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!
My freshman have started mastering the art of writing proofs. This is typically a difficult concept for students because they are used to making statements but stating the reason for each statement takes some getting used to. They were also having trouble understanding why they had to provide reasons for statements they felt where obvious. This is a common struggle for anyone writing proofs.
Khan Academy has a great introductory video on geometry and Euclid's (Greek Mathematician.) For example, did you know that until recently that Euclid's Elements (13 volume Geometry Textbook) was the 2nd most produced book after the Bible? Isn't that crazy that a math textbook was second only to the Bible! The video also shows how Abraham Lincoln would read Euclid during his lawyer days when he needed to refresh on the importance of proving a point.
This led to a comparison that if you where accused of murder do you want the lawyer that stands in the courtroom saying "Well, duh, this person is innocent" and then sits down or do you want the lawyer who proves to anyone in the room that you are not-guilty by showing evidence, cross-examining witnesses and brings in experts to represent you?
I would love to purchase Euclid's masterpiece soon and contribute to its success and the lasting legacy of Euclid.
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!
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!
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:
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.
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 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.
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
I am working for Georgia Teaching Fellows Atlanta (http://georgiateachingfellows.ttrack.org/Home.aspx) this summer. It has been an AMAZING experience!
I along with a fabulous co-workers recently presented on using technology in the classroom to our Fellows. Incorporating technology in the classroom is so important and a relevant way to get students engaged. Since technology was the topic I wanted to stay away from a PowerPoint and using paper so I created a website (on weebly of course) for our workshop. I also created tutorial videos (using screencast-o-matic) on how to use technology in the classroom. The website it linked to the picture to the left (www.gtfayi.weebly.com). Sakon and I hope that this can be a resource for teachers to use to get ideas and learn more about the technology available.
Enjoy! We had an awesome time bringing this to life.
Educator who loves math and working with students.