Competency Requirements for Mathematics

UNIT 4 RATIO AND PROPORTIONS

The student will demonstrate competency in simplifying ratios and solving
proportions with a minimum of 80% accuracy.

4.1

Simplify ratios involving work related ratios.

Example: Find the gear ratio involving 38 teeth of the driving gear
and 22 teeth of the driven gear.

4.2

Find the missing number using direct and inverse proportions.

Example: Find the diameter of the larger pulley when the ratio is 4:3
and the smaller pulley has a measurement of three inches.

4.3

Convert quickly and accurately between decimals, fractions , and percentages.

Example: .25 = 25% ¼ = 25% or .25

4.4

Solve problems involving a missing portion.

Example: Smith Company has a gross income of $85,000. If 34% of
the company’s income goes to taxes, how much will the Smith
Company have left?

4.5

Solve problems involving efficiency ratio, tolerance ratio, etc.

Example: Find the efficiency of the engine with an output of 85 HP
and an input of 70HP.

UNIT 5 MEASUREMENT CONVERSIONS

A student demonstrate competency in completing standard and metric conversions
with 80% accuracy. The student shall also demonstrate competency in accurately
measuring while using instructor assigned measuring devices.

5.1

A student will be able to calculate the precision and measurement accuracy of a number.

Example: 2.04 inches is precise to the hundredths and accurate to
three significant digits .

5.2

A student will be able to demonstrate the process of identifying correct wrench size to the nearest 32nd of an inch, and determine degree of error involved in using a fractional verses a decimal measurement .

Example: .432 x 32 = 13.824 = 14/32 inch. Error (14 – 13.824)/ 32 =
.0055 inch.

5.3

Convert standard measurements and demonstrate what measurements are needed to complete the conversion process.

Example: 15.5 in/sec. converted to feet/hour.

5.4

Convert standard measurements to the metric system equivalent .

Example: 12 inches equals how many centimeters?

5.5

Convert metric measurements

Example: How many centimeters are equivalent to 2.3 meters?

5.6

A student will be able to measure various parts using the measurement tools of a standard and metric tape measure as well as a standard and metric measurement micrometer.

Example: Measure the thickness of a part accurate to the
thousandths.

UNIT 6 INTEGERS

The student shall demonstrate competency with a minimum of 80% accuracy.

6.1

A student will demonstrate an understanding of an integer by accurately placing coordinates on a given number line.

Example: Place the set of numbers on a number line and state which
number is the smallest and which is the largest.

( -3, -8, 4, 0, 1 )

6.2

Consistently add integers without using a calculator.

Example: 4 + (-8) + (-6) =

6.3

A student will accurately subtract integers without use of a calculator.

Example: The temperature was 5 degrees F and dropped to 3 degrees
F below zero , what is the difference in the temperature?

6.4

The student will accurately demonstrate the process of multiplying and dividing integers without a calculator.

Example: -9 / 3 + 4 x (-3)

6.5

The student will demonstrate ability to accurately simplify a perfect and non -perfect square root while simplifying an expression .

Example: