Department of Mathematics at UTSA - User contributions [en]

MAT1163

2021-03-04T19:04:42Z

Christopher.duffer: /* Essential Elements in Mathematics II */

==Essential Elements in Mathematics II==

[https://catalog.utsa.edu/search/?P=MAT%201163 MAT 1163. Essential Elements in Mathematics II]. (3-0) 3 Credit Hours. (TCCN = MATH 1351)

Prerequisite: [[MAT1153|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.

{| class="wikitable sortable"
|-
! 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
|}

MAT1163

2021-03-04T19:02:00Z

Christopher.duffer: added weeks, modules, and filled in gaps. STILL NEEDED are prerequisite skills

==Essential Elements in Mathematics II==

[https://catalog.utsa.edu/search/?P=MAT%201163 MAT 1163. Essential Elements in Mathematics II]. (3-0) 3 Credit Hours. (TCCN = MATH 1351)

Prerequisite: [[MAT1153|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.

{| class="wikitable sortable"
|-
! 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 ]] || Example
||
* 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
|}