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# Math 053 Pre-Algebra

## COURSE DESCRIPTION:

A review of Arithmetic and an introduction to algebra. This is an adaptor course designed to strengthen arithmetic skills and introduce basic concepts of algebra in preparation for MAT 063.

## COURSE COMPETENCIES:

During this course, the student will be expected to:

1. Apply the four arithmetic operations to whole numbers, fractions, and decimals.
1.1 Apply the four arithmetic operations to whole numbers.
1.2 Apply the four arithmetic operations to fractions.
1.3 Apply the four arithmetic operations to decimals.
1.4 Apply the four arithmetic operations to any expression involving whole numbers, fractions and decimals.
1.5 Evaluate algebraic expressions using the four arithmetic operations.

2. Relate number theory to arithmetic calculations.
2.1. Write related sentences.
2.2. Write true number sentences using < or >.
2.3. Round numbers to a given place value.
2.4. Apply rules for exponential notation.
2.5. Simplify expressions using the rules for order of operations.
2.6. Find the factors and multiples of a number.
2.7. Find the GCF of two or more numbers.
2.8. Find the LCM of two or more numbers.

3. Execute calculations involving ration, proportion, and percent.
3.1. Write ratios and percents in fractional notation.
3.2. Write percents in decimal notation.
3.3. Write ratios and proportions for verbal problems.
3.4. Translate percent problems into proportions.
3.5. Solve proportions using variables.

4. Relate simple statistics to problems.
4.1 Interpret data from tables, charts, and various graphs.
4.2 Compute mean, medium, and mode.

5. Convert measurements within the Metric and U.S. Customary systems of measurement.
5.1 State the common units of measure of weight, mass, capacity, length, time and temperature.
5.2 Use unit fractions to convert between one U.S. Customary unit to another.
5.3 Convert from one Metric unit to another.
5.4 Convert between Celsius and Fahrenheit temperature scales.

6. Calculate the perimeter, area, and volume of various geometric figures.
6.1 Calculate perimeter and circumference.
6.2 Find the area of parallelograms (including squares and rectangles), triangles, trapezoids, and circles.
6.3 Calculate the volume of a rectangular solid, cylinder, sphere, and cone.
6.4 Calculate perimeter and area using variables.

7. Use square roots and the Pythagorean Theorem to solve right triangles.
7.1 Simplify expressions involving the square root of a perfect square.
7.2 find the length of the third side of a triangle using the Pythagorean Theorems.

8. Use estimation techniques to check the reasonableness of results.
8.1 Estimate sums and difference by rounding.
8.2 Estimate products and quotients by rounding.

9. Compute with integers.
9.1 Compare integers using <, >, or =.
9.2 Name the additive inverse of any integer.
9.3 Write the absolute value of any integer.
9.4 Determine the sum of two integers.
9.5 Determine the difference of two integers.
9.6 Determine the product of two integers.
9.7 Determine the quotient of two integers.
9.8 Use the order of operations to evaluate numerical expressions.

10. Simplify algebraic expressions.
10.1 Evaluate an expression for a given value of the variable.
10.2 Use the commutative or associative property to simplify a given expression.
10.3 Use the distributive property to simplify an expression.
10.4 Use the properties of 0 or 1 to simplify an expression.
10.5 Identify the value of a given expression with exponents.
10.6 Implement the order-of-operations rules.

11. Solve first-degree equations in one variable.
11.1 Solve linear equations involving one-step transformations using the addition property of equality.
11.2 Solve linear equations involving one-step transformations using the multiplication property of equality.
11.3 Solve linear equations involving two transformations.

12. Simply expressions involving whole number exponents.
12.1 Define a positive exponent.
12.2 Define a zero exponent.
12.3 Use exponent rules for products, quotients, and powers.

13. Compute with polynomials.
13.1 Define polynomial.
13.2 Evaluate a polynomial, given values for the variable.
13.3 Classify a given polynomial according to number of terms.
13.4 Find the sum/difference of two polynomials.
13.5 Multiply polynomials.
13.6 Apply the order of operations to simplify polynomials.

14. Graph using a number line and a rectangular coordinate system.
14.1 Graph rational numbers on a number line.
14.2 Plot a given ordered pair of rational numbers on a rectangular coordinate system.

15. Solve word problems involving any of the above.
15.1 Determine what information in a problem is pertinent.
15.2 Determine what operations will be necessary in solving the problem.
15.3 Translate word problems into equations or other strategies.
15.4 Check the feasibility of the answer.