Guitar

guitar
Originally uploaded by tkaminski.

I have been really impressed with the real life photos of circles that have been submitted so far. In this photo of a guitar what particular part of a circle do the strings represent?

Circle Geometry Site

So, we have spent the last week investigating circle geometry using Geometer's Sketchpad. We have looked at chords, inscribed and central angles as well as tangent lines.

There is a fellow by the name of Ron Blond (a former Alberta teacher) that has developed a number of very interesting applets to help summarize what we have learned about circle geometry. Check out his site. It will be very useful in helping you quickly review what we have learned.

P.S. Have you made your one page sheet summarizing all of the properties we have learned?? Remember you get to use this on your exam next week. If you have not started this summary sheet you need to have it completed for Monday. It will be very helpful in completing your assignment on Monday.

Cheers!!! Have a great weekend.

Steering Wheel

Steering Wheel
Originally uploaded by tkaminski.

Here is the latest real world picture of a circle. I hope Matt didn't take this picture while he was driving!!!!

Real World Pictures of Circles

Some of you have submitted real world pictures of circles to obtain your bonus mark on your next exam. What about the rest of you?? This is a great opportunity to exert a little bit of effort and impress me!!!! Find those really cool pictures and get them in to me.

Terminology

Today you need to find the definition for a Cyclic Quadrilateral. Our Math Dictionary does not have one. So, head out on to the Web and see what you can find!!

Inscribed and Central Angles

Here we are, the second day of circle geometry. Before we start our Geometer's Sketchpad investigations we need to define some more terms. Please use the Math Dictionary to write definitions in your notes for the following terms:

Inscribed Angle
Central Angle

Sometimes drawing a picture helps make your definition absolutely clear.

Do not forget about the challenge to find pictures of circles in real life and submit them for a bonus mark!!!!!

Daily Math Puzzle

Most of you have probably seen or maybe even try to complete the daily crossword puzzle in the Edmonton Journal. Now, if you are good with words (which are not my strong point) you probably quite enjoy completing crossword puzzles. Since I am good with numbers I prefer number related problems.

Yesterday I was sitting in my backyard enjoying the shade of my favorite tree reading the newspaper. There was an article about a number puzzle called Sudoku. Here is how Sudoku works:

You are given a 9 x 9 grid. The object is to fill in the grid so that every row, every column and every 3 x 3 box contains the digits 1 through 9. Sounds easy!!!! Well, I thought I would give it a try. I am hooked!!! I can't put down these puzzles until I solve them.

For a more detailed and pictorial explanantion of Sudoku check out this site.
If you get hooked on Sudoku and would like a new puzzle each day visit The Times of London website where they publish a new Sudoku puzzle each day.

Give Sudoku a try. I think you will like it.

Circles: Brondby, Denmark

Brondby, Denmark
Originally uploaded by tkaminski.

Is this a cool picture or what!!!! thanks for sharing this Chad.

Stonehenge

stonehenge.jpg
Originally uploaded by tkaminski.

Here is the first contribution of circles in the real world by one of your classmates. It is an artist's drawing of stonehenge.

Do you see any mathematical symbols in this picture??

Circle Terminology

Big Wheel
Originally uploaded by natalieb.

Before we start using Geometer's Sketchpad to investigate properties of circles we need to define some parts of the circle. Using the Math Dictionary link in our blog define the following terms:

Circle
Radius
Diameter
Chord

Mark sure to write these definitions in your notebook. You may even want to draw a diagram to help illustrate these parts of a circle.


This picture of a bicycle wheel illustrates some of the parts of a circle.

Challenge: The long weekend is before us. Anyone who brings in or e-mails me a picture of a real world example of circles receives a bonus mark on their next exam. Make sure that you can explain to me where this picture was taken, ie. the city or town, the building location etc... Wouldn't it be cool to post these to our blog!!!!!

Circle Geometry

church rosetta window
Originally uploaded by lunaryuna.

Tomorrow we start studying circle geometry. Many students always wonder where in the world circle geometry is ever seen or used. So, here is a Math Trail about circle geometry created by some teachers in Saskatchewan. It does an excellent job of illustating where in the world circles appear and are used.

