Welcome "Mind Your Decisions" Readers

Another bump in my stats, courtesy of Spiked Math's comic #445: Three Logicians Walk Into a Bar. Any time some blog discovers it and reposts it, an additional link is usually listed afterward for my own Coffee Logic comic from May 2011. Additionally, Mike has a link to Coffee Logic right beneath his own comic on his page, so people who see the repost of his comic and repost it themselves are still leaving the door open to finding their way here.

The most recent posting I've found was at Mind Your Decisions, with the post, Three "Mind Your Decisions" Readers Walk into a Bar. Another thousand readers have popped in in the past week or so because of this.

Thanks for the traffic.

A reminder about Copyright: I have no problem with educators re-using my images on free websites, so long as they aren't edited(*) and there's a link back to my site. Dropping a line to ask is always nice but I won't be offended if you honestly forget (but I'm less likely to link back to you if I don't know about it. Likewise, if you wish to use them in class in your presentations or on worksheets, I'd actually be flattered. However, if you put these assignments on a class or school website, then, again, I'd ask that you link back here. Thanks.

(*)As for editing, I mention this because I found one of my older comics on a "humor" site where my copyright notice and my initials where removed and filled in with the background color. Thankfully, this hasn't been repeated (that I know of), so I haven't resorted to using gradients as background, with would be harder to overwrite.

End of Year Review 2

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(C)Copyright 2013, C. Burke.

Though my professional life is in reruns, the comic isn't. So let's shake it up with a fill-in-the-blank. The punchline will be left as an exercise to the reader. Remember to answer in a complete sentence and to show your work!

Because people get their feed from multiple sites, get notifications from several more and have at least four places to respond (five, if you count email), I'll collect the best ones and publish them all in one spot.

It shouldn't be too difficult if I don't get too many responses. But feel free to make my life difficult!

By the way, this isn't my first "excess letter". Check out last year's Kiss Today Good-bye. Okay, now point me toward tomorrow.

LOST in Translation

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(C)Copyright 2013, C. Burke.

When students say they tried ''really hard'', I like to know how much.

Obviously, the answer given by the student in the first problem is an approximation to the best of his ability.
The second one would have L'O'S'T' somewhere off the plane, but L"O"S"T" would come back down to reality.

My initial instinct was to have a whole bunch (six? seven?) crazy translations and have the last last one messed up on purpose, but I wasn't sure that people would pick up on that or yell at me for making a "mistkae".


I meant to do that

Let's Talk Geometry Regents

EDIT: Welcome to my website. If you like the information in this blog entry or find it useful, please, feel free to leave a comment. Thank you for visiting. The extended-time tests are finished, so I assume that it's safe to talk about the New York State Geometry Regents exam given this morning.

By my count, in the multiple-choice, 15 problems were definitions, theorems, postulates, formulas, etc, with no calculations involved. That is, you either knew it, or you didn't, but there wasn't anything to work out. The other 13 required some kind of calculation or working through of steps. (Your opinion of what counts as working through steps may vary.)

For the test as a whole, I notice four questions regarding the equation of a circle. If you didn't know

(x - h)² + (y - k)² = r² then there were a bunch of points lost. Yes, that means if you forget that subtracting a negative number means adding a positive number, then you had problems. (Don't worry, I won't make you write the contrapostitive of that statement.)

Additionally, there was a question involving the vertex form of a parabola, just to be different.

There were two transformation problems: one multiple-choice, one open-ended. The open-ended was also a composition. You did do it right to left, right? You did the Translation of the Dilation, and not a Translation followed by a Dilation. You'll probably get a point for doing the wrong thing, if it's done correctly.

Two locus questions.

Two constuctions: one multiple-choice, which hopefully provided some assistance to the open-ended question. For an added twist, you needed to make the equilateral triangle with sides congruent to the diagonal of a given triangle. That just tells you how wide to make the compass. I really wonder how many scorers are going to measure those triangles.

Two questions involving right triangles and one more that used the distance formula.

And there was one question using quadratic equations. (Two, if you didn't know the vertex form of a parabola and had to work it out.)

Personally, I had two problems when I took the test. (Yes, I take the tests along with the students. Sometimes I can't assess the difficulty of a question until I actually do it. It may or may not look at difficult as it is.)

My biggest problem was question 24, the similarity problem:

24. In trangles ABC and DEF, AB = 4, AC = 5, DE = 8, DF = 10 and [angle A is congruent to angle D].
Which method could be used to prove [triangle]ABC ~ [triangle]DEF?

