Revisiting lines

My older son is participating in an amazing program called Idea Math and I wouldn’t be able to say enough great things about this program if I tried. Last weekend I had the pleasure of listening to the academic director – Dr. Zuming Feng – lay out his philosophy for the program. It was wonderful!

You can see him talking a bit in the beginning of this old video about the 2006 US IMO team:

The program intentionally does not give out much homework, maybe just an hour or so per week. Probably less, actually, though we are obviously brand new to it, so I don’t really know the exact number. Today my son started in on one of the homework problems about lines.

It has been a long time since we talked about lines, so I was really happy to see that he’s studying lines again. The first part of the problem involves drawing some lines given the equation of those lines and then estimating the coordinates of the intersection points:

The follow up question asked him to find the solution to the two equations using algebra. He seems to be fairly naturally inclined towards calculation, so this part was fairly straightforward for him. I’m excited to talk about the final part of this problem tonight – describe what happens geometrically when you add these to equations for a line together?

A problem that led to an interesting math conversation this morning

My younger son’s math club had a homework problem that boiled down to this idea:

Your backyard is 600 square yards. You want to pay someone to mow the yard for you, but want to pay less than 5 cents per square yard. What is the maximum amount of money you can pay?

It was interesting to me how both of my kids interpreted this problem differently than I did.