MAT 045 - Fundamentals of Math

1. Compute by hand, using the four arithmetic operations to whole numbers, fractions, decimals, and integers
   1. Compute whole numbers, fractions, decimals, and integers using the four arithmetic operations
   2. Compute and apply the order of operations to any numerical expression involving whole numbers, fractions, decimals, and integers
   3. Compute algebraic expressions using the four arithmetic operations
2. Relate number theory to arithmetic computations
   1. Write related sentences
   2. Build true number sentences using <, >, or =
   3. Round numbers to a given place value
   4. Utilize rules for exponential notation
   5. Find the factors and multiples of a number
   6. Find the GCF and LCM of two or more numbers
3. Compute calculations involving ratio, proportion, and percent
   1. Write ratios and percentages in fractional notation
   2. Write fractions and percentages in decimal notation
   3. Write decimals and fractions in percent notation
   4. Write ratios and proportions for verbal problems
   5. Translate percent problems into proportions and equations
   6. Solve proportions and equations using variables
4. Relate simple statistics to problems
   1. Classify various representations of data
   2. Interpret data from tables, charts, and various graphs
5. Convert measurements within the Metric and U.S. Customary systems of measurement
   1. State the common units of measure of weight, mass, capacity, length, time and temperature
   2. Use unit fractions to convert between one U.S. Customary unit to another
   3. Convert from one Metric unit to another
   4. Convert between Celsius and Fahrenheit temperature scales
6. Calculate the perimeter, area, and volume of various geometric figures
   1. Calculate perimeter and circumference
   2. Find the area of parallelograms (including squares and rectangles), triangles, trapezoids, and circles.
   3. Calculate the volume of a rectangular solid, cylinder, sphere, and cone
   4. Calculate perimeter and area using variables
7. Utilize square roots and the Pythagorean Theorem to solve right triangles
   1. Simplify expressions involving the square root of a perfect square
   2. Find the length of the third side of a triangle using the Pythagorean Theorem
8. Utilize estimation techniques to check the reasonableness of results
   1. Estimate sums and difference by rounding
   2. Estimate products and quotients by rounding
9. Examine integers
   1. Compare integers using <, >, or =
   2. Name the additive inverse of any integer
   3. Write the absolute value of any integer
10. Evaluate algebraic expressions
    1. Evaluate an expression for a given value of the variable
    2. Utilize the commutative or associative property to simplify a given expression
    3. Utilize the distributive property to simplify an expression
    4. Utilize the properties of 0 or 1 to simplify an expression
    5. Assess the value of a given expression with exponents
    6. Apply the order-of-operations rules
    7. Solve first-degree equations in one variable
11. Simplify expressions involving whole number exponents
    1. Define a whole number exponent
    2. Make use of the exponent rules for products, quotients, and powers
12. Graph using a number line
    1. Graph rational numbers on a number line
    2. Graph decimals on a number line
13. Solve word problems using algebraic methods
    1. Determine what information in a problem is pertinent
    2. Determine what operations will be necessary in solving the problem
    3. Translate word problems into equations and solve them using various strategies
    4. Check the feasibility of the answer