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CCOG for MTH 212 Winter 2024

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Course Number:
MTH 212
Course Title:
Foundations of Elementary Math II
Credit Hours:
Lecture Hours:
Lecture/Lab Hours:
Lab Hours:

Course Description

Examines the conceptual basis of K-8 mathematics using collaborative learning through in-class group interaction. Provides opportunities to experience using manipulatives to model operations with rational numbers including fractions, decimals, percents, and integers. Explores the set of irrational numbers, the set of real numbers, proportional reasoning, and simple probability and statistics. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 211 and (WR 115 and RD 115) or IRW 115 or equivalent placement. Audit available.

Addendum to Course Description

This is one of the two courses that follow MTH 211.

Intended Outcomes for the course

Upon successful completion students should be able to:

  • Apply an understanding of the theoretical foundations of mathematics focusing on real number operations, probability, and statistics as taught at the K-8 level in order to develop mathematical knowledge and communication skills necessary for teaching.
  • Use various problem solving strategies and statistical reasoning to create mathematical models, analyze real world scenarios, judge if the results are reasonable, and then interpret and clearly communicate the results.
  • Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.
  • Foster the mathematical practices in the Common Core State Standards.

Quantitative Reasoning

Students completing an associate degree at Portland Community College will be able to analyze questions or problems that impact the community and/or environment using quantitative information.

General education philosophy statement

Mathematics and Statistics courses help students gain tools to analyze and solve problems using numerical and abstract reasoning. Students will develop their abilities to reason quantitatively by working with numbers, operations, and relations and to reason qualitatively by analyzing patterns and making generalizations.

Course Activities and Design

In-class time is devoted primarily to small group problem solving activities and class discussion emphasizing the use of manipulatives and appropriate technology. The student’s role is to actively engage in positive collaboration with peers. The instructor’s role is to facilitate and model teaching and learning practices described in the Common Core Standards. 

Outcome Assessment Strategies

Assessment must include:

1.     Successful completion of a non-calculator math diagnostic assessment covering pre-requisite material for the MTH 211, 212, and 213 sequence is required.  The student must pass this assessment with a minimum of 90% to receive a passing grade for the course. Multiple opportunities and interventions will be offered.

2.      At least two proctored examinations, one of which must be a cumulative final.

3.      At least one writing assignment

4.      At least two of the following additional measures:

a.         Take-home examinations.

b.         Graded homework.

c.         Quizzes.

d.         Individual/Group projects.

e.         In-class activities.

f.          Portfolios.

h.         Field experience.

Course Content (Themes, Concepts, Issues and Skills)


The instructional goal is to understand integer operations and use manipulatives to model these operations.

1.1      Model integer arithmetic with drawings and manipulatives.

1.2      Estimate and perform mental calculations with integers.

1.3      Solve applications requiring integers.


The instructional goal is to understand rational numbers.  

2.1      Determine equivalence, order and density of rational numbers. Use manipulatives to model fractions.

2.2      Use manipulatives to model fractions. 

2.3      Use manipulatives to model basic operations on fractions.

2.4      Investigate non-standard manipulatives to add, subtract, multiply, and divide fractions.

2.5      Investigate and convert relationships between fractions, decimals and percents using base ten.

2.6      Use decimal squares, base ten pieces, and other manipulatives to model decimals and basic operations on decimals.

2.7      Represent ratios, proportions, and percents using manipulatives.

2.8       Solve applications involving ratios, proportions, and percents. 


The instructional goal is to explore topics of the real numbers.

3.1      Classify real numbers as rational or irrational.

3.2      Explore the Pythagorean theorem as an application of real numbers.

3.3      Use number sense to approximate square roots.


The instructional goal is to explore topics of probability and statistics. 

4.1      Model, investigate and interpret the common measures of central tendency (mean, median, mode).

4.2      Model, investigate, and interpret the numerical measures of dispersion (range, variance, standard deviation).

4.3      Construct and interpret visual representations of data and recognize the misuse of data. 

4.4      Model, investigate, and interpret measures of relative standing: percentile ranking, Z score, quartiles.

4.5      Explore topics related to theoretical and experimental probability including experiments, sample space, independent events, complementary events.

Standards of Mathematical Practice

While learning the mathematical content contained in the course, the following practices will be embedded throughout and students will be assessed on their ability to:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.
  9. Foster a growth mindset.