Course Description:
Covers linear equations, linear systems, linear inequalities and quadratic
equations in verbal,
numerical, graphical and symbolic forms . Also covers negative exponents,
scientific notation
and dimensional analysis. Explores topics using a graphing calculator as well as
traditional
approaches.
Performance-Based Learner Outcomes:
Upon successful completion of the course, students should be able to:
1. Create mathematical models of abstract and real world situations using linear
equations, linear systems, linear inequalities and quadratic equations.
2. Use inductive reasoning to develop mathematical conjectures involving linear
equations,
linear systems, linear inequalities and quadratic equations. Use deductive
reasoning to
verify and apply mathematical arguments involving these algebraic concepts . Be
able to
distinguish between the concepts of inductive and deductive reasoning.
3. Use mathematical problem solving techniques involving linear equations,
linear
systems, linear inequalities, quadratic equations and dimensional analysis.
Techniques include the use of tabular, graphical, symbolic and narrative
representations.
4. Make mathematical connections to, and solve problems from, other disciplines
involving
linear equations, linear systems, linear inequalities, quadratic equations and
literal equations .
5. Use oral and written skills to communicate about linear equations, linear
systems,
linear inequalities and quadratic equations.
6. Use appropriate technology to enhance mathematical thinking and
understanding, to
solve mathematical problems involving linear equations, linear systems, linear
inequalities and quadratic equations, and judge the reasonableness of results.
Course Content:
1. Number Sense: Describe recursive patterns in linear data. Solve linear
equations,
linear systems of equations and quadratic equations from data.
2. Symbolism: Create a symbolic form of a linear equation in two variables from
data
and graphs. Solve linear equations, systems of linear equations, linear
inequalities and
quadratic equations symbolically and with the use of data tables and graphs.
Solve
literal equations symbolically. Use the distributive property to change
polynomials
from factor to term form and term to factor form. Model the distributive
property as
area of a rectangle. Confirm and use the Pythagorean Theorem and its converse.
Develop the distance formula and the relationship of slopes of perpendicular
lines
using right triangles.
3. Problem Solving: Apply appropriate mathematical concepts and mathematical
models, including linear equations, systems of linear equations, linear
inequalities,
quadratic equations and dimensional analysis, to solve abstract and real world
problems.
4. Technology: Use a graphing calculator to investigate the nature of linear
equations,
linear systems and quadratic equations. Use the graphing calculator to aid in
numerical calculations and decimal approximations.
5. Communication: Communicate mathematical ideas using appropriate terminology
by
reading, writing, listening and speaking in group and individual settings.
Course Content Outline:
I. Linear Equations
A. Review input-output tables and Cartesian coordinate graphs
B. Identify and calculate linear slopes and rates
C. Write equations of a line in slope- intercept form
D. Identify slope and y intercept from an equation of a line
E. Represent a line graphically from slope intercept form and using a
graphing calculator
F. Solve linear equations using data tables, graphically and symbolically
G. Solve linear equations using a graphing calculator
H. Model linear relationships with an approximation of the line of best
fit
I. Applications of rates and linear equations
J. Solve literal equations
II. Linear Systems of Equations
A. Solve systems of equations with data tables and graphs
B. Solve systems of equations by substitution
C. Solve systems of equations by elimination
D. Solve systems of equations using a graphing calculator
E. Applications using systems
III. Linear Inequalities
A. Define inequality
B. Write an inequality relationship
C. Solve inequalities graphically and symbolically
IV. Exponents , Polynomials and Other Algebraic Expressions
A. Representations of polynomials
B. Multiplying polynomials using the distributive property
C. Factoring polynomials
D. Laws of exponents
E. Scientific notation
F. Solve quadratic equations using data tables, graphically, by square
root method, by factor method and quadratic formula
G. Solve quadratic equations using a graphing calculator
H. Applications including Pythagorean theorem, distance formula
V. Dimensional Analysis
A. Convert between measures of mixed units
B. Use rates to set up the appropriate unit fraction
