# 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