8.4 has a nice investigation where students break a regular polygon up into triangles, and find the area of each triangle, then multiply this area by the number of sides. Interesting how the number of triangles and the number of sides are the same, eh?
I started this by asking the students to try the Investigation as homework. It is my hope that some of them will notice the pattern on their own and better understand the formula. Only a few students seam to have made an attempt at the homework, but the people who have tried seamed to do well on it.
In class we looked at a regular polygon inscribed in a circle and looked at how as we add more sides to the polygon it is becoming more like a circle. I am trying to prepare students for tomorrow's area formula.
Tuesday, February 26, 2008
8.3 Area Problems
8.3 Brings together all the area formulas we have found so far. And it is bringing them together in word problems. I am used this lesson to go over how to approach word problems.
1: Read the problem carefully
2: Draw a picture and label the apropriate parts
3: Think of what equations might help with solving this problem
4: Fill the equations with the parts from the picture and solve
I would like to come up with a nice concise way of explaining word problems for my Geometry students. Any help would be appreciated.
1: Read the problem carefully
2: Draw a picture and label the apropriate parts
3: Think of what equations might help with solving this problem
4: Fill the equations with the parts from the picture and solve
I would like to come up with a nice concise way of explaining word problems for my Geometry students. Any help would be appreciated.
8.2 Areas of Triangles, Trapezoids, and Kites
Three more shapes come to join our area finding party.
As I worked through these problems it became apparent to me that students need to understand how to set up problems and solve for a variety of quantities. I like these problems because they require students to pull out their old algebra hats, dust them off, and get a little dirty working out these problems. It was a fun time for me, not sure if the students appreciated this as much as I did.
As I worked through these problems it became apparent to me that students need to understand how to set up problems and solve for a variety of quantities. I like these problems because they require students to pull out their old algebra hats, dust them off, and get a little dirty working out these problems. It was a fun time for me, not sure if the students appreciated this as much as I did.
8.1 Areas of Rectangles and Parallelograms
In this chapter students are visited by an old friend, the area of a rectangle. Something students should know from early days of multiplication. But a new friend comes to join the party, the parallelogram hangs out to mix things up a bit.
The parallelogram and the rectangle have the same area formula: A = bh
I tried to look at two reasons why this is true.
The first uses translations, just like we did last unit with tessellations. We can translate part of a parallelogram to make a rectangle, by translating a triangle. This doesn't work as easily for some parallelograms, so another idea is important to look at.
I looked at skewing a parallelogram. I showed this by looking at a stack of calculators, when I skew the stack the area stays the same. The same thing would be true if I skewed a stack of paper. I like this idea because it starts a more calculus based way of thinking.
I'd like to hear more thoughts on this.
The parallelogram and the rectangle have the same area formula: A = bh
I tried to look at two reasons why this is true.
The first uses translations, just like we did last unit with tessellations. We can translate part of a parallelogram to make a rectangle, by translating a triangle. This doesn't work as easily for some parallelograms, so another idea is important to look at.
I looked at skewing a parallelogram. I showed this by looking at a stack of calculators, when I skew the stack the area stays the same. The same thing would be true if I skewed a stack of paper. I like this idea because it starts a more calculus based way of thinking.
I'd like to hear more thoughts on this.
Wednesday, February 20, 2008
Tessellation Packet
This semester we have been using a homemade Tessellation packet instead of chapter 7 in the book. I am going to summarize everything from that packet into a single post, please comment if you would like to add comments to what I have.
I think that Tessellations are a great way to learn about math. There are a few things I wish I would have done differently.
First I wish I would have looked at this as more of an Art Unit. Great art is born under constraint, or at least that is what I heard some rock and roll group say on the radio one day. With tessellations we are constrained to the operations on tessellating shapes. The next time I teach tessellations I would like to challenge my students to think more creatively about the subject. I think I had too much of a cut and paste approach, until the final project the students were never asked to create their own tessellation.
Second, I would like to increase the math content I use in my discussion. While I did discuss vectors briefly I found that I didn't go in depth because little was asked of the students in the packet. Tessellations would be a good topic to lead into, or follow a discussion on transformations acting on points in a coordinate plane.
I'm still waiting for my final projects to come in, and when I have some pictures I will try and post them.
Cheers,
Mr. Sevre
I think that Tessellations are a great way to learn about math. There are a few things I wish I would have done differently.
First I wish I would have looked at this as more of an Art Unit. Great art is born under constraint, or at least that is what I heard some rock and roll group say on the radio one day. With tessellations we are constrained to the operations on tessellating shapes. The next time I teach tessellations I would like to challenge my students to think more creatively about the subject. I think I had too much of a cut and paste approach, until the final project the students were never asked to create their own tessellation.
Second, I would like to increase the math content I use in my discussion. While I did discuss vectors briefly I found that I didn't go in depth because little was asked of the students in the packet. Tessellations would be a good topic to lead into, or follow a discussion on transformations acting on points in a coordinate plane.
I'm still waiting for my final projects to come in, and when I have some pictures I will try and post them.
Cheers,
Mr. Sevre
Friday, February 15, 2008
What I'm Doing Here
Hello!
I am Mr. Sevre, a math teacher at Roosevelt High School in South Minneapolis. I am creating this blog to share my thoughts on what I am teaching with other math teachers. By posting my reflections here it is my hope that these ideas will be easily accessible in the future. I am hoping to use these in the future, and I hope that other teachers find this useful as well. If you happen to find your way to this blog and find it useful please let me know, this will help motivate me to be diligent about my blogging.
This Semester I am teaching geometry from the Discovering Geometry text. If you want to know more about the book check out the site: http://www.keypress.com/x5233.xml
I promise to do my best to post everyday and have an active blog of geometry topics!
I am Mr. Sevre, a math teacher at Roosevelt High School in South Minneapolis. I am creating this blog to share my thoughts on what I am teaching with other math teachers. By posting my reflections here it is my hope that these ideas will be easily accessible in the future. I am hoping to use these in the future, and I hope that other teachers find this useful as well. If you happen to find your way to this blog and find it useful please let me know, this will help motivate me to be diligent about my blogging.
This Semester I am teaching geometry from the Discovering Geometry text. If you want to know more about the book check out the site: http://www.keypress.com/x5233.xml
I promise to do my best to post everyday and have an active blog of geometry topics!