MAT1163

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