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:

(a)
Kate_A

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)

Kate_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)

Kate_C

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

(d)

Kate_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)

Kate_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)

Kate_F

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

(g)

Kate_G

This one also went pretty smoothly.

(h)

Kate_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)

Kate_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.

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