Friday, November 21, 2014

Activity: Drawing Triangles -- Based on Section 7-1 (Day 69)

Here it is, the last day before Thanksgiving vacation. This means that I should be taking all of next week off on this blog and wait to post Day 70 on Monday, December 1st.

But here's the problem. I've been wanting to purchase a new computer to replace my current PC. It is seven-and-a-half years old, and you know how computers fail when they are so old. Not only do I finally have the money to pay for a new computer thanks to my new job, but coming up is the perfect opportunity to buy it on a day when many retailers will have huge discounts -- Black Friday.

Now if I get the new computer, it's likely that I'll have to call our phone company to make an appointment to restore my Internet service -- and you know how things like that go. So, after taking a week off from this blog to celebrate Thanksgiving, I take another even more time off since I won't be able to post until my Internet is restored. And all of this will right when I'm supposed to post on Chapter 7, the chapter on triangle congruence. Even before Common Core, this is one of the most important chapters in the book, and now it's even more critical with the new standards.

Instead, what I was considering doing is treating Monday, Tuesday, and Wednesday as regular school days, even though my districts are closed those days. Then I could observe a full Thanksgiving week beginning on Turkey Day itself. I would start posting Chapter 7 next week and then continue it on Thursday, December 4th, is Day 73 -- by which point, I'd have a new computer with the connection to the Internet complete.

If the Internet is disconnected for much longer than I expect and I'm forced to skip days, no matter what happens, I will post Section 7-2, the Triangle Congruence Theorems SSS, SAS, and ASA. This is because this lesson contains these three theorems proved Common Core Style -- that is, using reflections and other transformations. Teachers can obtain lessons from the other sections after 7-2 from sources other than this blog. My duty here on this blog is to introduce geometry from the perspective of Common Core, and that means the mid-level proofs of SSS, SAS, and ASA. I don't mind skipping the higher-level proofs that one can read anywhere.

So instead, what I decided to do is take a chance and observe next week as Thanksgiving week, as scheduled in the schools. But since we finished Chapter 6 yesterday and said that I would post an activity today, why not let the activity be based on Section 7-1? After all, Section 7-1 of the U of Chicago text is on Drawing Triangles -- and what better activity is there to do than drawing? So Section 7-1 naturally lends itself to being an activity anyway. If I'm able to post on Monday, December 1st, then I might do Lesson 7-1 in more detail, but if I have to skip any days, then I can go straight to Lesson 7-2 without any trouble. After that, I'll cover the rest of Chapter 7 based on how many days I have to wait before my Internet is restored.

There are nine triangles to draw for this activity, based on Questions 11-19 from Section 7-1 of the U of Chicago text. The students are to draw a triangle ABC with the given information, and then conjecture whether all other accurately drawn triangles will be congruent to theirs -- so this can be done in groups. To add some fun to this pre-holiday activity, the students may cut out and glue their triangles to another sheet. They should label the triangles SS, AA, SA, SSS, ... based on the condition to which the triangle corresponds. Then they can compare their triangles with those of the other group in order to make their congruence conjectures -- possibly even before gluing them.

Note: SSS is the hardest one to draw, unless one uses a compass or possibly even strings cut to the correct lengths. But I don't necessarily want to make the students to a hard ruler-and-compass construction during a pre-holiday lesson. Most of the others could be drawn with just a protractor and a ruler.

This concludes the activity. During the Thanksgiving week, I won't post any school lessons, but I may post the my next Common Core pros and cons entry. In October I discussed Grades K-3, and this time I'll focus on Grades 4-7. I should be able to get that posted before the big purchase.

I won't post a worksheet for this activity -- instead I just give the conditions right here. This is why I'm buying a new computer next week -- one problem on my old computer is that so often, Windows Explorer locks up and I can't open up any new programs that aren't already open. So I can't access the word processor to type up the activity without turning the computer off and on. Rather than do that (since another problem is the infamous blue screen when I restart the computer), I will just post the nine questions right here:

For each triangle:
a. Accurately draw a triangle ABC with the given information.
b. Conjecture whether all other accurately drawn triangles will be congruent to yours.

1. SS condition: AB = 2", BC = 1 3/4".
2. AA condition: angle A = 70, angle B = 38.
3. SA condition: AB = 4 cm, angle A = 60.
4. SSS condition: AB = 4 cm, BC = 5 cm, AC = 6 cm.
5. AAA condition: angle A = 41, angle B = 100, angle C = 39.
6. SSA condition: AB = 2", BC = 1", angle A = 20.
7. SAS condition: AB = 2", BC = 1", angle B = 20.
8. ASA condition: angle A = 55, AB = 3", angle B = 90.
9. AAS condition: angle A = 40, angle B = 60, BC = 3 cm.

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