Calculators

CALCULATOR USAGE ON TESTS AND QUIZZES

In some math classes, a teacher often faces a situation in which he or she is giving a quiz or test and which the teacher wants the student to use a calculator on part of the test but not on the other part of the test. I found a good way to handle this. You can do it in either order but I had the students place their calculators on the table in the front of my room and they took a marker out of a box on that front table. (I would put enough markers in the box so that each student could get one.) When they start the test they do all the questions on the test that I want them to do without a calculator. I would group those questions together or designate them in some way so that the student knew which ones they were. They had to do their work, if needed, with the marker, and write the answer(s) with the marker. When they had completed those questions, then they would put their test face down, take the marker back up to the front table, put it back in the box, and then pick up their calculator to finish the rest of the test.

When working with the calculator they show their work with pencil and write their answer(s) with pencil. Because their answers to the non-calculator questions are written with a marker they can't use their calculator to redo the question and change their answer (when they have their calculator, the marker is back in the box). Ink pens can be used instead of markers as long as students use a pencil with their calculator. This method works very well. Students should know ahead of time what kinds of questions they will be doing without the calculator (ideally when you are first teaching the skill). Also the day before the first time I use this method, I tell them about it and show them where they will put their calculator and where the markers will be and so on.

E-commerce at Risk?

I came across an article that points out a potential flaw in the security of online transactions. It also illustrates one of the current uses of mathematics that is designed to protect those transactions. I do plan on continuing to buy things online until I hear otherwise. However I always told my students that, when someone says that a code or system is totally safe, that it isn't necessarily true. What man puts together, man can take apart and sometimes man can make an honest mistake.

Here is the link.

Movie Review #1

ACROSS THE UNIVERSE

What in the world is a movie review, an amateur one at that, doing on “Practical and Creative Ideas for Math Teachers?” Well I just thought it would be something interesting and teachers are people too, right?

Being a long time fan of the Beatles I thought I should see this movie. I had read good and bad things about it. It turned out to be very enjoyable – but it did not “change my world.” The basic story is a very common one – lonely boy meets lonely girl, they fall in love, they fall out of love, they get back together. The End.

The various plot points are illustrated by about thirty Beatle songs, sung mostly by a group of young, talented actors. In many cases the arrangements are slightly different from the Beatle originals but still recognizable. Some lyrics are given more emphasis, some less, in service to the plot. A series of stunning visuals accompany the songs, again in moving the story forward, or at least sideways. The creativity of director Julie Taymor is commendable, as well as her audacity to try to use music that is sacred to many people in a way that some may not like. I did like and admire what she did. She shot for the moon, only made it into orbit, but certainly didn't stay on the ground. How many of us have made it into orbit?

The movie is actually a series of music videos, strung together by the love story of the plot. Bono has a good part singing, “I Am the Walrus”. Joe Cocker is involved in an enjoyable take on “Come Together.” Other segments built around, “Strawberry Fields Together”, “I Want You (She's So Heavy)”, Hey Jude”, and “Let it Be” were also highlights. I also liked the multiple Selma Hayeks, but not necessarily the setting of the song, “Happiness is a Warm Gun.” The actors playing a Janis Joplin type character (“Sadie”) and a Jimi Hendrix type character (“Jo Jo”) were very good. I do wish the writers would have done more with the title song, “Across the Universe”, one of my all time favorite John Lennon compositions.

Watching this movie reminded me once again of the genius of the Beatles and showed the timelessness of their music. In fact there were many other Beatle songs that could have been used, but there is only so much celluloid. One thing I did wonder about – did they write the story and then pick which songs would go with that story, or the other way around?

I read something the other day (“oh boy”) about the fact that a lot of tweens, after watching the movie, are going out to buy the soundtrack album. New Beatle fans are being created every day. This movie is like the popcorn that many people ate while watching it – very tasty, very enjoyable but, in the end, not nutritious. But not everything has to be nutritious. I did enjoy this movie and am glad I went to see it.

Numerous other professional reviews of “Across the Universe” can be found on the movie review sites on the web.

Bush v. Gore part 2

A VERY CLOSE ELECTION
SOLUTION PLAN

Florida

Bush – 2 912 790 votes, Gore – 2 912 253 votes.
Total is 5 825 043 votes. Bush won by 537 votes. Using a proportion: 5 825 043 votes / 100yd. = 537 votes / X yd. Therefore:
5 825 043 X = 100 (537) Solving for X, we get
X = .009218816 yd.
.009218816 yd. multiplied by 36in./yd = .331877376 in.
4/16 = .25, 5/16 = .3125. 6/16 = 3/8 = .375

Therefore if all the votes in Florida were represented by a 100 yard distance and rounding to the nearest sixteenth of an inch, Mr. Bush won by about 5/16 of an inch.

Using the same information but with the 84 ft. basketball court and using a proportion, Mr. Bush won by .007743805 ft. or about 3/32 of an inch.

