Thursday, December 18, 2014

(blog): Another Jeopardy Math Category

Just a couple weeks after Jeopardy had its Non-Common Core Math category during Kids Week, they ventured again into that academic field, but this time with adults. They fared a little better. For one thing, they made it through all five clues, including a Daily Double, and they didn't wait until everything else was exhausted.

Unlike the kids' clues, these didn't all have to do with the numbers 1, 2, 3, 4, 5 being added and multiplied.

The first question involved calculating a 20% tip on a $16.00 fare. The contestant managed to calculate the tip correctly ($3.20), but got the answer wrong. Neither of his opponents picked up that his calculation was correct, but that the clue wanted the total, which was $19.20, as Alex pointed out. (He will always point things like this out. I think he delights in that sort of thing. But to continue . . . )

The second clue asked for the greatest common factor of 84 and 105. Oddly (to me), the first contestant said 7, which was incorrect. I had already checked 3 (yes) and 9 (no) using simple Rules for Divisibility when the second contestant said, 3, which is smaller than 7. Had he or the third contestant realized that 7 was, in fact, a common factor as well as 3, then they should have realized that the GCF was 21. I have to say that if you don't see 7 right away, you won't get 21 in the allotted time. On the other hand, 7 was called and it should have been a quick check.

The third clue checked your knowledge of time. If your friend meets you 130 minutes after 11:30 am, when would you meet him? Two hours and ten minutes later would be 1:40 pm.

The fourth clue, the Daily Double, dealt with the surface area of a cube 10 cm wide. (I don't remember the actual unit, so I'll say it was centimeters, but it was definitely 10.) The contestant started to answer, paused and then answered correctly that it was 600 square centimeters.

Finally, the $1000 clue was a simple two-step equation: If 3x - 11 = 43, then was it x? Alex was surprised at how fast the answer was given. I was still dividing 54 by 3 -- there was $1,000 on the line, and I didn't want to rush and get it wrong.

Overall, the topics were spread out a bit, and with the exception of the clock math, they were good questions for an Algebra Regents review sheet -- especially, the one asking for the total and not just the tip.

The dangerous part for me in all this? The only thing worse than being a math teacher who didn't make it a true Daily Double would be being the math teacher who made it a true Daily Double and got it wrong. Luckily, that wouldn't have been a problem.

On the other hand, I had the same fear with the million-dollar question on Are You Smarter Than a Fifth Grader?, so I guess it's a good thing that I don't go on these shows!

Update: Typo fixed in question 3.

Wednesday, December 17, 2014

Order of Operations Mnemonic

(Click on the comic if you can't see the full image.)
(C)Copyright 2014, C. Burke.

Remember to place all your holiday orders of operations early so they'll arrive in time ... and in the correct order.




Tuesday, December 16, 2014

(blog): 360, 180, 90, 2 and 1/2: I'm Talking Arcs and Inscribed Angles

Assisting today in a Geometry class. It was Day 2 of Arcs of a Circle. Yesterday, the teacher covered central angles with the class, which meant that today's lesson moved to the inscribed angles. She carefully and diligently explained what makes an inscribed angle, and how the line segments intercept an arc in a similar way that they saw in the previous lesson. And then we got into the relationship between the arcs and the two types of angles.

The measure of an arc of a circle is equal to the size of the central angle which intercepts it. The measure of the inscribed angle is half the size of the arc it intercepts. Pause. What does this make the relationship between the central and the inscribed angle. Pause. Wait. Rephrase? Response? Good -- but try again in a full sentence...

"It's half the size." sounds good. No, really, it does -- it means someone's paying attention and either getting it, or somewhat getting it. Following up: "What is half of what?" The inscribed angle is half of the central angle.

Okay. So if the inscribed angle is 60 degrees, how big is the central angle? Let them think about it. Did they come up with 120 degrees? Or 30 degrees? If the smaller angle is half the bigger angle, then the bigger angle is ... ? (Okay, it's a leading question, and I hate leading questions, but sometimes you do need to just pull that one number out of them so you can move on.)

They moved along with the notes and did a couple of practice problems before moving on to the next step. What if two inscribed angles intercepted the same arc? What could we conclude about the two angles? The teacher waited to see if they could reach the statement before she gave it. It took a moment to realize that A was half the arc and B was half the same arc, so angles A and B had to be congruent even if we didn't know how big the arc was. We didn't need to know. But if we did, we could work things out.

