CliffsNotes CBEST - BTPS TESTING Ph.D., Jerry Bobrow Ph.D. & 8 more 2021

Measurement
Math reasoning problems

Now that you have reviewed arithmetic, algebra, statistics, and probability topics, it’s time to put these concepts together using math reasoning. Because most questions on the CBEST appear as word or graph problems, this section will give you a chance to solve problems in the same format as the actual test. These types of problems may challenge your thinking process, but remember that they may also provide you an opportunity to excel.

You will be required to use reasoning skills as you analyze different numbers represented by multiple sources:

· Measurement (units—feet, yards, pounds, and perimeter)

· Word problems (text statements)

· Graph interpretation (graphs, charts, tables, and diagrams)

Once you learn the key strategies to solving these types of problems, you will be able to use your reasoning skills to logically make sense of questions.

Measurement

Units of measurement problems draw on your knowledge of arithmetic and reasoning. Review the measurement equivalents that follow to make sure you are comfortable with the terminology of unit quantities. In addition, it is important to understand how to solve basic geometric measurement questions related to perimeter, and:

· Understand and use standard units in the U.S. measurement and metric systems, including length, temperature, weight, and capacity.

· Measure length and perimeter.

· Convert from one measurement unit to another.

The English customary system of measurement is used throughout the United States, although the metric system is being phased in to the classroom. It would be valuable to memorize most of these basic units of measurement.

Unit of Measurement Equivalents

Length

Weight

Volume (Capacity)

Time

Converting Units of Measure

Using your knowledge of measurement and arithmetic skills, you can solve these types of problems on the CBEST.

Units of Measure — English System

Examples:

1.   How many inches are in 9 yards?

Since 1 yard = 36 inches, 9 yards = 9 × 36 = 324 inches.

2.   If 36 inches equal 1 yard, then 3 yards equal how many inches?

Intuitively, 3 × 36 = 108 inches.

By proportion, using yards over inches:

Remember to place the same units across from each other—inches across from inches, and yards across from yards. Cross-multiply to solve:

3.   How many miles are in 7,040 yards?

Since 1 mile = 1,760 yards, 7,040 yards = 7,040 ÷ 1,760 = 4 miles.

4.   How many pounds are in 352 ounces?

Since 1 pound = 16 ounces, 352 ounces = 352 ÷ 16 = 22 pounds.

5.   How many pints are in 7 gallons?

Since 1 gallon = 4 quarts, 7 gallons = 7 × 4 = 28 quarts.

Since 1 quart = 2 pints, 28 quarts = 28 × 2 = 56 pints.

6.   How many weeks are in 3 decades?

Since 1 decade equals 10 years, 3 decades equal 30 years. Since 1 year equals 52 weeks, 30 years = 30 years × 52 weeks = 1,560 weeks.

Notice that this was converted step-by-step. It can be done in one step:

3 × 10 × 52 = 1,560 weeks

7.   If 1,760 yards equal 1 mile, how many yards are in 5 miles?

1,760 × 5 = 8,800 yards in 5 miles

8.   How many weeks are in 343 days?

Since 1 week = 7 days, 343 days = 343 ÷ 7 = 49 weeks.

9.   How many minutes are in 6 days?

Since 1 day = 24 hours, 6 days = 24 × 6 = 144 hours. Since 1 hour = 60 minutes, 144 hours = 144 × 60 = 8,640 minutes.

Units of Measure — Metric System

Note: Use the Unit of Measurement Equivalents tables to find the equivalents for the following examples.

Examples:

1.   1 kilometer = 1,000 meters

2.   1 milligram = 0.001 gram

3.   1 centiliter = 0.01 liter

4.   1 meter = 100 centimeters

5.   1 liter = 10 deciliters

6.   1 gram = 0.001 kilogram

7.   1 centimeter = 10 millimeters

8.   1 decigram = 10 centigrams

9.   1 deciliter = 100 milliliters

Measuring Perimeter

Measurements for some basic figures, such as squares, rectangles, parallelograms, and triangles, are not difficult to calculate if the necessary information is given and the proper formula is used. You should first be familiar with the formula of perimeter.

Perimeter (P) is the distance around the outside of a figure (called a polygon). The perimeter of any polygon can be determined by adding up the lengths of all the sides.

Rectangle

The perimeter of a rectangle is equal to 2 × length + 2 × width. The formula for the perimeter of a rectangle is

P = 2l + 2w

For example, if you add the four sides of a rectangle, the result is the perimeter.

Top side + bottom side + right side + left side = perimeter

Perimeter(P) = 20 + 20 + 9 + 9 = 58

Square

The perimeter of a square is equal to the length of all four sides. The formula for the perimeter of a square is

P = 4s (s = length of side)

For example, if you add the four sides of a square, the result is the perimeter.

Top side + bottom side + right side + left side = perimeter

Perimeter(P) = 15 + 15 + 15 + 15 = 60

Examples:

1.   Find the perimeter of the rectangle shown.

2.   If each square in the figure shown has a side of length 1, what is the perimeter?

A.  8

B.  12

C.  14

D.  16

E.  20

Mark or draw the known facts:

Now you have a calculation for the perimeter: 10 plus the darkened parts. Now look carefully at the top two darkened parts. They add up to 1. (Notice that sliding the top square over illustrates this fact.)

The same is true for the bottom darkened parts. They add up to 1. Thus, the total perimeter is 10 + 2, or 12.

All of the squares are identical in size. To check your work, move the top and bottom squares to form the figure below:

Because each side has a length of 1, the perimeter becomes 12 groups of 1, or 12. The correct answer is choice B.