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CCOG for ABE 0782 Winter 2024

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Course Number:
ABE 0782
Course Title:
Foundations of Math 1
Credit Hours:
Contact Hours:

Course Description

Introduces mathematical concepts numerically, graphically, and symbolically, in oral and written form. Covers whole numbers, fractions and decimals to write, manipulate, interpret and solve application and formula problems. Recommended: (Placement into RD 80 or higher or CASAS reading score of 221 or higher) and placement below MTH 20.

Addendum to Course Description


Reading Placement: Accuplacer Reading 26 or higher/ Accuplacer Next Gen 210 or higher;

ABE 0790 or higher/CASAS Reading score 217 or higher.

Recommended Math Placement:  below Math 20; CASAS Math score 193-214.

Total contact hours: 60-72

Intended Outcomes for the course

Upon completion of the course students should be able to:

  • Use mathematical and other problem-solving strategies to formulate problems, to solve problems using multiple approaches, to interpret results, and to use technology strategically.
  • Choose and perform accurate arithmetic operations in a variety of situations with and without a calculator, with particular emphasis on scientific problems.
  • Present results numerically, symbolically, and graphically in written and oral form.
  • Estimate and compute personal needs relating to life skills through mathematics.

Aspirational Goals

Aspirational Goals

  • Appreciation of learning mathematics
  • Use math in a powerful way to achieve goals
  • Ability to apply scientific reasoning in daily life
  • 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
  • Continue life-long learning by participating in educational opportunities when possible

Course Activities and Design

  1. Interpret and apply a few common patterns, functions, and relationships, using technology strategically.
    1. Recognize and develop repeating patterns and generalize the relationship with a table, rule, graph, or one‐step formula (e.g., I make $7 an hour. If I work 30 hours a week, I can figure out how much I make in N weeks by multiplying N x 7 x 30, or Total wages = N(7 x 30).)
    2. Identify, describe, and use common properties of operation (e.g., associative and distributive property)
  2. Read and interpret common symbolic information.
    1. Show repeated multiplication for simple whole numbers using exponents (e.g., 34 = 81)
    2. Use variables to explain real‐life situations (e.g., “If there are 8 items in each box, then I can figure out that the total number of items, N, is 8 times the number of boxes, or N = 8b.”)
    3. Apply order of operations to evaluate expressions
    4. Write statements of equality and inequality (e.g., 3 > 4 3)
    5. Solve simple one‐step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation
  3. Read and interpret common data and statistical information.
    1. Extract discrete information from lists, tables, bar graphs, pictographs, or line plots
    2. Describe how the scale in a bar or line graph can distort interpretations of data
    3. Make statements and numerical comparisons about relative values on a bar graph (e.g., “One category is 3 times greater than another.” or “This bar extends more than halfway between 25 and 50.”)
    4. Identify the range, median, mean and mode of small data sets (e.g., the ages of the students in the class)
  4. Pose questions that can be answered with common data and collect, organize, and represent the relevant data to answer them.
    1. Design simple data investigations to address a question and collect categorical data
    2. Organize categorical data and represent them in a line graph or stem‐and‐ leaf plots
    3. Verify that data represented are the actual data collected
    4. Make simple, straightforward inferences based on the data
  5. Interpret and apply basic probability concepts.
    1. Predict and then conduct simple probability experiments with outcomes limited to between one and four choices (e.g., fourcolor spinner)
    2. Connect a percent (0%, 25%, 50%, 75%, or 100%) and their fraction equivalents to the expected probability (e.g., of a fourcolor spinner)
    3. Compare the likelihood of two uncertain outcomes using simple language (e.g., one spinner with half red and half yellow and another spinner with one fourth red and three fourths yellow, asking students, “Do you think you will have the same chance at landing on red in each of these spinners? Why?”)
  6. Read, write, interpret, and apply common types of information related to measurement and geometry, using technology strategically.
    1. Recognize and use commonly used standard units of measure to the nearest eighths, tenths, and thirds
    2. Use measurement units to describe the environment (e.g., Do you measure wire thickness in inches or mm? Is your height measured in cm or m?)
    3. Recognize and describe two‐ dimensional shapes, including basic angle descriptions (such as acute, right and obtuse) and properties of lines (e.g., perpendicular; parallel)
    4. Measure and compare radius, diameter, and circumference of a circle and informally develop an equation for determining the diameter or circumference (e.g., C is about 3d, so pi is about 3)
    5. Make conjectures about the formulas for simple two‐ dimensional shapes (e.g., “Since I can cut a rectangle into two equal triangles, I think that I can find the area of a triangle if I can create the rectangle it came from.”)
    6. Demonstrate an informal understanding of the coordinate graph system (e.g., find locations on a map using a grid system)
  7. Select and apply mathematical procedures, using technology strategically.
    1. Identify and use appropriate tools to measure to the nearest benchmark fractional unit (both decimal and fraction), including metric units
    2. Make simple conversions within the same measurement system (e.g., inches to feet; cm to m)
    3. Use direction, distance, labels, simple scales, and symbols to read and use maps and plans
    4. Determine whether two‐ dimensional shapes have similar attributes and properties (e.g., Are they congruent?)
    5. Determine the area and perimeter of common two‐ dimensional shapes and ex‐ plain what happens to the area and perimeter when a dimension is changed
    6. Measure size of angles and use benchmark angles (e.g., 90° and 45°) to estimate size of angles
    7. Use ratio and proportion to solve problems involving scale drawings or similar figures
  8. Apply common types of mathematical information and concepts to real‐life and theoretical problems involving whole numbers/integers, using technology strategically.
    1. Use the knowledge that multiplication and division are inversely related to develop efficient and accurate strategies for multiplying and dividing three‐digit numbers by one‐digit numbers
    2. Multiply and divide to solve a variety of problems, including those related to geometry, measurement, and data
    3. Estimate to predict answer when an exact answer is not needed or to determine reasonableness of computation
    4. Recognize and apply negative integers in real contexts (e.g., The temperature was 20 degrees but went down to 5 overnight. How much did the temperature drop?)
    5. Identify prime and composite numbers and describe the difference between them
    6. Use divisibility rules for 2, 3, 5, 10 and explain why they work
  9. Apply common types of mathematical information and concepts to real‐life and theoretical problems involving rational numbers, using technology strategically.
    1. Use the commutative, associative, and distributive properties to create equivalent representations of numbers up to 10,000 (e.g., 8,900 = 9(1000) 100) and to the nearest hundredth (e.g., $28.98 = 2(1.000) + 9.00 .02 )
    2. Extend benchmark fractions to equivalent decimals and percents (1/8, 1/6, 1/10, 1/100, etc.) and explain how these relate on a number line
    3. Explain ratios as equivalent forms of benchmark fractions (e.g., 2/4 = 1/2)
    4. Demonstrate that multiplying by a fraction is the same as dividing by the whole number in the denominator (e.g., 10 x 1⁄2 is the same as 10 ÷ 2.)
    5. Use benchmark fractions, decimals, and percents (e.g., 3⁄4 and 1/10) to estimate relative sizes (e.g., 11/16 is close to 3⁄4 because 12/16 is the same as 3⁄4.)
    6. Apply proportional reasoning to simple, one-step problems (e.g., If 5 pounds of potatoes cost $4, how much would 10 pounds cost?)
  10. Apply common types of mathematical information and concepts to real life and theoretical problems involving exponents, using technology strategically.
    1. Use the exponent 2 to express the area of two‐dimensional figures