Then things started getting complicated because when you start putting in two many line segments and too many inscribed angles, triangles start forming. Wait! What are we supposed to do with those?! Treat them like three inscribed angles, of course, but don't forgot those properties of triangles, either. Particularly, the one about the sum of the angles!

So if we had a problem that looked like this:

... we have enough information to fill in both angles BAC and BCA as well as arcs AC and BC. We just might not know that we know yet. Not unless we remember some other facts about circles and triangles. The total measure of the central angles in a circle is 360 degrees, so the total of the arcs of the circle is also 360 degrees. The sum of the angles of a triangle is 180 degrees. Notice that if each angle of the triangle is inscribed that make each part of the circle twice the size of inscribed angle -- and 360 degrees is twice as big as 180!

Excellent discovery, if they can make it on there own. One student was hovering about it while he was talking. If he made the connection, he didn't share it with me, but he was close to it.

Finally, why is 90 so important that I included it in the title?

Because many of these problems use diameters as one of the line segments. A diameter cuts the circle in half, into two semicircles, each 180 degrees. The central angle formed by the two radii joining into a diameter is a straight angle, measuring 180 degrees. Any inscribed triangle using the diameter as one of its sides would, by necessity, have an angle that measures half of 180 degrees, which is 90 degrees.

Wait a minute!

So any inscribed triangle using the diameter of a circle is a right triangle? And any inscribed right triangle has to include the diameter?

It's almost as if someone planned it that way. Maybe not, but that's how we planned the lesson.

Monday, December 15, 2014

(blog): Last Friday's #NYCMathTweetUp Meet-Up

As promised yesterday, more about my weekend meet-ups.

On Friday Night, a gathering of #mathednyc took place at the offices of Offices of New Visions for Public Schools on West 13 Street in New York City, dubbed the #NYCMathTweetUp. I'm not sure how the capitalization worked with hashtags. Prior to the event, I read that n > 30 had RSVPed, where n is "the number of people interested". However, upon arrival, I discovered fewer than that made it there on a cold night, but this didn't discourage anyone.

The icebreaker game started as soon as we stepped off the elevator and filled in our name tag. We had to pick another tag from the tree with the name of another guest. I thought to jokingly call these hashtags, but they actually contained our Twitter handles instead. The goal was to locate that person and start a conversation. I joked that I might find my partner, but she might excuse herself because she was still looking for her partner. And I say "she" because I did, in fact, locate @khatrimath before the evening ended. I didn't have many comments to make at that point, except that I thought that the two of us were the only ones with math in our Twitter handles.

Guests were asked to bring a math activity that we could try out. I promptly forgot all about that. Not a problem, however, because (1) David Wees @daidwees supplied us with a page of New Visions Math Tweetup Puzzles, and (2) we didn't actually do any. But that was fine, because the conversations were flowing nicely. (I even stopped talking long enough to allow other to speak... a few times, any way ...)

The one major activity of the evening (after eating too many sliders) was an activity entitled Things That Suck. As educators, we divided ourselves into three camps -- Totally Sucks, Does Not Suck, and Need More Info/Might (Not) Suck -- on each of several burning topics, including Homework, Regents exams and Professional Development. This last one being the reason I tweeted that the evening was "like Professional Development, but, you know, fun", and why the first response to that was "the kind that doesn't suck", by the aforementioned @khatrimath.

The evening wound down and the conversation continued at a local establishment a few blocks away, where the picture I posted yesterday was taken.


Update: What the heck, I'll add a little about Saturday night, too. I was debating whether or not to add a little more about the Celtic Cross concert because the readers here are usually looking for mathy-geeky comics or math-education discussion. But I'm Irish, and I had a good time, so why not? It's not blog, right?

I uploaded a couple of videos to youtube. I'll link you to their cover of Little Talks, which I referenced in a comic last summer. Search on user cjburke23 to find a bunch more. It was a fun show, and I had a sneak peek at their playlist so that I'd know when to film songs I hadn't gotten before. Unfortunately, they strayed from the playlist a few times. After the end of the evening, the crowd was screaming for "One. More. Song. One! More! Song!", and they obliged (and even played two).

It was at this point, the lead singer, Kathleen Vessey Fee called me over (I was close to the front) and said, "Chris, give someone your phone!". Then she handed me the Cowbell and the stick to play it. Unfortunately, I didn't know anyone well enough to hand over my videocamera (it's not a phone) who wasn't also dancing. The thing is: I knew that this would likely happen, given that it was a birthday night out for me, and this was secretly why I invited a bunch of people. So there isn't any video of it (not that I'm aware of), but I played along on the Black-Eyed Peas Tonight's Gonna Be A Good Night, which then led into Taylor Swift's You Belong With Me.

