### CCOG for ABE 0787 Winter 2024

- Course Number:
- ABE 0787
- Course Title:
- Foundations of Math 2
- Credit Hours:
- 0
- Contact Hours:
- 60-72

#### Course Description

#### Addendum to Course Description

Recommended Reading Placement: Accuplacer Reading 35 or higher/Accuplacer Next Gen 223 or higher; CASAS Reading score of 228 or higher.

Recommended Math Placement: CASAS Math score of 215 or higher.

Total contact hours: 60-72

#### Intended Outcomes for the course

Upon completion of the course students should be able to:

- Solve problems and make decisions using multiple and effective math strategies, with particular emphasis on scientific problems.
- Understand, interpret and work with concrete objects and symbolic representation (e.g. pictures, numbers, graphs, computer representations)
- Utilize technology to solve a mathematical problem, with particular emphasis on scientific problems.
- Apply scientific reasoning to problem-solving activities.
- Determine the degree of precision best suited to solve GED mathematical problems.

#### Aspirational Goals

- Appreciate learning of Mathematics
- Ability to apply scientific reasoning in daily life
- Use math in a powerful way to achieve goals
- Exhibit persistence, self-motivation, self-advocacy, and personal responsibility
- Reflect upon, assess, identify, and celebrate one’s own learning gains
- Explore, develop, and monitor appropriate academic and professional goals
- Advance knowledge and skills to make independent choices as a citizen, family member, worker, and life-long learner

#### Course Activities and Design

- Interpret and apply a variety of complex patterns, functions, and relationships, using technology strategically.
- Create and analyze a wide variety of relations, including linear and exponential functions
*(e.g., develop decay models based on relationship of data)* - Recognize, graph, and use direct or inverse proportional relationships
- Create different representations to illustrate complex patterns or relationships
- Solve two linear equations in two variables both algebraically and using a graphing calculator
- Analyze real life situations involving complex patterns, functions, and relationships
*(e.g., compare the cost of leasing vs. buying a vehicle)*

- Create and analyze a wide variety of relations, including linear and exponential functions
- Read and interpret a variety of complex symbolic information.
- Convert rational expressions to exponential expressions
- Solve quadratic equations by completing the square
- Develop the quadratic formula by completing the square of the standard form of a quadratic equation
- Combine and factor polynomials and expressions with rational exponents

- Read and interpret a variety of complex data and statistical information.
- Predict potential consequences from interpretations of data
- Make inferences based on the shape, spread, center of the data, and possible outliers
- Describe skewed distributions

- Formulate questions and design studies that can be answered with a variety of complex data and collect, organize, and represent the relevant data to answer them, using technology strategically.
- Develop a research question and analyze how the randomness of the sample will influence the results
- Compare two variables and informally estimate lines of best fit
*(e.g., in a scatter plot)*to test hypotheses - Make and evaluate inferences and predictions and formulate new questions
- Create two‐way tables, collect appropriate data, and describe any relationships among the categories

- Interpret and apply a variety of complex probability concepts.
- Estimate the probability of an event occurring, then test it out and record the results
*(e.g., predict how many times the coin would land on heads in 500 tosses, then toss the coin 200 times and observe the data changes)* - Find the theoretical probability of compound events using diagram trees, organized lists, or tables
- Develop a simple probability model and use it to find and compare probabilities of events occurring
*(e.g., A probability model for the probability of drawing an ace from a deck of cards is P(ace) = 4/52.)* - Apply and interpret probability and expected value to real life situations (e.g., weather forecast; fair game; stock market; etc.)

- Estimate the probability of an event occurring, then test it out and record the results
- Read, write, interpret, and apply a variety of complex mathematical information related to measurement and geometry, using technology strategically.
- Use the definitions of trigonometric ratios to find the sine, cosine, and tangent of the acute angles of a right triangle
- Develop and write simple informal geometric proofs
*(e.g., the Pythagorean theorem)*and explain the reasoning behind them - Create and explain rotations and reflections of rectangles, trapezoids, and parallelograms

- Select and apply sophisticated, multi‐step mathematical procedures, using technology strategically.
- Solve problems and informally prove theorems involving perpendicularity and parallelism
- Solve problems involving congruence and similarity of geometric figures
*(including three**‐**dimensional figures)* - Identify the characteristics of a 3‐ dimensional object from its 2‐ dimensional representation
- Solve problems involving circles
*(including arcs, chords, angles)*

- Apply a variety of complex mathematical information and concepts to real‐life and theoretical problems involving whole numbers/integers, using technology strategically.
- Use place value and the commutative, associative, and distributive properties to create equivalent representations of integers of any size
- Add subtract, multiply, and divide integers to solve a variety of problems

- Apply a variety of complex mathematical information and concepts to real‐life and theoretical problems involving rational numbers, using technology strategically.
- Determine to what degree a decimal result (product or quotient) is valid when used with measurements
*(e.g., Gas prices are shown to the nearest thousandth but we pay to the nearest hundredth.)* - Categorize real numbers as either rational or irrational
*(e.g., be able to explain that the decimal expression of an irrational number never ends and never repeats; recognize and use 22/7 or 3.14 as approximations for the irrational number represented by pi)*

- Determine to what degree a decimal result (product or quotient) is valid when used with measurements
- Apply a variety of complex mathematical information and concepts to real‐life and theoretical problems involving exponents, using technology strategically.
- Evaluate expressions with positive and negative exponents to solve problems such as growth or decay over time
- Use rational expressions to solve problems

#### Outcome Assessment Strategies

- Apply common types of mathematical information and concepts to real-life and theoretical problems involving rational numbers.
- Complete homework and/or computer-based assignments
- Read and interpret common data and statistical information
- Interpret and apply common patterns, functions and relationships using technology
- Move up a level in the Math CASAS Post Test and pass a teacher generated post test
- Pass at least one real-world application activity (Capstone)
- Pass the GED Mathematics Exam
- Pass the GED Science Exam
- Test into Math 60 or above

#### Course Content (Themes, Concepts, Issues and Skills)

**Themes:** Family, Citizen, Lifelong Learner, Worker, Science, Social Studies and Metacognition**Concepts:** goal setting, critical thinking, math vocabulary, decision making, confidence building, collaborative team work**Issues:** barriers to student success, access to resources, communication skills, learning differences, test and school anxiety, employability, testing strategies, cultural awareness, motivation, persistence, employment, and complex life issues**Skills:**

1.1.Ratios and Proportions

1.2.Advanced Applications of Percentages

1.3.Computing Interest

1.4.Mean, Median, Mode and Range and apply to scientific problems

1.5.Probability

1.6.Graphs, Tables, Charts and Graphic Methods of Data Analysis

1.7.Coordinate Plane

1.8.Slope Formula

1.9.Distance between two points (Coordinates)

1.10.Pythagorean Theorem

1.11.Absolute Value

1.12.Official GED Calculator

1.13.Algebra one step and multistep Equations

1.14.Quadratic Formula

1.15.Quadratic Factoring

1.16.Algebraic Factoring

1.17.Geometric Measurement (Area, Perimeter, and Surface Area)

1.18.Apply scientific reasoning to problem-solving activities