Thursday
Warm-up:
None - we have a lot to do today!
Activity:
I hand out two worksheets - a set of triangles that I have drawn and a worksheet where students will collect their work for the day. I also give out a ruler to each student. The instructions are simple: Using the centimeter side of the ruler, measure all three sides of each triangle. Then classify each triangle by its sides and by its angles.
For the file, check the link above or the Resources section below,
I had to hand-draw these triangles using a compass and ruler to ensure that the measurements were precise, but that's fine - I love constructing geometric figures. (In fact, I think kids should spend WAAAAY more time in geometry constructing figures of their own, but that's a side issue.)
This section of the class whips by pretty quickly, and I was able to help out any students who were struggling with using a ruler. They can all use rulers, but only if I really, truly force them.
On the back of their classification worksheet, I list a bunch of triangles by their sides and ask students to classify these triangles by their sides and angles. Pretty quickly, they realize that all the triangles are scalene, but how can you tell whether they are acute, right or obtuse? Mr. Haines? Mr. Haines? Can you come here?
At this point, I am walking from table to table distributing scratch paper and encouraging students to try to draw each triangle. There is a LOT of trial and error as students draw, then redraw, then redraw their 8, 9, 10 triangles or their 2, 8, 9 triangles. I don't worry too much about this. After all, I am giving the students a headache so they appreciate the aspirin.
Also, these are some really clever students I'm teaching! In two of my three classes, I had a student come up with the following strategy, which I will paraphrase:
"I pretend the triangle is a right triangle. So I draw the short side and the medium side with a right angle, and I try to connect them with the third side. If the third side reaches perfectly, it's a right triangle. If it's too short, the triangle is acute because the short side has to bend down to reach it. If the long side is too long, the triangle is obtuse."
Pretty cool, right?
By this point, we are edging right up against the bell, so I bring the students together, run through a quick check of their classifications, and then ask them why it took them so long. Lots of grumbling about erasing and redrawing. I mimic every announcer from every infomercial eve: "There's got to be a better way!"
The bell rings. Tomorrow, we meet Pythagoras.
Homework
None
Tomorrow's Goal:
Introduce the Pythagorean Theorem and use it to classify triangles.
Resources:
Triangle Worksheet (I tried very hard to get the scale of the triangles to remain after scanning and converting to a PDF. Hopefully this works for you, but it may depend on your printer. Or you could construct your own set of triangles!)