tried to see if we could find a fair division of a string with two colors using only two cuts:

Finally, to wrap up we tried to see if we could do a fair division of a string with three colors using three cuts:

This is a fun and relatively easy project for kids, and also a way for them to see some really fascinating advanced math!

# Having my younger son try out Matt Enlow’s algebra inequality problem

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:

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 he made some progress on the problem in the case when x > -4. Now we finished up that piece of the problem:

Now he tackled the case when x < -4. This part was not as difficult since we’d done most of the necessary work already:

Finally, we went to the computer to look at a graph of both equations. Here he talks about how these graphs help us see the solution to the original equation:

I liked this problem and was happy that my son was able to work through it. Definitely a nice problem for students learning algebra to think through.