Probability is one of the most interesting topics to teach but it also can be controversial. A number of the hands-on activities associated with probability are 'games of chance' (aka casino games/gambling) and have to be presented in a different way.
A favorite in the probability world is calculating the chance of rolling a certain sum with 2 dice (or number cubes- the PC way to say dice). I have always use the game Beano for this purpose but while enjoying Friends one evening Monica and Chandler provided another illustration while playing craps in Vegas. Now, I would never use this example unless my audience was out-of-high school since it involves gambling and deciding to get married based on the sum of two dice. But is does provide an opportunity to discuss what is the probability that Monica rolls a sum of 8 (5/36) or a 'hard' 8 (rolling 2 fours- 1/36).
The clip from the episode is below. Enjoy. And in the words of Monica Geller, "It just got interesting."
I spend the class before a test reviewing. This can be a very useful day for students or a complete waste of time where nothing is accomplished. I have found that providing a VERY structured class helps students more than just saying: "Work on your study guide for class."
I try to switch activities at least every 15 minutes to keep it from getting stale. Below you will find two different layouts I use to review. The document/files attached are in relation to the first method described.
Example of a review day in class (The PowerPoint is in reference to this layout):
0:00-0:10 Take a 7 minute time trial and take 3 minutes for checking and questions (Kuta has some great resources)
0:10-0:17 Return recent quiz/homework and take 7 minutes to go over (loving my document camera for this!)
0:17-0:18 Stretch break (hope they enjoy the cartoon clips I found)
0:18-0:23 "I have..., who has..." vocabulary game. (See file attached below)
0:23-0:33 Take 10 minutes to go over questions from the study guide as a class (I set a timer to keep this to 10 minutes)
0:33-0:43 4 Corner Activity to go over a concept that students typically struggle with
0:43-0:55 Free study time (work with a partner, finish your study guide, ask Ms. Turbiville a question, etc...)
Another example of a review day in class:
0:00-0:10 Work on your study guide individually with no notes. Highlight problems that you are having trouble with. You may not ask Ms. Turbiville questions.
0:10-0:20 Work on your study guide individually with your notes/book. Make a strong attempt to answer the questions you highlighted. You may not ask Ms. Turbiville. (I want them to learn to relay on what they know so I do not allow students to ask me questions for the first 20 minutes) Solution keys will be posted on the board and they may refer to those.
0:20-0:35 You may work with a partner and ask Ms. Turbiville questions.
0:35-0:55 We go over questions as a class. At the end, I do allow students to take pictures of the solution key.
What an interesting concept. I have mentioned that I have used an article in class to introduce even, odd, or neither even or odd function and it turned out well. Just google "zero even odd hurricane sandy" and you will come across articles with comments made that show full on arguments if zero is even of odd. I find that students may have difficult distinguishing between the difference between zero and none. For example, with my Algebra I students we covered x-and y-intercepts and some found it difficult to write "none" instead of zero when identifying the y-intercept for an equation like x = 5.
Below are great videos that explore zero and one (another good topic) a little bit further. This, I admit, is a rambling post but love these resources! I am starting to use TED Talks in some of my classes. TED-Ed has fabulous lessons that I would recommend checking out.
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!
Yes. The answer is yes you can study mathematics. There is apparently a rumor going around telling students that math cannot be studied. This is a lie. Run from the darkness.
The issue is students need to learn how to study math. This is where I, as the teacher, come in to hopefully fly in to save the day. Here is the list of ways I personally have studied math and instruct my students to do so.
Cheat Sheet (See photo to the left)
Start reviewing notes, power-points, textbook, or whatever form the material being tested was presented on and on a blank sheet of paper write out problems, equations, formulas, and helpful hints on the material you do not 100% understand. This is your "cheat sheet." Writing the topics you do not feel comfortable with allow your brain to process the material from start to finish and you get to "feel" how the topic is worked out. When I was a student, I would do this multiple times on separate days before a test. Your cheat sheet should get shorter and shorter the more times you complete this exercise. On the last night my sheet would short so I had less material to work through. I like this method because it works for all subjects and it a great to hold onto for use in studying for finals. The picture shown is one of my students "cheat sheets" that he created for his final test (that I did let students use). This does take time but with more repetitions on the same topic the quicker the process will go.
This is a fabulous tool to use with units where there is vocabulary, properties, and formulas that will tested. Old-school using lined index cards and new-school sites like quizzlet are great tools to use while studying. I prefer old-school paper index cards because I learn best when I write the material down (my love of cheat sheets is explained) but I have seen more students lean more towards quizzlet-like sites. The advantage of quizzlet is that you can share your creating with others.
I have written of my love for YouTube as a teaching method I use in class so it should be not surprise that I am using it again. I believe that YouTube gets rid of the excuse for students that they do not understand the material on test day (even if they were absent.) It has EVERY TOPIC YOU CAN IMAGINE on it. Simply type to topic in the search bar and 1,000s of videos will appear. I recommend starting with the first one that pops up. You do not like the person on the video you say? pick another one!
Extra Practice Problems (the whole problem, on a clean sheet of paper without referring to the worked out example)
As a coach, I know what my athletes do during practice is a direct implication on how they will preform on game/match/race/meet day. I also know that an athlete does not become an expert by watching me practicing the stroke/running technique but rather by practicing the technique. The same is true with math. Working out extra problems from start to finish does help. I find that students give into the lie that if they understand a problem by watching me going through it problem, hearing my explantation for it, and seeing my work on the board for it that they understand that topic. NOT REALLY TRUE. A student really knows the topic if they can work out a problem from start to finish without assistance. This is why I give my students a study guide/practice test for each test.
Bottom line...to study math you have to take time to study the math. You will not be able to magically get all topics, it will take work. Take the time to figure out what works. There are plenty more ideas, these are just the top
Work with different strategies to see what works. One method may work for one topic but not for the next.
How do you study mathematics?
While I am on Pinterest, I notice some funny math posters/ideas/the thing where you add a saying to a picture.
Here are some of my favorites. These are great to look at for a quick laugh and I have used some in lessons as an introduction or ending. The pizza one shown first on the slide show is a new one for me and I will be using it for volume this upcoming year.
Have fun and laugh a little.
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.
Educator who loves math and working with students.