Solution for June 2010 Brain Teaser

Find the average of all multiples of 7 between 7 and 777, inclusive.   Answer: 392

This is like the Gaussian problems (adding consecutive numbers) as it is the pairs of numbers that allow us to more easily solve these types of problems.
For example, adding the numbers 1 - 10 can be done by grouping the smallest and largest 1 and 10 to make 11, (then the next smallest and largest) 2 and 9 to make 11, 3 and 8, 4 and 7 and 5 and 6 to get 5 pairs of 11.  So the sum of the numbers form 1 to 10 is 5 x 11 = 55.

From 7 to 777 inclusive is just like 1 to 111 inclusive (divide each by 7).
One of Math educator and writer Polya's methods:  Solve a Simpler Problem.  Step 2: Devise a Plan

Choosing easier numbers can often make the solution easier and simpler to understand.
To find the average of 1 to 111, find the average of each pair -- the average of 1 and 111 is  56 (1+111)/2.
The average of 2 and 110 is 56 and so on.

So the 392 is the average of 7 and 777 and also the average of 14 and 770 (the next two multiples) is also 392.

Please visit the Excel spreadsheet on docstoc and scroll down to see that the answer is 392!!
http://www.docstoc.com/docs/45498081/Math-Confidence-Brain-Teaser-June-2010

M is for Mental Fitness

On-Line Learning of 100 Pairs by Math Confidence

Quick, what number plus 43 adds up to 100?  Studying 100 pairs (for example, 60 and 40 are 100 pair as they sum to 100) can help people with mental Math and cash register Math.
Math Confidence 100 Pairs Activity on Quia

If you can't divide 300 by 2, should you qualify for a loan?

Weak Math Skills Linked to Default -- borrowers with poor Math skills were three times more likely to go into foreclosure.

This article starts off "If you can't divide 300 by 2, should you qualify for a loan?"
The survey led by a Columbia University prof, Stephan Meier, had five questions -- only two were in the article -- the one listed above and "How much is 10% of 1000?"
16% of the respondents got one of these 2 questions incorrect.

Financial education is heavily based on Math education and personal finance is an excellent application of understanding numbers and how they affect life.  In addition, practicing problem-solving can build the mental skills and perseverance that can help people to read the fine print on a mortgage.

Researchers study cues to predict students’ math performance - The Boston Globe

Researchers study cues to predict students’ math performance - The Boston Globe