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CCOG for MTH 211 Winter 2024

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Course Number:
MTH 211
Course Title:
Foundations of Elementary Math I
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 problem solving, numeration systems, operations, patterns and change, and number theory. Emphasizes quantitative and algebraic reasoning. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 95 or MTH 98 or higher, and (WR 115 and RD 115) or IRW 115 or equivalent placement. Audit available.

Addendum to Course Description

 This is a prerequisite course for MTH 212 or MTH 213.

Intended Outcomes for the course

Upon successful completion students should be able to:

  • Apply an understanding of the theoretical foundations of mathematics focusing on numeration systems and operations 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 algebraic 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

  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 3 hours of field experience with written reflection
  5. 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.

Course Content (Themes, Concepts, Issues and Skills)


The instructional goal is to develop problem solving ability.

1.1         Utilize and develop effective problem solving strategies with an emphasis on quantitative reasoning.

1.2         Identify deductive and inductive reasoning when problem solving.

1.3         Explore patterns and sequences, and their relationship to problem solving.

1.4         Use algebra and algebra manipulatives to problem solve.

1.5          Solve application problems utilizing functions and graphs.

2.0     SETS

The instructional goal is to learn the fundamental concepts of set theory.

2.1         Explore attributes and classification.

2.2         Represent set concepts using Venn diagrams.

2.3         Understand and use the concepts and symbols of subset, intersection, union, and complement of a set.

2.5         Utilize set theory in application problems.


The instructional goal is to develop an understanding of numeration systems. 

3.1         Explore numeration systems of other cultures.

3.2         Define the set of whole numbers and their properties.

3.3         Model, compute, and investigate whole number operations in several bases.

3.4         Understand place value and base 10.

3.5         Estimate and use mental arithmetic.


The instructional goal is to understand elementary concepts of number theory and how these concepts are used in the elementary curriculum.

4.1         Explore divisibility.

4.2         Explore the properties of prime and composite numbers, and prime factorization.

4.3        Use symbolic and visual models to investigate least common multiple and greatest common divisor/factor

4.4         Use clock arithmetic and other simple modular arithmetic applications.

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.