## Saturday, December 19, 2009

### Conics Around Our School

We have just finished studying Conic Sections in Pure Math 30. At the start of the unit I informed my Gr.12 students that, for 1 bonus mark on their unit exam, they needed to use their cellphone or digital camera to take a picture of a real life example of a conic section. Many of the students took me up on this challenge, but I was kind of disappointed. The vast majority of the students brought me a picture of a circular object. While this an example of a conic section, I was hoping for ellipses, hyperbolas and parabolas.

So, on Thursday I decided to put the student to work and actually have them find examples of every conic section. At the start of Thursday's class I told my students we were going on a scavenger hunt. This got their attention!!! I informed them that they needed to use their cellphone to collect pictures of objects around the school. They needed to find a real life example of a circle, an ellipse, a parabola and a hyperbola. Immediately one student said, " Can we half a half an hour to do this?". I informed them they had 10 minutes to collect their pictures. So, off they went. They were like little kids in a candy shop. They were so excited!!!

In under 5 minutes, every student,(there were 20 of them) had collected their real life examples. It was really amazing to see how quickly they could find real life examples of conic sections around the school. I then asked the students to e-mail me their pictures from their cellphones. Here are some of the pictures my students sent me.

My students even explained to me that they took these 2 pictures above because they were examples of degenerate hyperbolas. Cool!!!

This little extension of Conic Sections was definitely worth the 10 minutes of class time that it took!!

Try sending your students on a scavenger hunt with their cellphone. You will be really pleased with what they find.

## Tuesday, December 8, 2009

### Using Wolfram Alpha to Discover Properties of General Equation of a Conic

Today, my Pure Math 30 students, took out our department laptops and logged into Wolfram Alpha.

We were investigating the general form of an equation of a conic. Ax^2+Cy^2+Dx+Ey+F=0.

I had the students graph many different equations and observe what graph Wolfram Alpha created.

The students then had to compare the equations with their graphs and answer the following questions.

1. Describe what values you must use for A and C in order to generate a circle?

2. Describe what values you must use for A and C in order to generate an ellipse?

3. Describe what values you must use for A and C in order to generate a parabola?

4. Describe what values you must use for A and C in order to generate a hyperbola?

Wolfram Alpha made this investigation quite easy for the students. All they had to do was type the equations into Wolfram Alpha and it gave them nice, easy to read graphs.

I could have just lectured for this lesson. However, I believe that the discovery approach I used was much more powerful.

Some math teachers would say that they could have their students use their graphing calculator to do the same thing. You are right. I have had the students use a graphing calculator for this lesson before. However, I had to install a special program on the calculator for the students to complete the activity. Wolfram Alpha is accessible to all students with a computer and an Internet connection. It is a far more valuable tool than a graphing calculator. Wolfram Alpha can do so much more than a graphing calculator.

Wolfram Alpha was an awesome "TOOL" in my math classroom today.

If you have not looked at Wolfram Alpha I think every mathematics teacher should.

We were investigating the general form of an equation of a conic. Ax^2+Cy^2+Dx+Ey+F=0.

I had the students graph many different equations and observe what graph Wolfram Alpha created.

The students then had to compare the equations with their graphs and answer the following questions.

1. Describe what values you must use for A and C in order to generate a circle?

2. Describe what values you must use for A and C in order to generate an ellipse?

3. Describe what values you must use for A and C in order to generate a parabola?

4. Describe what values you must use for A and C in order to generate a hyperbola?

Wolfram Alpha made this investigation quite easy for the students. All they had to do was type the equations into Wolfram Alpha and it gave them nice, easy to read graphs.

I could have just lectured for this lesson. However, I believe that the discovery approach I used was much more powerful.

Some math teachers would say that they could have their students use their graphing calculator to do the same thing. You are right. I have had the students use a graphing calculator for this lesson before. However, I had to install a special program on the calculator for the students to complete the activity. Wolfram Alpha is accessible to all students with a computer and an Internet connection. It is a far more valuable tool than a graphing calculator. Wolfram Alpha can do so much more than a graphing calculator.

Wolfram Alpha was an awesome "TOOL" in my math classroom today.

If you have not looked at Wolfram Alpha I think every mathematics teacher should.

## Tuesday, December 1, 2009

### Assessment for Learning in Circle Geometry

I have been "dipping my toes" into the assessment for learning stream. The last couple of weeks we have been studying circle geometry in my Applied Math 20 class. The students ALWAYS struggle with this unit. It stretches their minds and really makes them use their problem solving skills. Needless to say, the students do not "like" this unit. It is hard!!!

Every semester I give a two page assignment with about 15 different circle geometry problems. In the past, I have taken this assignment in, marked it and returned it to the students. While this method gave me another mark for my mark book it really did not HELP the students to learn to solve circle geometry problems any better.

So, today, I switched things up. I gave the same assignment. However, I explained to the students that I was not taking this assignment in for marks. I explained that I wanted them to learn to solve circle geometry problems better. I asked them to solve problem #1 then bring it too me and I would mark it and discuss it with them. Then go on to problem #2 and do the same. You would have thought that the students would have grumbled that they were doing an assignment for no marks. Not one single complaint.

In this class we have had a number of discussions about how all of the work in a unit is to help them learn the material. They get the "marks" when they write their unit exam at the end of the unit. The more questions they ask and the more learning they do during the unit the better they will do on the end of unit exam.

I am struggling with the fact that I have less marks in my mark book. However, I really like the fact that my students are learning and understanding mathematics better.

Stay tuned for more adventures of the Transformed Educator!!!

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