# Competency Requirements for Math

# 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 32 ^{nd} of an inch, and determine degree of error involved in
using a fractionalverses 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:**

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