Portland Community College | Portland, Oregon

Course Number:
MTH 211
Course Title:
Foundations of Elementary Math I
Credit Hours:
Lecture Hours:
Lecture/Lab Hours:
Lab Hours:
Special Fee:

Course Description

Examines the conceptual basis of K-8 mathematics. Provides opportunities to experience using manipulatives to model problem solving, numeration systems, operations, patterns and change, and number theory. Emphasizes quantitative, proportional, and algebraic reasoning. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 95 or higher, and WR 115 and RD 115 or equivalent placement test scores. Audit available.

Addendum to Course Description

 This course is the first in a three-course sequence. It 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 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.

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 instructor's role is to facilitate and model teaching and learning practices described in the Common Core Standards.  Students may also read, write about or discuss journal articles, or engage in field observations or teaching demonstrations. 

Outcome Assessment Strategies

  1. At least two proctored examinations.
  2. At least one writing assignment
  3. At least 3 hours of field experience with written reflection
  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 participation

                 f.  In-class activities.

                 g.  Portfolios.

                 h.  Individual projects exploring the Common Core State Standards.

                 i.  Individual or team teaching demonstration(s).

                 j.  Community based learning

Course Content (Themes, Concepts, Issues and Skills)


The instructional goal is to develop problem solving ability.

1.1         Utilize effective problem solving strategies.

1.2         Develop problem solving strategies, including quantitative reasoning, making a drawing, guessing and checking, making a table, using a model, and working backward.

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.


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

2.1         Explore attributes and classification.

2.2         Use set theory symbolism.

2.3         Represent set concepts using Venn diagrams.

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

2.5         Utilize set theory in application problems.

2.6         Apply deductive reasoning.

2.7         Use symbolic logic to explore premises, conclusions,  and validity.


The instructional goal is to develop an understanding of systems of numeration and the system of whole numbers.

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         Identify prime and composite numbers.

4.3         Prime factor numbers and determine when numbers are €œrelatively prime.€

4.4         Find the least common multiple (LCM) and the greatest common divisor/factor (GCD/F) of two or more numbers.

4.5         Use €œclock 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.