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1. Division:

  Sciences & Mathematics

2. Course Discipline:


3. Course Number:


4. Course Title:


5. First semester this new version/new course will be offered: Fall 2018




General Course Information


1. Units: 6.0                 Variable units N/A

2. This Course is:

Degree-Applicable Credit - Non-Transferable


3A.  Cross-List: 


3B.  Formerly:




Course Format and Duration


4. Standard Term Hrs per Wk


5. Standard Term Total Semester Hrs
















By Arrangement:



By Arrangement:


Total Hrs per Wk



Total Hrs



6. Minimum hours per week of independent work done outside of class:    12


Course Preparation – (Supplemental form B required)


7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)


7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)


7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)




Catalog Description And Other Catalog Information


8. Repeatability:

Not Repeatable

Please Note: 8. (Repeatability) does not refer to repeating courses because of substandard grades or a lapse of time since the student took the course. A course may be repeated only if the course content differs each time it is offered and the student who repeats it is gaining an expanded educational experience as stipulated in Title 5.


Skills or proficiencies are enhanced by supervised repetition and practice within class periods.

Active participatory experience in individual study or group assignments is the basic means by which course objectives are attained.

Course content differs each time it is offered.


Explanation for above repeatability selection:


9a. Grading Option:

Standard Grade

9b. Catalog Description:

Practical Mathematics is a one semester course for non-math, non-science majors covering the topics of numeracy, proportional reasoning, algebraic reasoning, trigonometric reasoning, data analysis and critical thinking through real world applications. Students will develop the marketable skills needed to apply mathematics and technology to analyze and interpret data. Algebraic, geometric and trigonometric topics covered include: real numbers and their properties; proportions; measurement of lengths, areas and volumes; first degree equations and inequalities; graphs of linear, quadratic, power, exponential and logarithmic equations; quadratic, exponential, and logarithmic equations; and basic right triangle trigonometry. Not intended for students on the Calculus track.




Course Outline Information


10. Course Objectives: (Course objectives for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Course objectives must be related to items listed in Section 11.)

Upon successful completion of this course, the students will be able to:

1. Execute basic order of operations and demonstrate the effects of common operations with signed numbers, fractions and decimals in both words and symbols.
2. Apply estimation techniques using technology in a manner mathematically appropriate for the context of the situation.
3. Demonstrate the ability to measure and perform dimensional analysis with variety of units of measure such as length, area, volume and weight.
4. Demonstrate competency in the use of magnitude in the context of place values, fractions and numbers written in scientific, engineering and pre-fix notation.
5. Read, interpret, analyze and make decisions based upon data collection and computer processed results given including from line graphs, bar graphs, root graphs, exponential graphs, logarithmic graphs, scatter plots, charts, and tables.

Proportional Reasoning
6. Recognize and compare proportional relationships presented in different ways.
7. Apply quantitative reasoning to solve applied problems with proportional relationships.

Algebraic Reasoning
8. Understand the use of variables to represent quantities or attributes in a variety of forms such as equations, formulas, tables and graphs.
9. With the use of technology, describe the effects of changes in variable values on algebraic and basic trigonometric relationships.
10. Construct and solve equations and inequalities representing relationships involving one or more unknown quantities for applied problems.

Trigonometric Reasoning
11. Apply the Pythagorean Theorem in a variety of contexts to solve applied problems.
12. Estimate and measure angles and solve practical problems involving missing angle measurements.
13. Construct and solve basic right triangle trigonometric equations representing relationships that arise in a variety of applied settings.

Data Analysis
14. Translate data using technology from a variety of sources including from line graphs, exponential graphs, logarithmic graphs, scatter plots, charts, and tables into mathematical representations.
15. Convert mathematical representations including linear, polynomial, root, exponential and logarithmic equations into visual, graphical interpretations with the use of technology (i.e. Excel, Desmos or another graphing calculator).
16. Describe the behavior of common types of functions (including linear, polynomial, exponential and logarithmic) using words, algebraic symbols, graphs and tables generated manually and by computer software.
17. Use appropriate terms and units to describe a rate of change for a variety of applied settings.
18. Identify the appropriate mathematical models for a given set of data and consider alternative models.
19. Demonstrate an understanding of the error involved when using mathematical models to estimate real world scenarios.

Critical Thinking
20. Use online and print resources to construct mathematical models, apply estimation techniques, analyze data and appraise validity of claims.
21. Operate appropriate mathematical tools such as calculators, computer algebra systems (CAS), electronic graphing and modeling tools, and measuring tools to solve applied problems.
22. Demonstrate critical thinking by analyzing ideas, patterns and principles.
23. Demonstrate flexibility with mathematics through various contexts, modes of technology and presentations of information.

