Investigating Geometry, Probability and Statistics
 Course: MAT257 First Term: 2014 Summer Final Term: Current Final Term: 2020 Spring Lecture   4 Credit(s)   4 Period(s)   4 Load       Credit(s)    Period(s)    Load Subject Type: Academic Load Formula: S- Standard

Description: Explores geometry, measurement, probability and statistics. Uses visualization, technologies, problem solving, reasoning and proof to develop a conceptual understanding of these topics.

MCCCD Official Course Competencies
1. Describe, illustrate, and apply the basic geometric concepts of a point, a line, a ray, an angle and a plane. (I)
2. Define, identify, visualize, draw, classify and analyze two-dimensional and three-dimensional shapes including the characteristics/attributes of and properties of these shapes. (I)
3. Develop, make sense of and apply appropriate techniques, tools and formulas to determine measurements in one-, two- and three-dimensions including angle measure, area, perimeter, circumference, volume, surface area and apply the Pythagorean Theorem. (I)
4. Investigate, apply and explain the use of proportional reasoning, similarity and congruence techniques to relationships between length, area, perimeter, surface area and volume of geometric shapes. (I)
5. Use appropriate techniques to create geometric constructions. (I)
6. Use geometry software to perform geometric transformations; i.e. perform translations, rotations, reflections and dilations of a geometric figure. (I)
7. Explore levels of the van Hiele Theorem of geometric development. (I)
8. Analyze and explain the structure of and the relationships between the US Customary System and the Metric System of Measurement. (I)
9. Illustrate, explain and distinguish between theoretical and experimental probabilities. (II)
10. Apply the concept of probability by conducting experiments and simulations using technology and concrete modeling to gather and analyze data with respect to both theoretical and experimental probabilities. (II)
11. Illustrate, explain and distinguish between complementary, mutually exclusive, independent and dependent events and determine probabilities of simple and combined events. (II)
12. Apply and interpret probability in real world situations including the determination of whether a game is fair. (II)
13. Explore and interpret patterns and trends found in data using technologies and concrete models. (III)
14. Identify, illustrate, explain and compare uses of mean, median and mode as well as analyze data using an appropriate statistical measure. (III)
15. Investigate and explain the characteristics of standard deviation and normal distribution. (III)
16. Represent and interpret data in multiple ways including bar graphs, line graphs, circle graphs, dot plot, box and whisker plot, scatterplot and histogram and compare the appropriateness of the representations with a variety of data sets. (III)
17. Use current technologies appropriately for investigation, visualization, computation and representation for geometry, measurement, probability and statistics. (I, II, III)
18. Develop definitions for geometric, probabilistic and statistical terms to deepen understanding of mathematical concepts and facilitate mathematical communication. (I, II, III)
19. Develop through experience the Common Core Standards of Mathematical Practice. (I, II, III)

MCCCD Official Course Outline
I. Geometry, measurement & visualization
A. Euclidean Geometry
1. Definitions
2. Identification and classification of figures in two- and three-dimensions.
B. Measurement
1. Units of measure
a. US Customary
b. Metric
c. Nonstandard
2. Angle measure
3. Two-dimensional figures
a. Perimeter
b. Area
c. Angle measure and polygons
4. Three-dimensional figures
a. Surface area
b. Volume
5. Characteristics of similar figures
a. Length
b. Area
c. Volume
d. Angle measure
6. Pythagorean Theorem
7. Euler`s formula for polyhedra
C. Transformational geometry
1. Rigid: Translation, rotation and reflection
2. Non-rigid: Dilation
3. Congruent versus similar
4. Symmetry
D. Applications of technology

II. Probability
A. Theory
1. Definitions: Probability, complementary, mutually exclusive, independent events, dependent events
2. Experimental versus theoretical probability
3. Simple events and combined (compound) events
B. Experimental versus theoretical probability
C. Applications
1. Simulations
2. Fairness

III. Data analysis
A. Statistical measures
1. Mean, median, mode
2. Standard deviation and normal distribution
B. Multiple representations of data
1. Graphs: Line, bar and circle
2. Plots: Dot, box and whisker, scatterplot
3. Histogram
C. Technology

MCCCD Governing Board Approval Date: April 22, 2014

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.