It was at this point that the jaw of the young lady pictured below dropped halfway to the dance floor as did those of several of her friends, all of whom were surprised that I appeared to know the song and could sing along with it. So I got a picture with my first "groupie", Jill. The gentleman with her took it, so I'm safe. And it was about time we were introduced because she and her friends are regulars at these shows, and we've bumped into each other on the (very small) dance floor before.

So no math discussions that night, not even about the Guinness t-test, unless that was a taste test.

Sunday, December 14, 2014

(blog): It Was a Meet-Up Weekend

Until recently, I had a lot of make-up weekends, lost Saturdays and Sundays were I made-up the backlog of work that I let snowball from Monday to Friday (or the week or weeks before). However, this weekend was a Meet-up Weekend, where I got to meet up with people I didn't know personally beforehand, but now I can say I have.

Warning: These meetups keep me out late -- not complaining. On the contrary, glad that I'm out of a rut. On the other hand, I haven't made up the sleep yet, so this is a short intro post, and the actual events will get described tomorrow. (No comic tomorrow, either. I haven't done one yet, and don't intend to in the next 20 minutes or so.)

Friday night, if you are a math educator in or near New York City and you blog, tweet or post anything about education, you should have joined us at the NYC Math Education Tweetup at New Visions for Public Schools. According to my email, about 30 people were scheduled to attend; however, I think the weather might've scared a few off. Likewise, parking in Manhattan (I took a train) can be a nightmare and finding the correct address was a minor adventure in oddly-labeled buildings. Again, I'll go into more detail tomorrow. I didn't have a decent camera on me, but pictures were taken, and I'm waiting for more to show up online or in email. One picture did show up at the "after-party" -- that's me on the right.

I got a little turned around in the village and thought I was heading in the correct direction for the train. I should've taken the hint when I was standing at the corner of West 4th Street and West 12th Street that something was amiss. I did figure it out, and eventually trains did get me home much later than I expected.

Unfortunately, my body won't sleep late once the sun's up unless it's extremely cloudy, so I lost a couple of hours. However, that didn't prevent me from joining Celtic Cross at a concert. (By joining, I mean that we were all at the same place at the same time.) The music didn't start until after 10pm. Funny thing, back in college, I never went to a late-night show like this. Now, I seem to do it every couple of months. It was an extra-special outing for me in that some family and friends were going to join me for a change to celebrate my birthday last week. Unfortunately, by showtime, every one of them had a legitimate reason for not being there. But I didn't care. I met other people, fans of the band, some of whom I've seen before, even if we hadn't spoken. I also found out others were having birthdays. At one point, three of us met and discovered that we were 30, 40 and 50. Unfortunately, one of us walked away before we could get a picture. I won't mention which it was, but here are the other two (me and Elizabeth).

I wore a red shirt to be festive for Christmas and all that, but by that part of the evening, it was too hot, so I wore it open. I got some compliments on the Celtic Cross design on my shirt, which has no connection to the band other than their name. (That is, their logo is different.)

Again, I can go into detail about the fun I had in a post tomorrow, but if you need to know why I like this band so much and follow them around, here's a little bit of a hint:

(me and Kathleen Vessey Fee)

Saturday, December 13, 2014

(blog): Happy Consecutive Number Day!

It's seems like every day, like every number, has something special about it, but as George Orwell might've said, but wisely chose not to, "Some dates are more special than others". (Had he said something about some numbers being more equal than others, that could've been a problem, but would've fit well into his theme. But that's a subject for another blog post.)

Today is Consecutive Number Day because it is 12/13/14. We've had a Consecutive Number Day for each of the past 11 years -- TWO, if you use the Commutative Property of Dates (also known as the DD-MM-YY format). This last fact makes this year's date even more special because there won't be a 12-13-14 is London or Madrid or pretty much everywhere else in the world where they use that format because there isn't a 13th month.

Finally, it's special because after 12 years in a row, this one will be the last one for a long time. Now, don't fret yourself into a worry. You don't have to wait until 2103 for another one ... unless you're some kind of crazed purist. Me? I like to run the numbers, have fun with the numbers.

The first Consecutive Number Day that I took note of happened when I was in ... kindergarten, no, wait, Pre-K! Yeah! That's the ticket! ... in 1978. It was 5/6/78 and we even had to pause at 12:34 pm (I was asleep for 12:34 am) to note that it was 12:34 5/6/78.

