This video demonstrates students plotting polar coordinates by actually moving their feet. It's just another way to move and learn. When you physically plot the point with your feet it cements the process in your mind. Use blue masking tape on the ground and plot some points with your students. It's as easy as that.
The students are plotting the point (3, 150 degrees) on the ground. They found out another way to plot it was (3, -210 degrees)
I would you encourage you to buy some blue tape and plot ANY type of point or graph with FEET! You will be amazed at the retention that your students will have.
Pick a question that you asked today in class. Try to reverse the question. Make the answer the question and the question the answer. You might notice the question might be a lot more open ended? Is it a higher level question than your original? So next time you are making a worksheet, reverse a few of your questions and mix them in along side some of your original type questions. Then see if your worksheet has a better mix of conceptual and procedural questions.
Examples
Geometry: Original Question: What is the area of this parallelogram given the height is 4 cm and the base is 10 cm? Reversed Question: Find the base and height of a parallelogram given the area is 40 square cm.
Algebra: Original Question: Solve this equation 5x + 10 = 30 Reversed Question: Find a two step equation that has a solution of x = 4.
Precalculus: Original Question: What is sin (30 degrees)? Reversed Question: Sin of what degree value(s) give an answer of .5?
Here is a cool site full of examples from a class using Desmos http://padlet.com/wall/rvkica26qi
Here is one of those examples. Click on it to make it interactive.
This is one of the "spokes" of the Student Engagement Wheel. The Student Engagement Wheel is show below. Use the Student Engagement Wheel to help you measure the student engagement in your class.
This is one of the "spokes" of the Student Engagement Wheel. The Student Engagement Wheel is show below. Use the Student Engagement Wheel to help you measure the student engagement in your class.
I have always had trouble with teaching the Ambiguous Case. It seemed that whatever I did, the explanation was not good enough. The kids came out of my class with their heads exploding with all the things they had to remember. A couple colleagues and I created a hands-on activity that really explores the heart of the ambiguous case and the Law of Sines SSA example. After going through this lesson, I really feel like the students had a grasp on the ambiguous case conceptually. My work is not finished, because I have to now finish the procedural process and we should be good.. The first video is the explanation of the original challenge. The second and third videos where students explain their partial and full answers.
Triangle Challenge Rules and Guidelines SMARTBoard Notebook LessonPDF Lesson
1. Use one pipe cleaner that is 8 inches long (light colored) and put it as side two
2. Angle A is exactly 30 degrees.
3. Side one is a second pipe cleaner (darker color) and starts at 12 inches long. It can be shortened by 1 inch increments.
4. Create as many triangles as you can using the above restrictions.
5. Hint: There are more than 10 solutions.
Here is a Grocery Store problem. I went to the store and video taped all the different Gatorade options. (And yes, I did get some looks at the store) My student's will have to decide which is the best deal. I want my students to try to use problem solving skills to get at the best deal. I want them to struggle a little bit with the complexity of the problem. They will somehow need to get all of the 5 different options on the same unit measure playing field. I have given a couple of answers below. I was looking for students to justify their work with equations, diagrams or graphs. They are not bound by any particular method. However, they must show their work and give their answer in complete sentences. In the video their is an example of what kind of work I expect. I debated on whether to include this. My end thinking was that I wanted them to see that their needed to be some work shown and a complete sentence answer. So I showed them a couple of solutions in the video. But the exemplar solutions are NOT in the worksheet.
Of course I loved the traditional approach of figuring out the price per oz. However, if you notice she also write that the Large Can was equal to 3 of the Smaller cans. (24qts = 3(8qrts)) I love it.
This was a different student's paper. This was another favorite answer because she wrote a diagram of two of the smaller bottles equaling the larger bottle.
All this really makes me realize how different we think. I have to get myself out of teaching a certain method and saying that is the only way to do it. It just is not right. Think of your choice of cars. Why are there so many cars choices out there? It is because we all are different and like different things. In math, it is the same way. The plain and simple truth is that understanding our method of choice thoroughly first, then branching out to understanding other answer methods will benefit us. I know I will forever be learning how to teach better. This is exciting and daunting at the same time. I will keep on trying to get better.
