The MCCCD Official Course Description for MAT091 is as follows.

```   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.

Requisites: Prerequisites: A grade of "C" or better or satisfactory
Math Diagnostic Assessment score for (MAT051, MAT052, MAT053, and MAT054),
or MAT081, or MAT082.
```

The MCCCD Official Course Competencies for MAT091 are as follows.

```1. Build a case for algebra based on prior knowledge of number sense.
2. Define Algebra, Variable, Expression, Equality, Inequality, Equivalence.
3. Interpret the structure of and evaluate expressions.
4. Assign a variable based on reasonableness.
5. Apply properties to manipulate expressions.
6. Create equations or inequalities that describe numbers or relationships.
7. Use additive and multiplicative identities and properties to solve
linear equations and linear inequalities in one variable.
8. Demonstrate solving is a process of reasoning through the
explanation of steps.
9. Validate solution(s) through a reasonable mathematical defense.
10. Transfer and apply knowledge through a process of sense making
and reasonableness in mathematical problems and practical
application situations.
11. Read, construct and interpret quantitative information
when presented numerically, analytically, graphically
or verbally, while looking for patterns.
12. Recognize and describe the meaning of each entry in an ordered pair.
13. Recognize that on a graph an ordered pair represents a horizontal
and vertical distance from the origin.
14. Describe the distinction between continuous and discrete data.
15. Demonstrate how each point or collection of points on a graph
represents the solution to a relation.
16. Identify and interpret horizontal and vertical intercepts when
presented numerically, analytically, graphically or verbally.
17. Describe how the change in one quantity (input) affects the
other quantity (output).
18. Model, solve and interpret solutions to contextual problems.
19. Construct logical arguments about mathematical relationships and
critique the reasoning of others in written and verbal form.
20. Describe a mathematical relationship as a correspondence between
two quantities and determine when a relationship is a function.
21. Represent functions in multiple ways, including tables, algebraic
rules, graphs and contextual situations, and make connections among
these representations.
22. Use and interpret function notation in terms of input and output,
graphically and in contextual situations.
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).
24. Analyze and build tables and graphs using rate of change and a data point.
25. Describe how the rate of change of a linear function relates to the
behavior of the graph.
26. Interpret the rate of change (slope) and the constant term (vertical
intercept) of a linear model contextually.
27. Construct logical arguments about linear behavior and critique
the reasoning of others in written and verbal form.
28. Model data that exhibit a constant rate of change with linear
functions, equations and graphs.
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.
30. Describe the relationship between vertical and horizontal lines
and the concept of slope.
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.
32. Model contextual problems with systems of two linear equations, solve
using graphing and algebraic techniques and interpret the solutions.
```

Creator: Gerald Thurman [gthurman@gmail.com]