Earth Hour
Birthday polynomials!
I posted last week about “birthday triangles” (in short, turn your birthdate of November 23, 1972 into a triangle with coordinates (1,1) (2,3) (7,2) – or a quadrilateral by including (1,9) – and then perform coordinate geometry or transformational geometry tasks using them.)
Sam, in the comments, suggested using birthdays to create polynomials. Cool. (How will this work?)
And then I remembered “family curves”
Express a birthday (yours, your mom’s, doesn’t matter who) as three coordinates: (1,1), (2,3), (7,2) – and write the equation of the parabola that passes through these three points. I used this as an early transition to polynomial functions last time I taught precalculus. It was also probably the only time the kiddies saw a system of 3 equations, 3 unkowns, before college
I’ll leave it to commenters to solve. Or solve your own. Or discuss which birthdays don’t make vertically oriented parabolas (parabolae?) or any parabola/s/e at all.
Edit – a friend points out that a (0,b) coordinate should either be required or somehow banned, as the work with and without the y-intercept given is of considerably different difficulty.
At last, a space
Yesterday I got the call. After seven years in my building, a parking space came open, and I was at the top of the list. $80/month, a real New York bargain.
(my annual parking rental will be more than the value of my car. And I am delighted. Go figure.)
Birthday Triangles
Birthday triangles. Family Quadrilaterals. Personal Polygons.
Take a date, turn it into a figure.
How?
October 31, 1993 –> 10/31/93 –> (1,0) (3,1) (9,3)
March 24, 2008 –> 03/24/2008 –> (0,3) (2,4) (2,0) (0,8)
November 28, 1966 –> (1,1) (2,8) (6,6)
July 4, 1776 –> 07/04/1776 –> (0,7) (0,4) (7,6) or (0,7) (0,4) (7,6) (1,7)
Kids seem to work much harder when they are working on their ‘own’ birthday, or their favorite baseball player’s, etc. In some cases kids who don’t usually work, actually do. Others will go on to do the same work they would normally do, but with more care. They take their own birthdays quite seriously.
Really?
Yup. Best evidence, (and mind this, please) almost every class, when they first plot their own birthday triangle, there is one or two sad looking kiddies (it’s not come to tears, but I’ve seen the quivering lip) who thinks their own triangle is ugly. “Nooo” I say “Yours is obtuuuse. Does anyone else have an obtuse triangle that looks as nice as Anna’s?” (it’s usually a girl)
And do what with these?
Anything you would do with coordinates.
classify
find slopes
find midpoints
find distances (perimeter)
find area
write the equations of the sides
transform
“show” stuff (particular cases of general laws. Eg, take a quadrilateral and show its midpoints form a parallelogram)
Some more open questions can be nice. I’ve sent kids to look for someone with an equilateral triangle for their birthday (led to a great discussion the next day), find the family member with the greatest (or least) perimeter or area, etc.
Pitfalls?
The upset kid.
April 4. (pretend you were born a day later, or choose someone else)
collinear points (degenerate triangles)
Worth it?
Definitely.
NCAA Sweet 16: The biggest loser
Anyone can pick the tournament winner. But the biggest loser?
The biggest loser will lose to a team, who immediately loses to another team, who loses to another team…
Last week I picked Baylor to be the biggest loser in the men’s NCAA basketball tournament. Joel picked Villanova. (he should get a repick, Villanova won, twice, and is in the Sweet 16)
So, who’s left? These are the teams who lost to teams who lost:
East: Indiana, George Mason, Saint Joseph’s, South Alabama
South: Oregon, Oral Roberts, Kentucky, St. Mary’s
Midwest: Kent St, Vanderbilt, Southern Cal, UMBC
West: BYU, UCONN, Baylor, Belmont
My pick is still Baylor, but Belmont, UMBC, Kentucky and St. Joseph’s should be favored to be the furthest four from the final four.
It’s not too late to pick (especially since there are no prizes!)
Math Ed, must read: Math Panel, Lockhart, Schmidt
1. The National Mathematics Advisory Panel issued its final report last week. Dave Marain (Math Notations) was concerned about the lack of active teachers involved – I shared the concern. Now it’s time to read and find out what they recommended.
