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.

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.

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!!!

Tweet Cloud

Everyone using twitter should check out Tweet Cloud

Here is a tweet cloud of my twitter posts for the past year.

Nominations for Edublog Awards 2009

My Nominations for The 2009 Edublog Awards are:

Best individual blog: Thinking in Mind - Neil Stephenson
Best individual tweeter: Dean Shareski @shareski
Best resource sharing blog: Free Technology for Teachers
Best educational use of video / visual: dy/dan - Dan Meyer
Lifetime achievement: David Warlick - 2 cents Worth

Make sure to submit your nominations for The 2009 Edublog Awards

Using Wolfram Alpha in Math Class

Yesterday we were studying Solving Systems of Equations using Elimination Method with my Pure Math 20's. We had solved a few problems together on the board. Then I said, " I want to show you Wolfram Alpha". So, I walked over to my computer, went to Wolfram Alpha and typed in the same 2 equations we had just solved. Voila!!! Here is what Wolfram Alpha spit out at us.


In less than 2 seconds we had the answer to the question. I then asked my students, "How could you use Wolfram Alpha to help you with your homework?". They thought about it for a second. One student said, "Well I can just type every question into Wolfram Alpha and get the answer. My homework would be done in 5 minutes!!" I reminded the students that Wolfram Alpha ONLY gives the answer. It DOES NOT show us all of the work to arrive at the solution.

I then talked to my students about how Wolfram Alpha let's me ask them "different" questions. Things like, "Explain what the solution (-1, 4) means in this problem." This is a much deeper question and shows their understanding of the problem.

I informed the students that I recently read that every high school student in Denmark was going to be allowed to use a computer with Internet access on ALL of their final exams. This really got the discussion going!!! We talked about how their would be NO multiple choice questions. The students would have the ability to "collaborate" during an exam. Wow!!! Different way of thinking about education.

I asked my students to imagine what it would be like if every one of them had a laptop for every class at school and how that would change the way they learned. They really started to get excited.

I informed my students that I am thinking of wheeling a cart of laptops into class and turning them loose on the students. I also informed them that I am thinking of giving them a unit exam where they all have computers and Internet access. One student said,"Please do not do that. We will have to think a lot harder on an exam like that!". She really gets it.

Yesterday's discussion really opened the doors in my mind and in my students minds about how the world we know could be very different.

Stay tuned to find out what happens!!!

Catapult Project Day 2

Today we finished off the catapult project by having each group fire their catapult from the top of a desk instead of flat along the floor. The students had to modify their original equation to factor in the height of the desk. Then they had to use their new equation to predict where a target should be placed on the floor. Part of their grade was based on how close they came to hitting a bullseye!!!

I had one group hit the bullseye dead centre. Most of the groups were within about 15 cm of the bullseye.

We ustreamed the final catapult firings so that anyone that wanted to watch was able to.

Thanks to Jared Nichol and Neil Stephenson for following along and chatting during the ustream. My students thought that was quite cool!!

I have also created an excel spreadsheet to help grade this project.

You can obtain the description of the actual project and the rubric from yesterday's post.

Catapult Project

Today my Pure Math 20 class carried out the catapult project. I have been waiting for this day for 2 weeks. Ever since I built the catapults I have been excited to see how the project would play out for a whole class. I broke my class of 30 students down into groups of 3, handed out the project to them and gave them some guiding words on collecting their data.

My first words of wisdom were practice, practice, practice the firing of the catapult before you ever collect data.

The students took my words of advice and did an awesome job of carrying out the project. Some groups even realized once they started trying to calculate the equation of the flight path of their marble that their data was not good enough. So, they redid the data collection!!! Wow, most students would have just given up.

We ran out of time to finish the project today. So tomorrow, the students will use their equations to predict where they should place a target on the floor. Then we will see how good their math calculations really are!!!! I plan to ustream the event tomorrow at approx. 10:30 a.m. mountain time. I will tweet the url for the ustream. You can follow me on twitter at kaminskiterry.

Here is a video of one group collecting data.

Check out more pictures here on flickr.

I have posted the detailed handout for the project.

I have also posted the scoring rubric I am using for the project.

I have to thank Sean Sweeney for sharing this project over at his blog. It is because of his sharing that my students are getting to enjoy a truly awesome mathematical experience. Thanks Sean.

M&M Catapult

Last weekend I came across an M&M catapult project on Sean Sweeney's blog. This really got me excited because I was just starting to teach the unit on Quadratic Functions with my Gr.11 Math 20 Pure students.

I read and reread Sean's blog post this past week. Last night I made a list of materials I needed to construct these catapults for my class. Today I built 10 of these awesome little devices.




The building of the first catapult took a little bit of time. After I constructed the first catapult I then tested it to see how well it worked. I was getting distances of between 2 and 3 feet with the catapult. Not bad, I thought, this will be good for a classroom setting.

