I love it when what is going on in life is relevant to what I am teaching.
I am getting married this summer and am finding out just how expensive weddings are. Every site and article I read always seem to state the average cost of a wedding, however, I know from all the statistics classes I have taken that the mean is not always the best way to represent the typical value.
My Advanced Pre-Algebra students are currently learning about the limits of basic statistics and the cost of a wedding in the United States is the perfect tie in for the debate of mean vs. median and the impact of outliers.
On the quiz I gave my students Monday, I asked them the following...
In part (a) I was looking for the use of the vocabulary of outlier and mentioning that there were expensive weddings that were bringing up the mean but not effecting the median.
In part (b) I was looking for the students suggesting that the newly engaged couple be told the median since that value is not as influenced by the high outliers like the mean is.
Below are some shots of my student's explanations.
Before I returned graded quizzes, I had my students read Will Oremus' article: The Wedding Industry's Pricey Little Secret. Mr. Oremus does a great explaining that the averages are more than what most couples spend. He continues to point out that the sources who provided the public with the average (TheKnot.com, New York Post, etc...) typically exclude the poorest and most low-key couples from their samples simply because those couples are not on those sites or responding to the surveys.
I especially enjoyed this section:
Oremus goes on to explain why the median is not used as the statistic: Americans do not understand what the median is. TheKnot .com told Oremus that is does not publish the median along with the mean since they don't want to "confuse" people. When Oreums asked the editor in chief of TheKnot.com to expand more on why the median is not used, this was her response:
She did not understand what the average was. Her reasoning is the typical error of most people-that the average tells you 50/50. The average serves as the balance of data, and not (usually) the indicator of the middle. That's the median.
We had a great discussion as a class after they read they article. Thank you Will Oremus for a fantastic article that got my students talking about statistics and providing me some insight as I plan my wedding.
Readers, I leave you with the closing remarks of Mr. Oremus:
"There's nothing wrong with spending 28 G's in 24 hours if you've got the means. Just don't fool yourself into thinking that there's anything average about it" (emphasis added)
(The file below is the word document I made from the article to print nicely. I printed 2 pages to 1, double sided.)
Math is everywhere! I always get excited when I see math used in tv shows, movies, and articles. I typically use these artifacts as class openers to introduce a topic or as a closer to make drive the point home. Now, I will say that some of the examples shown show math in a silly or intimidating way. This is very representative of society's view of mathematics: a difficult complex science that cannot be mastered. I will explain this for each.
Sherlock Homes: A Game of Shadows (Pascal's Triangle)
This came over during the Holiday Break of the 2011-2012 school year. I reluctantly saw it with a friend (ended up loving it) and was excited to see Pascal's Triangle on the board of the evil dude as a ciphering code for his notebook with his plans to take over the world. I had covered Pascal's Triangles with my 9th graders in the fall and was curious to see if any of them noticed it (the movie did zoom in on it and I think it is the scene shown in the picture.) They did! The link above leads to a publication which goes way more into detail on the math used. I just used is as a "you actually learn stuff in this class that you will see in the media." Now, this is an example of math being used by a super genius trying to ruin the world so it may not have a great vibe on the math but Sherlock had to use math knowledge to save the world so that is good right? I told my students I was showing them math that they could use to take over the world or save the world.
Go On (Fibonacci Sequence)
Season 1 Episode 12
This was my first summer completely off so I watched some television shows (thank you Netflix/Hulu) that I probably would of not seen if not for my restlessness. Matthew Perry's character in Go On does a sports segment with some famous sports guy who decides to change the focus of his show from sports to philosophy topics. He asks Matthew about his opinion on Fibonacci and Matthew is confused and lists off the first sequence he can think of...911. It is another not so positive jab at math but at least 50% of the people in the discussion know about Fibonacci. I am still in debate if I will use this clip in my classes this year.
Raising Hope (Area of a Circle)
Season 2 Episode 11
Alright, it is hard to show math being portrayed in modern media. This would actually be an interesting topic for a research paper or article (maybe that will be a goal of mine this semester). Here is another poke at mathematics were the only person who knows anything about calculating the area of a circle is the memory challenged grandmother. I know I teach this topic in Pre-Algebra this school year so it would fit in easily but once again I am debating on the message it sends about the inaccessibility of math.
I love solving problems. There is something very satisfying to me about figuring out a solution. This is amplified when a friend asks me a math question and when the answer has real world applications.
This past Wednesday, a dear friend who is pericardiac physical therapist sent me the following text (shown to the left) asking me to convert feet/seconds to miles/hour. I was thrilled to but I was shopping with no pen and only had receipts for paper. I paused shopping and worked out the problem (thank you dimensional analysis) after borrowing a pen from a cashier.
I took a picture of my work and sent her the solution. Excited to teach dimensional analysis this year and use this as an example.
Whoops. The conversion is actually 8.2 miles per hour. I forgot to type in a '0' in phone calculator and messed up the decimal. Thanks for pointing this out NS!