2. Lockhart’s Lament got a plug in Devlin’s Angle, and has been making the rounds this month. I think the analogy (math is art, music is art, extend for 25 pages) becomes weak very quickly. There is something to how badly much of our math is taught. However, many of his complaints do not extend to classes where teachers reason. His critique is of the classes that are taught “out of the book” and by not so smart people. Still, limited as it is, there is some merit, and it deserves real attention. I may return to it.
3. The new issue of the AFT‘s magazine, American Educator, is devoted to standards. Hirsch wrote a, well, Hirsch-piece. More interestingly (and a bit strange), the general piece on state standards finds math standards generally better than standards in other subject areas. (???)
But of most interest is William Schmidt’s “What’s Missing from Math Standards?”
Schmidt’s answer – rigor, coherence, focus – makes sense. His plea for fewer topics at greater depth makes sense. And his suggestion that we consider collaboration among states (already begun) or even look at national or federal standards deserves some attention, and perhaps consideration.
Marxist Set Theory
River to River against the war
Today, noon.
Manhattan.
14th Street.
Until 2.
Come out.
If you can’t come,
do something,
say something,
tell someone.
A prime carnival
Mathematics. #29. At Quomodocumque. Which is, apparently, a mathematician’s blog, but not a math blog. Let him explain.
It’s good, it’s weighted to the research side of things, and you should visit it.
If you do nothing else, follow the link to Emmanuel Kowalski’s blog, and look at: Les fabuleuses aventures de Schlomo Cohen le Mathématicien détective.
What makes a school hard to staff?
Let’s not talk about reality, but about categories. Because teachers who teach at “hard to staff schools” in NYC are eligible for certain financial considerations. (tuition assistance and/or student loan forgiveness, I think).
Let’s talk about Herbert H Lehman High School, straddling the Hutchinson River Parkway, in the east Bronx. Whether or not Lehman is in reality “hard to staff,” it is not designated “hard to staff,” so its teachers are not eligible for these incentive programs. Years ago it was on the list, now it’s off the list, and no one who I know can tell me how or why.
One school, not hard to staff? No tuition help for teachers
Same school, struggling? The new principal gets $25k
Where’s this designation come from? Beats me. I am not even certain if it is “hard to staff” or “high need” or “program eligible” But does it seem arbitrary? It does. Probably, when we learn more, we will find that it seems arbitrary because it is in fact arbitrary, but let’s wait for more information.
“Jonathan,” you might ask me, “you are blogging about the NYCDoE being arbitrary? That’s hardly news.” And you would be right. But read on.
(more —>) Read more…
March 19, 2008
No twists. No subtleties. No nuance.
Five years is five years too long.
Out. Now.
Problem: triangle area ratio
Consider equilateral triangle ABC. Circles with centers A, B, and C and radii 
Now consider the largest equilateral triangle, DEF, that can be inscribed in that gap. What is the ratio of the areas ABC:DEF?
Put questions below. To share answers, click this answer link.
Solutions: triangle area ratio problem
Consider equilateral triangle ABC. Circles with centers A, B, and C and radii
Now consider the largest equilateral triangle, DEF, that can be inscribed in that gap. What is the ratio of the areas ABC:DEF?
Share answers by commenting here. To ask questions, click the problem link.
NCAA Pool: The biggest loser
Anyone can pick the tournament winner. But the biggest loser?
It’s not the runner up. The runner up will have beaten many fine teams along the way. And it’s not going to be Portland State, most likely. The 16th seed will lose to a #1, who will win a few more games, maybe go all the way. No shame in that. Losing to the champ, or the runner up, or a sweet sixteen – no embarassment there.
No, the biggest loser will lose to a team, who immediately loses to another team, who loses to another team…
If every game is won by a higher seed, and North Carolina beats Memphis in the final, then the biggest loser will have been… #11 in the western region, Baylor, who will have lost to #6 Purdue, who will have lost to #3 Xavier, who will have lost to #2 Duke, who will have lost to #1 UCLA, who will have lost to South champ Memphis, who will have lost to tournament winner North Carolina.
