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CCOG for MTH 213 Winter 2024

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Course Number:
MTH 213
Course Title:
Foundations of Elementary Math III
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, 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 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 completion of the course 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 and communication skills necessary 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.

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 State 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.

g.         Field experience

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         Explore the various  kinds of relationships between lines and angles.

1.3         Investigate and classify by name closed geometric figures in a plane and in 3-space.

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      Explore systems of measurement, primarily the metric system and the U. S. Standard system, and develop a sense of their magnitude.

2.2      Demonstrate and apply an understanding of ratios when converting units of measure within a system and between systems.

2.3      Investigate a variety of measurements, using both non-standard and standard measuring tools. 

2.4      Investigate perimeter, area, volume, and surface area of various objects.

2.5      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      Explore and apply congruence properties of triangles and other figures.

3.2      Use straightedge and compass to construct various geometric figures.

3.3      Examine congruence and similarity mappings.

3.4      Create and explore three dimensional drawings and nets.

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.