Conics are EVERYWHERE. I just took a flip video and taped of a few clips of some conic sections around town and then put them in a 1 minute video. I asked the students to remember as many of the images that they could. They were to try to identify the shape (parabola, ellipse, hyperbola, or circle) and what the object was. It was very interesting to hear the discussion.
Some observations the students made.
The Taco-Bell clip looks like the bottom of the bell is an ellipse, whereas the top part looked like a parabola. There were some arches that looked like a semi-ellipse.
Someone pointed out the circle that is the steering wheel and the tires on cars.
The tower was a parabolic dish.
McDonald's had two parabolas.
The gas station had an elliptical sign.
There was a big argument about the wires on the sidewalk. The only thing it was not called was circular.
The stone arrangement looked like a semi-circle. Since the video is from an angle it almost looks like an semi-ellipse.
The bridge had some discussion as well between a hyperbola and a parabola.
The last clip was simply a nuclear plant shaped like a hyperbola.
Most of all, it created some great MATH discussions. Give it a try.
Dave
Here are some reasons why I'm THANKFUL for being a teacher!
1. Every Day is Different
Actually every class is different, every student is different, every parent is different... and so on. I love the fact that the activities are always varied, and thus always fresh.
2. I get to answer questions.
There is a certain amount of pride in answering questions. If students ask questions, I know that they want to know something more.
3. My Students.
I love the energy of young people. I thrive working with students and the fresh ideas they bring. Spending time with young people keeps me young.
4. I get to use new technology daily.
SMARTBoard, Flip Videos, Laptops, Tablet Laptops, Computer Lab, and of course MY CALCULATOR.
5. Problem Solving.
Teaching gives me a chance to problem solve on a daily basis. I find the challenges engaging. They give me a sense of accomplishment. How do students best learn? How can I make the material engaging?
6. My Colleagues
I love working with the people in my department and my school. They are so supportive and downright fun to be with.
7. Coaching
Coaching gives me a chance to work with my students in a different way. I love working with a team to try to accomplish something you can't alone.
8. Our new facility
Our school finished the renovation project this year. It is gorgeous. Check out my room in this video.
9. Math
I love math. I love numbers. I get to work with numbers everyday.
10. Stories
First of all, I get to tell my family stories about my adventures in teaching. Secondly, I realize that I need to find out each student's story.
11. Former Students
It is so rewarding to have former students stay in touch with me. I recently saw a former student of mine and she is currently a teacher herself. It was terrific to see her passion for her students and for her profession.
12. I get PAID for doing something I love!
13. I'm also very thankful for vacations. Thanksgiving, Holiday Break, Spring Break, and SUMMER!
I got this activity from my brother-in-law and really like it. It is called "Sum of Three". In essence you have students in groups of three each doing a different problem. Then you have them add the answers together to be the sum of the three answers. They will bring this number up to you and ask if this is correct. If they are correct, then they get to move on to the next problem set. If they are incorrect, then they must decide how to go about getting the correct answer. This is the best part of the activity. When the students get the problem wrong, they automatically think it is somebody elses mistake. They then will systematically go through the process of how to do the problem with everyone. It is a great group activity. Here are my directions. I have given a couple examples as well. 1. Get your class into groups of three. I always do this on a random basis. Let's say you had 26 people in your class. Take 26 kids divided by 3 and you get 8 full groups of three. Count students one, two, three, and so on till eight, then start back at one, two, three and keep doing this until you run out of people. In this case, you will have 6 groups that have 3 in it and 2 groups that have 4 in it. Now the ones get together and the twos get together and so on. 2. Hand out a problem set A in paper form to each group. This will have three problems in it. A1, A2, and A3. Each student will work on a different problem. The group will then add the sum of all three answers. 3. When a group thinks it has a sum, they bring up THEIR PAPER to show you their answer. Don't have the students SAY the sum. This might give it away for the other students. If they are correct, give them the problem set B in paper form. If they are incorrect, then they must go back and find out where they made a mistake. 4. I have my students do all their work on a separate piece of paper to be turned in. This creates a little accountability as well as a place for them to work. 5. You will have to decide how many sets of problems you will want. I typically have 3 to 4 sets. I have the last set as extra difficult.
Here are a couple of examples of the "Sum of Three" activity.
This is a problem set for multiplying fractions in Intro to Algebra
This is the answer sheet that I use when the students come up to give me their SUM.
This is an Algebra "Sum of Three" problem set. I have the students add the y-intercepts of the line.
Now I really like this one. I like it because it is very easy to use. It can graph my lines in color. It can graph an inequality. It is absolutely free. Just go to the site below and use away. It doesn't have all the bells and whistles that a TI-84 would have. I think I like it for displaying multiple graphs at once. This makes it so much easier to see the different graphs. You can say "Where the green function and the red fucntion intersect". Let me know what you think.
