Description

Math 1030 Video Overview
*A one semester course generating 3 credits of post-secondary study at Utah Institutions of Higher Education. *
Prerequisite: Math 1010 or Equivalent.

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Concurrent Enrollment Mathematics 1030 requires students to use advanced mathematical concepts to make decision and communicate ideas within five domains: statistics, logic, probability, mathematical modeling, and financial management. The course necessitates students to reason abstractly and quantitatively to make decisions about situations and then communicate their decisions using a mathematical argument. Further, students will use appropriate tools, including technology, to model their mathematical thinking, and use structure and regularity to describe mathematical situations and solve problems.

Mathematics 1030 consists of five modules: Statistics, Logic, Probability, Modeling with Mathematics, and Financial Management. The modules are presented in the syllabus below in a recommended order, however it is up to the Institution of Higher Education (IHE) with which a secondary institution has a contractual agreement to decide the order of the modules or whether to let the instructor decide for him or herself the order. Additionally, there are modules at the end of the syllabus that should be part of a yearlong high school *Mathematical Decision Making* course but are not part of Math 1030.

At the end of each module, it is recommended that students take the Utah System of Higher Education (USHE) module assessment as a formative indicator of student progress. At the end of the course there is also a required USHE final assessment. Based on this final assessment, students will receive one of three designations: "exceeded expectations," "met expectations," or "did not meet expectations." Individual high schools and IHE's determined high school and college credit and grades for Math 1030.

Each module identifies the "Mathematical Foundation" and "Application of Mathematics" for module topics. The Mathematical Foundation identifies the content that is to drive the understanding, communication and decision contexts identified by the Mathematical Foundation list. The Mathematical Foundation topics only identify the broad mathematical concepts within the course. It is understood and expected that the course involve rich mathematics and real application. The ultimate goal (as explicated in the Expected Learning Outcomes section below) is that students leave the course with a fundamental ability to apply mathematical reasoning to a variety of contexts they are likely to experience in the future.
Text: Although the materials being prepared for this course are meant to suffice for instruction, we recommend, where feasible, adopting the text used in most Utah higher education institutions:

*Using and Understanding Mathematics*, by J.O. Bennett and W.L. Biggs, Second Edition, Addison-Wesley (see http://wps.aw.com/aw_bennett_usingandun_2/)

Learning Outcomes

- The student is able to apply mathematics-based skills used in college and career, including reasoning, planning and communication, to make decisions and solve problems in applied situations.
- The student is able to analyze numerical data using a variety of quantitative measures (tables, graphs, statistics) and numerical processes.
- The student analyzes and evaluates risk and return in the context of everyday situations, making decisions based on understanding, analysis and critique of statistical information.
- The student can communicate methods and results in statistical studies and reports.
- The student can model data in a variety of ways, generate predictions and evaluate their validity.
- The student uses mathematical models to represent, analyze and solve problems involving change.
- The student uses mathematical models and analyses to make decisions related to earning, investing and borrowing.
- The student can generate network models to organize data, make decisions and solve problems.

Course Modules

Module 1: Logic (Numbers, Sets, Logical Thinking And Counting)

Standard I: Students will use the mathematics of logic to make decisions.
*Mathematical Foundation:*

Inductive & Deductive Reasoning

Logic, statements and definitions & Critical Thinking

Relationships in Sets & Counting

Set operations & Venn diagrams

*Application of Mathematics:*

Objective 1: Understand and interpret logical arguments.

- Identify an argument’s premise and conclusion.
- Critique an argument by being able to recognize logical flaws (e.g., begging the question, confusing evidence with proof.)
- Analyze an argument and support your critique using precise logic statements.
- Analyze inductive arguments based on the strength and validity of the evidence presented, using real examples from contemporary news.
- Use precise language to explain relationships among sets using categorical propositions or Venn diagrams.
- Evaluate arguments using strength for inductive arguments, validity and/or soundness for deductive arguments, validity for Venn diagrams, and/or chains of condition

Module 2: Modeling with Mathematics

Standard II: Students will use mathematical models to organize, communicate, and solve problems.
*Mathematical Foundation:*

Linear, Exponential, Logarithmic and Geometric Models

*Application of Mathematics:*

Objective 1: Use various mathematical models to understand, explain, and make decisions about real world situations

