Tuesday, May 1, 2012

SAT CHALLENGE - ODD NUMBERS OF FACTORS

How many positive integers less than 1000 have exactly

(a) 3 positive integer factors
Ans: 11

(b) 5 pos int factors
Ans: 3

(c) 7 factors
Ans: 2

Is this topic in the middle school core standards? Under divisibility? Factors?

Have you seen questions like these on state tests? SATs?

What strategy would you like your 6th-8th graders to use? Assuming they don't know a 'rule' for this problem, how can they best discover a pattern? Would it make sense for students to make a 2-column table of integers and number of factors?

Why am I addressing middle school curriculum when the title of this post refers to SATs?

Is this question not worth all the time it would consume?

Do you believe this question is only for the 'mathletes' who take math contests?



Sent from my Verizon Wireless 4GLTE Phone

2 comments:

OrangeMath said...

SAT Math is Middle School Challenge Math as a rule of thumb. While this isn't really an SAT question, it is part of the mindset necessary to succeed on the SAT. If a student can play with it, then he or she can work the SAT well.

Dave Marain said...

I agree essentially with your knowledgeable thoughts.

Many parents and students do not realize how many middle school topics appear on SATs. Yes, the questions can be challenging for that age group but I am suggesting that the middle school math curriculum itself needs to be more challenging and not only for advanced groups. Introducing students early on to higher order reasoning can only benefit them down the road. Of course, as teachers we need to present age-appropriate explanations and help them recognize the BIG IDEAS embedded in the problem.

Understanding WHY only even powers of primes (and their products) can have an odd number of factors is more than some esoteric concept of limited use IMO. Number theory is an area which has traditionally been neglected.