Mathing...

the synthetic division is used to solve equations...

2015-08-30T07:53:59.371-07:00

the synthetic division is used to solve equations with superior grade

Thanks for the links. I like the other area proble...

2013-07-23T13:55:19.044-07:00

Thanks for the links. I like the other area problem too. Two great questions about the same concept.

For me the numerical solution came quickly if I as...

2013-07-23T13:49:43.622-07:00

For me the numerical solution came quickly if I assumed its area is constant however we change the unknown sides. I just made the top unknown segment zero, essentially dragging the red dot to the left mentally (I hadn't built the applet then).

The more interesting question to me was why was the area constant. The question wouldn't make sense if it changed, but why? For some reason, I didn't make the connection earlier even though I found the area by mentally drawing that segment so I could calculate the base of the triangle in he bottom left.

Perhaps we both found joy in the question because the problem was easier than it seemed at first. It's "how didn't I know that I knew it" kind of happy realization.

May be I should've used common or straightforward instead of boring.

The problem was originally posted here: http://fiv...

2013-07-22T18:38:57.567-07:00

The problem was originally posted here:
http://fivetriangles.blogspot.com/2012/04/area-problem.html

And here was some discussion about it on Reddit:
http://www.reddit.com/r/math/comments/1c46c7/does_this_quadrilateral_area_problem_really/

I made an equation in two variables, and asked wol...

2013-07-20T13:13:28.318-07:00

I made an equation in two variables, and asked wolfram alpha to give me integer solutions. The one they gave me made me laugh. Turns out my joy and yours are probably unrelated. Even with the added line, this problem doesn't look boring to me. I'll have to keep thinking about geometric solutions.

You never know when skills you learn will come in ...

2013-06-29T13:50:25.910-07:00

You never know when skills you learn will come in handy. I think I learned this technique for transfer in 5th grade. Would love to hear your experience with it.

I had not seen that version yet. Perfect example o...

2013-06-29T11:21:05.118-07:00

I had not seen that version yet. Perfect example of how people still don't believe the evidence (in this video, at least initially) even after the experiment.

Around 5:17 du Sautoy asks "Do you believe in the maths now?" and Davies (?) responds "It still seems like an exceptional result for you."

I think they sum up the counter-intuitiveness of this problem very well.

Around 5:53 du Sautoy says "And that's the power of maths. This is totally counter-intuitive. I didn't get this the first time I looked at it. I thought surely it was 50/50, but I followed the math through. I put on my x-ray spanx that makes me see the world in a mathematical way and suddenly I could see this pattern emerging. And that gives me power!"

Love that last line. Thanks for the link!

Really like this idea. I think it could be used wi...

2013-06-28T22:50:02.451-07:00

Really like this idea. I think it could be used with other problems where the answer isn't intuitive or readily determined without computation, but can be reasoned about.

You might want to check out Marcus du Sautoy (mathematician) and Alan Davies (comedian) version of testing the Monty Hall problem from there BBC program http://www.youtube.com/watch?v=o_djTy3G0pg

Absolutely brilliant. Thank you for a great teachi...

2013-03-09T17:16:35.565-08:00

Absolutely brilliant. Thank you for a great teaching and learning idea! Will be using this with my class in Sydney in a few weeks.

I'm glad it is of use to you. Credit goes to T...

2012-09-09T18:46:17.353-07:00

I'm glad it is of use to you. Credit goes to Touch Mathematics for creating it first. I like how they put the unit circle and graphs together in their flash applet.

Thanks for providing this useful tool.The best way...

2012-09-06T05:04:56.791-07:00

Thanks for providing this useful tool.The best way to learn trigonometry is to work on it everyday. Spending a little time reviewing class notes and solving a couple of problems will pay off in a few months, when tests and exams are near.
types of angles

I just laughed out loud. This is hilarious.

2012-06-29T09:11:12.254-07:00

I just laughed out loud. This is hilarious.

@Melina: I did this in Pre-Calc when I taught it. ...

2012-06-29T00:07:33.963-07:00

@Melina: I did this in Pre-Calc when I taught it. Inverse functions is in the Algebra 2 standards in California, so students *should* know them by the time they get to Pre-Calc. The sheer number of standards in Algebra 2 means it may not be taught or covered as thoroughly as it should be. Many don't really understand it or even remember it. I review the topic by going over the definition of functions and inverses along with the relationship between the graph of a function and its inverse. So it's not a surprise when students actually do this activity.

I can see how this could be a discovery-based lesson. Perhaps, students plot points for a function in one color and points for its inverse in a different color, then follow the steps in the video by sketching the first function, folding, and then transferring to reflect over the line y=x. If they plotted the points and sketched the graphs accurately, the reflection should connect all the points of the inverse. They can then describe the relationship between the graphs.

