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!
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 have always taught how to identify if functions are even or odd by substituting in -x for x and then multiplying the original function by -1. For my honor students this is still the way I approach it but I tried a different approach for my on-level students this year.
I started the class by each student reading an article from the BBC released in December 2012 about Superstorm Sandy and if '0' is even or odd. New York residents were limited to the days they could pump gas based on the last number of their licence plate number. Odds went one day and the evens (add those ending with '0' as the mayor said) could pump gas the next day. The article is easy to read and shows why zero is indeed zero. As a class we discussed the major points of the article.
Then each student received notes and we went went over it together. The approach is if all exponents of the function is even (and a constant has an even exponent of zero) then the function is even, if all exponents are odd then the function is odd, and if the exponents are a mixture of even and odd then the function is neither even or odd.
I 'borrowed' the powerpoint from a teacher in Georgia and then added in a few polleverywhere.com polls at the back end. I had each student send their response to the question asked by texting on their phone. The program is free (up to 40 responses) and you can choice how people can respond. There is an option to embed the poll in your powerpoint and the poll will automatically update as answers are submitted. My students LOVED this. I did have to reset it after each class and make sure you have internet connection! You can answer my questions by selecting the following links below:
I only use the free options provided by the site but the paid options look fabulous. I honestly know I would not use them to the fullness of their abilities and it would be waste to spend that money.
I ended the class by having students answer 5 questions for a ticket-out-the door. I graded that sheet for correctness and that was entered in my gradebook as their homework grade for that objective.
I introduced (well, this is technically like the 10th time my Juniors have seen end behavior in their math careers) end behavior to my 11th graders in January by showing quick video, going over some notes, and playing a game for closing. The video is short and the guy was entertaining enough where my students mimicked for a few days. Even to this day if we talk about end behavior my students will use this guys expressions.
The game was created by Rebecka Peterson. I did not think I would of been able to watch everyone's hands (especially odd functions with my direction facing them) so each student was given a laminated graph and pipe-cleaner to bend to create an example. I have moved away from my students using dry erase boards because in my tiny room and 33 open markers I was having KILLER headaches (smell is my one strong scent). Pipe-cleaners for a variety of topics and this is one of them!
When you think of the wonders of the world, you think of Stonehenge, the Colosseum, and the Great Wall. Which are actually all feats of engineering...go STEM! Mr. Franklin called compound interest the Eight Wonder of the world and I do not know I did not hear about this till this past summer after listening to the Podcast "Stuff You Should Know."
The story goes, a French mathematician basically made fun of Franklin's Poor Richard's Almanack and mocked the American optimism that Franklin exhibited. Franklin, not to be made fun of, accepted the challenge and left 1000 British pounds to both Boston and Philadelphia in 1790 (year of his death.) Both accounts would earn 5% yearly interest and were not the be used till 200 years later (1990). At the end of the 200 years, the accounts were brought to courts on the legality but at the end Boston received $4.4 million and Philadelphia received $2 million. (Court fees lowed Philly's balance) Wow!
I had my students read an article about Franklin and the accounts as the start to the class and then we discussed the formula and more examples. It was a neat way to get my students to read math, introduce a topic, and tie in the content to history. I used this lesson in both my Advanced Algebra (Algebra II) and Common Core Coordinate Algebra. I still get comments from my students about it--and its been 2 months since!
Franklin's story is interesting and makes the math more relatable for students.
Links to articles:
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
I love teaching probability! It is relevant to my student's life. they do not complain about it, and they see the relevancy! (Yay!) And there are super fun techniques to use! BEANO is one of them. Once again, this is not a concept/worksheet that I developed. It was presented to me during the TI Conference in Atlanta, GA during the spring of 2010.
2 dice (or number cubes as we call them in Georgia)
BEANO Worksheets (I give each student their own)
Dry Beans (I used black-eyed peas since they were the cheapest--these are great to have for BINGO)
I tell my students we are playing a game (insert excited students) and have them place their twelve beans on the front of the worksheet. I usually let them read the instructions on the front and figure it out! Then we play! You can roll the dice and say the sum, have a student do it (I opt for this option), or use a graphing calculator with the probability simulator program. When the dice are rolled by hand I will chart the frequency of the sums on the board for use later!
Then we complete the backside. You may have to explain filling in the sum chart for some and I usually will plot the box graph with them. Then answer the questions (it discusses probability and you can add more questions if you want to!) and play BEANO again!
The second time around and the questions prompt students to look at which sum (6, 7, 8) are most likely to come up and how they arranged the beans on their boards will noticeable change (see pictures below) or at least they should if they were paying attention. You can play a couple rounds and I usually have the winner be the next roller. The BEANO games played after the worksheet are way quicker then the game at the beginning of class!!! Also, keep track the frequency of the sums and you can use the theoretical chart from the worksheet for use of comparison of the experimental chart you keep track of in class. The more trials, the more like the theoretical the experimental will look like.
Educator who loves math and working with students.