# Going through a Kate Nowak exercise

Tonight on twitter Kate Nowak published an exercise she was planning to use in her geometry class tomorrow. I may need to, um, borrow this exercise for my son tomorrow since I may need to run off to work early. I decided to go through it carefully just in case I get any questions at work. That short exercise helped me see the problems much better than just reading the list. Here’s are my thoughts, but first the twitter post:

For this one I used the ruler to draw the 3 inch side and the compass to draw the range of points 5 inches away from one of the endpoints of that side. Lots of possible triangles and hopefully a good start to the lesson.

(b) Here I started with the 3 inch side at the bottom of the page. That was lucky because 5 inches and 6 inches are longer on the paper that I expected. If you put the 3 inch side in the middle of the paper, you’ll not have room (on 8 x 11 paper anyway!). I used my compass to draw a 5 inch circle centered at one of the endpoints of the 3 inch side and then used it again to draw a 6 inch radius circle centered at the other endpoint. One of the intersection points for these two circles was on my paper and allowed me to draw the triangle.

I used the compass again only for problems (d) and (i).

(c) Had to use the protractor for the first time on this one. Lots of possible choices of triangles here.

(d) I like this one. After drawing the 120 degree angle it took me a bit to figure out where to put the 5 inch side. Then I remembered the compass and picked a random point on one of the sides and drew a 5 inch radius circle. Just reading this one I missed that it would be more challenging than some of the other problems.

(e) Having measured the 120 degree angles in the last problems in the right hand side of the protractor, I did the same thing here with the 30 degree angle at the start and accidentally began by nearly drawing a 150 degree angle. Oops! I’ll be interested to see if the students notice the similar triangles from the different groups on this one.

(f) Now that I was a pro at drawing acute angles, this one went pretty smoothly 🙂

(g) This one also went pretty smoothly.

(h) I found it easier on this one to draw the 100 degree angle and then the 30 degree angle on the other side of the 6 inch side. I sort of feel like I cheated, but I didn’t see where the intersection point with the 50 degree angle would be right away so I solved a different problem.

(i) Hey, two possible solutions!! I’d like to hear what the kids have to say about this one, too!

So, fun little exercise. If I do have to run off to work early tomorrow, I’ll definitely give the worksheet to my son and have him attempt to create all of these various triangles.