My classes have been doing investigations (or will be doing investigations) based on ideas we have come across in the world outside the mathematics classroom. We haven't analyzed the data yet so I have no idea what it will show. I used to fear that these would be "wasted" days in the math classroom. Now I want to have more of these days. Why? I want my students to read/see something and ask questions.
"Is this true?"
"Could we prove it?"
"What would happen if...?"
My students aren't independently there yet, but I hope I can guide them there.
Current investigation 1: We looked at the Noah basketball website http://www.noahbasketball.com/optimal_arc.php
and the press it is getting http://www.youtube.com/watch?v=2FEmBY-n71Y to set up an investigation in advanced mathematics. We used flip cameras(?) to videotape students shooting 10-20 shots. We shot from the free-throw line, three-point line, and half court. Next week we will analyze the data to see if it fits the Noah site and discuss why our results match/don't match as well as drawbacks in our data collection.
Upcoming investigation 2: The math and physics involved in sledding. I need to collaborate with the physics teacher to get some equations so we know what data to collect. Now hopefully we get a fresh batch of snow soon. (It's Iowa so I'm sure I won't have to wait too long.)
I also hope to fit quadratic models into this investigation as well. Snowballs will need to be used...Oh boy, I think this will test my classroom management strategies, but I can't wait!
Saturday, January 29, 2011
Monday, January 10, 2011
My favorite math lesson
So I guess it's time to start fulfilling my "New Year's Resolution." We'll see how long it lasts. :) Basically, I want to post a weekly blog about something that is happening in my classroom. If you are a new reader, please understand that this blog was previously my location for describing my missionary experiences in West Africa and then a place to post ramblings as I transitioned back into American culture.
Enjoy :)
The Sine Function
Here is my favorite math lesson to teach and I get to cover it at VM next week! It's over the sine function and how it is created from the unit circle values. I love hands-on activities, and I had that "Aha" moment when I completed the activity the first time.
(Note: This was adopted from an NCTM article that appeared many years ago. They used cooked spaghetti. Perhaps someone has the original article and can share the link with everyone!)
Supplies: Bulletin board paper (a large piece) and pull-n-peel licorice
My preparation beforehand:
Take a large piece of bulletin board paper and draw a large set of axes. Then make a circle with the radius equal to the length of one-pull-n-peel licorice strand. Create a unit circle marking the standard points. (I usually have my students fill in the point values and the radian measurement.)
Introduce lesson by asking them how we graph functions
1. Explain sine, cosine etc are functions. Ask them why we can’t call it a function on the circle.
2. Explain to the students how the circle was made.
3. Complete the following in groups.
Pull-n-peel Trigonometry
1. For the marked points, label the angles on the circle. (Use radians)
2. Place the string along the circle with one end at 0 radians and transfer the radian marks from the circle to the string.
3. Stretch the string along the line and transfer the marks on the string to the line. The end of the string that was at 0 radians on the circle must be placed at the beginning of the line. Label all the new points with the radian measures.
4. Use the pull-n-peel (pnp) to form a right triangle on the circle. (Pretend we are using pnp instead of drawing all the triangles.)
5. Move the piece of pnp that is the vertical leg of the triangle to the line and place it perpendicular to the line at the appropriate radian measure.
6. Now make a dot on the paper at the top of the piece of pnp to show the length of the vertical leg of the right triangle.
7. Do this for all the points.
a. Remember to think about values on the axes as well as what the triangles would look like in the 3rd and 4th quadrant.
b. Also, think about all the triangles and whether you need to construct them all.
8. Show Miss Pettit what your new graph looks like. Then connect all the points.
Questions:
1. What does the graph look like? Why?
2. What would the graph look like if you used the horizontal legs of the triangle instead of the vertical ones? How do you know?
3. What concept did you use to create the scale on the x-axis?
4. What would happen if we wanted to continue the graph. What value would be at 5π/2?
At -π/2? How do you know?
5. Explain why you really only needed to make 3-6 triangles instead of 14-17.
6. Explain how the sine function is created. Be specific. It is important that you know this.
Enjoy :)
The Sine Function
Here is my favorite math lesson to teach and I get to cover it at VM next week! It's over the sine function and how it is created from the unit circle values. I love hands-on activities, and I had that "Aha" moment when I completed the activity the first time.
(Note: This was adopted from an NCTM article that appeared many years ago. They used cooked spaghetti. Perhaps someone has the original article and can share the link with everyone!)
Supplies: Bulletin board paper (a large piece) and pull-n-peel licorice
My preparation beforehand:
Take a large piece of bulletin board paper and draw a large set of axes. Then make a circle with the radius equal to the length of one-pull-n-peel licorice strand. Create a unit circle marking the standard points. (I usually have my students fill in the point values and the radian measurement.)
Introduce lesson by asking them how we graph functions
1. Explain sine, cosine etc are functions. Ask them why we can’t call it a function on the circle.
2. Explain to the students how the circle was made.
3. Complete the following in groups.
Pull-n-peel Trigonometry
1. For the marked points, label the angles on the circle. (Use radians)
2. Place the string along the circle with one end at 0 radians and transfer the radian marks from the circle to the string.
3. Stretch the string along the line and transfer the marks on the string to the line. The end of the string that was at 0 radians on the circle must be placed at the beginning of the line. Label all the new points with the radian measures.
4. Use the pull-n-peel (pnp) to form a right triangle on the circle. (Pretend we are using pnp instead of drawing all the triangles.)
5. Move the piece of pnp that is the vertical leg of the triangle to the line and place it perpendicular to the line at the appropriate radian measure.
6. Now make a dot on the paper at the top of the piece of pnp to show the length of the vertical leg of the right triangle.
7. Do this for all the points.
a. Remember to think about values on the axes as well as what the triangles would look like in the 3rd and 4th quadrant.
b. Also, think about all the triangles and whether you need to construct them all.
8. Show Miss Pettit what your new graph looks like. Then connect all the points.
Questions:
1. What does the graph look like? Why?
2. What would the graph look like if you used the horizontal legs of the triangle instead of the vertical ones? How do you know?
3. What concept did you use to create the scale on the x-axis?
4. What would happen if we wanted to continue the graph. What value would be at 5π/2?
At -π/2? How do you know?
5. Explain why you really only needed to make 3-6 triangles instead of 14-17.
6. Explain how the sine function is created. Be specific. It is important that you know this.
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