# Guessing Ages Activity

This semester I tried a Guessing Ages Activity as a first day activity in my statistics classes.  My version of the activity is adapted from page 11 of Teaching Statistics: A Bag of Tricks.  I found this activity to be a good ice breaker for the first day of class.  The students really enjoyed working in small groups to guess the ages of people and it gave me a chance to briefly review how to find the mean with students, a concept that they should already know from Pre-Algebra class.  Of course, later on in the class we talk about properties of the mean above and beyond what is learned in a Pre-Algebra class.  But this was an excellent way to review how to compute the mean.  It was also a good way to have the students do some calculations on the first day to break up the long list of definitions that is covered in Chapter 1 in the textbook.  Overall, I found this to be a successful activity.  And of course, the results from this activity can be used for further analysis later in the semester, but I have other activities I use down the stretch to get the students active again rather than just referring back to the same results again.

# 1.653*Pi Day

Happy 1.653*Pi (5/19) Day!

Yes, I know that Pi Day was way back on 3/14 and that 2*Pi Day is coming up on 6/28.   But celebrating 1.653*Pi Day is a little more fun, don’t you think?

Here are few resources that you may be able to use in your classroom:

Pi Day Activity

My Pi Day Exponent Activity from Pi Day 2011

Pi Day Rap Videos

# Justin Verlander’s One Hitter

Warning:  I don’t normally write about baseball.  But you can’t deny that being at Justin Verlander’s One Hitter game is something special.

I have to admit that I went into this game not expecting much from the Detroit Tigers.  The Tigers should have been able to sweep the Twins and they didn’t.  Villarreal shouldn’t have had to come out of the bullpen at all on Thursday afternoon.  There are a lot of things that are simply making me angry about this Tigers team.  Let’s put it this way, the AAA people were passing out rally towels outside Comerica Park before the game and I told the woman passing them out to keep it because I didn’t think it would help.  She insisted that I take the rally towel anyway.

Anyway, my seat in Section 110 was absolutely lovely.  The people were very friendly for the most part and most people were paying attention to the game.  The person who stood out the most for me, though, was the little old woman sitting to the left of me.  She seemed to know absolutely nothing about anything, including baseball, and I’m still not quite sure why her son brought her to the game.   I think I want my season tickets for next year to be somewhere over in right field around this area.  It seems to be a good place to sit.

I have to say that I now know why people like Justin Verlander so much.  Up until now, I thought that people were just buying into the unnecessary hype of how great Verlander really is.  I thought that maybe Verlander was on his way out.  You have to admit, he’s been struggling a little bit this season, just like the rest of the team.  But tonight, for the first time in a while, Verlander brought his A-game.  Tonight Verlander threw a game the way that I would expect Verlander to throw given all the hype about how great he is.  I am very happy that I was at Comerica Park for this game.

I think I can pinpoint the time the excitement started as right around the sixth or seventh inning.  I think that everyone could tell by that point in the night that it was going to be a special game.  Well, everyone besides the old woman sitting next to me.  When Verlander gave up his one hit of the night in the ninth inning, the woman really had no idea what had happened.  Her son tried to explain to her that the no hitter had been botched, but finally just told her that he would have to explain it to her later.  It was actually slightly amusing how naïve she was throughout the entire game.

I must admit that after the eighth inning when Verlander was closing in on 100 pitches, I was actually considering the possibility that Leyland might bring in Benoit or Dotel or Coke for the ninth inning.  Given how Leyland has been managing the team this year, it truly wouldn’t have surprised me if he would have made a knuckle-head move like that.  But Verlander stayed in the game and although it didn’t end up being a no-hitter, the fact that he threw a complete game seemed to satisfy most people.

The only problem I see is that the Tigers are definitely not out of the woods yet.  They are still below .500, and at this point in the season, I would like to see them at least 4 or 5 games above .500.  In fact, I guess this wouldn’t even be bothering me as much if the Tigers would at least win more than 1 game in a row.  The fact that this team can’t win more than one game in a row and can’t seem to sweep anyone is very disappointing.