Eleven years later, digital watches were common and we knew the correct time to the second, if we ever bothered to set it correctly, so we knew when it was 1:23:45pm 6/7/89. We could do the same the following year, although 7/8/90 wasn't quite as much fun.

Two thoughts come out of this. First, given the accuracy of today's computing, I had to wonder if the atomic clock could tell us when it was exactly 1:23:34567891011 12/13/14 (and, if so, did some geek take a selfie of it?). Second, it gives us something closer to look forward to.

Hold the date now in your datebook app for 1/2/34. Sadly, there isn't a 5:67 am or pm. Not even in London. Or even in Pasadena, where they'll be hosting the Rose Bowl because New Year's Day is on a Sunday.

Friday, December 12, 2014

(x, why?) Mini: Catching a Cab in the Rain

(Click on the comic if you can't see the full image.)
(C)Copyright 2014, C. Burke.

It's all about the green, about the green, no yellow...

If you think about it, the Flash's powers wouldn't help him catch a cab, although he could beat it to where he wanted to go.

And if Green Arrow shot one with an arrow, he'd need to use another trick arrow to jack up the car while he changed the tire.

Of course, the probability of Batman catching a cab in the rain is 100%, metaphysical certitude, because, you know, he's Batman.




Thursday, December 11, 2014

What's It All About, Algie?

(Click on the comic if you can't see the full image.)
(C)Copyright 2014, C. Burke.

It's all about the pun.
And it's about a month later than I planned it.

And once I'd decided on going with an allusion to What's It All About, Alfie, I had to lose the examples that didn't go with Algebra. There were a number of variations that I had written down (some better than others) and some I forgot because I wasn't near that piece of paper. Going to happen.

But if you're going to round the bases, make sure you know who's on first. I don't know.


Update: So I discovered that Get Smart used the title What's It All About, Algie decades ago in Season 5, Episode 23, which is very illuminating according to the Law of Fives.
"The Law of Fives" was also the name of a (x, why?) comic published 5/23/10.




Wednesday, December 10, 2014

(Blog): MATHice in Scienceland

Only three days into my new substitute assignment, and I have a few observations. Now, i don't want to get political or start anything -- that's not me. I try to roll with it, whatever it is, and not stir the pot. Especially, considering that I have to revisit this pot for the next month. But, here goes ...

One of the school's Living Environment teachers has been out sick. (I don't know how many the school has.) I've covered her classes every day this week, so far, and likely will continue to do so. I don't mind, but the kids do. They're objecting to the work posted on the board with no one to teach them. They're frustrated and confused and don't like to be told to read the text book. Some of them do what they have to do and try their best. Some of them, I think they just want a teacher to tell them the answers to the questions. And some don't seem to care at all. And none are happy that there's a math teacher in their science class.

Today, I tried to talk to a few of them. It was a good day for this because many of the freshmen were gone on a trip and some of my classes had fewer than a dozen students present. Unfortunately, they just wanted to complain (which is fine, so far as that goes), but they didn't want to hear any solutions -- not the ones that are possible or likely. They need to step up and take matters into their own hands, but they don't have the maturity for it.

Have you heard me complain lately that today's freshmen are less mature than the junior high school students I needed to get away from a dozen years ago?

I don't have all the facts, just some anecdotals. At my last school, while they were losing teachers to budget cuts, I knew that the Living Environment (aka Biology) teachers were safe. (This is my impression, mind you, not a statement of facts.) They were needed more than any of the other science teachers because they were the freshmen class, and everyone has to pass that class and Regents exam. If I extrapolate this, Living Environment teachers are likely in high demand, meaning that they have options as to what school they teach in. Which means that they'll leave a poor school in a heartbeat if something better becomes available.

Without passing judgment, I tried to explain to the kids that if someone was looking for a position, would they pick a school that's been around for 50 years or one that was reopened in the past five? That's not the perfect measure for adults, but that's something the kids could understand without feeling insulted.

Not all 50-year-old schools are great, but they've "reorganized" the poorer performing ones in recent years. But if you're looking for a position (which I've done too much of in recent years) and you see a school where, say, 80% of the kids graduate in 4 years and 70% go on to college, and a second one where, say, 40% of the kids graduate in four years and who wants to contemplate the low number going to college, which do you think the teacher is going to lean toward? If one school has staff who have been there for more than a decade, and the other is only five years old and no one's been there for more than three of those five years, which do you think the teacher is going to lean toward?

