Course Description
Presents topics in Introductory Geometry; Measurements and Units; Mensuration; Real Numbers and Algebraic Thinking; Data Analysis/Statistics; Probability; Congruency, and Similarity with Constructions.
Prerequisite: MATH 2132: Understanding Elementary Math I
Credit Hours: 3
General Course Purpose
This is the second of two courses that focus on developing the mathematical understanding of students who are preparing to be licensed as Elementary Teachers.
Course Purpose
Teachers who teach mathematics in the elementary grades need a solid understanding of the mathematics they teach to
their students.
For instance, a fifth-grade teacher must know why it is necessary to get a common denominator when adding two fractions
with unlike denominators, to be able to adequately explain the conceptual basis of fraction addition to his or her students.
Furthermore, teachers need to feel comfortable and confident that they can offer mathematically correct conceptual
explanations for the mathematics that they teach.
If teachers do not feel confident in their ability to explain mathematical concepts to their students, they are likely
to pass that lack of confidence on to their students, which can inhibit those students ability to learn other
mathematical concepts and operations in the future.
Thus, two primary purposes of Math 2132 and 2133 are to ensure that students taking these courses have accurate knowledge of the concepts and operations of
the elementary mathematics curriculum, and have the confidence to teach those concepts and operations to their own students.
Upon the successful completion of this course, students will satisfy these objectives:
Course Objectives
(1.) Introductory Geometry
(a.) Explain the basic terms in Geometry.
(b.) Discuss the concepts of lines, line segments, and angles.
(c.) Name, classify, and measure angles.
(d.) Discuss geometric shapes.
(e.) Determine the measures of the interior and exterior angles of polygons.
(f.) Solve problems involving lines and angles.
(g.) Solve problems involving geometrical shapes.
(2.) Mensuration
(a.) Analyze the relationships between different physical quantities. (Dimensional Analysis)
(b.) Discuss the main systems of the measurements of physical quantities.
(c.) Identify a measurement and measurement unit needed to solve a problem.
(d.) Convert units within and between standard and metric measurement systems.
(e.) Solve real-world problems involving measurements and units.
(f.) Discuss the mensuration of geometric figures.
(g.) Solve applied problems involving the mensuration of geometric figures.
(h.) Solve applied problems involving the Pythagorean Theorem.
(3.) Algebraic Thinking
(a.) Discuss the concepts of: Expressions, Equations, and Functions.
(b.) Translate word phrases into algebraic expressions. (English to Math)
(c.) Translate sentences into algebraic equations. (English to Math)
(d.) Solve algebraic expressions.
(e.) Solve, and check the solution of algebraic equations.
(f.) Determine the domain and range of functions.
(g.) Derive the formulas for the sum of the n terms of arithmetic and geometric sequences.
(h.) Solve applied problems involving expressions, equations, and functions.
(4.) Data Analysis and Introductory Statistics
(a.) Define the term, Statistics.
(b.) Discuss the basic concepts/topics in Statistics.
(c.) Design experiments to collect data.
(d.) Organize data.
(e.) Present data.
(f.) Analyze data.
(g.) Determine the descriptive statistics of data.
(h.) Differentiate between association and causation.
(i.) Analyze the relationship between two variables as applicable.
(j.) Solve applied problems in Statistics.
(k.) Solve applied problems involving Correlation and Regression.
(5.) Probability
(a.) Discuss the topic of Probability.
(b.) Discuss the applications of probability in several disciplines.
(c.) Discuss the types of events.
(d.) Determine the probability of an event.
(e.) Determine the odds in favor of an event.
(f.) Determine the odds against an event.
(g.) Apply the rules of probability.
(h.) Discuss Conditional probability.
(i.) Calculate the expected value of a random variable.
(j.) Solve applied problems involving probability.
(6.) Combinatorics
(a.) Discuss the basic concepts used in Combinatorics.
(b.) State the Fundamental Counting Principle.
(c.) Determine the number of ways two tasks can be done consecutively.
(d.) Determine the number of ways multiple tasks can be done successively.
(e.) Determine the number of permutations of items.
(f.) Determine the number of permutations of duplicate items.
(g.) Determine the number of permutations of total items taking some items at a time.
(h.) Determine the number of combinations of total items taking some items at a time.
(i.) Apply the rules of probability in combinatorics.
(j.) Solve applied problems involving combinatorics.
(7.) Congruency and Similarity with Constructions
(a.) Discuss the concept of Congruency.
(b.) Explain geometric constructions leading to the SSS, SAS, ASA, AAS, and HL congruence properties.
(c.) Discuss the concept of Similarity.
