This week’s assignment in the 8-week Explore the MathTwitterBlogosphere project is to provide “A Day in The Life” of a math teacher. It’s Monday morning, and here is my day….
It’s 6:30AM, and I’ve just arrived at my desk. I’ve always been an early-riser; I don’t like feeling stressed in the morning so it’s always been custom for me to be in my classroom well before kids start rolling in at 7:20. Weekend e-mails include a student seeking guidance on entering the PA Statistics Poster competition, an update on the Math Madness competition for our math club, and a few items from my local math teacher group, ATMOPAV. Today in Algebra 2, we will be doing a test review for an exam on exponential and logarithmic functions. Thanks to the great site Problem Attic, I was able to quickly assemble an assortment of review items for hanging around the room.
We have block scheduling here. My day consists of 3 assigned periods, and a prep at the end of the day. This semester, I teach all honors students and will have a more traditional schedule in the spring.
7:30, Homeroom – such a strange time of the day. A group of students I see for only 5 minutes a day wander in, their attendance is verified, then they move on with their day. Is there any “real life” analogy for this? The DMV perhaps? Very difficult to get to know kids this way. On Friday,
I had a conversation with a homeroom student who was excited to travel into the city to visit the Philly-famous Reading Terminal Market. I encouraged her to visit the Amish people and their fine foods, but the student admitted an irrational fear of the Amish folks. This led to an assignment from me: have a meaningful conversation with an Amish person, and report out to the homeroom. I’m happy to share that Kianna talked to a few Amish people, found them “fun”, and is no longer scared of them. A good start to the morning.
7:40, Learning Resource Center – my day begins with an assigned period in our LRC, where I help out any students seeking math assistance. Some come from study halls, others will visit if they have been absent a few days. It’s a neat assignment, but can be stressful when a student comes seeking Pre-Calc help, and you realize that you haven’t thought about trig identities for a long time.
This morning’s deep discussion: how many spaces are you supposed to put after the period at the end of a typed sentence? Young folks say 1; old-heads say 2. Damn you Twitter and your shortening of everything.
9:00, Algebra 2 – Today is test review day for exponential and log functions. What I like to do on days like these is to post problems through the room, let students wander, have conversations, work through problems, and ask questions. What I don’t want to have happen is to have students working quietly and isolated. Many students have the same needs and misconceptions; I strive to create an environment where those questions bubble to the surface, and it is OK to need help. At the end of class, we did a quick review of polynomial division as a table-setter for the next unit. I love having students write on desks, as I can wander around the class and assess work. It’s a great strategy for facilitating group discussion; just have a bottle of Formula 409 handy.
During this period, my AP Statistics colleague e-mailed me with an issue which will alter my plan for next period. For years, I have used the “Against All Odds” video series for part of my Statistics class. My favorite video provides a summary of the Physicians Health Study of 1981. I love this video, as so much of the vocabulary we stress in experimental design is discussed in a real-life application. The video is old, to be sure, but effective. As of last week, the video ran fine on the site. But today, all of these old videos from the series have been replaced with newer versions. What to do when a resource you have used for so many years seems to have disappeared? I have 30 minutes to figure this out…
10:30 AP Statistics – With a quick preview of a new experimental design video snuck in while my Algebra 2 students completed their review, I am set to go. For homework, these students completed an actual AP exam item from last year which deals with survey design and bias. This is a problem I graded last year in Kansas City in my role as AP reader, and I saw about 1,500 student responses. It’s great to be able to discuss the grading procedure with students, and the exercise of working through the College Board rubrics and discussing them so intimately has improved my instructional practice.
ONE OF MY FAVORITE STRATEGIES: To go over the problem, I use my handy 24-sided die to choose a student at random. Their problem is placed under the document camera and critiqued by the class. This can be intimidating for the student, but I assure the class that everyone eventually will have their work assessed via camera during the year. By this point in the year, I hope students have been through this enough times to see the positive value in peer evaluation. I often start classes now by handing out index cards and asking a quick understanding question. For example, a day after we had gone over the required elements when describing a scatterplot, the day’s opener asked students to describe a relationship and the use of r-squared. Many examples went under the camera, and we had a snapshot of where we are as a class.
