Response to NYT on Math Ed

This proposed sequence would help students prepare for life especially with respect to Finance. Another important consideration is how to prepare students for SAT, ACT and college placement tests. Until the Common Core Standards are implemented, we can use the SAT and ACT as standards. The College Board's SAT book has extremely accurate sample exams while the free SAT Question of the Day can help students, parents, teachers and society gauge what students should know. By studying this content, students can fill in their gaps and expand their opportunities.

http://www.amazon.com/Official-SAT-Study-Guide-2nd/dp/0874478529/ref=sr_1_1?ie=UTF8&qid=1314246854&sr=8-1

http://sat.collegeboard.org/practice/sat-question-of-the-day

Robin A. Schwartz, MBA, BSEE

www.mathconfidence.com

August 2011 Brain Teaser Solution

How many integers less than or equal to 1,000,000 are both perfect squares and perfect cubes?

Answer: 10
Anything that is both a perfect square and a perfect cube will be a number to the 6th power.
The lowest one is 1 = 1^2 and 1^3
2^6 = 64 = 8^2 and 4^3
3^6 = 729 = 27^2 and 9^3
4^6 = 4096 = 64^2 and 16^3
5^6 = 15625 = 125^2 and 25^3
6^6 = 46656 = 216^2 and 36^3
7^6 = 117649 = 343^2 and 49^3
8^6 = 262144 = 512^2 and 64^3
9^6 = 531441 = 729^2 and 81^3
10^6 = 1,000,000 = 1000^2 and 100^3

For an example of why this works, let's examine 2^6  which is 2 x 2 x 2 x 2 x 2 x 2 then these 2s can be split into 2 groups of 3 as (2 x 2 x 2)^2 which can be rewritten as 8^2
or 3 groups of 2 (2x2)(2x2)(2x2) = 4^3