Page 1 Math Study Guide for the CBEST
No matter what your teaching specialization is, you will need to have some basic math skills to carry out the duties of your job. Math comes into play at some point in every area of teaching and a certain amount of knowledge in the subject is a must.
Here are the areas in which you will need to be competent in order to score well on this portion of the CBEST. Remember that most of the questions involve reading a word problem and that you are not allowed to use a calculator of any kind during the test.
Mathematics Estimation, Measurement, and Statistical Principles
Estimation and Measurement:
Measurement involves determining the size or dimension of a thing. You may measure length, surface area, volume or capacity, weight, temperature, and time. Measurement may be done using the metric system or the U.S. measurement system. In the U.S. standard, length is expressed in inches, feet, yard, and miles. Liquid is measured in fluid ounces, cups, pints, quarts, and gallons; mass or weight is measured using ounces, pounds, and tons. Surface area is expressed in square inch, square foot, square yard, and acre. The units for time are seconds, minutes, hours, days, weeks, months, and year, while the unit for measuring temperature is degrees Fahrenheit.
Length and Perimeter
Length is measured when there is a need to determine how long or tall a thing is, how far apart two things are, or the distance between places or locations. The units inch or foot are used for shorter lengths, such as the length of paper or cloth. A standard ruler measures 12 inches or 1 foot. For longer lengths, such as distances between cities, a mile is the applicable unit.
Perimeter is the distance around a closed flat shape. To measure the perimeter of a square, simply find the sum of the lengths of its sides. A square with a side of 5 inches, for instance, has a perimeter of 20 inches (5 + 5 + 5 + 5). The distance around a circle is called circumference (C) and is computed using the formula:
where r is the radius of the circle.
CBEST will have questions involving addition or subtraction of time. The key is to add or subtract seconds, minutes, and hours separately, and to remember that:
1 minute = 60 seconds 1 hour = 60 minutes
A question may go like this: You leave work at 10:08 a.m. after a 5-and-a-half hour shift. What time did you arrive for work that day?
The problem requires us to subtract 5:30 from 10:08. Do this by subtracting the minutes first, then the hours. However, subtracting 30 from 8 cannot be done directly, so we borrow 1 hour or 60 minutes from the hour side, and we now have 68 minutes instead of 8. Thus we have:
Minutes: 68 – 30 = 38 Hours: 9 – 5 = 4
The correct answer is 4:38 a.m.
Estimating involves calculated guessing. If fully developed, it becomes a very useful skill, not only for this test, but for everyday application. An intelligently estimated number or answer is close to an exact value, and is often useful when you need an answer quickly and there is no calculator available.
Estimate “497 x 60.5” by multiplying “500 by 60”. That’s easily 30,000. The exact answer is 30,068.5 ― our estimate is not that far from this amount.
This tip comes in handy when estimating. When you round one number up, round the other number down to minimize the discrepancy between the estimated value and the exact value.
Estimating answers is applicable whether you’re adding, subtracting, multiplying, or dividing. It is also useful to double-check answers obtained through computation. For instance, you just calculated “550,234 + 24,980” and came out with an answer of 552,732. From a cursory estimate adding the rounded numbers of 550,000 and 25,000, you know that the answer is something around 775,000. That’s significantly different from 552,732! Checking again, you realize that you left out the “0” in 24,980 and got an erroneous answer. This is the same technique used for estimating bills at a restaurant―you actually have a figure in your mind that shouldn’t be too far off from the actual bill. If the discrepancy is significant, it’s a clue that you need to check some items.