Best,
Dave http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.swf
1. Have your students stand up. 2. Have 5 "I am a..." questions ready to ask. (I have given you a few examples below) 3. Tell the students that they are not to shout out answers for this activity. They should think of the answer and be ready to give it when called on. 4. Explain to your students that you will be calling students at random for the answer. Also explain that they will be doing this completely by listening to the question. They will not be allowed to write out anything. 5. Give the question and then give the students some "think" time before you call on someone. 6. Call on someone to answer the question. Have them justify the answer. 7. Call a new person to verify or change the answer. Do this until you get 2 people in a row to verify an answer. 8. Verify the answer yourself and then move to the next question.
It is a great lesson on LISTENING and MENTAL MATH. It only takes a couple of minutes and the students like it. You get a high involvement rate because you are being called on at random. This is an activity that I do not assess. It is also a great review session that breaks up the regular day. Give it a try and let me know what you think.
Most math text books have examples that are completely worked out with the solution given. Take a piece of paper and hide the textbook answer and work, but show the question. Redo the problem and then check your work with their work and solution.
2. Study for Tests and Quizzes.
It is easy to just do the review homework and feel like you are ready for the test. You need to do this and more. Study for the test or quiz by going back through problems that have been given and solved in class. Actually redo them and check your work. Studying for math is DOING the MATH.
3. Make sure your homework is correct.
Check your answers with those that are in the back of the book while you are doing your assignment.
4. Do math EVERYDAY.
Do your homework every day. Try not to skip any days of homework. If you are cramming all your work into a short single session you will find this usually ends up in frustration as well as poor long term memory with the topic.
5. Attempt the most difficult questions.
The most difficult questions will usually teach you the most about the material. Never skip them. Try to get the most exposure to these problems as you can. Try to solve them on your own. Revisit them. Go in for help. Ask a question on the problems in class.
6. Take a break.
Give yourself a break when working with math. If you are being efficient, then three fifteen minute sessions in a day are better than one 45 minute session. Stand up. Stretch. Go for a walk. Move your work to a new place. A break is needed when working with math.
7. Have a good attitude.
Never think “I’m terrible at math”. You usually meet your own expectations. Believe that you can do it!
8. Go in for help with your teacher and bring a specific question.
When you bring in a specific question to your math teacher they can help you with where you are struggling. The teacher then can typically give you more examples that are similar to what you are struggling with.
9. 5 minutes.
Once your homework is done, then take an extra 5 minutes to look at these possible things: vocabulary, formulas, notes, projects, and book examples.
This is a collection of free video tutorials involving almost any math topic that you could think of. This is by far the most useful website that I have ever recommended for a math class.
Yesterday I made a math problem so that it took up one whole page of typing paper. I cut it up into 6 equal pieces that were approximately 3 by 3 inches. I put it a random order and put a paper clip on it. I did this for 5 problems in all and 2 sets of each for a total of 10 questions. I have 20 students in my class. So I had my students work in pairs. It is real easy to cut these problems up with a paper cutter. See the above cut out lines that I took with the problem.
Then I put the 5 stations with 2 sets of the same problem around the room. Four people, or two pairs of partners would be at each station. I would then have them start on the problem and set the timer for ONE MINUTE. The partners together would have to unscramble the pieces and then solve the problem. They would write their answer down on their paper. Once they were done, they could check the answer that is provided at each station. After the minute was over and students had checked their answers, I told them to rotate. They went to the next station and we did the process all over again.
I was happy with the outcome because they seemed to enjoy trying to figure out the puzzle and do the math. It also helps the students to MOVE and LEARN. They are moving after each problem.
As a math teacher, I give a lot of problems to my students that are equations. This provides a great opportunity for students to work together to solve a problem. Put one student on the left side of the problem and another student on the right side of the problem. Then they can only do things on their "side" of the problem. It was amazing. Basically, it forced my students to work in tandem and at the same speed. Even better was the fact that they had to talk the math out. So one person added something to her side of the equation. That meant that their partner had to add something to their side as well. They would each discuss what had to be done next. If one student tried to do something to one side, the other person would not do anything to their side until things were explained. It was a magical moment. So here is how I designed it.
We were doing 2 step equations in Introduction to Algebra
1. Have the students working in pairs. Have them move their desks next to each other.
2. Have one sheet of paper per pair of students.
3. Tell the student in the left desk that they are only allowed to write on the left side of the equation. Also, the person in the right desk are only allowed to write on the right side of the equation.
4. Give a question to your students that is an equation.
5. Watch your students work together to solve the problem.
6. Monitor your students to see when they might be getting done.
7. Pick a student at random to come to the board with their partner and explain the problem. The pair should bring up the paper they were working on to guide them.
