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:

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 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.

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

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.

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.