MATH 106 Page 4 of 4
CUYAMACA COLLEGE
COURSE OUTLINE OF RECORD
MATHEMATICS 106 – INTERMEDIATE ALGEBRA FOR ENGLISH LANGUAGE LEARNERS
3.5 hours lecture, 1.5 hours laboratory, 4 units
Catalog Description
This is an accelerated one-semester algebra course for English language learners. Students enrolled in this course should concurrently enroll in ESL 021. This course leads to Math 075, Math 076, Math 078, Math 120 and Math 160. This course covers core concepts from arithmetic, pre-algebra, elementary and intermediate algebra, and general education mathematics. The core arithmetic and algebra skills needed to understand the concepts, formulas, and graphs used in Intermediate Algebra are investigated in a “just-in-time” approach. Intermediate Algebra topics include: solving and graphing linear equations and inequalities in one and two variables, solving and graphing systems of equations in two variables, arithmetic operations and factoring polynomials, solving quadratic equation using factoring, problem solving, and modeling with linear, quadratic, and exponential functions. Recommended for ESL students with little or no recent knowledge of algebra. A graphing calculator is required for this course.
Prerequisite
None
Course Content
1) Basic arithmetic operations, exponents, and order of operations
2) Estimation and number sense
3) Scientific notation
4) Interpreting and drawing visual displays of data
5) Functions
6) Solving application problems analytically that involve linear and quadratic equations and systems of equations
7) Solving application problems graphically that involve linear, quadratic, and exponential equations
8) Connections between graphical, numeric, and analytic representations of equations and functions
9) Dimensional analysis
10) Rates of change
11) Inductive and deductive reasoning
12) Inverse and direct variation
13) Linear, quadratic, and exponential regression
14) Arithmetic operations and factoring with polynomials
Course Objectives
Students will be able to:
1) Percentages and charts
a. Compute percentages
b. Create and interpret pie charts and bar charts using a spreadsheet and by hand
2) Crate and interpret Venn diagrams
3) Estimation and number sense
a. Make educated guesses
b. Plot points on a number line
c. Compare numbers using inequality symbols
d. Approximate square roots
4) Basic mathematics skills
a. Identify when it’s appropriate to add quantities
b. Interpret bank statements
c. Use Excel to compute sums
d. Calculate perimeter of rectangles and triangles
e. Interpret multiplication as repeated addition
f. Refresh multiplication and division skills
g. Distinguish between simple interest and compound interest
h. Interpret exponents as repeated multiplication
i. Apply the order of operations to simplify expressions
5) Comparing linear and exponential growth
a. Recognize patterns and use them to make predictions
b. Distinguish between linear and exponential growth
6) Dimensional Analysis
a. Identify units for area and volume
b. Convert units by multiplying and dividing
c. Articulate the meaning of scale in models and maps
d. Convert units using dimensional analysis
e. Interpret percentages in terms of scale
7) Rates of change
a. Interpret and use rates of change
b. Convert units involving rates
8) Relative difference
a. Compare difference and relative difference
b. Apply relative error
c. Find conversion factors for square and cubic units
9) Writing applied expressions
a. Distinguish between inputs and outputs
b. Evaluate expressions and formulas
c. Write and interpret expressions
10) Inductive and deductive reasoning
a. Use inductive reasoning to make a conjecture
b. Disprove a conjecture by finding a counterexample
c. Use deductive reasoning
11) Polya’s problem solving procedure
a. Identify the four steps in Polya’s problem solving procedure
b. Solve problems using a diagram
c. Solve problems using trial-and-error
d. Solve problems requiring calculations
12) Algebraic expressions in decision-making
a. Consider major life decisions that involve answering “Which is better?”
