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: Question #1 Question #2 Question #3 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.
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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!
Conic Sections is a great topic to get a hands on with. To introduce the topic I had students work in groups of 4. They 3 activities for the lesson. 1st: A sheet on basic algebra skills (graphing, factoring, writing equations of lines, etc...). Each member had to have the correct answers and correspsodning works to move to the 2nd activity. 2nd: Conic Sections with Paint. Students cut paper cone cups to represent each conic section. 3rd: A round-the-school instagram activity (#conicsectionschs--some of the picture are still available to view) I have used instagram for my freshman to complete a geometry scavenger hunt and for cross country--it is one of my new favorite ways for students to prove they found certain shapes. A majority of the students have instagram linked up with facebook so I am proud to say that a bunch of high-schooler's facebook newsfeed had conic section identifications. Once a group finished with an activity they moved to the next. I wanted to each group to get through the 1st and 2nd. The 3rd activity was my early finisher activity. Once the first group left the room with directions to take pictures and post them on instagram, the other groups kicked it into gear to finish so that they could complete the 3rd. The 1st activity took the longest. It was a fun day that everyone enjoyed!
I found this on Pinterest and decided to make a powerpoint to use during the first day back with my students. I selected shots that used the math we had covered in Advanced Algebra this past semester. I am excited to use this! Pictures and more photos on: http://spikedmath.com/movie-math-quiz/
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: http://www.crackerjackgreenback.com/the-basics/compound-interest-a-lesson-from-benjamin-franklin/ http://sensuouscurmudgeon.wordpress.com/2008/12/31/ben-franklin-compound-interest-and-evolution/ http://www.globalinvestmentfoundation.org/powerCompInt.html http://www.upstatenh.com/Finances/BenFranklinsLessonForToday.html My school's freshman, sophomores, and juniors took the PSAT today. I took the day before to review test taking skills, complete a 25 minute practice test, and then reviewed the answer. It is just as important to know how to take a standardized test as it is to know the material. Especially when 1/4 point is subtracted from your score for each incorrect answer. Layout of the class: 1) Students grabbed the attached article as they entered the classroom, read it, and highlighted key information 2) I answered questions and pointed out key information that was not asked by class 3) Students completed Section 4 of the practice they received in advisement 4) Reviewed answers 5) Answered content questions (not as much time left as I hoped...6 minutes tops) And just to show how some of the math they have learned in the past is relevant...I showed them the expected value of their score if they were to guess on every single problem. (Keep in mind that there are usually 5 answer choices for each question) E(x) = (-0.25)(0.8) + (1)(0.2) = (-0.2) + (0.2) = 0 So, if you guessed on every single question, you can expect a score of 0. I wanted my students to be able to focus of the content the day of the PSAT and not be worried about the directional instructions of the test. The article I had my students read before starting class is shown below. If you wish to download the document, simply click the "Download" selection. Enjoy! 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. Materials: 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 Solution: 1) C 2) J 3) K 4) G 5) B 6) D 7) L 8) I 9) A 10) F 11) E 12) H
The traditional math classroom is: In Class: Listen to a lecture Outside of Class: Complete concept exercises FLIPPED Classroom: Outside of Class: Watch lecture online (YouTube is my choice) In Class: Complete concept exercise (under guidance of teacher) Great Visual: http://www.knewton.com/flipped-classroom/ What I have noticed... 1) It is an adjustment. Be patient and be prepared to answer ALOT of questions! 2) The response from my honor classes have been more positive than my on-level classes I presented at my county's professional development day on incorporating reading and writing in the high school math classroom. There are great ways to use both tools in our math classrooms. I do not know even close to all the different sources but I would love to hear how you use reading and writing in your classroom. My presentation is below. Enjoy! Video Links:
Flatland Trailer: http://www.youtube.com/watch?v=C8oiwnNlyE4 The Number Devil: (having trouble finding it) Writing and Math: http://www.youtube.com/watch?v=Vq9wGg24tVI |
Natalie Turbiville
Educator who loves math and working with students. Archives
May 2016
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