## Course Content and Outcome Guide for ALC 60

Date:
02-OCT-2012
Posted by:
Heiko Spoddeck
Course Number:
ALC 60
Course Title:
Basic Math Skills Lab
Credit Hours:

Lecture hours:
0
Lecture/Lab hours:
0
Lab hours:
0
Special Fee:

#### Course Description

In conjunction with the instructor, students choose a limited number of topics in Basic Math (MTH 20) and/or Introductory Algebra (MTH 60 and 65) to review over the course of one term. Instruction and evaluation are self-guided. Completion of this course does not meet prerequisite requirements for other math courses.

#### Outcome Assessment Strategies

Assessment shall include at least two of the following measures:

1. Tests
2. Attendance
3. Portfolios
4. Individual student conference

#### Course Content (Themes, Concepts, Issues and Skills)

Basic Math

THEMES:

1.     Mathematical vocabulary
2.     Number sense
3.     Computational proficiency
4.     Critical thinking
5.     Appropriate use of technology
6.     Team work

SKILLS:

1.0           ORDER OF OPERATIONS

1.1           Vocabulary (Define and use)

1.1.1      Grouping symbols

1.1.2      Exponents

1.1.3      Square roots (perfect squares)

2.0           SIGNED NUMBERS

2.1           Vocabulary (Define and use)

2.1.1      Absolute value

2.1.2      Opposite vs. negative vs. minus (subtract)

2.2           Number sense

2.2.1      Compare signed numbers using inequality and equality notations

2.2.2      Place signed numbers on a number line

2.3           Computation

2.3.1      Add, subtract, multiply, and divide signed numbers

2.3.2      Simplify signed numbers to exponents

2.4           Order of operations with signed numbers

2.5           Applications with signed numbers

3.0           FRACTIONS

3.1           Vocabulary (Define and use)

3.1.1      Proper fractions, improper fractions, mixed numbers

3.1.2      Reciprocal

3.1.3      Prime number

3.1.4      Composite number

3.1.5      Divisibility Rules 2, 3, 5, 9, and 10

3.2           Number Sense

3.2.1      Compare fractions using inequality and equality notations

3.2.2      Place signed fractions on a number line

3.3           Computation

3.3.1      Add, subtract, multiply, and divide signed fractions

3.4           Order of operations with fractions

3.5           Applications involving fractions

3.5.1      Write answers to application problems as complete sentences and using proper units

3.5.2      Ratios and rates

4.0           DECIMALS

4.1           Vocabulary (Define and use)

4.1.1      Place values

4.1.2      Powers of ten

4.1.3      Terminating, repeating and non-terminating

4.2           Number sense

4.2.1      Compare decimals using inequality and equality notations

4.2.2      Place signed decimals on a number line

4.2.3      Rounding decimals

4.3           Computation

4.3.1      Add, subtract, multiply, and divide signed decimals

4.3.2      Convert between fractions and decimals

4.4           Order of operations with decimals

4.4.1      Round at the end of the calculation

4.5           Applications

4.5.1      Write answers to application problems as complete sentences and using proper units

4.5.2      Rates and ratios

4.5.3      Unit rate and unit price

5.0           PROPORTION AND PERCENT

5.1           Vocabulary

5.1.1      Proportion

5.1.2      Percent

5.2           Number sense

5.2.1      Convert between fractions, decimals, and percents

5.3           Computation

5.3.1      Solve proportion problems for missing value

5.3.2      Solve percent problems

5.4           Applications

5.4.1      Write answers to application problems as complete sentences and using proper units

5.4.2      Identify and solve problems that involve reasoning about proportions

5.4.3      Solving percent increase and percent decrease problems

5.5           Technology

6.0           GRAPHS

6.1           Introduce, read and interpret graphs

7.0           FORMULAS AND CONVERSIONS

7.1           Perimeter and area of rectangles, squares and triangles

7.2           Computing mean, median, and mode

7.3           Introduce unit conversions within each measurement system

7.4           Money, \$0.35 vs. 35¢ (students often write 0.35¢)

Introductory Algebra I

THEMES:

1. Algebra skills
2. Graphical understanding
3. Problem solving
4. Effective communication
5. Critical thinking
6. Applications, formulas, and modeling
7. Functions