The new video on experimental design is nice, but not as great as the older one. The experimental design chapter is one of my favorites, with so many opportunities to think creatively. Hoping to talk share our “old wives’ tales” project for this unit in a later post. Looking forward to my “hallway bowling” activity for next time, which provides need for matched-pairs.
12:00 – Directed study – All students here have have a half-period directed-study built into their schedule. Most teachers are assigned one to watch. Fortunately, many of the kids in my directed study are in orchestra, so they choose to leave and go practice. Many days I will have visitors seeking math help, but today is pretty quiet.
1:15 – After a lunch-time spent dissecting the Eagles victory with colleagues, I had my prep period at the end of the day. Most of my time was spent writing and revision tomorrow’s Algebra 2 test. Such a tough balance trying to develop an exam with enough rigor for honors students, yet be a fair measure of student growth. The students should be in good shape. Getting ready for the next chapter in stats, thinking out how my portfolio project for Algebra 2 will work, and a track and field discussion with a colleague round out the time.
Time passes…nice walk…dinner…Monday Night Football and….
9:00PM – #alg2chat – one of many weekly twitter chats I keep my eye on, this is a nice community of folks who share their successes, pains, ideas, and resources. This week, the discussion bounced around from completing the square (where a twitter colleague looks forward to trying the box method), to synthetic division (and Dr. James Tanton’s railing against it), to a discussion of matrices and where they fit in a HS math sequence (answer – all over the place). For me, this is the most powerful aspect of the MTBoS, having a network of enthusiastic educators looking to share ideas and make their lessons better.
Since I was a little kid, I loved watching the Price is Right. I know all the games, many of the prices, and of course can name the “back in the day” models without batting an eye (Dian, Holly, Janice). I even made the pilgramage to Television City a few years back to see Bob Barker in his last years of hosting.
This is the most simple probability game on the show. The contestant is shown a prize, and two possible prices for the prize. If the contestant guesses blindly, they then have a 50% of choosing the correct price, and winning the prize. In all of these games, the pricing aspect is a “clue” to the player, which hopefully increases their chance of winning. But in all of these examples, we will look at the games as random chance experiments.
The smaller prize has 3 distinct digits in its price, which the contestant is given. They must place the digits in the correct order to find the price. With 3 digits to place in order, we have 3! = 6 possible prices. BUT, in this game, the price always ends in zero (they don’t tell you this, but it’s always true), which means this is essentially a 50-50 game. For example, if the 3 given digits are 0, 9 and 5 – then there are only two possible prices, $950 or $590.
To make their guesses, the contestant places markers either above or below each digit in the dummy price. If they are correct with all 4 digits, they win the prize. If they are wrong, they can go back and make changes. A total of 30 seconds is given to make as many guesses as they can, running back and forth between the game board and the guessing buzzer.
Moving onto the next prize, 4 digits are given, 3 of which make up the next price. In theory, there would be 4 x 3 x 2 = 24 choices here. But again, given that the price will always end in zero, there are only 3 x 2 = 6 viable choices.
This is one of the most difficult games on the show to win, and is often played for a luxury car. The game is played with 8 wooden disks, which are placed in a bag and shaken. 5 of the disks have number on them; digits in the price of the car. The other 3 disks have red “strikes” on them. A disk is drawn, and if a number is drawn, the player must tell which position in the car’s price the number represents. If they are correct, the disk is removed from circulation. And if the player is able to complete the price of the car before drawing all of the strikes, they win the car.
Now, I could go through and count the number of these 56 that produce wins, but I think it might be simpler than that. The game really comes down to the last item on the list. If the last item is an X, then you will have won the game. If the last item is an N, then you have lost. The chance that the last item is an X 3/8, so the probability of winning the game, assuming perfect play, is 3/8.
This game is played for a car, with 3 smaller prizes as well. The 3 smaller prizes have prices with 3 -digits, 2 digits, and 3-digits. The prices of these smaller prizes are used to fill in the middle 3-digits in the price of the car, as shown on the game board here. This give 3 x 2 x 3 = 18 possible outcomes. The nice part about this game is that the contestant is given a second chance, and is told how many digits they have correct after the first attempt. If the player needs their second attempt, it would be interesting to analyze how many choices of the 18 remain, given that they have 0, 1 or 2 of the digits correct.
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