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Praxis Study Guide, Part 1: Mental Math

This article is the first in a series of five study tips to get you ready for taking the Praxis Core tests.

1) Mental Math
2) Read
3) Learn from your Mistakes
4) Beating Test Stress
5) Using a Study Schedule

Use and Abuse of the Calculator

Fact: On the Praxis Core Mathematics Test, you get an onscreen calculator that you can use at any point during the test.

Fact: If you use the onscreen calculator every single time you need to do a calculation on Praxis Core Mathematics Test, then you will never finish the test in the allotted time.

Yes, you get access to a calculator on the test, but it is a BIG mistake to lean on this calculator. Every Praxis math problem can be solved without a calculator. When I did the online Praxis practice Mathematics Test, I did all 56 problems without touching a calculator. That’s an ideal that might be a little hard for some folks, but let’s say that you goal should be to use the calculator fewer than five times during the course of the Mathematics Test.

How are you doing to do most of this math without a calculator?

Praxis and Mental Math

My first piece of advice is: in all your Math practice problems, do not touch a calculator. Do not touch a calculator anywhere in your life between now and when you take the Praxis Math test. Do all math in your head without a calculator.

You have to think of doing math as an exercise like running. Suppose I know I have to run a marathon in a couple months. If I don’t run at all, and then try to run that marathon, I am going to be seriously hurting: I might even do serious injury to myself! But, if I follow a training schedule, running every day, I can build up to it. If I have not done much running, it will be painful at first, but my body will adapt.

Well, if you are a person who never liked math, chances are good that, for years, you have avoided it at every turn. To get yourself in shape for the Praxis math, you need to do math every day. Every day, add, subtract, multiple, and divide in your head. You should be able to do things such as (4 × 17) or (37 + 28) or (91 – 17) or (87 ÷ 3) in your head. One way to practice is to hand a roommate or friend a calculator, and then have them, holding the calculator, do calculations and ask you to do them in your head. Again, like running for the first time in years, it may be painful at first, but you will build “math stamina” over time.

In the Magoosh lessons, you will learn several perspectives that make this mental math easier.

Patterns

In addition to comfort with the basic arithmetic, there are also patterns that are good to learn.

One set of patterns are the divisibility tricks. You can look at a large number and tell relatively quickly whether it is divisible by different single digit numbers. If a number is even, then it has to be divisible by 2. If a number ends in 5 or 0, then it is divisible by 5. Those two are reasonably obvious to most folks. A slightly more interesting one is the pattern for divisibility by 3: if the sum of the digits of N is divisible by 3, then N itself it divisible by 3. For example, consider the current year, 2015, as a number. This number is odd, so we know that it is not divisible by 2. This number has a units digit of 5, so it must be divisible by 5. If we add up the digits, we get 2 + 0 + 1 + 5 = 8, and since 8 is not divisible by 3, this means that 2015 is not divisible by 3. The Magoosh lessons discuss the divisibility tricks in more depth, and here’s a GMAT blog article that discusses this concept more.

Another pattern is called doubling and halving. This works if you are multiplying an even number by some multiple of 5, 25, 50, 250, 500, etc. For example, suppose you had to multiple (14 × 45). Of course, many folks would be tempted to run for their calculator, but we are trying to build mental math and not touch the calculator. Notice that 14 is even, and 45 is a multiple of 5. Think about it this: we can “halve” 14, that is, take a factor of 2 away from it, and give this factor of 2 to 45, so that the 45 will be “doubled.”

Thus
(14 × 45) = 7 × 90
Well, (7 × 9) = 63, so we just add a zero to the end.
(14 × 45) = 7 × 90 = 630

Let’s try another example. Suppose we had to multiply (24 × 500). That looks scary, but we will just take half of 24, making that 12, and double 500, making that 1000, and this makes the multiplication easy:
(24 × 500) = 12 × 1,000 = 12,000

The Magoosh video lessons have a lesson on Doubling and Halving, and this GMAT blog article also discusses this pattern.

Summary

One day, when you are a teacher, there will come moments when you are surrounded by munchkins and a math problem arises and a calculator will be nowhere in reach. If you are comfortable with mental math at that moment, you will provide an invaluable example to your students in this respect.
Keep practicing math, and keep an eye out for the next Praxis Study Guide installment!

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