The choices are AA, SAS, SSS, and ASA.
This is a STUPID question.
The only postulate or theorem which gets used to prove similarity is AA, because two triangles are similar if their angles are congruent. But we only know about one pair of angles, and we don't even know their size. There's no way to find information on any other.

Now, you are given information about the pairs of sides which include the congruent pair of angles. That much is true. But those sides are NOT congruent. SAS is used for congruence. If two triangles are congruent, then, of course, they are similar. But these aren't congruent. The sides are proportional, as corresponding sides of similar sides should be, but that in itself isn't proof. (For one thing, we don't know about the third pair of sides.)

So I have a problem with this question. They were looking for Number 2. The only answer which makes sense is Number 1, and that one isn't useful, either.

You may argue and disagree all you like, but SAS for similarity is NOT in the curriculum.

My second problem was question 36. They laid a trap and I fell into it. Three times. I wouldn't have gotten the right answer, despite the fact that I knew I had the wrong answer.
How did I know? Test-taking Strategies and Number Sense. Basically, the part that said "Determine the length of OA" gave me trouble because I got an irrational answer. However, the answer COULD NOT be irrational because they neither stated "round to the nearest ####" or "give the answer in simplest radical form".

What was the confusion? The setup was complicated enough, and I just through all the hoops fine, except for the last one. It gave CF = y + 10 and CD = 4y - 20. I read the latter part as FD. So on top of all the radii you had to pencil in, and using the Pythagorean Theorem, and knowing that when a radius is perpendicular to a chord it bisects the chord (into two congruent pieces), you had to know enough to double y + 10 into 2y + 20 before setting it equal to 4y - 20.

So I had y = 10, instead of y = 20, which was correct, but not the answer. You then had to substitute to get the length of DF. You know, the segment that I thought was 4y - 20, but was really half as big. So DF = 30.

Now the last answer was obvious to me (once corrected) because 16 and 30 are part of a Pythagorean Triple. That being said, just because the answer is obvious doesn't mean that you don't show the work!!! OA is 34. (I don't have to show it. Exercise left to the reader and all that.)

So how did you do?

Any questions?

All Heart

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(C)Copyright 2013, C. Burke.

I put my Cardioid in her care, and she something something.

More information here.

And a shoutout to @KatieLinendoll, who inspired this, in part, by wearing that equation on her shirt yesterday.

"Review" Material on the Algebra 2 Regents

Disclaimer: I have never taught Algebra 2/Trigonometry in high school. Yes, I am familiar with the material. No, I am not familiar with the acutal curriculum.

On any test, you have to vary the level of difficulty of the questions. You can't make the students sweat every single question. It's the rollercoaster approach: let them catch their breath on the next climb before the next drive drop.

That said, my first look at last Friday's (June 14, 2013) Algebra 2/Trigonometry Regents shows some questions which my Algebra students might have been able to answer. However, as I look at this, I can't help wondering: if it's on this test, why am I cramming so much material into the Algebra 1 curriuculum?

Some questions my Algebra 1 students should've been able to answer (whether or not I covered the material as is):

7. What is the graph of the solution set of |2x - 1| > 5?
I didn't cover this, but I covered inequalities, and simple checking of the answers would yield the correct choice. (My students could get this only as a multiple-choice.)

8. What is the range of the function below? (graph omitted)
I covered domain and range, so they should have gotten this one easily.

Which ordered pair is in the solution set ... ?
It doesn't matter the actual equations. The fastest solution here is to plug in x and y and check. Using the simple equation, 3y - x = 0, choices (1) and (3) can be eliminated immediately. Choice (2) is obviously wrong for the first equation even if you accidentally reversed the co-ordinates, which I'm expecting is what the test makers were expecting when they wrote it. The answer, by quick elimination before I even checked it, is (4).

13. Sue invests $500 ...
Compound interest is now in Algebra, rather than just simple interest. However, they do make you solve for time in these problems. However, because its multiple choice and the fact that the formula is given and the avaiability of calculators, it doesn't take long to plug in all four answers.

17. Which problem involves evaluation 6P4?
Okay, fun time. Do I or don't I explain 6P4 on the blackboard? Do I cover permutations and how do I cover it? Yes, I cover permutations, but there's a time issue. I may explain how it's done without writing "6P4", and certainly without writing a complicated factorial formula for it. However, this year's Algebra regents had a factorial problem totally devoid of any statistics, so maybe I should be teaching that.