Outcome Assessment Strategies

  • Complete a post-test of math word problems using a GED approved calculator
  • Take COMPASS test and place into Math 20
  • Take CASAS math pre and progress test and improve one level
  • Pass at least one real-world application activity (Capstone)
  • Pass at least five in-class examinations - Whole numbers, fractions and decimals testing without calculator. No more than 50% of any test can be multiple choice
  • Complete at least two or more of the following measures: At least one written explanation of a mathematical concept, take-home examinations, Graded homework, Quizzes, Group projects, In-class activities, Attendance, Portfolios, Individual projects, Individual student conference, Community based service learning

Course Content (Themes, Concepts, Issues and Skills)


  • Life (e.g. family and citizen) and employability (i.e. worker) planning
  • Life-long learning
  • Metacognition
  • Goal setting
  • Critical thinking skills
  • Team work
  • Science
  • Social Studies


  • Time management (attendance and completing tasks)
  • Social skills (communication and diversity)


  • Confidence building
  • Communication styles
  • Employability attributes
  • Access to resources for students success
  • Math anxiety


1.0 Basic Arithmetic Facts

1.1 Solve numerical and application problems with GED specific calculator

1.2 Perform order of operations accurately using whole numbers

1.3 Develop skills in estimation and number sense

1.4 Master fraction and decimal vocabulary

1.5 Solve numerical and application problems with fractions and decimals

1.6 Round a given number to a specified place

1.7 Arrange numbers in numerical order

1.8 Perform order of operations accurately using fractions and decimals

1.9 Determine whether a given whole number is prime or composite

1.10 Evaluate expressions containing exponents and square roots

1.11 Perform operations accurately using fractions, decimals, and percents

1.12 Solve application problems with fractions, decimals, and percents

1.13 Read and interpret data from bar, pictorial, line, circle graphs, tables, charts and various graphs

1.14 Find statistical measures such as median, mode, mean and apply to scientific problems

1.15 Apply scientific reasoning to problem-solving activities

1.16 Scientific Notation