SKILLS:
1.0                REAL NUMBERS

1.1                Review prerequisite skills – signed number and fraction arithmetic

1.2                Simplify arithmetic expressions using the order of operations

1.3                Evaluate powers with whole number exponents; emphasize order of operations with negative bases

1.4                Simplify arithmetic expressions involving absolute values

1.5                Order real numbers along a real number line

1.6                Identify numbers as elements of the subsets of the real numbers

2.0                VARIABLES AND EXPRESSIONS

2.1                Simplify algebraic expressions

2.2                Evaluate algebraic expressions

2.3                Recognize equivalent expressions and non-equivalent expressions

2.4                Distinguish between evaluating expressions, simplifying expressions and solving equations

2.5                Translate from words into algebraic expressions and vice versa

2.6                Apply the distributive, commutative, and associative properties

2.7                Recognize additive and multiplicative identities and inverses

2.8                Distinguish between factors and terms

2.9                Apply the product rule, product to a power rule, and power-to-a-power rule to expressions with positive integer exponents emphasizing the logic behind these rules of exponent

3.0                GEOMETRY APPLICATIONS

3.1                Evaluate formulas and apply basic dimensional analysis

3.2                Know and apply appropriate units for various situations; e.g. perimeter units,  area units, volume units, rate units, etc

3.3                Memorize and apply the perimeter and area formulas for rectangles, circles, and triangles

3.4                Memorize and apply the volume formula for a rectangular solid and a right circular cylinder

3.5                Find the perimeter of any polygon

3.6                Evaluate other geometric formulas

3.7                Use estimation to determine reasonableness of solution

4.0                LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE

4.1                Identify linear equations and inequalities in one variable

4.2                Understand the definition of a solution; e.g. 2 is a solution to x < 5; 3 is the solution to  x + 1 = 4

4.3                Distinguish between solutions and solution sets

4.4                Recognize equivalent equations and non-equivalent equations

4.5                Solve linear equations and non-compound linear inequalities symbolically

4.6                Express inequality solution sets graphically, with interval notation, and with set-builder notation

4.7                Distinguish between solutions to equations and equivalent equations (e.g. “The solution is 2.” vs. “x = 2”)

5.0                GENERAL APPLICATIONS

5.1                Create and solve linear equations and inequalities in one variable that model real life situations (e.g. fixed cost + variable cost equals total cost)

5.1.1           Properly define variables; include units in variable definitions

5.1.2           Apply dimensional analysis while solving problems

5.1.3           State contextual conclusions using complete sentences

5.1.4           Use estimation to determine reasonableness of solution

5.2                Apply general percent equations (A = PB)

5.3                Create and solve percent increase/decrease equations

5.4                Create and solve ratio/proportion equations

5.5                Solve applications in which two values are unknown but their total is known; for example, a 50 foot board cut into two pieces of unknown length

6.0                LITERAL EQUATIONS AND FORMULAS

6.1                Solve an equation for a specified variable in terms of other variables

6.2                Input values into a formula and solve for the remaining variable

7.0                INTRODUCTION TO TABLES AND GRAPHS

7.1                Briefly review line graphs, bar graphs and pie charts

7.2                Plot points on the Cartesian coordinate system; determine coordinates of points

7.3                Classify points by quadrant or as points on an axis; identify the origin

7.4                Label and scale axes on all graphs

7.5                Interpret graphs in the context of an application

7.6                Create a table of values from an equation

7.7                Plot points from a table

8.0                INTRODUCTION TO FUNCTION NOTATION

8.1                Determine whether a given relation presented in graphical form  represents a function

8.2                Evaluate functions using function notation from a set, graph or formula

8.3                Interpret function notation in a practical setting

8.4                Identify ordered pairs from function notation

9.0                LINEAR EQUATIONS IN TWO VARIABLES

9.1                Identify a linear equation in two variables

9.2                Emphasize that the graph of a line is a visual representation of the solution set to a linear equation

9.3                Find ordered pairs that satisfy a linear equation written in standard or slope-intercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs

9.4                Find the intercepts given a linear equation; express the intercepts as ordered pairs

9.5                Graph the line using intercepts and check with a third point

9.6                Find the slope of a line from a graph and from two points

9.7                Given the graph of a line identify the slope as positive, negative, zero, or undefined.  Given two non-vertical lines, identify the line with greater slope

9.8                Graph a line with a known point and slope

9.9                Manipulate a linear equation into slope-intercept form;  identify the slope and the vertical-intercept given a linear equation and graph the line using  the slope and vertical-intercept and check with a third point