In any case, each of the four choices should be answerable in Algebra
- How many different four-digit ID numbers can be formed using 1, 2, 3, 4, 5, and 6 without repetition?
- How many different subcommittees of four can be chosen from a committee having six members?
- How many different outfits can be made using six shirts and four pairs of pants?
- How many different ways can one boy and one girl be selected from a group of four boys and six girls?

The answers, respectively, are 6P4, 6C4, 6 * 4, and 4 * 6. (The last two are basically the same question.)

18. Which equation is represented by the graph below?
I have one Geometry class per day. This was covered. There's nothing special about this problem that those students couldn't have done it.

24. Which expression is equivalent to ... ?
A fraction with variables and negative exponents. Nothing tricky about it. Laws of exponents.

So I hope everyone caught their breath on those and saved their your energy for the rest of the exam. Some questions were trickier than others, but some (especially the multiple choice) weren't too hard to work out.

One last question, which is beyond my regular Algebra class:
30. Find the number of possible ten-letter arrangements of STATISTICS. There are 10! arrangements of the any 10 letters, but there are duplicates you have to divide by 3! for the repeated S's, by 3! for the repeated T's, and by 2! for the repeated 2!.
So the answer is 10! / (3! * 3! * 2!), which is 50,400.

Frankly, I'm surprised at this question, because that's pretty much the standard challenge question I use when teaching the subject. The other word I'll use is "MISSISSIPPI". I can't believe that they used it.

More on the Algebra Regents

It's been almost a week, and the tests are graded, so I don't suppose anyone still cares about this, but I'll go ahead anyway.

First off, if you weren't familiar with the word bivariate, you could have broken it down into bi-, meaning "two", and -variate, which looks like "variable", right? So bivariate: two variables. Which of the tables is measuring two variables and will give a scatter plot, as opposed to a bar graph. The answers, unfortunately, doesn't matter because the question was thrown out. A "lack of specificity" was the reason.

Likewise, if you took the test in Chinese, two answers were accepted to question number 1 because of a translation error. That happens a lot.

As for the Factorial question, a.k.a. "the question with the exclamation point", I was able to guess that answer without doing any work for one simple reason: the last step was to subtract 10, but only one answer was 10 less than another. That answer was the correct one. (I checked my guess afterward, of course.) For the record: 6! + 5!(3!)/(4!) - 10 can be done with the scientific calculator, if you know where to look, but it isn't necessary.
6! = 720, 3! = 6, 5!/4! = 5, so 720 + 5 * 6 - 10 = 720 + 30 - 10 = 740

I wanted to review some of the open-ended questions.

Question 31. An inequality with a negative multiplier. The trick was to remember to reverse the direction of the inequality symbol.

That is, -5(x - 7) < 15, when divided by -5 becomes (x - 7) > -3.
The final answer is x > 4.

Question 32. A volume question on the Algebra test. Silly. If they at least gave the Volume and asked to find, say, the height, you could argue it was an Algebra task, but, as is, it's a middle-school problem.

The formula for volume of a cylinder was in the back of the booklet: V = (pi)r^2*h.
The trick here is that the gave the diameter instead of the radius, so you had to divide 13 by 2 to get 6.5. If you didn't, your answer was four times larger than it should've been, but you most likely got 1 out of 2 points.

The final answer is 1,014*pi. Note: The question said "in terms of [pi]", so if you multiplied by 3.14 or used the pi key on your calculator (i.e., you did extra work!), you lost a point for not answering the question that they asked.

Question 33. A distance question with big numbers, with a conversion added on. Two questions on the test involved converting between hours and days and weeks. This was one of them.

The distance from Earth to Mars is 136,000,000 miles. A spaceship travels at 31,000 miles per hour. Determine, to the nearest day, how long it will take the spaceship to reach Mars.

Divided 136,000,000 by 31,000 to get the number of hours (4387.096774...) and then divide by 24 to get the number of days (182.795698...).
The final answer is 183 days.

Question 34. The Counting Principle. How many options are on the menu? They've given this question many times before, but this is the largest number of items that they've ever used. The Principle remains the same.

There are five main courses, three vegetables, five desserts, and three beverages. To find the number of possible means, multiple the four of them: 5 * 3 * 5 * 3 = 225.
How many have chicken tenders? That's 1 * 3 * 5 * 3 = 45, which is one-fifth of the total.
How many have pizza (1), corn or carrots (2), a dessert (5) and a beverage (3): 1 * 2 * 5 * 3 = 30

If you showed your work, you likely got one point for each correct answer.

Question 35. Trigonometry. Find the angle of elevation.
You have a right triangle with a height of 350 feet and a base of 1000 feet, and you want to find the angle on the ground. You have the opposite (350) and the adjacent (1000), but you don't know the hypotenuse, so that means that you need to use tangent to solve the problem.