Tonight reminded me of some things that are wrong with this team.  Tonight was the night that I thought Fielder would break .300.  And he didn’t.  Tonight was the night that I thought Rayburn should have built on the energy of everyone else and made a hit.  And he didn’t.  Even Santiago made a hit.  Once Jackson is back, maybe it would make sense to remove Rayburn from the line-up and put in Kelly instead.  I actually like Don Kelly.  I can’t say it enough that I think he really is a talented player.  Kelly can and would do anything that he is asked to do.  That’s the type of talent the Tigers have in Don Kelly.  Of course, I’m not counting Don Kelly to be the Tiger’s savior, but I do think that he’s better than Rayburn.

And that’s all I have to say.  On the night I went into Comerica Park really not expecting that much, Justin Verlander blew my mind and threw a one hit game.  I won’t forget this night any time soon.  (And it was definitely a good night for the first fireworks of the season!)

# My Search for a New Laptop

This week I bought a new laptop.  My search came down to the final three.  I ended up buying the Toshiba, but I thought it might be helpful to others to post the thoughts that went through my mind while picking between the three, as well as the specs on each of the machines from Best Buy.

 Pros Cons HP ·         Low price point; cannot beat the quality for the price. ·         Can do the basic stuff such as use the Internet and create documents for my classes. ·         Had bad experiences the HP in the past, but that was well over 10 – 12 years ago. ·         Sony looked slightly better. Sony ·         Previous Sony Viao held strong for 3 – 4 years; the only reason that I was even looking to replace my laptop is because the battery life was only 15 minutes and the Z-key was broken. ·         Security in knowing exactly what I would be getting from having owned a Sony in the past. ·         When I tried to buy a new battery for my old laptop, I found out that Sony discontinued the battery for my model. ·         Having broken Z-key is very annoying when you want to use ‘Ctrl+Z’. ·         New Sony Model would probably have a low battery life, just like the old model. ·         Sony used to have a Sony Store at the local mall that I could visit in person for more selection and for more personalized service, but it closed without notice. Toshiba ·         Price was not much more than the price of the Sony. ·         Machine is very lightweight, which makes it very easy for me to take with me wherever it needs to go. ·         Machine has a very long battery-life (at least compared to all of my previous laptops). ·         Machine has a solid state drive; this was a very big pro for me since I have had multiple fan failures with my past laptops. ·         Have never owned a Toshiba in the past so I would have no idea of what to expect from previous experience. ·         Every time I have seen a Toshiba in the stores in the past, they have always been heavy, hot, and on display with an extra cooling fan under it. ·         My personal perception of Toshiba is that it could end up being a lemon, just like the Averatec laptop I had before the Sony.

Product_Detail_-_Compare_Page.pdf

# Teaching Control Charts

The other day in my statistics class, I talked about Control Charts.  I really wanted to drive home the point about the difference between individual runs charts and control charts.  So, I did a version of Deming’s Experiment with my students.

First of all, it was very difficult to get 1,000 marbles on very short notice, and even harder to get them in two specific colors.  I ended up going to the dollar store and buying the gemstones that people generally put in vases or in the garden.  The gemstones are sold in bags that are 14oz, but I can tell you now that there are about 100 per bag.  The hardest part for me was picking two colors of gemstones that I could actually tell the difference between since I am colorblind.

Next up was getting the cups for the students to scoop the gemstones up with.  Since I had students working in groups of 4, I had about 8 cups.  As described in the activity, I marked 7 of the 8 cups at a line for 50 gemstones, making sure to write ‘50’ on the bottom of the cup.  And I marked the 8th cup at a line for 30 gemstones, making sure to write ‘30’ on the bottom of that cup.  If you do not remember to do this, it is not a big deal.

The execution in class was pretty seamless.  I had each group take five samples and record their results from each of the five samples in tables on the board.  Then the students found the averages for the ‘total #’ and the ‘proportion red’.

