MATH 090 - Beginning Algebra

4 Credit: (4 lecture, 1 lab, 0 clinical) 5 Contact Hours: [Prerequisite: Math Level 3 ][Pre- or co-requisite: GNST 100 ]

1. Work collaboratively in small groups.
2. Investigate the structure of a mathematical system and its notation.
3. Apply appropriate problem solving strategies (solve simpler problems, use manipulatives, draw a picture, make a table, look for a pattern, make a graph, guess & check) using Polya’s four-step approach.
4. Explore connections among number systems (natural, whole, integers, rational, irrational, real).

Goal 2:  Students will investigate algebraic expressions and equations, and apply algebraic properties.  (Chapter 1)

1. Order numbers on a number line.
2. Identify variables, constants, numerical coefficients, and expressions.
3. Translate English phrases into algebraic expressions.
4. Translate English sentences into algebraic statements.
5. Identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
6. Find the absolute value of a real number.
7. Define and apply exponents.
8. Simplify expressions using the Order of Operations.
9. Use a calculator to verify the Order of Operations.
10. Determine whether a number is a solution of an equation.
11. Apply the Commutative and Associative properties.
12. Apply the Distributive property.
13. Apply the Identity property.

Goal 3:  Students will investigate equations and inequalities. (Chapter 2)

1. Identify terms, like terms, and unlike terms.
2. Combine like terms.
3. Apply the Distributive property to parentheses.
4. Write word phrases as algebraic expressions.
5. Define linear equations.
6. Apply the Addition Property of Equality.
7. Apply the Multiplication Property of Equality.
8. Use the calculator to check solutions to equations.
9. Identify identities and conditional equations.
10. Identify linear and nonlinear equations.
11. Apply Guess and Check tables.
12. Solve word problems.
13. Use formulas to solve problems.
14. Solve literal equations.
15. Solve percent problems using equations of the form a%  b = c.

Goal 4:  Students will investigate inequalities (Section 2.8).

1. Define linear inequalities in one variable.
2. Graph solution sets of inequalities on a number line.
3. Solve simple linear inequalities.
4. Solve simple inequality applications.

Goal 5:  Students will investigate the graphs of linear equations in two variables. (Chapter 3)

1. Read and interpret graphs.
2. Identify quadrants, axes, the origin, ordered pairs, and coordinates.
3. Identify linear and nonlinear equations.
4. Determine whether an ordered pair is a solution to a two-variable equation.
5. Find the missing coordinate given one coordinate.
6. Graph paired data.
7. Graph a linear equation given two points.
8. Explore the roles of parameters m and b in y=mx+b using a calculator.
9. Identify intercepts of a graph.
10. Find the slope and vertical intercept from an equation.
11. Find horizontal and vertical intercepts of lines.
12. Graph a linear equation using intercepts.
13. Identify and graph vertical and horizontal lines.
14. Find the slope of a line given two points.
15. Find the slope of a line given an equation.
16. Find the slope of a line from its graph.
17. Find the slope of a line from a table.
18. Graph a line given a point and a slope.
19. Find the slopes of horizontal and vertical lines.
20. Compare the slopes of parallel and perpendicular lines.
21. Interpret slopes as rates of change.
22. Interpret the meanings of intercepts in terms of the units of measure.
23. Use a slope and vertical intercept to write the equation of a line and graph the line.
24. Graph and write the equation of horizontal lines.
25. Graph and write the equations of vertical lines.
26. Determine a linear equation given ordered pairs of data.
27. Determine a linear equation given a graph.
28. Recognize the slope concept in real life applications.
29. Determine relationships among numeric, algebraic, and graphic representations of lines.

Goal 6:  Students will investigate systems of 2x2 linear equations. (Chapter 4)

1. Determine if an ordered pair is a solution of a system of equations in two variables.
2. Solve a system of equations by graphing.
3. Solve a system of equations by substitution.
4. Solve a system of equations by elimination (multiplication/addition).
5. Apply appropriate problem solving strategies to set up and solve a system of equations for an applied problem.

Goal 7:  Students will investigate exponential expressions. (Sections 5.1 & 5.5)

1. Develop exponent properties using the meaning of exponents.
2. Use a calculator to explore patterns in exponents.
3. Simplify exponential expressions using the meaning of exponents.
4. Simplify multiplication, division, and powers of exponential expressions.
5. Use the Product Rule for exponential expressions.
6. Use the Power Rule for exponential expressions.
7. Use the Power Rule for products and quotients of exponential expressions.
8. Use the Quotient Rule for exponential expressions
9. Define a number raised to the 0 power by applying the Quotient Rule for exponents.
10. Simplify exponential expressions using negative exponents.
11. Convert numbers from standard notation to scientific notation.
12. Convert numbers from scientific notation to standard notation.
13. Perform operation on numbers written in scientific notation.
14. Estimate and use a calculator to perform operations on numbers written in scientific notation.

Goal 8:  Students will investigate polynomial expressions. (Sections 5.2-5.4 and Chapter 6)

1. Identify monomials, binomials, and trinomials.
2. Add and subtract polynomials.
3. Multiply monomials.
4. Multiply polynomials with algebra tiles.
5. Multiply polynomials with generic rectangles (tables).
6. Multiply polynomials using the Distributive Property.
7. Square a binomial.
8. Identify patterns in the products of binomial squares.
9. Multiply the sum and difference of two terms.
10. Identify patterns in the products of the sum and difference of two terms.
11. Find the greatest common factor of a list of integers.
12. Find the greatest common factor of a list of monomials.
13. Factor a polynomial with algebra tiles.
14. Factor the greatest common monomial factor from an expression.
15. Factor with a generic rectangle (table).
16. Apply appropriate problem solving strategies (make a systematic list).
17. Factor using the guess and check strategy.
18. Factor special products.
19. Solve quadratic equations by factoring and applying the zero product rule.
20. Make a table and graph for a quadratic function.

Goal 9:  Students will investigate proportional reasoning. (Section 7.6)

1. Identify ratios.
2. Identify proportions.
3. Solve proportions.
4. Use proportions to solve applied problems.
5. Solve percent problems using proportions.
6. Apply unit conversion.

Goal 10:  Students will investigate averaging. (Appendix F and additional material)

1. Find the mean of a data set.
2. Find the mode of a data set.
3. Find the median of a data set.
4. Find the midpoint of a line segment.
5. Find the weighted average of a data set.

Goal 11:  Students will investigate squares and square roots and related expressions and equations. (Section 10.1 and additional material)

1. Develop number sense regarding square roots of numbers.
2. Find the principal square root of a number.
3. Solve square root equations and formulas by squaring both sides.
4. Solve quadratic equations by taking the square root of both sides.
5. Use the Pythagorean Theorem to write equations and solve for missing sides of right triangles.
6. Use the converse of the Pythagorean Theorem to determine whether triangles are right triangles.
7. Use the Pythagorean Theorem to solve applied problems.
8. Apply the Pythagorean Theorem to find the distance between points on a coordinate system.