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Saturday, September 24, 2011

Destroy My Problem Set, Please.

Students should be able to complete this in groups without too much assistance from me. We already had a lesson on what the cube root means and simplifying cube roots to simplest form, which was also a refresher on how to simplify square roots. When it says "check on a calculator" they will have access to a CAS calculator for this lesson. I realize that if the roots don't come out rational, the calculator displays the answer with a fractional exponent. I don't know what to do about this yet. Maybe I will just put the answers on cards they can check instead of futzing with the CAS's.

The goal is for them to practice multiplying and simplifying, and investigate multiplying conjugate pairs to set us up for rationalizing denominators, both monomial and binomial.

I know the two questions at the end are kind of weird but it seems like a shame to waste the opportunity.

So...

  • okay?
  • Crappy?
  • Suggestions for decrapifying?
  • Am I missing any relevant opportunities to make connections?
  • Or show multiple ways of seeing something?
  • How are the kids going to noob this up in ways I'm not anticipating?

Also, I am a Latex beginner so no making fun of my typesetting. It took me four hours to make this.

12 comments:

  1. Looks pretty good! What do you think about a part that is like \sqrt{8}\cdot \sqrt{\frac{1}{2}} in order to hint at division having the same property?

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  2. The typesetting is pretty good. You might want to add \clearpage before problem 5 to keep the problem all on one page.

    Is this class a regular class, an advanced class, or a slow class? The exercise set seems like a lot of drill—way too much for an advanced class.

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  3. What about some reversal problems? Like 'write 8 as a product of 2 square roots.' Or another way to get at division, sqrt(10)*___=20 or sqrt(160) or...

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  4. It looks like the margins are different for even/odd pages. Are you using one of the book document class rather than article?

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  5. I love how it looks (didn't notice the odd/even margin thing).

    May not matter, but I was looking for a simple exponent or two inside the radicals in parts 2 and 3. \sqrt{a^2} or something like that.

    And the kids won't do it, but I think I'd like to refer to the Pythagorean Theorem when answering number 6. You've already got the familar a's and b's.

    ReplyDelete
  6. @gasstation It's a regular class. This isn't intended as "drill." The repetition is intentional. I haven't shown them how to do very much. The repetition is supposed to help them notice patterns.

    I uploaded a new version...check it out. Some of the additions will look awfully familiar.

    ReplyDelete
  7. Yay typesetting! If you are using TI's you can put a decimal point anywhere in your expression and it will give you a decimal answer. This won't verify that they simplified completely, but if their answer and the calculator's have the same decimal they haven't messed up yet. Hope that's helpful but it may be old news/not what you were looking for.

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  8. I just started with Latex myself. My first document took me 3 hours - maybe I shouldn't have started with tables...

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  9. If you don't want the 0.1, 0.2 section.. You can do:

    \section*{Title}

    If you every have latex questions.. email me
    nicholas.bennett@dc.gov. I am pretty decent and also do alot of graphs using psTricks

    ReplyDelete
  10. First impression: where does that rule in 0.1 come from? Was that presumed covered before this lesson? Have they done complex numbers? The actual rule restricts a and b to be non-negative: a, b >= 0.

    3(b) is a great problem. I would lead with more like these, even as problem 1. A target skill is the ability to square both sides, so something like sqrt(20) * sqrt(a) = 10 could lead right to that.

    4 is very good: what is your plan for handling 4(f)?

    Love #7. Well done here.

    Your definition of "conjugate pair" is not accurate.

    In #8g, are you missing an extra "square" or is that deliberate?

    I would never enjoy #9, can you throw more of the other stuff into it? #9a suffers the same fate as #4f.

    Good style. Questions you could add (to homework or otherwise)... Calculate the sum (6+a) + (6-a) and the product (6+a)(6-a)... then find two numbers whose sum is 12 and product is 35... 34... 33... 32... 21... 10... -100... p.

    ReplyDelete
  11. Thank you for the feedback Bowen.

    >>First impression: where does that rule in 0.1 come from? Was that presumed covered before this lesson? Have they done complex numbers? The actual rule restricts a and b to be non-negative: a, b >= 0.
    you know...I don't really know? We did a lesson before this developing radicals as sides of squares and rectangles with non-perfect-square areas. I'm not totally sure that's enough justification though. I changed the > vs >= thing though.

    3(b) is a great problem. I would lead with more like these, even as problem 1. A target skill is the ability to square both sides, so something like sqrt(20) * sqrt(a) = 10 could lead right to that.

    >>4 is very good: what is your plan for handling 4(f)?

    I would expect kids to think of numerical examples and generalize...I stopped class to highlight the difference in the domain restriction between 4(e) and 4(f).

    >>Your definition of "conjugate pair" is not accurate.
    I guess I don't really know what a conjugate pair is, then? I got around it by changing the wording.

    >>In #8g, are you missing an extra "square" or is that deliberate?
    It was deliberate, but I added another one with a square.

    >>I would never enjoy #9, can you throw more of the other stuff into it? #9a suffers the same fate as #4f.
    I don't enjoy it either, neither do they, I just want them to apply their understanding of how things work to disconnected, annoying problems like they are going to see on their Regents exams.

    >>Questions you could add (to homework or otherwise)... Calculate the sum (6+a) + (6-a) and the product (6+a)(6-a)... then find two numbers whose sum is 12 and product is 35... 34... 33... 32... 21... 10... -100... p.

    Good idea...done.

    ReplyDelete

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