So tan(x) = (350)/(1000) and, therefore x = tan-1(350/1000), which is approximate 19.29.
The final answers is 19 degrees
Partial credit likely for using sine or cosine, or if you answer is expressed in radians or if rounded incorrectly.

Question 36. Summation of radicals. I cover this in Geometry. I have simplified them when dealing with Pythagorean Theorem but I don't usually cover this as it requires an extra day or so that I don't have.

Bear with me as I try to type this without any graphics:

(25)^.5 - 2(3)^.5 + (27)^.5 + 2(9)^.5
"^" means raise to a power, "^.5" means raise to 1/2 power, which means square root.
Calculators and spreadsheets understand this.

The square root of 25 is 5 and twice the square root of 9 is 2*3 = 6. That leaves the root 3 term, which is in simplest form, and root 27, which simplifies to (9*3)^.5 = 3(3)^.5. So 5 + 6 = 11 and -2(3)^.5 + 3(3)^.5 = 1(3)^.5.
The final answers is 11 + (3)^.5. In other words, 11 + the square root of 3.

Question 37. Algebraic fractions.

This is the one time where your teacher may have given you bad advice. Actually, it was good advice, if you know when to use it, but this isn't the time.
I have colleagues who will tell students (the ones who hate fractions or just "can't do" them) to multiply by the denominators to get rid of them. In this case, that would make a big mess. Don't do that.
This is one approach you could take:

2 / 3x + 4 / x = 7 / (x + 1)
2 / 3x + 12 / 3x = 7 / (x + 1)
14/ 3x = 7 / (x + 1)
At this point, cross-multiplying will yield the equation 14(x + 1) = 21x
The final answers is x = 2.

Question 38.Probability. I was expecting more of a twist for a four-point problem. This one isn't too bad if you know what you're doing.
Five red marbles and three green marbles make eight marbles total
These are dependent events, and their probabilities will be multiplied.
P(red then green) = 5/8 * 3/7 = 15 / 56
P(both red) = 5/8 * 4/7 = 20 / 56 = 5 / 14
P(both red or both green) = P(both red) + P(both green) = (20 / 56) from above plus 3/8 * 2/7 = 6 / 56. The total is 26/56, which reduces to 13/28.
I recommend to my students to reduce fractions, but I can't say if it's required for full credit in this problem.

Question 39. An Area problem, which I have never covered in Algebra.
You needed to find the area of the rectangle, then the area of the semicircle, and then subtract the latter from the former.
The tricky part here was understanding the frickin' question! Seriously, they went out of the way to be obtuse about it, making this more of a reading comprehension problem than an actual math problem.
In the diagram, AB = 5, and AB = BC = DE = FE, but CD = 6, which means the radius, which can't be named because they didn't name the point at the center of the circle, is 3.

The rectangle is 5 X 16, so the area is 80.
The semicircle is 1/2(pi)(3)^2 = 4.5(pi), which is approximately, 14.13716694.
The shaded area is 80 - 14.13716694 = 65.86283306, which rounds to 65.86.
The final answers is 65.86 square inches.

STUPID QUESTION ALERT! The folks who write these tests know very well that students have been taught for years to approximate pi as 3.14, whether or not they have a calculator which has a "pi" key on it. Using 3.14, the numbers will change in this problem. The semicircle will become 14.13, and the final answer 65.87. Whether or not a student loses a point on this may very well depend upon the teacher scoring it.

Floating

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(C)Copyright 2013, C. Burke.

When you think about it, a floating error would be sinking!

If you're curious about the cuties lounging around the pool, they've been taking in the sun since this comic.

One of the interesting problems I have with every comic is How big do I make it?
Seriously, I never know. I want them to fit on the screen, but every screen is different, and you have no clue what settings are being used. There's some discrepancy in my earliest comics depending on whether I worked on the comic at home or at work -- and which PC in the Teacher Center I might have used.

I'm not looked into one particular format -- and I'm not planning any books which might require one -- but I'd like to have some consistency.

My problem today was that this comic because of the nature of floating-point numbers, had to be wide to accomodate the Sixes and 9.0000002. The width was over 1000, which doesn't display properly on the blog. Moreover, it the right side had been cut off, so would part of the joke. I could've reduced it, but the it might've been too short. Decisions, decisions. So I moved the Sixes down, giving the comic a little more depth, but that gave me a lot of empty space that stood out. Luckily, there have been enough beach scenes over the past 5+ years to find something adaptable.