- Distinguish contexts in terms of change: linear (additive change); exponential (multiplicative change)
- Model and solve problems by recursive relations, identifying and distinguishing among linear, exponential, cyclical, and logistic processes
- Model mathematical problems with algebraic and geometric tools
- Attain flexibility in the use of tables, algebraic expressions, graphs and charts to represent the various modeling strategies.
- Use models to predict future or past values and justify the models
- Explain factors that limit or affect models in real life situations

Module 3: Probability

Standard III: Students will use the mathematics of probability to make decisions.
*Mathematical Foundation:*

Fundamentals of Probability

Independent and Conditional Probability

Calculating Probabilities

Probability & Odds

Expected Value

Introduction to counting

*Application of Mathematics:*

Objective 1: Understand and use probability in a variety of contexts.

- Apply appropriate probability rules to real life situations.
- Use predicted outcomes to make decisions about real life situations.
- Understand and explain real life incidences relative to probability.
- Given a set of facts, be able to make a reasonable argument about the likelihood of an event.

Objective 2: Use the rules of probability to calculate independent and conditional probabilities in real contexts.

- Calculate probabilities using addition and multiplication rules, tree diagrams, and two-way tables using correct probability notation.
- Calculate conditional probabilities of compound events using two-way tables and Venn diagrams.
- Use permutations and combinations to find probabilities.

Objective 3: Analyze risk and return in the context of everyday situations.

- Construct and analyze tree diagrams, Venn diagrams, and area models to make decisions in problem situations.
- Construct and interpret two-way frequency tables of data.
- Weigh the possible outcomes of a decision using expected values and probabilities to payoff values
- Use probabilities to make fair decisions.
- Analyze decisions and strategies using probability concepts.

Module 4: Statistics
Standard IV: Students will use statistics to make decision.
*Mathematical Foundation:*

Describing data: mean and median, variation and SD;

Sampling and measures of central tendency;

Bivariate data: correlation, best fit, causality;

Basic distributions: differences among various distributions, relation to context.

*Application of Mathematics:*

Objective 1: Use and communicate data in written and quantitative forms.

- Calculate a mean, median, and/or mode of data, describe its spread, identify outliers and communicate the significance in interpretation of the data to make an argument or decision about the data and its use.
- Discuss shape of the distribution: peaks, symmetry, skewness , variation and standard deviation as part of the interpretation of the data set.
- Understand and use measures of variation in interpreting and using data.
- Use and interpret bivariate data to make an argument or decision.

Objective 2: Understand and communicate statistical information.

- Report results of statistical studies in both oral and written form including graphical representations.
- Describe strengths and weaknesses of sampling techniques, data and graphical displays, and interpretations of summary statistics.
- Describe the relationship between various distributions and the contexts and or processes to which they relate best.
- Identify uses and misuses of statistical analyses.

Module 5: Financial Management

Standard V: Students will use mathematical analysis to manage personal resources and make financially sound decisions.
*Mathematical Foundation:*

Increments as addends or percentages

Simple Interest

Compound Interest

Relationship of recursive definition of processes and formulae for end results.

*Application of Mathematics:*

Objective 1: Determine, represent, and analyze mathematical models for various types of income calculations.

- Analyze models related to investing and income growth.
- Differentiate between rates proportional to the original amount and the previous amount.
- Select the most advantageous interest rate given two different sets of conditions.
- Create mathematical models that represent projected income or growth.

Objective 2: Determine, represent and analyze mathematical models of various types of loan calculations.

- Understand terms and conditions of loans, how they may vary and how to compute total amount repaid at any stage during the loan.
- Understand and use amortization tables and use them in making financial decisions.
- Understand loan payment and/or prepayment/principal payment strategies and how they affect total interest paid over the lifetime of a loan.
- Create amortization tables for a variety of situations.

Sample Videos

V Financial Math Introduction (6:43)
V1.2 Successive Discounts (10:22)
High School Modules:

These materials constitute that part of the course, Mathematical Decision Making for Life, that is not included in the above, and are recommended for the full year course. References are to the USOE Standards for this course

Module 6: Modeling with Matrices

Quarter B, Standard II, Objective 1

Module 7: Design of Experiments
Quarter C, Standard III, Objective 3

Module 8: Models of Choice

Quarter A, Standard I, Objectives 1,2: Personal Budgets

Quarter D, Standard V, Objectives 2,3,4: Selections, Flow Charts, Networks