USA

Taking the same approach as above, Mr. Gore would have won on the football field by about 19 3/16 inches. On the basketball court Mr. Gore wins by about 5 12/32 inches.


An interesting way to use one of your answers to get another answer is as follows:

In Florida we calculated that Mr. Bush would have won by
about .331877376 in on a football field. We could use that answer to figure out the answer to a basketball court.
(100 yd. = 300 ft.) Again using a proportion:
300 ft./84 ft. = .331877376 in./ X in. Solving for X we get X = .092925665 in. which is virtually identical to the answer we got the other way (.092925666 in.)

If you want more information about this solution plan, write a comment at the bottom of this post.

Brain Development

I saw an interesting article this morning on the New York Times website that I thought you might find interesting. It is self explanatory.
Here is the link:

It is exciting to think that as time goes on we will be able to find out more about how the brain actually works. That will enable us to figure out better ways of addressing the problems that teachers and parents observe in their children.

Three Answers

RIGHT, WRONG, NOT WRONG

When students give answers to math questions they sometimes will give an answer that is not what the teacher really wants but it is equal to the correct answer or is written in a different way. For me, those answers fell into the "Not Wrong" category. That told the students two things. First and most important to them, their answer was not counted wrong. Second, there was something else I wanted for that answer. They got the benefit of not counting the answer wrong but they knew there was a different answer or a different way of writing the answer that I wanted them to understand.

There are answers that are "Right." There are answers that are "Wrong." There are answers that are "Not Wrong." Here is an example:
Let's say the student is asked to solve P=2L + 2W for L.
For me the "Right" answer is L=(P-2W)/2.
A "Wrong" answer could be L=P-W.
A "Not Wrong" answer could be L= -W + .5P.
Some teachers might very well consider that that last answer is just as "Right" as my first answer and that is fine. My point here is that there are situations in which the student may give an answer in a way that really isn't wrong but is not in the form that the teacher might want, in that situation, at that time. In the above example if the teacher had specifically told the students that there were to be no decimals or negative signs in a formula, then that "Not Wrong" answer would be "Wrong."
My experience with most students is that when they hear that an answer is "Not Wrong", they will attempt to understand the different type of answer that the teacher wants and try to do it that way next time.

There are other situations in which there are multiple right answers. A simple example would be the following:
What is the probability that a card randomly drawn from a standard deck is a diamond?
"Right" answers could be 13/52, 1/4, 25%, or .25. Of course if the directions had stated that the answer had to be a fraction in simplest form, then the only "Right" answer would be ¼.

The concept of "Not Wrong" might also apply to the method that a student uses to find an answer. It is good for students to know that there are multiple ways of solving a problem. However the teacher might want the student to use the most efficient method and/or a method that can be applied to many other problems. For example a student might use the Guess and Check method to successfully solve a certain problem. The teacher might call that method "Not Wrong" if they had wanted the student to use a more efficient strategy.

As you can imagine the concept of "Not Wrong" is in the eye of the beholder and the situation. What is "Not Wrong" to one teacher might be "Wrong" to another teacher and "Right" to another teacher. The concept of calling some answers or methods, “Not Wrong” can be an effective teaching tool that shows respect for student thinking but also teaches that there is something else they need to learn.

Bush v. Gore

A VERY CLOSE ELECTION

The 2000 Presidential Election was one of the closest in history. To get some perspective on how close that election was, I came up with the following questions that I believed the students would find interesting, as well as using some good mathematics. This makes for a very good extra credit situation although it has lost some of its interest to today's students. It does suggest an approach that teachers could take with a similar situation in the future. The problem uses the visual images of a basketball court and a football field. This type of familiar image will help students understand the closeness of the vote. Older students and adults will also enjoy this.

In the state of Florida in 2000, the official “certified” voting results showed that George Bush got 2 912 790 votes and Al Gore received 2 912 253 votes. Imagine that the combined votes of these two candidates equaled the length of a football field, from goal line to goal line (100 yards). If the two candidates had received exactly the same number of votes, then they would each have 50 yards. However they didn't receive the same number of votes. Based on the vote totals above, Mr. Bush won Florida by what distance? Round your answer to the nearest sixteenth of an inch.

Using the same vote totals from above, assume the combined vote total is the length of a high school basketball court (84 feet). In this case, Mr. Bush won Florida by what distance? Round this answer to the nearest thirty-second of an inch.

In the total USA vote in 2000, Mr. Gore received
50 996 582 votes and Mr. Bush received 50 456 062 votes. Assuming the combined vote total of the two candidates is a football field, as above, Mr. Gore won by what distance? Round to the nearest sixteenth of an inch. Assuming the combined vote total is the length of the high school basketball court, as above, Mr. Gore won by what distance? Round to the nearest thirty-second of an inch.

The answers and my solution plan will appear in a future post.