Portland Community College | Portland, Oregon

Course Number:
MTH 213
Course Title:
Foundations of Elementary Math III
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, explore patterns and relationships among geometric figures and develop spatial reasoning. Explores informal geometry, transformational geometry, and measurement systems. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 211. Audit available.

Addendum to Course Description

This is the third term of a three-term sequence (MTH 211, 212, and 213). 

Intended Outcomes for the course

Upon successful completion students should be able to:

  • Apply an understanding of theoretical foundations of mathematics focusing on geometric principles as taught at the K-8 level in order to develop mathematical knowledge for teaching.
  • Use various problem solving strategies and geometrical 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 State Standards.  Students may also read, write about or discuss journal articles, or engage in field observations or teaching demonstrations.

Outcome Assessment Strategies

Assessment must include:

1.            At least two proctored examinations.

2.            At least one writing assignment

3.            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

f.          Portfolios.

g.         Individual or group teaching demonstration(s).

h.         Field experience

i.         Community Based Learning

Course Content (Themes, Concepts, Issues and Skills)


The instructional goal is to understand the ideas of intuitive geometry regarding the plane, space, and simple geometric figures and relationships.

1.1         Develop and use the geometric vocabulary needed to discuss figures and their properties.

1.2         Understand the various  kinds of relationships between lines and angles.

1.3         Classify by name closed geometric figures in a plane and in 3-space (polygon, polyhedron, circle, sphere, cone).

1.4         Identify reflection and rotation symmetries for two- and three-dimensional figures.

1.5         Investigate tessellations.


The instructional goal is to understand the attribute to be measured as well as what it means to measure.

2.1      Know that measurement is a comparison between a given unit and the object to be measured.

2.2      Study systems of measurement, primarily the metric system and the U. S. Standard system.

2.3      Convert units of measure within a system and between systems.

2.4      Investigate a variety of measurements, including temperature and weight.

2.5      Find perimeter and area using a variety of techniques.

2.6      Find volume and surface area using a variety of techniques.

2.7      Estimate perimeters, areas, and volumes of various objects.


The instructional goal is to study relationships and develop spatial sense by constructing, drawing, measuring, visualizing, comparing, transforming, and classifying geometric figures.

3.1      Define and apply congruence properties of triangles and other figures.

3.2      Use straightedge and compass to construct various geometric figures.

3.3      Study congruence mappings (translations, reflections, and rotations).

3.4      Study similarity mappings.

3.5      Introduce networks.

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.