9.10            Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined

9.11            Given the equation of two lines, classify them as parallel, perpendicular, or neither

9.12            Find the equation of a line using slope-intercept form

9.13            Find the equation of a line using point-slope form

10.0            APPLICATIONS OF LINEAR EQUATIONS IN TWO VARIABLES

10.1            Interpret intercepts and other points in the context of an application

10.2            Write and interpret a slope as a rate of change

10.3            Create and graph a linear model based on data and make predictions based upon the model

10.4            Create tables and graphs that fully communicate the context of an application problem

11.0            LINEAR INEQUALITIES IN TWO VARIABLES

11.1            Identify a linear inequality in two variables

11.2            Graph the solution set to a linear inequality in two variables

11.3            Model application problems using an inequality in two variables

Introductory Algebra II

THEMES:
1.       Functions
2.       Graphical understanding
3.       Algebraic manipulation
4.       Number sense
5.       Problem solving
6.       Applications, formulas, and modeling
7.       Critical thinking
8.       Effective communication

SKILLS:

1.0                SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES

1.1                Solve and check systems of equations graphically and using the substitution and addition methods

1.2                Create and solve real-world models involving systems of linear equations in two variables

1.2.1           Properly define variables; include units in variable definitions

1.2.2           Apply dimensional analysis while solving problems

1.2.3           State contextual conclusions using complete sentences

1.2.4           Use estimation to determine reasonableness of solution

2.0                WORKING WITH ALGEBRAIC EXPRESSIONS

2.1                Apply the rules for integer exponents

2.2                Work in scientific notation and demonstrate understanding of the magnitude of the quantities involved

2.3                Add, subtract, multiply, and square polynomials

2.4                Divide polynomials by a monomial

2.5                Understand nonvariable square roots

2.5.1           Simplify using the product rule of square roots

2.5.3           Rationalize denominators

2.5.4           Estimate square roots

3.0                FACTORING POLYNOMIALS

3.1                Factor the greatest common factor from a polynomial

3.2                Factor a polynomial of four terms using the grouping method

3.3                Factor trinomials that have leading coefficients of 1

3.4                Factor trinomials that have leading coefficients other than 1

3.5                Factor differences of squares

3.6                Recognize and factor sums and differences of cubes

4.0                QUADRATIC EQUATIONS IN ONE VARIABLE

4.1                Solve quadratic equations using the zero product principle (factoring)

4.2                Solve quadratic equations using the square root property (see Section 2.5)

4.4                Make choices about the appropriate method to use when solving a quadratic equation

4.5                Understand that the solutions satisfy the original equation by checking the solutions

4.6                Distinguish between a linear and a quadratic equation and be able to solve both kinds of equations when mixed up in a problem set

4.7                Create and solve real-world models involving quadratic equations

4.7.1           Properly define variables; include units in variable definitions

4.7.2           Apply dimensional analysis while solving problems

4.7.3           State contextual conclusions using complete sentences

4.7.4           Use estimation to determine reasonableness of solution

5.0                QUADRATIC EQUATIONS IN TWO VARIABLES

5.1                Identify a quadratic equation in two variables

5.2                Create a table of solutions for the equation of a quadratic function

5.3                Emphasize that the graph of a parabola is a visual representation of the solution set to a quadratic equation

5.4                Graph quadratic functions by finding the vertex and plotting additional points without using a graphing calculator

5.5                Algebraically find the vertex, axis of symmetry, and vertical and horizontal intercepts and graph them by hand

5.5.1           The vertex as well as the vertical and horizontal intercepts should be written as ordered pairs

5.5.2           The axis of symmetry should be written as an equation

5.6                Determine whether quadratic functions are concave up or concave down based on their equations

5.7                Create, use, and interpret quadratic models of real-world situations algebraically and graphically

5.7.1           Evaluate the function at a particular input value and interpret its meaning

5.7.2           Given a functional value (output), find and interpret the input

5.7.3           Interpret the vertex using proper units

5.7.4           Interpret the vertical intercept using proper units

5.7.5           Interpret the horizontal intercept(s) using proper units

6.0                RELATIONS AND FUNCTIONS

6.1                Use the definition of a function to determine whether a given relation represents a function

6.2                Determine the domain and range of a function given as a graph or as a table

6.3                Apply function notation in graphical, algebraic, and tabular settings

6.3.1           Understand the difference between the input and output

6.3.2           Identify ordered pairs from function notation

6.3.3           Given an input, find an output

6.3.4           Given an output, find input(s)

6.4                Interpret function notation in real world applications

6.4.1           Evaluate the function at a particular input value and interpret its meaning

6.4.2           Given a functional value (output), find and interpret the input