MA 240 - Geometry and Measurement for Elementary Teachers

1. Classify various geometrical concepts figures in one, two, and three dimensions.
2. Correctly use metric, English, and non-standard systems of measurement in one, two, or three dimensions and be able to convert from one system to the other.
3. Correctly identify the relationship different sets and their elements have to each other and use operations on sets.
4.  Select and use pedagogical resources to convey mathematical content and to assess and analyze student learning and thinking.
5. Demonstrate an understanding of how to use teaching practices and strategies to develop a learning community which builds respectful relationships between students and students and teachers.

  A. Basic Concepts of Geometry

      1. Know basic terms such as point, line, line segment, ray, angle, and plane.

      2. Classify pairs of lines as parallel, perpendicular, or skew.

      3. Measure and classify angles.

  B. Two-Dimensional Figures

      1. Know the defining attributes of polygons and be able to categorize them.

      2. Identify triangles by both measures of sides and angles.

      3. Justify that the sum of the angles in a triangle is 180°.

      4. Identify quadrilaterals by defining attributes.

      5. Classify 2-dimensional figures in a hierarchy based on their properties.

      6. Identify polygons based on the number of sides.

      7. Differentiate between regular, convex, and concave polygons.

      8. Determine the measure of interior, exterior, and central angle for polygons

      9. Identify lines of symmetry or complete a diagram to create symmetry.

    10. Identify rotational symmetries.

  C. Three-Dimensional Figures

      1. Classify 3-dimensional objects.

      2. Identify planes of symmetry and axes of rotation.

      3. Identify cross-sections.

      4. Represent 3-dimensional figures using nets consisting of polygons.

II. Measurement

  A. Length and Perimeter

      1. Demonstrate an understanding that length is a 1-dimensional measurement.

      2. Use standard and non-standard units to estimate and measure lengths.

      3. Select appropriate tools for measuring length

      4. Demonstrate that perimeter and circumference represent a 1-dimensional measurement of length around a 2-dimensional figure.

      5. Informally justify the formula for circumference of a circle.

      6. Prove the Pythagorean theorem and use it to solve real-world problems.

   B. Area and Surface Area

      1. Demonstrate that area is a 2-dimensional attribute of planar figures.

      2. Measure area of rectangles and approximate areas of other shapes.

      3. Develop the formula for the area of a rectangle.

      4. Develop the formula for the area of a parallelogram.

      5. Develop the formula for the area of a triangle.

      6. Develop the formula for the area of a trapezoid.

      7. Informally justify the formula for area of a circle.

      8. Demonstrate that area is additive.  Use that property to find the area of composite shapes.

      9. Demonstrate that surface area is a 2-dimensional measurement of area to cover a 3-dimensional object.

  C. Volume

      1. Demonstrate that volume is an attribute of a 3-dimensional solid.

      2. Measure the volume.

      3. Develop the formula for volume of a rectangular prism.

      4. Develop the formulae for the volume of any prism or cylinder.

      5. Relate the volume of a pyramid or cone to the volume of the corresponding prism or cylinder.

      6. Know and utilize the formula for the volume and surface area of a sphere.

      7. Utilize the displacement method with liquid to determine the volume of irregular shaped objects.

III.  The Metric System

  A. Know the prefixes for the metric system and their relationship to powers of ten.

  B. Convert between like measurement units of different size.

  C. Relate the relative size of each unit in the metric system to real life objects.

  D. Use unit analysis to convert between like measurement units in any system of measurement.

IV. Other Geometric Topics

  A. Write and solve simple equations for an unknown angle in a figure.

  B. Constructions

      1. Perform basic constructions using a straightedge and compass.

      2. Draw geometric shapes with given conditions.

      3. Construct triangles from three measures of angles or sides.

  C. Rotations, translations, reflections, and dilations

      1. Verify experimentally the properties of rotations, reflections, and translations.

      2. Solve problems involving scale drawings of geometric figures.

      3. Demonstrate congruence and similarity using physical models.

      4. Demonstrate that a two-dimensional figure is congruent to another if it can be obtained from the first through a sequence of rotations, reflections, and translations.

      5. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using a coordinates system.

      6. Demonstrate that a two-dimensional figure is similar to another if it can be obtained from the first through a sequence of rotations, reflections, translations, and dilations.

      7. Demonstrate the effects of scaling on 1-, 2-, and 3-dimensional measurement units.

V. Sets, Relations, and Operations

A. Introduction to Sets

1. Definition

2. Venn Diagrams

3. Subsets

4. Union and Intersection

VI. Core Teaching Practices in Geometry and Measurement

1. Identify appropriate resources and activities for a geometry and measurement lesson.
2. Lead and analyze classroom activities and interactions around teaching and learning of geometry and measurement content. 
3. Outline historical and cultural developments and contributions to mathematics and mathematics education related to geometry and measurement.

Facilitated Discussion: 10-60%

Collaborative Learning: 30-60%

 
Mandatory Course Components:
None
Equivalent Courses:
None