www.IGoogle.com Math Challenge Widget

Hi guys if you still take a look here and there at this blog! There is a cool math widget on the igoogle site if you have a google account, and use Igoogle as your homepage, you can search for "math" or "nick's math" and you will get great challenge problems to play with. I have been having fun playing with the following one...

Puzzle 159: Eight odd squares
Lagrange's Four-Square Theorem states that every positive integer can be written as the sum of at most four squares. For example, 6 = 2^2 + 1^2 + 1^2 is the sum of three squares. Given this theorem, prove that any positive multiple of 8 can be written as the sum of eight odd squares. 


...I can prove that every odd square is a multiple of 8 +1, and show a few initial cases of odd squares adding up to consecutive multiples of 8, but still working on how to prove that every multiple of 8 can be written as the sum of eight odd squares. 


Feel free to give it a try and show me what you have gotten! 

Goodbye Grade 10 and 11 IRHS Mathies!

For those who like to take a look at this blog, I will try to add challenges here and there for you to try! Feel free to post comments or suggestions of things you would like to see on here if you really enjoy it! As you get into 11th and 12th grade math and beyond, please do use me as a resource for you when you need some guidance!

I will miss all you guys at IRHS and I wish you all success and happiness in your future endeavors! Sad to leave, but happy to have been a stepping stone on your learning journeys (corny I know, but true!)

Thank you

Sine Wave Art!

Amazing Pendulum Wave Video

New Challenge!! Triangle Area Ratios

What is the Relationship between Triangles? 
In triangle ABC, segment AG from vertex A meets opposite side BC at a point G, with the length of CG 1/3 the length of BC. That is, point G is located 1/3 of the way along segment BC from C. Similarly, points E and F are located at 1/3 marks along the other two sides of triangle ABC. The intersections of these segments are the vertices of another triangle, IJH, in the interior of triangle ABC.
What is the relationship between the areas of triangles ABC and IJH?

Factory Balls: Best logic game ever

Note to self: Don't start this unless you have time to spare! It's as addicting as Snood once was

http://hoodamath.com/games/factoryballs2.php

Learning to Add

How many plus signs should we put between the digits 

987654321 

to get a total of 99, and where? 

(For those who get hooked on this problem: There are two solutions. To find even one is not easy, but the experience will help you put plus signs within 

123456789 

to get a total of 100.)

Logic Manipulatives

• http://nlvm.usu.edu/en/nav/frames_asid_118_g_4_t_2.html
• http://nlvm.usu.edu/en/nav/frames_asid_139_g_4_t_2.html
• http://nlvm.usu.edu/en/nav/frames_asid_182_g_4_t_2.html

Challenge: Unknown Averages Problem

In April 1998, the basketball players Michael Jordan and Shaquille (Shaq) O’Neal were vying for the season individual scoring title until the last game of the season. The scoring title is won by the player with the highest average of points per game, calculated by dividing the total number of points by the number of games the player has played. (Customarily, averages are rounded to the nearest tenth.)

Before the last game, Jordan had scored 2,313 points in 81 games and Shaq had scored 1,666 points in 59 games. No on else has a chance to win the title. 

1. Given the above information, what are all the possible outcomes?
2. What are the critical point totals in terms of a change in outcomes?
3. If Jordan scores more points in the last game than Shaq, will he necessarily win?
4. If Shaq scores more points in the last game than Jordan, will he necessarily win? 

Solve algebraically and graphically. How does one representation inform the other?

Grade 10: Classifying Quadrilaterals Venn

Where Parallelograms have 2 sets of parallel sides, Trapezoids only have 1 set.
Rectangles have perpendicular adjacent sides, Rhombuses have sides of equal lengths.
Squares have both! There are also Isosceles Trapezoids, where the non-parallel sides have
equal lengths!

Problem-Solving Cycle: Tool to Use!

Challenge Problem

Circles A, B, P, and Q are all inscribed (within) and tangent (touch at one point) to circle T. The Radii of Circles A, B, and T respectively are 2, 1, and 3. What are the Radii of Circles P and Q if they are tangent to circles A, B and T?

A Must Read Article!

ARTICLE: Debt, Key Lime Pie & Willpower (Click Link to Read)

The Marshmellow Experiment the Article References

Grade 11 - Great Online Practice for Transformations

http://archives.math.utk.edu/visual.calculus/0/shifting.7/index.html

http://www.regentsprep.org/Regents/math/algtrig/ATP9/funcprac.htm

Grade 10 - Intro to Circles!

What we are learning only goes up to time 3:40 in this video!!!

Grade 10 Review Substitution and Elimination

More on Substitution

More on Elimination - Word Problem!!

Grade 11 - Inverses of Functions

This is a fantastic way to learn function inverses. Check it out! Thanks Sal!

Do you ever wonder?

Polynomial Division: Understanding by NOT doing!

Challenge for All

 Find different ways to express 30 as the sum of two or more consecutive integers. Explain how you found your solution. How many solutions can you find?

Grade 11 Questions on "Imaginary" Number graphing

Hi people!

This site I am going to post contains a LOT of information on Complex numbers. Complex numbers are in the form of a real and a complex number (2+2i). "i" stands for the square root of -1. So (2+2i) is like saying (2+sqrt(-4)) or (2+2*sqrt(-1))... Sorry I don't have the symbols for radicals on this blog site. Check it out. Use Wikipedia if necessary!

http://home.scarlet.be/~ping1339/complget.htm

Challenge Problem to Try

For all who are feeling brave! 



1. When I sum five numbers in every possible pair combination, I get the values: 0,1,2,4,7,8,9,10,11,12.  What are the original 5 numbers?


2. When I sum a different set of five numbers in every possible group of 3, I get the values: 0,3,4,8,9,10,11,12,14,19.  What are the original 5 numbers?

For Grade 10 Number Types Review

Here are a few links with more details on the Number Types (e.g. Reals, Natural Numbers, Rationals, Irrationals, etc.) as well as information on the irrational number "e".


Explore the site for more information on each type of number!
http://www.mathsisfun.com/sets/number-types.html


"e" Euler's Number
http://www.mathsisfun.com/numbers/e-eulers-number.html

For Grade 11 Functions Unit: Intro to Notation

I wanted to share with you an interesting link/explanation on function notation. This includes why we have it, and how it extends to other subjects like science. We will briefly go over it tomorrow, but you will see that this link provides a much more detailed synopsis. 

http://mathmaine.wordpress.com/2010/02/22/function-notation/

Hi All!


Welcome to my new blog, my first blog ever, which I have created in order to provide you with resources that have the potential to help you with your math learning this year. 


We live in such an online connected world, so why not make best use of it? There are so many resources available that can help clarify your questions beyond what I can provide in a class period, so make best use of the internet. It's a fantastic resource! I will help!