Enjoy!!!!!

P.S. If you are no sure what a Math Trail is. Check out this video.

Does Blogging work??

It has been a couple of weeks since my last post. Things have gotten busy in the trenches. Even though I have not posted to the blog for 2 weeks not one of my students has complained about this. This really concerns me. I started this blog to help my Pure Math 20 students. I wanted to provide them with additional resources for the course.

If my students are not using my blog should I keep creating it?

Why wouldn't my students want to use these additional resources?

Maybe the content I am providing is of no use to them?

I have many questions that I need to answer for myself and for my students. I guess part of my class on Monday will be to talk to my students about the blog and try to get answers to my questions.

It concerns me that I think blogs are of incredible benefit to my students and they do not. I do not think they realize what they are missing out on if they are not blogging. I have to get them hooked on blogs some how!!!!

Linear Inequalities

We learned how to graph linear inequalities by hand and using our graphing calculator. Here is a gizmo to help you test yourself on whether or not you understand this concept. There is a second gizmo that you may like better.

I have a blogging prompt for you also. I would like you to answer this prompt by commenting here at the blog.

Blogging Prompt:
We have been using the mini-white boards for a couple of weeks now. Do you like using them? Are they helping you to learn? What ways to you think we could be using them better or differently?

Have a great weekend!!!!

Solving Systems of Equations Using Elimination and Substitution

We have learned two algebraic methods of solving systems of equations. The yesterday we learned the method of elimination or addition and subtraction. Today we learned the method of substitution. For a detailed explanation of each of these methods you can visit this site.

Then if you want more practice on elimination go to the sparknotes site. There is also more practice for substitution at sparknotes.

Have a great weekend and don't forget to watch Numb3ers.

Solving Systems of Equations Graphically

So today we started working in partners. How did you like your partner? How do you like using the whiteboards? Let me know if there are things I could improve on.

I have links to a couple of sites that have questions and answers related to solving systems of equations graphically.

The first site is Sparknotes. It is a site I will be using for this entire unit.

The second site is a website set up to practice for the Regents exam. It is an exam something like our diploma exam.

Preparing for Tuesday's Exam

Yes, that is right!!!! We have a unit exam this Tuesday on Ch.4 on Equations and Inequalities. Do not forget to check back at the links I have provided over the past 2 weeks. Some of the sites I have suggested contain online quizzes to test your knowledge of the material in this unit.

If I get my act together I may even have an online quiz up by tomorrow that will help you study.

Polynomial Inequalities

The following link shows a couple more examples of how to solve a polynomial inequality. For some of your seeing some more examples might help.

This second link shows how to solve polynomial inequalities graphically as well as using test intervals.

Zeros of Polynomial Functions

We are learning about how to determine all of the real zeros of a polynomial function. You can take a quiz to see how you are doing in this area.

Go to topic 16 at the following site and there are 5 questions you can test yourself on related to determining the zeros of polynomial functions.

Remainder Theorem and Synthetic Division

Today we learned about Remainder Theorem, Factor Theorem and Synthetic Division.
Use these links to review what we discussed in class.

This Synthetic Division link also contains some quiz questions on synthetic division as well.

Remeber that understanding synthetic division will really help simplify your life in higher mathematics!!!!

Quadratic Formula

Today we discussed the quadratic formula. We looked at how it lets us determine the exact value of the x-intercepts of a quardatic function.

For a summary of what we learned check out this link.

There is also a really good explanation on how the quadratic formula was derived using completing the square. This link talks about the history behind the quadratic formula and who was the first mathematician to use the formula.

Trivia question

For those of you that watched Numb3ers last night you might have seen this.

If you take a single piece of paper and fold it in half you have 2 layers. If you fold it in half again you have 4 layers. This represents a geometric progression.

2^1 = 2 layers
2^2 = 4 layers.

If you could fold the paper in half 50 times, how high would it reach?

What is the world record for the number of times a piece of paper can be folded in half?

If you find the answers to these questions I think you might be surprised!!!!!