# Foundations of Elementary Math III

## Course Description

Surveys mathematical topics for those interested in the presentation of mathematics at the K-9 levels. Various manipulatives and problem solving approaches are used to explore informal geometry, transformational geometry, and measurement systems. Prerequisite: MTH 211 and its prerequisite requirements. Audit available.

## Intended Outcomes

Upon successful completion students should be able to:

1. Understand the theoretical foundations of mathematics focusing on geometric principles as taught at the K-9 level in order to develop mathematical knowledge for teaching.
2. 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.
3. Participate in a teacher education program.
4. Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.

## Outcome Assessment Strategies

Assessment must include:

1. At least two proctored examinations.
2. At least one writing assignment and
3. At least two of the following additional measures:
1. Take-home examinations
3. Quizzes
4. Individual/Group projects
5. In-class activities
6. Attendance
7. Portfolios
8. Individual or group teaching demonstration(s)
9. Field experience
10. Service Learning

## Course Activities and Design

In-class time is primarily activity/discussion or lecture/lab emphasizing the use of manipulatives and problem solving techniques. Activities will include group work, field experience, or teaching demonstrations.

## Course Content (Themes, Concepts, Issues and Skills)

#### 1.0 GEOMETRIC FIGURES

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.

#### 2.0 SYSTEMS OF MEASUREMENT

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.

#### 3.0 GEOMETRIC MAPPING

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.

## Department Notes

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

Foundations of Elementary Math III is intended to examine geometric concepts and provide students with manipulatives to model problem solving, explore patterns and relationships among geometric figures, and develop spatial concepts. The content and pedagogy is based on the NCTM standards.  Emphasis is on why mathematics works as it does rather than on memorization of algorithms.