Together we constructed the individual run chart for all 40 of the values (8 groups with 5 samples per group) and we talked about how there was an obvious dip within each sample.  At this point, I had all of the groups turn their cups over.  Of course, it turned out that the dip was caused by the group with the ‘30’ on the bottom of their cup.  This allowed us to talk about the importance of making sure that your measuring tool is properly calibrated, etc.  And by the way, if you did not write the numbers on the bottom of the cups, it will still be crystal clear which group had the faulty cup.

After we did that, we constructed an x-bar chart for the average totals of each of the 5 samples.  We discussed how it is difficult to tell that the group with the ‘30’ was making a mistake when looking at the averages rather than the individual runs.  And finally, we constructed a p-chart for the proportion red.  I told the students to use 5 samples with n = 8 observations in each of the 5 samples.

This was definitely a worthwhile activity.  It allowed for reinforcement of individual runs charts, control charts, and an opportunity to talk about faulty measurement tools, which I would not have been able to easily incorporate into the discussion otherwise.

# Computer Tips and Tricks

This past week I have had to do a few things on the computer that appear not to be common knowledge.  Here is a brief run-down of computer tips and tricks that I think might be useful to everyone:

Microsoft Excel

The University of Wisconsin-EauClaire has a wonderful summary of functions needed to use Excel as a Gradebook.  My favorite one is the ‘SMALL’ function, which makes it very easy to drop the lowest score, the second lowest score, etc.

This week I also came across a situation where I had to add double quotes around a name and slanted brackets around an e-mail address.  This is very tedious to do for a list of hundreds of names.  But there is hope since there is a very simple formula that can be used to do this.

Turning off CAPS LOCK

This week a friend of mine asked me how to turn off caps lock.  It really is not that hard to do as long as you have the guts to alter the binary code.  Now it is dawning on me that this may have been a good exercise for my Everyday Math class when we studied our chapter on cryptography.

If you don’t want to turn off caps lock permanently, but you still find yourself typing with the caps lock more often than you would like, Convert Case is a very nice web-based tool that will allow you to convert your uppercase text to lowercase text without having to start again and retype it all.

Saving Webpages as PDF Files for Easy Reading

This semester I had my Everyday Math students do presentations on current events in the field of mathematics.  I picked about 35 articles from sources such as The New York Times, The Seattle Times, and Science Daily, and I wanted a way to keep the articles to about 1-page front and back each.   JoliPrint and PrintFriendly were absolutely perfect for this cause.  Once printed, I put all 35 articles up on the board around the classroom and had the students pick the article that interested them the most.  The students read the article at home and presented a summary of the article during the next class.  I found it to be a nice activity for this particular group of students.

# Teaching the Runs Test for Randomness

The other day in my statistics class, I was teaching the runs test for randomness.  One of my students keeps on asking for an in-class activity, and it happened that I had an extra half-an-hour of class time to spare.  So, I adapted this famous teaching experiment for use in my own class.

The set-up:  I split the class into 8 groups, with 3-4 students in each group.  Four of the groups were labeled ‘Group A’ and the other four groups were ‘Group B’.  Group A went into the hallway while I explained the assignment to Group B.

Group B was the coin tossing group.  They were asked to flip a coin 200 times and record the sequence of heads and tails that they observed.  Once I made sure that Group B understood the instructions, they went into the hallway while I explained the assignment to Group A.

Group A was the random listing group.  They were asked to write a sequence of 200 heads and tails that they thought was random without actually flipping a coin.  Once I made sure that Group A understand the instructions, both groups rejoined in the classroom and started their experiment.

Now, since neither group knew the instructions that the other group was given, or what we were going to do with the data that was collected, it made for a very interesting experiment in itself.  The students came up with very unique ways of recording the data.  Some groups assigned one recorder and then the other two people in the group alternated flips of the coin.  Other groups had everyone in their group flip the coin 50 times in a row simultaneously and then combined their results at the end.  I was OK with this since it would have been no different if the students would have just followed one another in their coin flips.