This is one of my favorite math music videos on YouTube. I believe it was completed for a class project but I honestly have NEVER seen a student produced video with such AMAZING quality (And I have done YouTube Video projects and they are great but not at this level). I find that videos over 2 minutes lose my student's interest but this one always captivates from beginning to end. Videos can help re-enforce or introduce a topic that has a lasting impact. I showed this to a Pre-Algebra class 2 years when I taught in Memphis and I had a former student contact me in January saying that she remembered the trigonometric ratios because of THIS video and it helped her in her Geometry class.
Share it. Pass it on. This is awesome.
Vocabulary is essential in mathematics. In the past I have strayed away from it mainly because it is 'boring' and the past methods I have used have been ineffective. Through online research and collaboration with other teachers, I have been exposed to a variety of methods that work.
"I have..., who has..."
My favorite vocabulary strategy. The first 4 attached files are in reference to this activity. 14-16 students each have a different card. The student how has the card that states "I have the first card" reads that statement and then the "Who has...". The student who has the answer to the "Who has..." reads "I have..." and then their "Who has...". This continues till the last student reads "I have..." and then "The end." You can make it shorter or loner depending on if you want each student in your class to have a card. I have an average of 32 students in a class so I shot for half to have a card. I will time each class to see which class can finish in the least amount of time. This game typically takes about 2-5 minutes depending on the vocabulary. I will start a class with this and then end it with this as well to see how much time each class can shave off their first time. It is also great to use with known vocabulary objectives. I like to use this when teaching logarithms and exponents because it makes each student SAY the proper form. I will have a student at the front of the room time the activity, pass out/collect the cards, and they may write the "Who has..." part on the board. If someone reads the incorrect "I have..." I make the student holding the current "Who has..." read it again. This is to save on complete random guessing. Some classes like to have everyone with a card stand up and then sit down when they read their card. I sometimes tack on some extra points to the class with the fastest time. This has become common place in my teaching. I keep the initial print out as a key and make a copy of it on card stock that I then cut-out and hand out. I did not create the blank word document...I found it online.
You do need 2 fly swatters (try to the Dollar Tree) for this game and I think elementary teachers use this one a good bit but my older students enjoy it! Have the vocabulary show on the board in two columns with an overhead or projector. I then read a definition and the 2 students with the fly swatters try to the first student to "swat" the correct word with the fly swatter. It is entertaining to watch but you do need to be clear the fly swatters are only to tap the words and not others. (I do one class of Juniors that I do not do this activity with). You could even have teams and switch out the "swatter" for each word. This is quick and a great closing activity.
I see no value in word searches but I do see value in crossword puzzles (with no word blanks...that would defeat the purpose in my opinion). The only completely free site I have found is from Discover Education. It is not the best and I have not figured out a way to save a copy but it works!
I love playing taboo and have always wanted to implement it for vocabulary. I plan on doing this in the future by giving each student a word and having this write the "taboo" words. This would be a great addition to any vocabulary day. I was thinking of using flashcards cut in half and adding the new words to the old words so that students were constantly reviewing previous vocabulary. I think groups of 8 (4 on each team) would be optional. Alright, I have convinced myself to do this.
If I am spending a day on vocabulary I will do:
1st: "I have..., who has..."
3rd: Fly Swatter
4th: "I have..., who has..."
I would love to hear what other people are using. This is an area I want to continue to grow in!
I LOVE projects! I love that they are another way to assess students and gives those students who are weak test takers another option to show what they know. What I do not love is those students who choose to not complete any project and therefore hurt their grade even more....anyway....
We have switched our 9th graders in Fulton County to Common Core and the county has given us "blueprints" to walk us through each unit. Each blueprint comes with multiple resources that are appreciated! I came across this Mathemagic activity and turned it into a project for Unit 2. (I did not create this, I simply used it!)
Students have to create a "math magic" trick where contestants are asked to choose a number and then operate certain steps on that number to get back to the original number or get to a certain number.
A great way to introduce the project is be opening with...
1) Choose any nonnneagtive number...
2) Square your number
3) Multiply the result by 9
4) Take the square root of the result
5) Add 15 to the result
6) Divide the result by 3
7) Subtract 5.
It's your original number!
I wish I had a magians hat for the occasion...oh well...
Students had to do the following with their trick:
1) Describe in words
2) Show an example #
3) Show why the trick worked with "x"
4) Justify each step (this showed students that whatever they did they had to undo!)
The biggest weakness was showing why the trick worked with the general example "x."
They enjoyed it and we had fun taking 5-10 minutes for a few days for the students to amaze their classmates with their tricks!
I used a round-the-room activity as a closing (20-30 minute closing) for my lesson on graphing using x-and y-intercepts. The night before, my students watched a video on graphing using intercepts and how to algebraically find them. We reviewed the concept and graphed with pipe-cleaners and laminated graph paper (not in love with the exact approach I used) and then they completed this activity.
I like using this activity because the answer is there, so if they have the incorrect answer it prompts them to ask me and then I can clear up misconceptions. It is also easy to check because I make them write the answer letter in the last column. This is a great alternative to a worksheet! I have a small room and 32 freshman had enough room to complete the activity.
1) Answer sheet - 1 per student
2) Question/Answer Sheets - Print 2 pages on 1 page so each page has a question and an answer
Educator who loves math and working with students.