After the first catapult was built and tested I changed a few things to speed up production. I had used wood glue to build the first catapult. While it holds well it takes a while to dry. On my wife's suggestion, I used her crafting glue gun to construct the second catapult. What a difference!!! The next 9 catapults went together in no time flat.

I can hardly wait to have my students work on this M&M catapult project. I think they are going to love it!!!

Hurry Up and Wait!!!

We have just finished the first 3 weeks in our new high school. For the most part the start up of the new school has gone off without a hitch. However, the technology end of things is still in chaos. It started with not having Internet access because Telus was not coming to hook up our SuperNet connection until Sept.3. We would have to live without the Internet for awhile. This required ALL of us to think how we used to do things before we had the Internet and e-mail. Back to typing memos, printing them and photocopying them to distribute to staff members. We eventually received access to the Internet and that portion of our lives has returned to normal.

We are suppose to have 120 laptops on carts to use with students. At present not one of those laptops is in a cart and useable by students. How are teachers suppose to integrate technology into their classrooms when the computers are not even available?

Last May and June we tested some wireless networking at our old high school and determined that 20 concurrent users on one wireless router was about all the router could handle. Then users started dropping off of the wireless network. At that point, we informed our district IT people that they needed to install 2 wireless routers per classroom to ensure a class of 30 students could all access the wireless network at the same time. I thought they understood. However, it turns out they only installed one wireless router in each classroom and, guess what, the 2 classrooms where we are currently testing the wireless network are having issues. Once more than 20 students try to access the network computers start dropping off of the network. It would have been nice if our IT guys had just followed our advice from the start.

Then there is our 1-to-1 laptop program for our Gr.9's. With all of the network and wireless issues that the IT people have been dealing with, the 120 laptops for our Gr.9's are no where ready to distribute. We have not done any training with our Gr.9's yet because we need the carts of laptops to do this. It is going to be many weeks before these Gr.9s receive their laptops.

I know that opening a new school has its trails and tribulations. However, when we are trying to prepare our students for the 21st Century it just feels like we are being told "Hurry up and wait!!!"

New Way of Presenting Course Information

Yesterday, I was able to meet with all of the students in each of my courses for 30 minutes. In the past I would have handed out a course outline to them, talked AT them for who knows how long and bored them to tears!!!

Yesterday, I changed things. Instead of talking AT them I created a Keynote presentation that contained the key points I wanted the students to know. I placed some music in the background of the presentation and I had the students "READ". I also placed some interesting pictures in the presentation to help jazz it up.

Thanks to Darren Kuropatwa for sharing his "First Day" presentation. I have borrowed a lot of information from his presentation and mashed it up to my liking.

While my students were "watching and reading" the presentation I looked around the room and noticed that they were all engaged. I hope my first day with them was better than they experienced in their other classes.

You can view my "First Day" slideshow here.

First Day of Classes

Today marked the first official day of classes at Cold Lake High School. A number of our staff planned a much "different" first day for our students. It started off with all of our students meeting with their teacher adviser for one hour in their TAG (Teacher Adviser Group). Since we were opening a new school today and TAG was a new thing at our school there was lots to talk about in that first hour.

The second hour of the day were grade level assemblies led by each of our administrators. This where the students heard about all of the rules, procedures etc.. for Cold Lake High School.

From 11 a.m. until 1 p.m. the students returned to their TAG and were given a tour of the school, received lunch (free), had time to socialize and walk through the displays that highlighted the teams and clubs at our school.

From 1 p.m. until 3:20 p.m. The students attended 30 minutes of each of their 4 classes where their teachers had a short period of time to meet with them and discuss their courses.

The day blew by pretty quickly. Before we knew it 3:25 p.m. had arrived and the students were on the bus home.

The kids LOVE the new school. Let's hope that, as teachers, we are able to instill a LOVE of learning in them during the 2009-2010 school year.

The Beginning

About a week ago our staff was allowed to physically enter our new high school, Cold Lake High School. At that point, most of us began unpacking boxes, thinking about how to arrange our desks in our new classrooms (It took me 4 different arrangements before I was happy)and beginning the new school year in a totally new environment.
The transformation for me is not only the fact that I will be teaching in a new building but that I will now have access to a cart of laptops to use with my math students and a fully wireless network to use with those laptops. I will be trying many different things with my students. Some of them will fail miserably but I hope, at least some of them, will work out truly spectacularly. As I begin this new school year I am a little anxious because I am going to be traveling down a path that is new to me. However, I am excited because I truly believe that the changes I will be attempting to make will engage my students more and help them learn and understand mathematics better. No matter how uncomfortable I am, if my students end up happier and better educated I am all for it!!! I hope that you will leave me comments related to my blog postings so that we can make this journey of change together. There will be days I will need your help and encouragement and other days I want to "blow my own horn" because I have just delivered the most kick ass lesson of the week. So the journey begins.

**The pictures are from my new classroom at Cold Lake HS.