MATH 096 Intermediate Algebra in Context (7 credits)
Prerequisite Satisfactory placement, or MATH 054 with at least a 2.0, or instructor permission.
Course Description
This course integrates numeracy, proportional reasoning, algebraic skills, and functional reasoning. Students will represent quantitative relationships in multiple ways in order to solve problems from a variety of authentic contexts. Linear and exponential functions, along with logarithms and radicals will be studied and applied. Modeling and interpreting quantitative data is emphasized.
Student Outcomes
Numeracy
1. Demonstrate operation sense by communicating in words and symbols the effects of operations on numbers. Apply the correct order of operations in evaluating expressions and formulas.
2. Demonstrate an understanding of the magnitude of real numbers represented in many forms (fractions, decimals, scientific notation, square roots of numbers) by ordering and comparing them in mathematical and real-world contexts.
3. Estimate results in appropriate contexts, using appropriate precision; use estimation to detect errors and evaluate the reasonableness of answers.
4. Use dimensional analysis to convert units, rates, and ratios from any given units to other units. Include conversions among and between U.S. and metric units using a variety of metric prefixes.
5. Demonstrate measurement sense by determining the sizes of objects and angles using measurements and estimation. Determine perimeter, area, surface area, and volume using appropriate units in both the U.S. and metric systems.
6. Demonstrate an understanding of the connection between the distribution of data and various mathematical summaries of data (measures of central tendency and of variation).
7. Read, interpret, and make decisions based upon data from tables and graphical displays such as line graphs, bar graphs, scatterplots, pie charts, and histograms. Given data, choose an appropriate type of graphical display and create it using scales appropriate to the application.
Proportional Reasoning
8. Recognize a proportional relationship from verbal, numeric, and visual representations. Link and create verbal, numeric, visual and symbolic representations of the relationship.
9. Compare proportional relationships represented in different ways, considering units when doing so.
10. Apply quantitative reasoning strategies to solve real-world problems with proportional relationships using whole numbers, fractions, decimals, and percents as appropriate.
Algebraic Skills and Reasoning
11. Distinguish between variables and constants. Represent real-world problem situations using variables and constants. Construct equations to represent relationships between unknown quantities.
12. Simplify algebraic expressions by using the distributive property, combining like terms, and factoring out a greatest common factor.
13. Evaluate formulas with multiple variables in a variety of contexts, including science, statistics, geometry, and financial math. Solve simple formulas for a specified variable.
14. Distinguish between expressions and equations and apply appropriate methods to each.
15. Solve linear equations in one variable, including problems involving the distributive property and fractions.
16. Construct inequalities to represent relationships, solve simple and compound inequalities in one variable, represent solutions using interval notation, and interpret solutions in the context of the situation.
17. Use basic exponent rules to simplify expressions, including those with negative exponents.
18. Solve basic power equations of the form xn = b using radicals.
19. Use the Pythagorean Theorem when appropriate in problem situations.
Functional Reasoning
20. Translate problems from a variety of contexts into mathematical representation and vice versa (linear, exponential, simple quadratics).
21. Describe the behavior of common types of functions using words, algebraic symbols, graphs, and tables. Include descriptions of the dependent and independent variables.
22. Identify when a linear model is reasonable for a given situation and, when appropriate, formulate a linear model. In the context of the situation interpret the slope and intercepts and determine the reasonable domain and range.
23. Determine the exponential function for a situation when given an initial value and either the growth/decay rate or a second function value. Interpret the initial value and growth rate of an exponential function. Include compound interest as one application.
24. Translate exponential statements to equivalent logarithmic statements, interpret logarithmic scales, and use logarithms to solve basic exponential equations.
25. Use functional models to make predictions and solve problems.
General Skills
26. Extract relevant information from complex scenarios. Obtain any necessary additional information from outside sources. Synthesize the information in order to solve problems and make decisions.
27. Identify which mathematical skills to use and then apply them in diverse scenarios and contexts.
28. Clearly communicate solution processes. Write solutions in the context of the problem in complete sentences, including units. Use mathematical notation and vocabulary correctly.
29. Use technology appropriately including calculators and computers.
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