## Tuesday, April 29, 2014

### An easier challenge?

NOTE: Don't forget to submit solutions and/or questions via the NEW Contact form at top of right sidebar...

And the winner is...
I'm happy to report that no one submitted an incorrect proof for my Challenge. Then again no one submitted anything! Disappointed but not surprised. Of course I've learned not to take this personally since it was a last minute announcement but I will leave the Challenge open for now for anyone who still wants to submit their proof or a counterexample to show I'm wrong!
A comment from anyone who tried the Challenge would be appreciated.  I saw the large number of views so it's hard to determine why no responses...
I don't give up easily so here's another Algebra Challenge which might also elicit zero responses!
Note: These are really designed for students...
1^3 + 2^3 < 3^3
2^3 + 3^3 < 4^3
Show algebraically that if a,b,c are consecutive positive integers with a<b<c,  then
a^3 + b^3 > c^3 for a> 5.

## Monday, April 28, 2014

### Deadline for Contest Submission is Midnight Tonight!!

Time's running out on the MathNotations Contest. I'm guessing one of 3 possibilities"

1) There's an error in the statement and you think I'm asking you to reprove Fermat's Last Theorem!
2) It's too easy to be bothered!
3) It's harder than I thought??

Remember I corrected it to positive integer values for n greater than 2.  Just a start here...

The first step is to show that c^3>a^3+b^3 and that may be a little sticky but I know many can do it

Use new contact form at top of right sidebar to contact me directly! If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back and DETAILED SOLUTIONS/STRATEGIES for the 1st 8 quizzes. Suitable for SAT I, Math I/II Subject Tests, Common Core Assessments, Math Contest practice and Daily/Weekly Problems of the Day. Includes multiple choice, case I/II/III type and constructed response items. Price is \$9.95. Secured pdf will be emailed when purchase is verified.

## Saturday, April 26, 2014

### MathNotations Math Induction Challenge

Correction/Update: n is a positive integer

CHALLENGE
If a,b,c are the sides of a right triangle, c>a, c>b
prove by Mathematical Induction that
a^n + b^n < c^n, for n> 2

Submit detailed solution using the new contact form in the sidebar no later than Mon 5-28-14 11:59 pm EDT.

If your solution is too long for the contact form, indicate that that and I will contact you.

IMPORTANT NOTES:
1)Include your full name and state.
2)If you are a student, pls indicate grade level (or if in an Undergrad or Grad program).
3) If an educator,  pls indicate elementary,  middle, secondary or college.

The 3 best solutions will receive a free emailed copy of my Math Challenge Quiz Book and, of course,  recognition on this blog.

Note: If you feel there is an error in the problem or if the new contact form is not working, pls leave a comment.

## Thursday, April 24, 2014

### Parametric/Projectile Motion Simulated in Desmos - A Common Core Activity for Algebra/Precalculus

[Updated using folders to reduce amount of visible text. Click on the arrow next to the Folder icon to see the frames below. Thanks to Desmos team for this helpful hint!]

CLICK ON GRAPH TO ACTIVATE DESMOS...

The Desmos activity above is both an investigation of parametric representation and a tutorial for more advanced use of this remarkable WebApp. The The text in the side frames begins with a detailed background of the activity for the instructor and how Desmos can be used to demonstrate projectile motion using both parametric and rectangular coordinates. Some of the uses of slider 'variables' are demonstrated including animation, a powerful feature of Desmos.

In addition to showing how to use parameters in Desmos, the activity itself asks students to compare two different trajectories, representing an object dropped from some initial height, then a 2nd object two seconds later. The horizontal translation of the first graph is juxtaposed against the algebraic representations of these graphs using both system of coordinates.

The student activity starts about halfway down. There is a series of questions and actions the student needs to take in Desmos.

I'm hoping this will prove useful for both the instructor and the student.  Desmos is powerful but, in my opinion, some of the illustrative examples provided by Desmos do not flesh out the ideas behind the various uses of slider 'variables'. I'm hoping this will fill in some of those gaps.  I'm still a novice here so I'm sure more advanced users will be able to improve upon this...

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back and DETAILED SOLUTIONS/STRATEGIES for the 1st 8 quizzes. Suitable for SAT I, Math I/II Subject Tests, Common Core Assessments, Math Contest practice and Daily/Weekly Problems of the Day. Includes multiple choice, case I/II/III type and constructed response items. Price is \$9.95. Secured pdf will be emailed when purchase is verified.

## Sunday, April 20, 2014

### A Common Core Alg Activity Using Desmos - Piecewise Linear Functions and Squares

This is my first attempt to use Desmos, the outstanding free online graphing calculator (and a free iPad app). I'm sure many of you have been utilizing this powerful resource. There are already many available teacher samples you can use.

CLICK ON THE GRAPH TO LOAD THE APP.

Let me know if you can view the graph (you may have to adjust the window slightly). More importantly, what do you think of the activity and do you see its potential for deepening understanding of algebra?

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back and DETAILED SOLUTIONS/STRATEGIES for the 1st 8 quizzes. Suitable for SAT I, Math I/II Subject Tests, Common Core Assessments, Math Contest practice and Daily/Weekly Problems of the Day. Includes multiple choice, case I/II/III type and constructed response items. Price is \$9.95. Secured pdf will be emailed when purchase is verified.

## Tuesday, April 15, 2014

### Another Common Core Rant - not a video...

While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog.

The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control.

We're trying to set the bar higher for children without raising the bar for those responsible for implementing these changes. That is irresponsible at best and criminal at worst.

## Saturday, April 5, 2014

### Developing Fraction Sense Using Egyptian Fractions

This MathCast describes a procedure for writing proper fractions as a sum of unit fractions, e.g., 5/6=1/2+1/3. This exploration is appropriate for Gr5 on up.A simplified form of the Greedy Algorithm.
Watch "Developing Fraction Sense Using Egyptian Fractions" on YouTube: http://youtu.be/ulb6E4OcQ8g
I'm experimenting with embedding these MathCasts directly into my blog post, however, the audio may not come out right. May work on your computer but not your tablets or smartphones. Please let me know. If there is a problem you can just click on the link to YouTube.