Finally, each Group A exchanged papers with a Group B and analyzed the sequence using the runs test for randomness.  What I discovered is that because the students did not know why the data was being collected, they did not organize it very well, so the group that they passed it to had a very hard time figuring out what was going on.  This made for a good side discussion on the importance of organizing data properly while it is being collected.

Soon enough the students came up with a process for analyzing the data, most groups used a yellow highlighter to highlight the heads to make the runs a little easier to count.  Once their runs were counted, they were able to analyze their sequence using the runs test for randomness.  The students worked very well together verifying their calculations for the mean and standard deviation of the number of runs.

As suspected, it did turn out that Group A (the random listing group) ended up NOT generating random sequences and that Group B (the coin tossing group) did end up generating random sequences.  This made for an interesting discussion as well, since of course, Group A insisted that their sequence had to be random given the way that they collected their data.

# Observations on Plotting Points in Pre-Algebra

Disclaimer:  Some of this might seem very, very obvious.  But sometimes it’s good to state the obvious, right?

This semester I decided to teach plotting points differently than I have in the past.

I started the lesson by handing each student a piece of graph paper and a ruler.  Yes, I know college students should probably be accountable for bringing their own supplies to class. However, in this particular class we spend a grand total of 2 class periods discussing graphing.  I do not believe it is worth it for these students to buy a pack of 100 sheets of graph paper when we do not do 100 sheets worth of graphing in this class.

The first thing I had the students do is draw a vertical line and horizontal line down the middle of their papers.  I did not even bother mentioning the terms x-axis and y-axis at this point, as my major focus was on the drawing itself.  From observing my students, I found out that it is not OK to assume that they can draw straight lines, even when they do have a ruler.

Next, I had the students label the positive x-axis, negative x-axis, positive y-axis, and negative y-axis (in this order).  From observing my students, I found out that it is not OK to assume that they can properly number a number line, even though this is a skill that we also discuss in the chapters on whole numbers, integers, fractions, and decimals.  For the x-axis, which I was still calling the horizontal axis at this point, many of my students had trouble figuring out if the positive numbers should be to the right or to the left of the negative numbers.  Interestingly enough, they were better with labeling the y-axis.

After every student had their graph drawn properly, we started labeling the Quadrants, the x-axis, and the y-axis.  Then I talked about x being positive and y being positive in Quadrant I.  I had the students determine the direction of x- and y- in the other three Quadrants on their own.  Then we plotted one point in each of the four quadrants.

It seemed as if it was much easier for the students to plot points on a graph that they created themselves.  They seemed to have taken ownership of their graph at this point.  This is a stark contrast to how I have taught plotting points in the past.  My previous method was to either have the students construct a graph without graph paper, or give the students a pre-labeled grid.  I found out that neither of these methods is OK and I will never do either of them again.

I continued the lesson from here by having student plot the coordinates of a sailboat.  I did not tell the students that we were going to plot a sailboat.  Instead, I told the students that we were going to plot one point at a time, drawing a straight line connecting the points as we go.  Many students were resistant to connect the points as we went, causing for chaos in constructing their sailboats.  What I found out is that some of my students did not want to connect the points until they knew whether or not they were plotting the correct points.  Once they realized that we were plotting one point at a time so that I could walk around and make sure they were plotting it in the correct position, their nerves were calmed a little.

Finally, I had the students plot the coordinates of a coffee mug on their own.  This seemed to be a good reinforcement activity to clear up some of the odds and ends.  Of course since they were now ‘on their own’ and not being guided by me, some students went back to not connecting the points as they went.  And some students got (0,1) confused with (1,0).  However, since I was walking around the classroom, I was able to correct the majority of those issues before the students got too far into the drawing of the coffee mug.

Overall, I must say that this was a half-an-hour of very well-spent time.  I would definitely use this particular progression of steps to teach this lesson to students again in the future.