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Essential Elements in Mathematics II

MAT 1163. Essential Elements in Mathematics II. (3-0) 3 Credit Hours. (TCCN = MATH 1351)

Prerequisite: MAT 1153. Algebra, statistics and probability; geometric shapes; measurement; coordinate and transformational geometry. May not be applied toward a major in mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRS1 $45; MFSM $30; STSI $21.

Date Sections Topics Prerequisite Skills Student learning outcomes
Weeks 1-2 Module 1 Definition of Polygons
  • Understand the development of geometric (mathematical) definitions through examples and non-examples
  • Build definitions for the terms: closed, simple, polygon, convex, and regular
Weeks 1-2 Module 1 Properties of Polygons (Sides, Angles and Diagonals)
  • Build, express, and justify a pattern for the diagonals of an n-gon by using geometric reasoning
  • Use geometric reasoning to build and express the formula for the sum of interior angles of a polygon
  • Use geometric reasoning to build and express the formula for the internal angles of a regular polygon
Week 3 Module 1 Lines & Angles
  • Develop and use visual reasoning skills to decompose and identify angle measures based on a given a reference angle on a grid
Week 3 Module 1 Transversal lines
  • Explore relationships between angles formed between parallel lines and transversals and solve problems using these relationships
Week 4 Module 1 Classifying Triangles
  • Classify triangles by angles/sides and articulate relationships between classes
  • Create and use an ordered list to enumerate combinations of characteristics
Week 4 Module 1 Triangle Inequality
  • Informally justify and be able to use the triangle inequality
Week 5 Module 1 Triangle Congruence
  • Informally justify triangle congruence theorems by construction
Week 5 Module 1 Theorem of Right Triangles
  • Understand when and how to apply the Theorem of Right Triangles to calculate lengths
  • Use different models to informally justify the Theorem of Right Triangles
Week 6 Module 1 Definitions and Hierarchy of Quadrilaterals
  • Explore relationships between and the consequences of given definitions of classes of quadrilaterals
  • Build and integrate visual representations with thinking about logical statements
  • Understand relationships between classes of quadrilaterals
Week 7 Module 2 Measurement (LINEAR) Definition of multiplication (# groups x group size = total)
  • Describe measurement as an iteration of a constant unit
  • Develop an understanding of the Inverse relationship between size of unit and number of units needed to measure something
Week 7 Module 2 Measurement (LINEAR) – CONVERSION
  • Convert between different units of length measurement
Week 8 Module 2 Measurement (AREA)
  • Calculate areas on a grid using additive and subtractive approaches
Week 8 Module 2 Measurement (AREA) – CONVERSION
  • Convert between different units of area measurement
Week 9 Module 2 Area of Polygons - Formulas
  • Develop, relate, and justify area formulas for parallelograms, triangles, and trapezoids
Week 9 Module 2 Perimeter Area
  • Calculate perimeters of non-standard objects with right angles by reasoning about missing lengths
  • Calculate perimeters of objects on a grid using the Pythagorean theorem
  • Understand the relation and distinguish between Perimeter and Area
Week 10 Module 3 Rigid Transformations
  • Define the three basic rigid motions and given the result of a transformation, identify a correct sequence of rigid motions that maps the pre-image to the image
  • Define congruence as a result of properties of rigid motions
Week 10 Module 3 Symmetry
  • Identify rotation and reflection symmetry and use rigid motions to create figures with different types of symmetry
Weeks 11-12 Module 3 Similarity
  • Determine whether two figures are similar and justify this determination by referring to angles and scale factor
  • If two figures are similar, determine/describe the correspondence between the two
  • Use proportionality and scale factors (instead of additive thinking) to determine measurement of similar figures
Week 13 Module 4 Mathematical & Statistical Reasoning
  • Identify statistical and non-statistical questions
Week 13 Module 4 Display of Categorical Data
  • Given data, select a variety of appropriate displays
  • Identify and justify appropriate displays for a given type of data
Week 14 Module 4 Display of Numerical Data
  • select appropriate graphical and numerical methods and use those methods to analyze data
  • use appropriate tools for exploring (represent/ summarize/interpret) distributions including bar graphs, dot plots, stem & leaf plots, box-whisker plots, and measures of center
  • use sophisticated tools such as histograms, the IQR (interquartile range), mean absolute deviation, 5-number summaries, and boxplots for describing distributions, summarizing and comparing distributions, and for making inferences
Week 15 Module 4 Probability
  • Compare displays of empirical data with theoretical probabilities
  • Create and use an ordered list to enumerate combinations of characteristics
  • Identify equally probable outcomes and combine them to find the probability of events
  • Use probability to evaluate the fairness of games