Math Confidence
24. Demonstrate fluency with mathematical vocabulary, terminology, and notation through written and oral presentation.
25. Implement student-specific learning strategies and study techniques.


11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I.Basic operations with Real Numbers
a.Convert between decimals and fractions
b.Work with signed numbers
c.Exponents and exponent rules
d.Order of Operations

a.Measure length, area, volume and weight in both US customary units and metric units.
b.Estimation techniques
c.Evaluation and application of accuracy needed for a specific situation
d.Dimensional analysis for length, area, volume weight
e.Apply skills to real world scenarios

a.Scientific, engineering and pre-fix notation
b.Determine or interpret the appropriate notation for applied situations
c.Compare numbers and quantities expressed in different formats
d.Perform operations on numbers given in scientific notation

IV.Rates, Proportions & Percent
b.Rates of change
i.Appropriate units for rates of change
ii.Linear rates of change and slopes of lines
c.Interpret rates, proportions and percent from an applied context
d.Apply proportional analysis to set up equations and solve applied problems

V.Graphical Analysis
a.Cartesian Coordinate System
b.Independent/Dependent Variables and Axes
c.Generalize a pattern
d.Linear graphs
e.Polynomial graphs
f.Exponential graphs
g.Logarithmic graphs
h.Translations of curves and functions
i.Fit data with a curve
j.Use graphical analysis to describe a real world scenarios

a.Solve linear equations
b.Solve polynomial equations
i.Estimate solutions using quadratic formula
ii.Find solutions graphically
c.Solve exponential equations
d.Solve logarithmic equations
e.Formula manipulation for one variable using appropriate order of operations

VII.Linear Relationships
a.Express slopes as rates of change and with appropriate units for applied contexts
b.Given data in graphical and table form, determine if the relationship is linear and model with an equation
c.Write linear equations using rate of change and data points
d.Use linear equations to model applied problems and answer questions.

VIII.Exponential and Logarithmic Relationships
a.Exponential rates of change
b.Given data determine if the relationship is exponential growth or decay
c.Use exponential equations to model applied problems and make calculations
i.Population growth and decay
ii.Compound interest
d.Logistical growth models
e.Inverse relationship between logarithms and exponential functions
f.Solve exponential and logarithmic equations

IX.Data Analysis
a.Given real world data in graphical or numeric form, determine the equation of best fit (linear, quadratic, exponential, logarithmic, power, etc).
b.Determine domain and range of a data set
c.Apply real world constraints to domain and range
d.Use the appropriate technology to mathematically model data from a variety of types of sources into equations that could be used to make future predictions.

a.Angle measurement
b.Pythagorean Theorem
c.Right triangle ratios
d.Use trigonometric analysis to solve real world problems


12. Typical Out-of-Class Assignments: Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour, less for lab/activity classes.  List types of assignments, including library assignments.)


a. Reading Assignments: (Submit at least 2 examples)

1. Find and read an article utilizing measurements in scientific or engineering notation. State the numbers used in the article in both the given scientific/engineering form and in the equivalent standard decimal format. Describe why the authors chose to describe the numbers in this format rather than in standard decimal notation.
2. Read an article describing the growth of different social media such as MySpace, Facebook, Instagram, and Twitter. Research historical records of user data per month and make independent tables for each company, clearly labeling your independent and dependent variables. Using a graphing calculator, Excel or Desmos (a free app that is a powerful graphing calculator) create a graph of each company’s growth curve. Explain the type of growth experienced by each company, the factors that led to this growth and any conditions that did or will hinder future growth.


b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Using a thermometer and a cup of boiling water, take the temperature of the water every 4 minutes for at least an hour. Record the data, graph the relationship between time elapsed and temperature of the water, determine what is a model of best fit (linear, power, exponential or logarithmic), include a justification for your choice. Using either Desmos or Excel, graph the data and find the equation of best fit to use to answer: How long will it take for a cup of boiling hot coffee take to reach 140 degrees (considered an ideal temperature for drinking coffee)? How long will it take for a cup of boiling water to reach the room temperature?
2. Determine the number of grains of rice in a 20lb bag. First, make a guess as to how many grains you would estimate in the 20lb bag, then discuss in your group different strategies and methods for solving this problem. Summarize the steps your group members will take to find the number of grains of rice in a 20lb bag. Using the tools provided (scales, cups, rice samples, plates, etc.) and proportions to solve this problem.


c. Other (Term projects, research papers, portfolios, etc.)

