Two Grand Question

(You are not required to write a new post about this.)

I hope the field trip is an eye-opening experience. The Two Grand Question is doable than some other questions. I enourage you to try it. Let me know you did it before Tuesday and you win two small chocolates from Mr. Cheng!

Here is the question:
3 identical circles with radius r are touching (tangent) each other and inscribed in a larger circle as shown. What is the radius of the large circle in terms of r?


To solve this question, you need to use:
1) symmetry to draw triangles to help you find large radius
2) sin 30 degree = 1/2 = opp/hyp
3) Pythagorean Theorem

Math Field Trip Oct 21, 2010

"Who Wants to Be a Mathematician?"

I hope you have a wonderful experience with our first ever Math field trip! You are going to write a reflection about the experience. Here is The Assignment:

1) Write 10 new things you've learned about mathematics

2) What have you learned from The Talk?

3) How does The Workshop help you in future math learning?

Enjoy blogging. Save your posting from time to time.

Hyperframe - Shockwave game

Here is my highest score. Now is your turn! Go here:

http://www.shockwave.com/gamelanding/hyperframe.jsp

What does it mean to be good in math?

Pick top 3 qualities from the list below you think are most important in math learning. Explain.

Qualities for good math?
- hard working (diligent)
- patience
- think outside the box
- never give up - perseverence
- go Kumon (practice, repetition)
- basic math skills
- intelligence
- focus
- optimistic
- confidence
- good memory
- don't afraid to ask alot of questions
- willing to learn
- be able to think abstractly
- quick thinking
- follow through
- team work
- always double check your work
- humble

Mar 5 and Spring Break

As of Mar 5, you have added another posting about the 2006 Math Contest, the one given to you in the last two classes before spring break.

Over the spring break:
1) Complete all the postings. I will be commenting on your posting and give you a mark. Let me know if you make any changes after I assigned a mark.
2) To keep your brain running, work on the Practice Unit Test package I gave you before the break. They are good Prov. Exam. type of questions. Do the "Arithmetic Sequence" and "Radical/Exponents" section. The "Table and Sequence" section is no longer required by the exam, but you can do it anyway.

Hope you have a great Spring Break.

2010 Canadian Math Contests

We did it! Let's reflect on your experience. How do you feel? Did the pressure help you focused or make you anxious? How is your performance throughout the 60 minutes period (at the beginning, in the middle, near the end)? Do you guess any questions? How do you feel after you are done? When we went over the question? I hope you enjoy the challenge.

After you reflected on your experience, pick 1 question and talk about it.

Here are the answers for the contests (official):

Grade 10 Cayley
===============
1D 2C 3A 4E 5B 6E 7D 8B 9C 10B
11A 12E 13D 14C 15C 16B 17D 18E 19A 20C
21A 22C 23B 24A 25D

Grade 9 Pascal
===============
1D 2C 3C 4A 5C 6E 7B 8E 9B 10E
11E 12C 13B 14B 15D 16B 17A 18C 19A 20B
21D 22D 23A 24C 25E

Solving Radical Expression

For this posting, I want you to explain how to solve rational expression with negative or fractional exponent. If you don't have Word 2007 Equation Editor, just explain how to do it. I did the first one for you as an example. You can pick either the second or third.



1) I resolve the negative exponent x^-2 by flipping it to the top
2) Distribute the exponent 3/2 to all components
3) 3/2 means cube and then square root, so 16^(3/2)=64, 25^(3/2)=125
4) for the x term, power on power, so I multiply 3 with 3/2 to get 9/2
5) write x as a radical and simplify
Done!

Problem Set #2

Just like last time. Choose 1 of your favorite questions and write something about it.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.

My Pick: What is the largest x value that will satisfy the following inequality?

This question seems impossible at first because 3^500 is too big for the calculator to handle. To solve for x, first take 200th root for both sides! No one will ever take 200th root of a number in real life, but the principles of math work for both small and large numbers. Take 200th root is same as raise it to the power of 1/200 (this is what we just learned!!). And exponent law says power on power is to multiple the power. 3^(500/200) or simplier 3^(5/2) is something the calculator will accept. The largest x is 15.

I learned that big numbers are not scary because math principles work the same no matter how big or small the numbers are.

Problem Set #1

Choose 1 of your favorite questions and write something about it.
Ideas:
Explain how you solve it.
Why do you like this question?
What have you learned about the process of problem solving.
Have fun.

This one is my favorite. Find c.

I first tried to solve this system of equations by working backward, substitute each answer into the system to see which answer works. I found the answer but it takes a while. This question can be easily solved by adding the second and third equations together:

The interesting discovery is that we can substitute (a+b) by 3 without knowing what a and b are. System of equations is a topic in Math 11, but it doesn't mean we need to wait til grade 11 to understand it.

Tower of Hanoi

Describe the strategy and the formula for the puzzle Tower of Hanoi.

Embed a screen shot of the completed puzzle with 5 dics.