Monthly Archives: September 2014

Sunday Summary

It’s time for the weekly (ok, technically bi-weekly since I was at the beach last week for a very rejuvenating weekend with the parentals) #mtboschallenge 3-2-1 Sunday Summary!

3 Things I’ve Done Recently That Were Not Half-Bad.

1. Question Brainstorming

I usually try not to reward promoted links on twitter, but this article about students asking questions was too tempting not to click.  I read it Thursday night and then tried it out Friday morning in PreAP Precal where we were preparing for a test on Monday.  I handed each student a piece of scrap paper and let them have 3 minutes to jot down any question they had–it could be general (“how do you write an equation for a tangent graph?”) or specific (“how do you do #11 on the study guide?”).  Then I gave them 6-8 minutes to try to answer the questions in their groups–I saw A LOT of good peer helping at this stage!  Then I collect any remaining unanswered questions and answered them

…Except for “why is -1 used for inverse notation?” (unless you count “because it is” as an answer).  I did a little googling this weekend and all I was able to come up with was if you want to perform f on x, you write it f(x).  If you want to perform it twice, you could write it as f(f(x)), or f²(x).  Following that same notation, undoing f once could then be written as  f‾¹(x).  Anyone have anything better?

2. Using Graphing Calculators to Graph Absolute Value

I found great discovery activity worksheet online and actually used the entire thing with limited modifications (I took out graphing the piecewise lines because we hadn’t discussed piecewise yet and one battle at a time, amirite?)  It went over great!  The kids were enthralled at using their calculator to do this.  (Actually, they were more amazed that it could graph y = |x + 2| than the fact it could give you a line of best fit when given 15 different ordered pairs.)   Hint: Have them turn their grid on (under “format”-the top middle button on TIs) for better transferring of graphs to paper.

3. Linear Modeling in Algebra II

Totally stealing from Mimi’s (@untilnextstop) fabulous worksheet, I made some math libs of my own.

Capture1(doc file here)We did these by hand (well, as in putting equation in point-slope form and then converting to slope-intercept).  Things I need to change: kids have no idea about having to pay a fare just for getting in a taxi nor do they understand #4 at all.  I should throw something in there about having to pay for both AOL and internet service just to complete date myself.  Also it’s best not to have a question about a rod expanding or growing if you’re teaching high school boys.

Then I made another worksheet to use the linear regression on the calculator.

Capture4 Capture3(doc file here) As I said, I did steal the first two questions directly from Mimi.  One thing that I didn’t notice until a kid pointed it out is that the answers to 4D don’t correspond very well to the chart, which led to a great discussion of what the line of best fit can and can’t do for us.

You can’t see it in the picture, but the next problem has the y-scale in billions which was something good to discuss as well.

We then did Mathalicious’s Reel Deal lesson, which was using a scatterplot and line of best fit to determine the movie lengths.  Maybe it was because I was pressed for time, but it did not go over as well as I thought it would.  I think next time I will just add it as another example to discuss in class.

Two Things That Are Not So Great

1. Even after all the work we did with the linear equation mad libs (and we did more work in bellringers and study guides) some students still had trouble telling me what the slope or intercept meant on the quiz.  (As in being able to fill in the blanks: for every _____, the something will increase _____.  At the beginning, there was _____.)  Maybe I should have done Mathalicious’s Domino’s activity instead of Reel Deal.  I also waver back and forth between “they should know this already!” and “they need to know this and they don’t so I need to spend a lot of time on it!”

2. Time is still a huge stress, since we are also nearing the end of the nine weeks and I am struggling to get in 6 major test grades.  Do I just have one test on a single topic to get the required six?  Or cram a lot of material in to have the test cover more than one topic?  Ugh.

One Thing I’m Looking Forward to This Week

Trig Identities!!!!!!!!!!!!!!!!!!!!!  I could do those all day.

Ok, so maybe I just like them for the puns.  🙂

MTBoS Challenge Sunday Summary

3 Favorite Questions From My Favorite Activity This Week:

We did these extension questions in PreAP Precal for 2 days: (.doc file here)

These came from a variety of places–textbook, MTBoS, a resource with free-response-questions for Precal level, my own mind. My three favorite questions:

1) Take a look at #6 there.  With 5-7 groups in each class, we got 5-7 different orderings.  What rich discussions we had!  What beautiful diagrams they drew (big whiteboards, I want to marry you)!  MIND-BLOWING FACT FOR ME: The absolute value of tangent of an angle is always bigger than the absolute value of its sine value. 

Good topics to bring up: how does tangent relate to slope?  what does “approaching undefined” mean?  what is a good way to discuss numbers whose absolute value is bigger, but since we’re in negative land, it means they are smaller?  what is a good way to organize these?

2) Ah, the fabulous #7. We had just discussed odd and even functions in the previous chapter so this was a great opportunity to bring up the algebraic definition and how it relates to the graph of these guys!  (Not going to lie to you, this is first time I realized that the graphs of sine/tangent are odd and cosine is even)

3) Here are the answers they will tell you for #10: (1, 1) (1, -1) (-1, -1) (-1, 1).  Then they will not believe you when you tell them that it is incorrect.  Then they will draw a picture to prove it and tell you the square root of one squared plus one squared is 1.

2 Awesome Things That Happened This Week

1) My version of Math Maintenance bellringers paid off!  Since bellringers are “non-negotiable” this year, I thought I’d take advantage of the fact that they don’t have to be ACT review questions until the 2nd nine weeks.  So I’ve been throwing review questions up, not from the day before, but from the previous week.  My kids did somewhat better on those sections than the teacher who did just random review, and I know I’m not a better teacher than her!  So I’m going to have to say that it was the math maintenance bellringers that made the difference!

2) I made it through the entire week without crying, which is a first for this school year.  Winning!

1 Thing I’m Looking Forward To

Trying my first Mathalicious lesson in Algebra II!  A little worried, but hey, gotta grow sometime!

Category: Precal | Tags: ,

Special Unit Circle Angles Worksheet

If you want to know how my week went, I’d have to go with

So let’s focus on the positive, which was a worksheet that I’m kind of in love with. I used it last year for Alg II w/ Trig and yes, again in Precal as we reviewed trig. One previous student remarked that it looked like the one from last year and another kid said, “hey, if it’s a good resource, then she’s just being smart!” which made me want to give him a gold star. Anyway, the file is available here (note: it does use Running for a Cause font at the top, easily downloaded or you can just change it) and these are the screenshots:

Capture2I am a visual person so I think of my triangles as short, medium, and tall, but some of them in Precal wanted to put 30, 45, 60.  Go for it, dudes.

We did stop and talk about radians for a while, using the wonderful applet from Sam’s post.  And we talk about Math Teacher Mambo’s empinadas, except they turn into quesadillas from Moe’s (welcome to Moe’s!).  I do not teach how to convert radians to degrees because I find they want to resort to that instead of learning where they are (although a few figure out the conversion on their own and they love to tell me all about it and I tell them my reasoning as well).  They had to the back WITHOUT looking at the circles on the front, however (Or if you print two to a page, have them fold it half to prevent peeking).  Then it’s just a quick hop to talking about how tall/wide each triangle is and you’ve got sine, cosine, and tangent of special angles, which is what we’ll be discussing Monday!

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