Material Cost Project: Determine the cost to manufacture a product of your choice. The materials you use and the type of manufacturing is your choice. You may construct/build, weld, sew, design, etc.
-Write a paragraph explaining your project, design, the tools needed and how you would manufacture this product.
-Create a blueprint of your project complete with measurements of each piece.
-On the blueprint, state each measurement in both US customary units and metric units.
-On the blueprint, state your measurements in both fractional and decimal equivalents. (Note: Your design must include at least 5 fractional measurement, you may not use only whole numbers)
-On a separate sheet of paper, determine exact amount of material needed to manufacture your product. Include all areas and volumes necessary to complete your design.
-Using technological resources, determine the cost to manufacture your product based on the amount of material needed. Answer the following questions:
-- Can you purchase the exact amount of material needed? If not, what is the waste?
-- Would it be cheaper to produce more products?
-- What issues did you run into? How did you resolve these issues?


13. Required Materials:

a. All Textbooks, resources and other materials used in this course are College Level?




b. Representative college-level textbooks (for degree-applicable courses) or other print materials.

Book 1:


  Almy and Foes


  Math Lit: A Pathway to College Mathematics



Date of Publication:




Book 2:







Date of Publication:




Book 3:







Date of Publication:




Book 4:







Date of Publication:




Book 5:







Date of Publication:




c. Other materials and/or supplies required of students:

Course Packs (Volume 1 and 2), Scientific Calculator


Methods of Instruction


14a. Check all instructional methods used to present course content.


Laboratory and/or Activity

Distance Learning (requires supplemental form)




14b. Provide specific examples for each method of instruction checked above; include a minimum of two examples total. Reference the course objective(s) addressed by instructional method(s). Explain both what the instructor and students are expected to be doing and experiencing.

Interactive lecture format will be used to perform data analysis, graph real world information and model the behavior with an algebraic equation. Data will be projected to the class and graphed through a Computer Algebra System (CAS) such as Excel or Desmos. The class will discuss the trends in the data and which type of algebraic curve would best describe the data. Through lecture, discussion and demonstration the class guided by the instructor will develop the appropriate algebraic modeling equation.

Course Objectives Addressed: 14) Translate data using technology from a variety of sources including from line graphs, exponential graphs, logarithmic graphs, scatter plots, charts, and tables into mathematical representations. 18) Identify the appropriate model for a given set of data and consider alternative models.

Small group collaborative learning activity:
In small groups, students will be asked to design and build a seal-able container that will hold 3 ounces of popcorn. Each group will be given a piece of poster board, scissors, tape and a scale. There will be a large bag of popcorn at the front of the room, but there is no measurement given on the bag. The instructor will move around the room observing and guiding groups as needed. At the end of the activity, each group will get to test their container by pouring exactly 3 ounces of popcorn into the container to determine how close they met the criteria. As the groups are testing their containers, the instructor will facilitate a class discussion about the pros and cons of each design and the process of designing the containers.

Course Objectives Addressed: 2) Apply estimation techniques using technology in a manner mathematically appropriate for the context of the situation. 21) Operate appropriate mathematical tools such as calculators, computer algebra systems (CAS), electronic graphing and modeling tools, and measuring tools to solve applied problems.




15. Methods of Assessing Student Learning  


15a.  Methods of Evaluation:


Essay Examinations

Objective Examinations

Problem Solving Examinations

Skill Demonstrations



Classroom Discussions




Other (explain below)







15b. Based upon course objectives, give examples of how student performance will be evaluated. Provide examples for each method checked above; include a minimum of two examples total.




Projects and Classroom Discussions:
The following is an example of a classroom discussion that would lead into a group project started in class and finished for homework. The final product would be a group report turned in at the completion of the project. Student performance would be evaluated based on the detail provided about the students' specific project, each student's contribution to the group and the correctness of the solutions given.

As a class, the instructor will facilitate a discussion about the different ways to measure the height of very tall objects such as buildings or trees. If not brought up during the discussion, the instructor will introduce tools (including applications for cell phones) and mathematical formulas from trigonometry that can be used to determine heights and angles. The class will then take a field trip outside the classroom to find heights of specific objects around campus. The initial object measured will be demonstrated by the instructor and done together as a class. Then small groups will split off to find other objects around campus and determine the measurements necessary to find the height of the specified objects. The groups will use this data collection to complete an in class worksheet. At the end of class, each small group will be given the following assignment:
a. Find five objects off campus and determine the heights of these objects, pick objects that would otherwise be difficult to measure them with standard measuring tools (i.e. do not use the bookshelf in your room).
b. List all five objects, along with the subsequent measurements you found necessary to determine the height of the object.
c. Show all equations and calculations used.
d. Write a conclusion paragraph about this project. Include your contribution to the group data collection, how accurate your measurements were and discuss any difficulties your group encountered.

Objective and Problem Solving Examinations:
The following is an example of a problem from an exam which would entail problem solving, written explanations and objective solutions. Student performance would be evaluated based on the correctness of the solutions given the specific data set and on the depth of understanding displayed in written explanations to the question asked in the problem.

