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04-25-2013, 09:32 AM
If you are looking for a tool that will help you and your student cover 50 of the most complex math problem types that are on these college entrance exams, at no charge,there is a site that allows that.

Now, before anyone says "hey, don't spam us with an advertisement" This is NOT a spamed ad. I am real not a spambot, and I am the co-founder of the company. We have been using the tool as we have been developing it for the last 10 years with over 3,000 students for pre-algebra and algebra 1 and 2 as well as SAT/ACT Math.

The tool is useful in free mode, just limited in that no data is collected on the students use for reporting, we limit the time per problem type and problem types are selected randomly for presentation. Other than that, the student is getting the full tool, not some brain dead version that has been crippled.

Okay, so how is it useful? On the SAT for example there are problem types of 1-5 complexity and also X. X are experimental problems that they put on the tests to see how complex they are so they can add them to the problem bank. 1-3 are basic enough so a student who got a B in Algebra 1, 2 and Geometry should be able to get 90% of them right. 4 and 5 level are designed to stretch the student (under 50% will get it right for 4's and then under 20% will get the right answer for 5's). We took the 4's and 5's and in our proprietary language broke the question down to an algorithm that our tool uses to generate problems (we call them probes) for the student. So, using SAT as an example, the B student should get a 550-600 just by being a B student. But to get from 600 to 800 you have to do the 4's and 5's.

Now, how does our tool work, and how can you benefit from using it (even the free version works and you can benefit from it)?

Okay, a student starts using the tool and they are presented with a random problem. The problem is: Numbers & Operations: square of integers divisible by

The probe presented is:

The integer n is equal to the square of an integer and is divisible by 20 and by 45
What is the smallest possible value of n.

The student then has a fill in blank (not multiple guess, we want them to answer the question, not have a 20% chance of getting it right in a raw guess) and a button that says "show next step". If the student knows or thinks they know the answer, they can answer it. If they need help they can "show next step".

So, they show next step... what happens? On the side it will show one of four things. A Strategy for solving the problem, a Socratic question, the answer to the Socratic question or it will show the mathematical breakdown to the next step (a simpler problem). In this case the next steps would be:

1) Strategy
For an integer to equal the square of an integer, it's prime factors must occur in pairs. As an example 9 equals 3 squared (3 x 3), and 25 equals 5 squared (5 x 5).

We need to basically find the LCM of both integers and if any prime is not raised to an even power, increment it by one so that it is.

2) Question
What is the prime factorization of 20 and of 45

3) Answer
The prime factorization of these integers:
20 = 22 x 5
45 = 32 x 5

4) Question
What is the smallest possible value of n

5) Answer
The smallest value will occur when the unique common prime factors of both integers are raised to the smallest even exponent (in this case, squared) and then multiplied together.
n = 22 x 32 x 52
n = 900

In the free version of the tool we give the student 10 minutes to do the problem type. If they complete one problem of this type they can request to do another, and another and another until time runs out.

Remember at the beginning of this post where I said I'm not a spambot, well I hope you can see that I'm not. While the "free" version of the tool doesn't give you a great deal of control, provides no reporting and has time limits, it's still very useful. Feel free to go look at it and see if you can use it and if it meets your needs. If it does, use it with your students. If it doesn't, you took all of five minutes to look at it and see if it's useful.

I'll stay around and follow this thread so if you have any questions I'll be here to answer them. Thanks for your time and consideration.

Darn, forgot the link (more proof I'm not a spambot) http://collegeentrancetestprep.com/

04-25-2013, 07:19 PM
I got an e-mail from someone from here (or at lest they stated they followed the link) that asked about other resources and if we will link to them from within the question.

Great question, and we had considered it. The problem is that other sites can and do change links. Kahn Academy, who we used to link to in the past, and CK-12, also a great resource that we have linked to in the past, change their sites and this means that links die as content is moved around. So, while we would love to be able to provide resources to support the learning process while you are working on a probe, the problem is that since we don't own the resources and since they don't have stability, we can't provide links that are unstable.

Again, if you have a question, please don't search the site for the form to contact us, but just ask it here as I am following the thread here and will be more than happy to answer any questions that you may have.