MTH 240 - Geometry and Measurement for Elementary Teachers

Was previously MA 240

1. Classify and analyze geometric figures and relationships in one, two, and three dimensions, including transformations, congruence, and similarity.
2. Analyze geometric measurement attributes, including length, area, surface area, and volume, and convert within and between measurement systems, including metric, customary, and non-standard units.
3. Apply set concepts and operations to classify, compare, and analyze mathematical objects and relationships.
4. Communicate mathematical thinking related to geometry and measurement concepts using accurate and precise language, models, multiple representations, and mathematical discourse.
5. Interpret and analyze Birth–8 student thinking related to geometry and measurement concepts using student work and classroom interaction evidence.
6. Apply current PK–8 state and national mathematics recommendations to the design and instruction of geometry and measurement concepts.
7. Use research-based pedagogical practices to support students’ mathematical communication, reasoning, and conceptual understanding of geometry and measurement ideas in PK–8 learners.
8. Plan, facilitate, and reflect on standards-aligned instruction on sets, set operations, geometry and/or measurement that responds to and advances student thinking and incorporates formative assessment.

A. Core Teaching Practices

1. Lead whole-class and small-group mathematical discussions

2. Explain and model mathematical content, practices, and strategies

3. Build respectful and inclusive relationships with students

B. Elicit, Interpret, and Respond to Student Thinking

1. Elicit and analyze children’s mathematical thinking related to geometry, measurement, and classification

2. Examine developmental progressions in students’ spatial and measurement reasoning

3. Use evidence of student thinking to inform instructional decisions

C. Students’ Strategies and Instructional Planning

1. Analyze videos and/or classroom experiences to identify student thinking and reasoning processes

2. Analyze student work to identify strategies, misconceptions, and levels of understanding

3. Develop instructional plans that respond to and advance student thinking and understanding

II. Mathematical Content

A. Sets, Classification, and Mathematical Structure

1. Sets and attributes

a. Defining sets and elements

b. Measurable and non-measurable attributes

c. Sorting, classifying, and comparing sets

2.  Set relationships and operations

a. Subsets and universal sets

b. Union, intersection, and complement

c. Venn diagrams as representations of set relationships and operations

B. Geometry

1. Foundations of Geometry and Spatial Reasoning

a. Basic geometric terms (point, line, line segment, ray, angle, plane)

b. Classification of lines (parallel, perpendicular, skew)

c. Measuring and classifying angles

2. Two-dimensional figures

a. Defining attributes and classification of polygons

b. Triangles classified by side length and angle measure

c. Angle relationships in triangles and informal justification of angle sum

d. Quadrilaterals classified by defining attributes

e. Hierarchies of two-dimensional figures

f. Regular polygons, convex and concave polygons

g. Symmetry in plane figures (reflection and rotational)

h. Interior, exterior, and central angles of polygons

3. Three-dimensional figures

a. Classification of three-dimensional objects

b. Planes of symmetry and axes of rotation

c. Cross-sections of three-dimensional figures

d. Nets and representations of three-dimensional figures

C. Measurement and Measurement Systems

1. Measurement concepts and processes

a. Attributes of measurement (length, area, surface area, volume, capacity, weight)

b. Units of measure (metric, customary, and non-standard)

c. Direct and indirect comparison

d. Iteration and tiling

e. Estimation as a tool for understanding measurement

2. Length, perimeter, and circumference

a. Measuring length using standard and non-standard units

b. Perimeter and circumference as linear measurements

c. Informal justification of the circumference formula

d. Pythagorean Theorem as a geometric relationship

3. Area and surface area

a. Area as a two-dimensional attribute

b. Developing area formulas for rectangles, parallelograms, triangles, and trapezoids

c. Informal justification of the area of a circle

d. Area as additive and decomposition of composite figures

e. Surface area as area covering three-dimensional figures

4. Volume

a. Volume as an attribute of three-dimensional solids

b. Developing volume formulas for prisms, cylinders, pyramids, cones, and spheres

c. Relationships among volume formulas

d. Measuring volume using displacement

5. Measurement systems and unit conversion

a. Metric and customary measurement system (including prefixes and powers of ten)

b. Selecting appropriate units and tools for measurement tasks

c. Converting within measurement systems

d. Converting between measurement systems using unit analysis

e. Interpreting measurement units in real-world contexts

D. Geometric Constructions, Transformations, Congruence, and Similarity

1. Constructions and geometric reasoning

a. Constructing congruent segments and angles

b. Constructing perpendicular bisectors and angle bisectors

c. Constructing parallel and perpendicular lines

d. Writing and solving equations for unknown angle measures

e. Informal geometric proof and justification

2. Transformations

a. Translations, reflections, and rotations as rigid motions

b. Dilations as non-rigid transformations

c. Effects of transformations on geometric figures

3. Congruence

a. Congruence defined through rigid motions

b. Congruent segments, angles, and figures

c. Congruence in two- and three- dimensions

4. Similarity and scaling

a. Similarity defined through dilations

b. Scale factor and proportional relationships

c. Effects of scaling on one-, two-, and three-dimensional figures

Facilitated Discussion: 10-60%

Collaborative Learning: 30-60%

Technology Supplemented Learning: 10-30%

Alternative grading will be used in this class.
Mandatory Course Components:
Math Play Activities
Equivalent Courses:
None