American Math Challenge

The American Math Challenge 2010 is around the corner... Registrations are now open at www.americanmathchallenge.com.

The actual event will take place over 48 hours, beginning on October 26, 2010 at 9 a.m. EST. This is a FREE online Challenge where U.S. students of all ages and skill levels compete against each other in a series of one-minute mental math games, as well as self-challenged curriculum-based activities.

October 18 will open a "practice competition week" open to all registrants.

Registration will close on October 22. 

Another guess my secret number game

Here's another one of those "guess my secret number" games where the computer tells what number you thought of originally.

http://myframeshoppe.ca/math/

First you need to choose your "secret" number between 1 and 10,000.

I thought some of you might enjoy trying to figure out how it works... I enjoyed it.

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By popular demand I want to share some of why it works. So DON'T READ if you want to think about why it works!

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In the LAST step, the computer guesses which digit you left out. For example, maybe you put in the number as 75x711. Now, the key to "guessing" or figuring out what the missing digit is, is the fact that this number is divisible by 9. Recall that before coming to this step, you had multiplied your number by 3, and again by 3. That means you multiplied it by 9, so it is now divisible by 9.

The numbers that are divisible by nine have a special property: the sum of their digits is also divisible by nine. OK, my number 75x711 IS divisible by nine. The sum of the digits I see is 7 + 5 + 7 + 1 + 1 = 21. The next bigger number after 21 that is divisible by 9 is 27. So the digit sum must be 27, and the missing digit is 6.

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The game goes like this:
1) Choose a number between 1 and 10,000.
2) Multiply it by 4.
3) Add 5.
4) Multiply it by 75.
5) Choose any two digits from your number and add the number formed by those to your number.
6) Multiply it by 3.
7) Multiply it by 3.
8) Replace one of the digits by X and submit.
9) Computer guesses your number.

I already explained how the computer finds out the missing "secret" digit. Then of course, the program can easily go backwards any step that had adding or multiplying (by doing the opposite operation).

In step 5, where you choose two digits and add them, the program isn't trying to guess what number you added. The key idea is that no matter what number you add, it's less than 100, AND the number you got in the end of step 4 is divisible by 75 and ends in 5.

So, to undo step 5, the program ONLY looks for a number that is divisible by 75, ends in 5, and is no more than 100 less than the number from step 6.

Resources for multiplication tables

This time of year many students tackle multiplication tables. These resources can be of help:

1. This video explains my method for "structured drilling" of multiplication tables. We don't start with random drill (that comes later) but with drill that is using the structure of the tables. The tables are also practiced "backwards", which will facilitate the learning of basic division facts.
   
   Over the years I have hears from many individuals who have gotten their child to learn the tables using this method, but recently  I got word from a a principal of an English medium school in Pune, India, that they have already implemented my multiplication drilling method and it is working beautifully with their children! I feel flattered a whole SCHOOL is using it... and glad it is working.
   
   
2. Math Mammoth Multiplication 1 book. First it has a long section that concentrates on the concept of multiplication, and then the last part has lessons to faciliate the same drilling as explained in the video.
   
   
3. There is a place for random drill, and you can use flashcards, or the way shown in the video, and/or GAMES. I have compiled a list of online multiplication games here.
   
   This card game is also noteworthy  (the "Product War" version). Essentially, each player is dealt two cards face up, players multiply those, and the person with highest product captures all cards in that round.
   
   Or, try a dice game called Damult Dice.

I feel that learning the multiplication tables well is more important than even mastering addition and subtraction facts. Why? Because knowing the tables well facilitates the learning of basic division facts, multidigit multiplication, long division, most fraction math and factoring. Even in algebra you still need to be able to simplify rational expressions and factor polynomials, perhaps even multiply matrices.

Or, we can say it this way: if you child does not know the tables, he/she will have a terrible time mastering all those topics. I'm not saying children won't learn those topics conceptually -- I mean they will have hard time completing the problems and exercises quickly, and can instead get all "bogged down" just by the multiplications.

That is why I feel every teacher/parent should put forth a good effort for their students to learn the times tables. Spend 1-2 months on it. It can pay off!

That said, there is a BALANCE, as in everything. IF you've already expended a considerable amount of effort and the child is not retaining them, please don't make the multiplication tables to be the reason why your student hates math. You can back off and try again later. Some give their students a "crutch" -- tables written out -- and eventually the kid notices how slow it makes him/her having to check the answers in the table instead of knowing them, and decides to memorize them.