b. Decide if one option is better by looking at values in a table
13) Solve equations and inequalities and interpret the solutions in context
14) Basics of graphing
a. Use a rectangular coordinate system
b. Connect data to graphs
c. Interpret graphs
15) Slope and rate of change
a. Define and interpret slope as a constant rate of change
b. Define and interpret the intercepts of a line
c. Write equations of lines by recognizing slope and initial value
16) Variation
a. Identify quantities that vary directly
b. Identify quantities that vary indirectly
c. Write and use variation equations
d. Solve problems involving variation
17) Linear relationships and lines of best fit
a. Write an equation of a line that models data from a description, table, or graph
b. Decide if two data sets are linearly related
c. Find the line of best fit for data using spreadsheets and calculators
18) Solving problems with linear equations and systems
a. Use linear equations and systems of linear equations to solve applied problems
b. Illustrate problems with tables and graphs
19) Pythagorean theorem and distance
a. Use the Pythagorean theorem to solve application problems
b. Read contour maps and calculate grade
c. Develop and use the distance formula
20) Quadratic equations
a. Recognize when a graph is parabolic
b. Solve problems using the graph of a quadratic equation
c. Solve equations using the quadratic formula
d. Find and interpret the vertex of a parabola
e. Study physical phenomena using quadratic functions
21) Write large and small numbers in scientific notation
22) Factoring and function notation
a. Explain what factoring is and why it is useful in algebra
b. Use and interpret function notation
c. Identify the connection between zeros and x-intercepts
d. Factor expressions
23) Exponential functions
a. Identify and interpret the growth rate for exponential growth
b. Solve problems using graphs representing exponential growth and decay
c. Find an exponential curve of best fit for data
d. Identify and interpret the decay rate for exponential decay
Method of Evaluation
A grading system will be established by the instructor and implemented uniformly. Grades will be based on demonstrated proficiency in subject matter determined by multiple measurements for evaluation, one of which must be essay exams, skills demonstration or, where appropriate, the symbol system.
1) Individual and group exploratory projects, in-class activities, homework assignments, or exams which measure students’ ability to exhibit numerical and algebraic reasoning and computational skills; use graphic, numeric, and analytic methods to model linear, quadratic, and exponential functions; and solve application problems involving the same.
2) Individual and group exploratory projects, in-class activities, writing assignments, or exams which measure students’ ability to apply deductive and/or inductive reasoning to writing basic proofs.
3) In-class activities, homework, math notebook, or projects that demonstrate students’ ability to apply effective learning strategies.
4) Computer laboratory assignments in which students use linear, quadratic, and exponential regression to model data and make predictions; apply algebraic principles and problem-solving techniques discussed in class; and identify gaps in their skill attainment and concept mastery to improve their symbolic manipulation abilities and problem-solving skills.
Special Materials Required of Student
1) Scientific calculator
2) Graphing calculator
3) Access to Microsoft Excel
Minimum Instructional Facilities
1) Smart classroom with writing boards covering three walls, overhead projector, graphing utility overhead viewing panels, projection screen
Method of Instruction
1) Individualized instruction: computer-aided instruction or in-class individualized tutoring
2) Collaborative learning: group work or peer review student work
3) Modeling: instructor led-demonstrations and discussion or guided-discovery
4) Active learning: use of manipulatives, interactive computer-based instruction, or in-class activities requiring student participation
5) Class activities and assignments developed by math faculty
Out-of-Class Assignments
1) Problem sets
2) Exploratory activities and/or projects
3) Reading and/or writing assignments
Texts and References
1) Required (representative example): Pathways to Math Literacy by Dave Sobecki and Brian Mercer, McGraw-Hill 2015 (with McGraw-Hill Connect Access Card); ISBN-13: 978-1259316661
2) Supplemental: Exploratory projects and classroom activities developed by math faculty
Exit Skills
Students having successfully completed this course exit with the following skills, competencies, and/or knowledge:
1) Perform basic arithmetic operations: addition, subtraction, multiplication and division using positive and negative numbers.
2) Perform calculations involving fractions, decimals and exponents. Express numbers in scientific (exponential) notation.
3) Calculate percentages. Interpret percentages in terms of scale. Convert percentages into decimal form and vice versa.
4) Calculate measures of center and associated measures of spread: mean, variance, standard deviation median, quartiles, percentiles.
5) Use a scientific calculator to perform the types of calculations described above in items 1-4.
6) Solve linear and quadratic equations; and solve word problems involving the same.
7) Recognize plane geometric figures such as triangles and squares; differentiate among the terms linear, planar and three-dimensional.
8) Perform calculations and solve equations involving ratio and proportion techniques.
9) Graph data in a rectangular coordinate system.
10) Make connections between graphical, numeric, and analytic representations of equations and interpret each.
11) Use inductive and deductive reasoning to support an argument.
12) Use Inverse and direct variation to solve application problems.
13) Use linear, quadratic, and exponential regression to model data and solve application problems.
Student Learning Outcomes
Upon successful completion of this course, students will be able to:
1) Apply numerical and algebraic reasoning and computational skills to solve contextualized problems.
2) Construct, use, and interpret mathematical models, specifically linear, quadratic, and exponential functions to represent and communicate relationships in quantitative data.