MCCCD Program Description

Introductory Algebra

Course: MAT091

First Term: 2024 Fall

Lecture 4.0 Credit(s) 4.0 Period(s) 4.0 Load
Subject Type: Academic
Load Formula: S - Standard Load

Description: Emphasis on meanings related to variable, equality, inequality, equivalence. The use of additive and multiplicative reasoning in solving linear equations and inequalities in one variable. Validation of solution(s) through a reasonable mathematical defense. Transfer and apply knowledge through a process of sense making and reasonableness in mathematical problems and practical application situations. Recognize patterns and organize data to represent situations where output is related to input. Understand the concept of function and be able to represent functions in multiple ways, including tables, algebraic rules, graphs and contextual situations, and make connections among these representations. Read, represent, and interpret linear function relationships numerically, analytically, graphically and verbally and connect the different representations. Model and solve real world problems involving constant rate of change.

MCCCD Official Course Competencies
1. Build a case for algebra based on prior knowledge of number sense. (I, II, III, IV, V) 2. Define Algebra, Variable, Expression, Equality, Inequality, Equivalence. (I, II) 3. Interpret the structure of and evaluate expressions. (I, II) 4. Assign a variable based on reasonableness. (I, II) 5. Apply properties to manipulate expressions. (II, III, IV, V) 6. Create equations or inequalities that describe numbers or relationships. (II, III, IV, V) 7. Use additive and multiplicative identities and properties to solve linear equations and linear inequalities in one variable. (II, III, IV, V) 8. Demonstrate solving is a process of reasoning through the explanation of steps. (III, IV, V) 9. Validate solution(s) through a reasonable mathematical defense. (III, IV, V) 10. Transfer and apply knowledge through a process of sense making and reasonableness in mathematical problems and practical application situations. (III, IV, V) 11. Read, construct and interpret quantitative information when presented numerically, analytically, graphically or verbally, while looking for patterns. (VI) 12. Recognize and describe the meaning of each entry in an ordered pair. (VI) 13. Recognize that on a graph an ordered pair represents a horizontal and vertical distance from the origin. (VI) 14. Describe the distinction between continuous and discrete data. (VI) 15. Demonstrate how each point or collection of points on a graph represents the solution to a relation. (VI) 16. Identify and interpret horizontal and vertical intercepts when presented numerically, analytically, graphically or verbally. (VI, VII) 17. Describe how the change in one quantity (input) affects the other quantity (output). (VI, VII) 18. Model, solve and interpret solutions to contextual problems. (VI, VII) 19. Construct logical arguments about mathematical relationships and critique the reasoning of others in written and verbal form. (VI, VII) 20. Describe a mathematical relationship as a correspondence between two quantities and determine when a relationship is a function. (VII) 21. Represent functions in multiple ways, including tables, algebraic rules, graphs and contextual situations, and make connections among these representations. (VII) 22. Use and interpret function notation in terms of input and output, graphically and in contextual situations. (VII) 23. Determine the rate of change between two data points and interpret the meaning in terms of change of output compared to change of input (co-variational reasoning). (VIII) 24. Analyze and build tables and graphs using rate of change and a data point. (VIII) 25. Describe how the rate of change of a linear function relates to the behavior of the graph. (VIII) 26. Interpret the rate of change (slope) and the constant term (vertical intercept) of a linear model contextually. (VIII, XI) 27. Construct logical arguments about linear behavior and critique the reasoning of others in written and verbal form. (VIII, XI) 28. Model data that exhibit a constant rate of change with linear functions, equations and graphs. (IX) 29. Utilize and justify the use of equivalent forms of linear equations, such as slope-intercept, point-slope, and other standard forms, for solving a given problem. (IX) 30. Describe the relationship between vertical and horizontal lines and the concept of slope. (IX) 31. Construct an equation of a line when given the slope and vertical intercept or given the slope and a point or given two points, and express the equation in the various forms. (IX, XI) 32. Model contextual problems with systems of two linear equations, solve using graphing and algebraic techniques and interpret the solutions. (X, XI)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
I. Define A. Algebra B. Variable (unknown/varying) C. Expression D. Equation (equality, equivalence) E. Inequalities II. Expressions A. Properties B. Vocabulary C. Evaluate D. Simplify III. Equations A. Solving B. Validate solution IV. Inequalities A. Solving B. Graph C. Symbolic representation D. Notation (Interval, Set) V. Practical applications A. Reasonableness B. Sensemaking VI. Representations of relationships A. Data/tables B. Graphs C. Verbal descriptions D. Formulas E. Connect representations VII. Functions A. Definition B. Notation C. Input/output D. Domain/range E. Intercepts F. Contextual VIII. Linear behavior A. Slope B. Initial value, intercepts C. Graphing D. In context IX. Equations A. Standard forms B. Graphs X. Systems A. Algebraic B. Graphical XI. Applications A. Solve linear equations B. Graph linear functions given data tables or an equation

MCCCD Governing Board Approval Date: May 1, 2018

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.