Given the data set of Instagram users after 2010 (when Instagram was initially launched):
a. Identify the independent and dependent variables.
b. Graph the data on a Cartesian coordinate system and label your axes and intercept(s). Write a sentence or two to describe the intercept(s) in context of the data given.
c. Determine which type of algebraic equation would best fit your data. Then find the appropriate equation.
d. Use the equation you found to predict the number of Instagram users in 5 years, in 10 years and in 100 years.
e. Does your algebraic model have restrictions in this context? Why or why not?












1. Program Information:  

In an approved program.  

Part of a new program.

Not part of an approved program.  

2. Course TOP Code:

   Program title - TOP Code:  

Mathematics, General- 170100


3. Course SAM Code:

 A  Apprenticeship

 B  Advanced Occupational

 C  Clearly Occupational

 D  Possibly Occupational

 E  Non-Occupational


4. Faculty Discipline Assignment(s):










General Education Information:  

1.  College Associate Degree GE Applicability:    

Communication & Analytic Thinking
Math Competency

2.  CSU GE Applicability (Recommended-requires CSU approval):

3.  IGETC Applicability (Recommended-requires CSU/UC approval):  

4. C-ID:  






Articulation Information:  (Required for Transferable courses only)



CSU Transferable.  

UC Transferable.

CSU/UC major requirement.  


If CSU/UC major requirement, list campus and major. (Note: Must be lower division)




List at least one community college and its comparable course.  If requesting CSU and/or UC transferability also list a CSU/UC campus and comparable lower division course.


Pasadena Community College, California: Math 150 - Quantitative Literacy II

Rock Valley College, Illinois: Math 96A - Mathematical Literacy for College Students

Cuyamaca College, California: Math 096- Preparation for Elementary Statistics





Planning and Resources - Please address the areas below:  

1. Evidence of Planning: connection to existing or planned degrees/certificates, place in general education; relationship to mission (basic skills, transfer, career technical education, lifelong learning); transfer university requirements; advisory/regional/national needs; or other planning considerations.

Math E provides non-STEM students with an accelerated pathway through applicable curriculum to either a degree (it will meet the AA/AS degree requirement as equal in rigor to a Math D, Intermediate Algebra course) or to a transferable level course. Successful completion of Math E will gain students access to Math 10, 13 or 18, all three of which provide non-STEM majors a transferable level math class.

Students placing at the lower levels of Math (Math 581/582/585 and A/D) are primarily non-STEM students in need of a pathway that will take them to a terminal transfer level math course, such as Statistics or The Nature of Math. Accelerated pathways consistently show higher results for success and retention of students through the sequence of math courses than more traditional approaches. Math E data from the last three years does show that 68% success and 87% retention rates which is significantly above the traditional approach of A and D, which has historically had success around 50%.

The course also provides CTE (Career and Technical Education) students with an applicable one semester math course to apply to an AA/AS degree in their chosen field.

2. Potential Impact on Resources: faculty, facilities, computer support/lab, library, transportation, equipment, or other needs.
All math faculty members meet the minimum qualifications to teach this course, but it is taught using hands-on, discovery based learning. The concepts are discovered by the students through group work, projects and activities. Therefore, professional development activities and training are necessary to equip faculty with the materials and pedagogy to effectively deliver the material.

Materials are also necessary for all of the projects and thus needs to be purchased through the department budget and stored for use in the classroom. Technology is also used significantly and therefore it will be necessary to purchase more classroom sets of laptops or tablets as the sections of Math E increase.





1.  Maximum Class Size (recommended):              28

2.  If recommended class size is not standard, then provide rationale:

Practical Math is taught in modality where students are learning using hands on, practical activities and exploratory learning. Discovery learning through group work is the foundation of the class and as such the need for a lower enrollment cap is necessary to allow the instructor sufficient opportunity to give each student the attention needed for meaningful learning. Students taking this course have often struggled with the traditional delivery of mathematics and this course gives them the chance to learn math in a more hands-on manner with practical applications. Also, because of multiple measures as a way to place students into higher math courses than we have historically seen, the level of preparation of the students in this course varies widely.
Daily activities involve constructing physical models and collecting data in a variety of ways, such as using scales to weigh objects or racing toy cars to measure speed. A typical day in Practical Math would involving the students “discovering” the physical meaning of slope. Groups of 4-5 students would first go outside to determine the rise and corresponding run of ramps around campus. They would then convert these ratios into percent grades determine if they meet ADA compliant ratios. This concept could then be expanded in the classroom to percent grade signs and elevation changes. The teacher is constantly on the move, answering questions and guiding the discovery based learning.