If a teacher were to walk into my classroom while I was subbing and saw what little respect the students had not only for me (the sub), but for the property of their actual teacher and (let's face it) for themselves, would they want to come to this school?

End result: if the school is poorly-performing, then you aren't going to be able to attract a qualified teacher whose future depends on the performance of immature individuals who have been taught to respect themselves above all else to the exclusion of having any respect for others, without actually recognizing that they aren't respecting their own future as they find "disrespect" in everything anyone tells them that is contrary to their own preconceived (and immature) notions of reality.

Is that the school's fault? Is it the kids' fault? The parents' fault? The teacher's fault?

I don't know. I'll play it safe. I'll blame Bloomberg. He didn't create the mess. He just made it worse by trying to remake the schools in his own image. And he's not my boss anymore, so I can get away with that now.

Tuesday, December 09, 2014

(Blog): 8 Lies Math Students Love to Tell!

In honor of the marking period ending and grade submissions coming due, we present to you ...

The Top 8 Lies Math Students Love to Tell

8. I'm doing my work!

7. Why am I failing? I handed in all my homeworks and passed all my testses (sic).

6. I was just about to get started.

5. Hey, why'd you erase it? I was copying that.

4. I said that!

3. I'm finished.

2. Mr. Burke, you the greatest math teacher evah! (week before grades are due and/or parents coming to school)

And the Number One Lie Math Students Love to Tell. . .

1. I did my best. I tried really, really hard.

Monday, December 08, 2014

Blog: Jeopardy and Non-Common Core Math

Last week, Jeopardy had a Kids Week and on Friday night, one of the categories was Non-Common Core Math. As a math teacher and just someone who likes numbers, I was curious what the category would be. The kids, on the other hand, well they were curious, too, at first, but then ran away.

It started innocently enough, with the $200 answer being: "1 + 2 + 3 + 4 + 5". Quick mental math gave the question, "What is 15?" A simple exercise in triangle numbers, which are formed by summing consecutive numbers. It's one of those things which most kids will see and do even before they hear the phrase "triangle numbers", and long before they know they memorize the formula. Besides, a small sequence like this is quicker to add (if you don't have it already memorized) than computing a formula.

Things got trickier with the $400 answer, "1 - 2 + 3 - 4 + 5". There was some hesitation as the contestants (I almost typed "students") worked that one out before one of them arrived at "What is 3?" (I didn't tape it, so I can't review it to see if someone got it incorrect first. I don't remember.) There are two short cuts for this problem, and both have to do with pairing. If you noticed that each pair "1 - 2" and "3 - 4" yield a result of "-1", you have -1 + -1 + 5, which is 3. If you noticed that "-2 + 3" and "-4 + 5" yield a result of "+1", then you had 1 + 1 + 1, which is still 3. If you just oscillated your numbers, you took more time and you probably didn't buzz in in time.

The kids gave up on the third answer: "1 * 2 * 3 * 4 * 5". Given the ages of the kids, I would have thought that at least one of them had seen factorial before, and this was the definition of 5!, although the numeric equivalent was needed. Perhaps they got stuck on 24 * 5, not thinking to reverse the order (20, 60, 120, 120). Whatever the reason, no one got the answer, and they bailed on the category.

It proved so unpopular that when Trebek cautioned "less than a minute to go" (a.k.a < 1 min), the two Math clues remained, and were the final ones of the game.

The $800 answer: "-1 * 2 * -3 * 4 * -5". This actually bothered me that none of the kids gt it. First, for the reason Alex gave. Second, because I had to listen to Alex give it. The previous clue had a result of 120. The numbers multiplied are the same, only some of the signs have changed. Multiply a negative times a negative times a negative and the product will be negative (times two more positives, which won't affect it). The question should have been "What is -120?", which should have been easy considering the previous question gave them the number, and they only had to add on the sign.

The final reason to be annoyed? Alex took so long to explain what should have been obvious that we didn't get to see the last clue. Would it have had division? Exponentiation? Mathematical minds want to know!

But that clue won't be revealed, and it's likely that they avoid such mathematical categories during future Kids Weeks.

Sunday, December 07, 2014

(x, why?) Mini: Eights

(Click on the comic if you can't see the full image.)
(C)Copyright 2014, C. Burke.

But four and four are eight, so whatever the problem, it's not a math problem.

But here's a bonus problem: when was the last time we saw these Eights together?