Happy Fathers Day 2013

I'd like to wish a Happy Fathers Day to all the Dads out there.

At this point, I'm calling it: there won't be a Father's Day comic this year.
I don't usually do Sunday comics anyway, because Saturday tends to be busy, and this time of is usually busy at school. Moreover, this year there are graduations going on, just adding to the craziness.

Through all of that, I did have something planned, and I could've gotten to it, but it was just something based on actual banter between my son and me, which I had a good punchline for, but no way to weed out extraneous words from the set-up. (Plus, I didn't want to plagiarize a Jeopardy question, which was the source of the merriment last week.)

So let me just say again, Happy Fathers Day!

Barring some serendipitous doodling on my iPad later today at the in-laws, leading to a last-minute comic, I'll be back tomorrow with a regular strip.

Super 3-D

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(C)Copyright 2013, C. Burke.

The path to world domination is through Canada, eh?

And stay tuned for Metropolis's new hit game show Luthor Consequences!

Celebrating Seventy-five years of Superman, and twenty-five since Julie Schwartz gave me my Superman tie pin at Lunacon in 1989. I still have it, and I'll probably be wearing it today.

Red Ink

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(C)Copyright 2013, C. Burke.

I've used all different colors of markers, but they bleed through the page. And red pens are just so much cheaper.
And not one student of mine has ever had a psychological reaction to red ink -- but that might be because they never actually look at anything other than the grade (before asking "Is that good?" or "What does 'S' mean?"

(If this sounds familiar, I've lamented this in the past on my twitter feed.)

Anyone (in New York) Have Any Reaction to the Algebra Regents exam?

The last Algebra Regents exam, in its current form, was given today. Next year's test will have to align with the Common Core Standards being implanted across the state and around the country. Problematically, some schools started their implementation this year, meaning that their students would be ill-prepared for this exam, which hardly lined up with those new standards.

Any thoughts on the exam? Please, share them. Let's have a dialogue.

EDIT: Thursday morning

In my opinion the dumbest question on the Algebra Regents was 6! + [5!(3!)]/4! - 10.

The question serves no purpose. It's order of operations... but with a twist! Sure, factorial gets covered with permutations, but this isn't any kind of combination/permutation question -- which, by the way, can be figured out without using an exclamation point.

There were too many statistics and probability questions, and there was no graphing. (Yes, there were a couple of multiple-choice questions which involved a graph, but students didn't need to make any graphs.) Statistics and probability are what get crammed in at the end of the year because there are so many topics in the Integrated Algebra curriculum, many of which are interconnected. Statitstics is a separate topic, and probability has been moved out of the curriculum under the Common Core standards. I feel sorry for any student whose school implemented the new curriculum a year early.

What else is there to complain about? (Anything to compliment?)

The 0'Factor, episode 14

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(C)Copyright 2013, C. Burke.

When it comes to the whole number line, the Whole Numbers are such a small part of it, and yet a very important part, especially if you ask my students their opinions of fractions.

A couple of returns today: we haven't seen the New Number 2 in quit a while, since 2009 it seems. And while Mr. 0 has been around, the last 0'Factor was back in 2010.

Funny thing: I've been wanting to do another 0'Factor for three years now. Funnier thing: this wasn't even the one that I've been planning to do. Funniest thing: I still find it hard to believe that I've been doing a webcomic for over three years and this bit has had a three-year hiatus!

Update:Title changed to episode 14 URL cannot be changed.

There's Cake!

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(C)Copyright 2013, C. Burke.

Sometimes you just have to step through and move beyond 'pie' jokes.

Wiki or Not Wiki. That is a Question.

You may or may not know that there's a wiki page for (x, why?) I don't mention it much, and it hasn't been updated in a couple of years. (What else is new?)

I've been thinking about whether or not to move it over to where my (out-of-date) Archive page page resides. However, if I were to do that, I'd most likely have to make it into another static page, not a wiki page. For one thing, all the links would point back to the current hosting site (including their banner ads), and for another, I wouldn't no how to program a wiki page.

On the other hand, if anyone wants to update the page now (and only one other person ever has, I believe), you have to be a member of Comic Genesis, which based on the utter failure of my Forum on their site, I don't think my readers are all that gung-ho to update my wiki anyway.

So the wiki would basically become just a generic Background page for the characters and the comics. Nothing wrong with that. Nothing exciting about that either.

Anyone have any thoughts or suggestions?

Try Not. DO!

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(C)Copyright 2013, C. Burke.

So far today, they've tried 'hard', 'very hard' and 'really, really hard'. Before today, ... not so much.