Had your students already seen inverse functions? ...

2012-06-27T16:54:13.291-07:00

Had your students already seen inverse functions? How did you introduce this? I love love it and was thinking of using it as a discovery-based lesson for students to get some exposure to inverse functions before seeing a formal definition (maybe even deriving their own definition by looking at relationships between various linear functions and their inverses). Thoughts?

I hope your students will enjoy seeing interesting...

2012-05-29T09:06:42.097-07:00

I hope your students will enjoy seeing interesting applications of stats as much mine did.

You might also like the video on Human Computation by Luis von Ahn. It's a little longer (runs about an hour) than TED talks. You may be able to work it into one of those days when half the class is gone. It's not about stats, but there are many examples from which to ask interesting questions.

http://mrhodotnet.blogspot.com/2010/08/human-computation-math.html

Great post - if I get to teach AP Stats again, I&#...

2012-05-23T22:26:08.486-07:00

Great post - if I get to teach AP Stats again, I'll use it. Thanks

@Rebecka: It takes about 10-15 minutes, depends on...

2012-05-18T15:13:51.858-07:00

@Rebecka: It takes about 10-15 minutes, depends on student ability and maturity. I speeded up the video so it plays faster. The pace in the video is probably a little fast for students.

It's a substantial chunk of class time, but I think it pays dividends in the long run. This is one activity former students who've gone on to AP Calc or who took regular calc still tell me that they remember from class. I think it's the novelty of it that helps them remember. I can see how this wouldn't have the impact it had, had the students done similar activities in previous classes (say Geometry or Algebra) before they did it in mine. But from this activity, many students remembered the relationship between exponential and logarithmic functions, at least graphically.

The activity works better when the students partner up. If they miss a little detail, their partners can fill them in.

Love this. About how long did you spend with it i...

2012-05-15T14:58:04.544-07:00

Love this. About how long did you spend with it in class?

I remember a high school teacher giving us a works...

2012-05-05T17:41:00.238-07:00

I remember a high school teacher giving us a worksheet with a long list of directions where the first was "Read ALL directions before beginning" and where the last was "Skip ALL directions and just write your name and birthday on the top and turn it in". I was one of the few who actually followed directions, yet I didn't do that on the test. May be I was too eager to do well on it. I suppose attention to detail is less of a skill and more of a habit.

Fixed! Interesting history. http://en.wikipedia.o...

2012-05-05T17:30:17.709-07:00

Fixed! Interesting history.

http://en.wikipedia.org/wiki/Sudoku#History

Love it! Such a valuable lesson for you... hopefu...

2012-05-04T00:43:12.445-07:00

Love it!

Such a valuable lesson for you... hopefully your students learn from it as well.

I remember taking a really important test in England called the "11 Plus", and found in the last few minutes that I had skipped two entire pages. Never did that again.

More seriously, this is surely about how we do math, and how to be successful at it? To succeed at solving math problems you have to use all your mental capacities, including the ability to read and understand the problem, organising the information, etc.

Thanks for sharing--I'm enjoying the Shikaku. ...

2012-04-06T09:51:30.713-07:00

Thanks for sharing--I'm enjoying the Shikaku. Nikoli wasn't the first to come up with Sudoku, though. Dell was publishing Sudoku puzzles for quite a while under the name "Number Place" before it became popular under the name Sudoku.

Thanks for the tip. It's the first I've he...

2011-09-25T14:57:22.714-07:00

Thanks for the tip. It's the first I've heard of Brian Dettmer. He's definitely done some interesting work, probably a little too complicated for the purposes of a calculus class, at least for the principle we're investigating.

First time I saw it, the video reminded me of Shawshank Redemption. I was thinking about matching up a solid pyramid or cone to the cut out space on a stack of paper. Show how that volume can be calculated from just a few sheets of paper, some simple modeling, and a little calculus. Even using sand or salt to fill in the void and measuring the volume that way.

As for guest post, I haven't considered that for this blog. Let me think about it. In general, I do not get much traffic here so guest posting in other more prominent blogs will be a better choice if you're looking to get more web traffic.

That is some intense papercutting right there. Lov...

2011-08-30T10:48:02.438-07:00

That is some intense papercutting right there. Lovely work though. Maybe you could get students to bring in old hardback books for this project rather than using new sheets of paper though, make little secret hiding places or do something à la Brian Dettmer's book autopsies.

Unrelatedly, do you accept guest posts for your blog? I would've emailed you but I can't seem to find your contact info. Drop me a line at nataliehntr86 at gmail, thanks!

@Tim Someone oughta try it. It's now my new fa...

2011-07-25T12:31:03.978-07:00

@Tim Someone oughta try it. It's now my new fave Zenoism. :)