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September 3rd, 2003
01:54 pm


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If you have some spare time
I'm editing some activities to go along with a pre-algebra book (most likely 8th grade). I'm thinking that this particular one might be too difficult (gotta love outside writers). It's meant to be an activity that a substitute can just give the kids. It should take up somewhere around a class period, but not more than two class periods.

They are given 31 angle measures: 10, 11, 25, 25, 40, 40, 53, 57, 72, 72, 73, 74, 8060, 80, 83, 85, 93, 94, 95, 95, 97, 100, 105, 116, 130, 140, 145, 150, 159, 160, 161

Then they are asked to use each angle measure exactly once to create the following polygons:
4 distinct triangles
2 distinct quadrilaterals
1 pentagon
1 hexagon

Then they're asked to sketch each one and write a short paragraph telling how they know their answers are correct.

So, I'm interested to know if people can successfully come up with a solution without knowing the answer first, and if there are multiple possible answers. I'm also curious to know how long it takes people to do something like this.

I covered up the answer and gave it a try. My first attempt started with trying to find the 4 triangles. I found 3, but then it was impossible to find a 4th. Was I just unlucky? Did avoiding the first obvious triangle (because I had already seen the answer) screw me up?

All of the other activities were relatively reasonable (if stupid). It's just this last one that looks to be a bear.

Current Mood: Hulk smash angles

(5 comments | Leave a comment)

[User Picture]
Date:September 3rd, 2003 11:26 am (UTC)
I began to think it was impossible, so I actually checked the answers given. One of the triangles is listed as 40-80-80. D'oh. So, change one of those 80s to a 60, and it should actually be a solvable problem.
[User Picture]
Date:September 3rd, 2003 12:11 pm (UTC)
I was bored, so I just did this exercise. It took less than a half hour to come up with:

Triangle #1: 130, 10, 40
Triangle #2: 95, 25, 60
Triangle #3: 83, 72, 25
Triangle #4: 95, 74, 11
Quadrilateral #1: 40, 80, 100, 140
Quadrilateral #2: 57, 93, 94, 116
Pentagon: 53, 85, 97, 145, 160
Hexagon: 72, 73, 105, 150, 159, 161

But I didn't waste time drawing out the things, I just solved it by the numbers. Without your edit substituting a 60 for an 80, the problem is, in fact, impossible; the numbers simply don't add up.

Which was the obvious triangle?
[User Picture]
Date:September 3rd, 2003 12:19 pm (UTC)
That certainly answers the question of whether there are additional answers.

The "obvious" triangle for me was the one that uses the first two angles: 10-11-159.

Something that takes someone like you 20 minutes to do could very easily take the average eighth grader 2 hours.

I'm struggling to decide whether I should rewrite the activity or whether I should just say "fuck it" and let it go. I mean, it really is on the border of too difficult, I think. However, I really don't want to come up with an idea for another activity.

I guess I'll go ahead and start making the edits in the other activities, and hold of on the decision about this one until tomorrow.

Thanks for sharing your findings.
[User Picture]
Date:September 3rd, 2003 03:03 pm (UTC)
I couldn't help but write a program to find these solutions; it seems that there are zillions of them. In fact, it seems that one can fall over a solution no matter where one starts, which I guess is a strength of this exercise.

I don't know anything about teaching 8th graders, but this exercise seems funny to me. It appears to have to do with geometry, but of course, drawing the figures is a waste of time. It is actually an exercise in bookeeping and arithmetic (that's why it was such an irresistable programming project). Is this busywork of any use to the 8th graders who will do it? I wouldn't have thought so.

[User Picture]
Date:September 3rd, 2003 03:14 pm (UTC)
Yeah, the one thing that really goes with what they're learning in this chapter is the sum of the interior angles of polygons. I agree, it does seem like an awful lot of busywork just for that one little point.

Of course, this is just an activity for substitutes to hand out. It is meant to be busywork, pretty much. I go back and forth between leaving it alone and chucking it. I'll probably en dup leaving it alone, consoling myself with the fact that most kids will never see this.

Really, ancillaries on the whole (and this is part of an ancillary full of activities) are crap. They're most valuable to the company as an item on a list, to say, "See, we have this and this and this to go along with these shiny textbooks," and only the textbooks get any scrutiny by the people making the buying decisions.

Mostly, I try not to think about these realities as I sit in my cubicle with my red pen.
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