8. The pair should "JUSTIFY" what they do. I like to have both students alternate talking.
Have you seen the new game called "Minute to Win It"? It is a great game. In the show there is something called the "Breakfast Scramble" where a cereal box is cut up in to 20 rectangular equal size pieces. Then they have two people working together to put the pieces back together again. Of course they have to do it in a Minute. Here is a video of the rules. While I was watching the show I thought of using my new DUAL TOUCH 800 Series SMARTBOARD. Perfect for our DUAL TOUCH SMARTBoard! Here is what I did in class. 1. I found a picture that would be easy to put back together. 2. Then I cut the problem up into 12 square pieces. (I used the screen capture tool by placing a light gray dotted grid over the picture) We did a podcast on this very topic with instructions. All you have to do is go to podcast number 81 at http://www.teachingwithsmartboard.com/ 3. I deleted the picture and scattered the 12 pieces around the page. 4. I put a timer in the corner. (optional) 5. Now I chose two students to come up to the board and UN-SCRAMBLE the picture. This was really engaging and it was fun to see people working together. Here are my students working on the new DUAL TOUCH 800 Series SMARTBoard. Today I made a problem in my Introduction to Algebra class and then cut it up into 12 pieces. I asked two students to come up and put the problem together and then solve it. The rest of the class has to wait until the problem is revealed before they could start on the rest of the problem. Check out the video below. It turned out to be a very engaging activity. I'm excited to learn more tricks with the board. This is my third day with the new board. I anticipate a lot of new FUN. Do you have a 800 Series SMARTBoard? Let me know. How are you using the dual touch feature? All the Best, Dave
I keep trying to find activities for my kinesthetic learners. This activity helped students to actually "DO" the math. There were some definite ahah moments for some of my students. I took out some pipe cleaners and handed them out to my pre-calculus class. Pipe cleaners are great for teaching transformations of graphs. Students had to physically move the graph up, down, left or right. We predicted shifts and we found multiple answers to graphs. See below.
1. Either have your student make their own scale on a piece of paper or hand out a scale for your students. 2. With the paper scale in hand, ask them to make a certain graph. I asked my students to make a y = sin x graph. They proceeded to bend the pipe cleaner into a sign wave. The graph could be a parabola, or cubic or even a line. 3. Then I asked them to shift the graph up. Explain what the new equation would be. For my class I then had them shift the graph to the left until it turned out to be the same graph as the original. They shifted it over one period. we found our new equation to be y = sin(x-2π) 4. Have them shift it left or right and predict the new equation 5. Have them move the pipe cleaner into a certain location and then ask for an equation.
6. Ask them to reflect the pipe cleaner over an axis or the origin.
Here are some of the things we graphed and explored in my pre-calculus class.
Find 5 other graphs that are equivalent to y = sin(x+2π)including at least 1 cosine graph. Find 3 other graphs including at least 2 sine graphs equivalent to y = cos(x)
I tried to reach my kinesthetic learners with this activity. Basically, the students are laying down on the floor and making right triangles. Then there is some right triangle trigonometry going on. I think it reinforced the SOHCAHTOA concept in a new way.
Here are my instructions:
1. Your group of four will make a single video of some Trig problems. 2. Each person will take a turn taking the video. (with a FLIP Video Camera) 3. The other three people will form a right triangle on the floor by laying down. Make sure you make a CLEAR right angle. When you are laying down, make sure you are in a head to feet order. 4. The person running the flip video will explain where the right angle is, and then call out a trig function and an angle like SIN of ALEX. Once the trig function is named, the person who is the Opposite side will wave and say "opposite". Then the person who is the hypotenuse will wave and say "hypotenuse". 5. Change the person who is taking the video and form another triangle with the remaining people. 6. Repeat the process for each person who is using the flip.
We watched some of the videos after they finished. I think this just further reinforced the concept. You will get the idea with the video below. This is just a clip of a 2 minute video.
What do you think should be in the list of the 13 most important Virtues for TEACHERS? It was extremely difficult for me to choose only 13. I'm sure that yours would differ. It is a good exercise for all teachers. Try it yourself and leave your 13 virtues in a comment to this post. I got the idea from Ben Franklin, who came up with 13 Virtues that we all should live by. They are at the bottom of the post.
Here are some words that were close but didn't make my list. Attitude, Caring, Compassion, Consistency, Determination, Dignity, Facilitate, Fairness, Forgiveness, Hopeful, Humility, Instruction, Intelligence, Passionate, Professionalism, Organization, Questioning, and Trust.
Ben Franklin's 13 Virtues 1.Temperance. Eat not to dullness; drink not to elevation. 2.Silence. Speak not but what may benefit others or yourself; avoid trifling conversation. 3.Order. Let all your things have their places; let each part of your business have its time. 4.Resolution. Resolve to perform what you ought; perform without fail what you resolve. 5.Frugality. Make no expense but to do good to others or yourself; i.e., waste nothing. 6.Industry. Lose no time; be always employ'd in something useful; cut off all unnecessary actions. 7.Sincerity. Use no hurtful deceit; think innocently and justly, and, if you speak, speak accordingly. 8.Justice. Wrong none by doing injuries, or omitting the benefits that are your duty. 9.Moderation. Avoid extremes; forbear resenting injuries so much as you think they deserve. 10.Cleanliness. Tolerate no uncleanliness in body, cloaths, or habitation. 11.Tranquillity. Be not disturbed at trifles, or at accidents common or unavoidable. 12.Chastity. Rarely use venery but for health or offspring, never to dullness, weakness, or the injury of your own or another's peace or reputation. 13.Humility. Imitate Jesus and Socrates.