So, do you want to try your hand at picking the biggest loser? (I’m sticking with Baylor)
(by the way, this is men’s since I just watch. This year I’ll be rooting for UCONN in the women’s tournament.)
Demonstrations this week
Wednesday, March 19, City Hall, Against the budget cuts. 4PM.
The UFT is making a major push for this. (make it bigger on the webpage, please). But it also involves parent and community organizations. It will take work to make sure people in your school understand this is important.
Unfortunately, this got proposed while much of the membership was not yet on board about the scope of the cuts and how they affect us, so those of you who know you are coming will need to explain to others in your school why they should come too. Assume that you can convince a few more people, and then do it. If we all bring extra people, this could be big.
Saturday, March 22, 14th Street. River to River, against the war in Iraq. Noon.
UFT endorsed this one.
Private factoring
I factor permutations of subway car numbers to pass the time on rides when I have nothing to read. (Last night, 1157, but I only got two-thirds done, since I had had some wine and started not so far from home).
Commenter Sara factors to help herself fall asleep.
I factor/do long division to hold my composure.
And Mr. Munroe?
This sort of factoring is soothing, calming. It requires focus. It is a solitary activity. Silence, or white noise, or unengaging background helps. And it is kind of nuts.
Is 8303 divisible by 17?
If yes, we can add multiples of 17, and the sum will still be multiples of 17.
Assume 8303 is 17n.
Then 8303 + 17 = 17(n+1)
8320 = 17(n+1)
Divide both sides by 10.
832 = 17k (where k = (n+1)/10 )
850 – 832 would be 50(17) – 17k, or 17(50-k)
that’s 18 = 17(50-k).
no good. k is not an integer, n is not an integer, 17 doesn’t divide 8303.
Is it prime?
Not fancy, computer-type stuff. I factor numbers. Mostly 4-digit, sometimes 5-digit. Permutations of subway car numbers. And sometimes they don’t factor.
8303? Not even. 8+3+3 = 14, so no 3. Not a multiple of 5.
Subtract 303 – 8 = 295. 7, 11, 13 none go into 295, so they don’t divide 8303.
17? 8303 + 17 = 832. 850 – 832 = 18, so 17 doesn’t go in (what?? if all these numbers were multiples of 17, then their sums and differences would be too. 850 is 50 17s. Since we got 18, one of the numbers was off. That would be 8303)
19? 8303 + 57 = 836
836 – 76 = 760. Hurray! 8303 is not prime.
I find it easy to amuse myself for a full subway ride…
Teacher’s Potluck – Pi Day Edition
![[pipie.jpg]](https://i0.wp.com/bp3.blogger.com/_ZZ1YVMMovvU/R9npDz0RAdI/AAAAAAAAATA/ID_vrqKfheE/s1600/pipie.jpg)
Run over to Meeyauw to catch it.
Recipes. Teacher Stuff. Pie (of course). Even a picture of a Pie-shaped lolzcat.
Of course I forgot to submit again. Even with this wonderful photo (left) from Whatsit to remind me!
But Andrée does serious recipes. Look closely at those pistachio cookies!
What does this map show?
UFT Accountability Reports
UFT President Randi Weingarten announced today an answer to the New York City Department of Education’s embarassingly poorly designed “Progress Reports.” The UFT’s proposal gives schools four separate ratings:
- Academic Achievement
- Safety, Order and Discipline
- Teamwork for Student Achievement
- Department of Education Accountability to the School
But these categories are broad. To understand the ‘feel’ of the report, click on the samples. (Elementary school, middle school, high school). And for more background/details, try the other links:
- Press release
- Highlights
- Weingarten speech
- November Delegate Assembly Resolution on creating an alternative to the miserable Progress Reports
The right questions are asked. The calculations look transparent. The comparison groups are clear. I am not sure that we are right to buy into the rating the schools business in the first place. But that’s UFT policy. Given that this is what we are doing, it looks like we’ve done it well.
Picking nits?
We should, all of us, read these things carefully, and post to here, or to EdWize, or e-mail your DR or someone with ideas. A good document could always use some picking to make it stronger.
I’ll pick a bit (maybe more later). (Below the fold —>) Read more…
JD2718 