(d.) Determine if two triangles are congruent.
(e.) Determine if two figures are similar.
(f.) State the theorems for determining similarity for triangles.
(g.) Solve problems involving congruent triangles.
(h.) Solve problems involving similar figures.
This week we will focus on...
Week 1 Learning Objectives:
Upon completion of this week, students will:
(1.) Explain the basic terms in Geometry.
(2.) Discuss the concepts of lines, line segments, and angles.
(3.) Name, classify, and measure angles.
(4.) Solve problems involving the basic terms in Geometry.
This week we will focus on...
Week 2 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss geometric shapes.
(2.) Determine the measures of the interior and exterior angles of polygons.
(3.) Solve problems involving lines and angles.
(4.) Solve problems involving geometrical shapes.
This week we will focus on...
Week 3 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss geometric shapes.
(2.) Solve problems involving geometrical shapes.
(3.) Analyze the relationships between different physical quantities. (Dimensional Analysis).
(4.) Discuss the main systems of the measurements of physical quantities.
(5.) Identify a measurement and measurement unit needed to solve a problem.
(6.) Convert units within and between standard and metric measurement systems.
(7.) Solve real-world problems involving measurements and units.
This week we will focus on...
Week 4 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the mensuration of polygons.
(2.) Discuss the mensuration of circles.
(3.) Solve applied problems involving the mensuration of polygons.
(4.) Solve problems involving the mensuration of circles.
This week we will focus on...
Week 5 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the Pythagorean Theorem for right triangles.
(2.) Solve applied problems involving the Pythagorean Theorem.
(3.) Calculate the distance between two points using the Distance Formula.
(4.) Determine the equation of a circle.
This week we will focus on...
Week 6 Learning Objectives:
Upon completion of this week, students will:
(1.) Convert units within and between standard and metric measurement systems.
(2.) Solve real-world problems involving measurements and units.
(3.) Discuss the mensuration of solids.
(4.) Solve problems involving the mensuration of solids.
This week we will focus on...
Week 7 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concepts of: Variables, Expressions and Equations.
(2.) Translate word phrases into algebraic expressions. (English to Math).
(3.) Translate sentences into algebraic equations. (English to Math).
(4.) Solve algebraic linear expressions.
(5.) Solve, and check the solution of algebraic linear equations.
(6.) Solve applied problems involving linear expressions and linear equations.
This week we will focus on...
Week 8 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concepts of: Relations and Functions.
(2.) Translate word phrases and sentences into functions.
(3.) Discuss linear functions.
(4.) Discuss the slope concept.
(5.) Determine the slope of linear functions.
(6.) Interpret the slope of linear functions.
(7.) Determine the intercepts of linear functions.
(8.) Interpret the intercepts of linear functions.
(9.) Determine the zeros of linear functions.
(10.) Interpret the zeros of linear functions.
(11.) Convert between various forms of linear functions.
(12.) Graph linear functions.
(13.) Interpret the graphs of linear functions.
(14.) Derive the formula for the sum of the n terms of an arithmetic sequence.
(15.) Derive the formula for the sum of the n terms of a geometric sequence.
(16.) Solve applied problems involving linear functions.
This week we will focus on...
Week 9 Learning Objectives:
Upon completion of this week, students will:
(1.) Define the term, Statistics.
(2.) Discuss the basic concepts/topics in Statistics.
(3.) Compare observational studies and experiments.
(4.) Contrast observational studies and experiments.
(5.) Design experiments to collect data.
(6.) Obtain a simple random sample.
(7.) Obtain a stratified sample.
(8.) Obtain a systematic sample.
(9.) Obtain a cluster sample.
(10.) Explain the sources of bias in sampling.
(11.) Perform sampling techniques using technology.
(12.) Solve applied problems in Introductory Statistics.
This week we will focus on...
Week 11 Learning Objectives:
Upon completion of this week, students will:
(1.) Complete all outstanding assignments.
This week we will focus on...
Week 11 Learning Objectives:
Upon completion of this week, students will:
(1.) Organize data.
(2.) Present data.
(3.) Differentiate between association and causation.
(4.) Analyze the relationship between two variables as applicable.
(5.) Solve applied problems involving Correlation and Regression.
This week we will focus on...
Week 12 Learning Objectives:
Upon completion of this week, students will:
(1.) Analyze data.
(2.) Determine the measures of center of a dataset.
(3.) Determine the measures of spread of a dataset.
(4.) Determine the measures of location of a dataset.
(5.) Determine the measures of shape of a dataset.
(6.) Solve applied problems in the descriptive statistics.
This week we will focus on...
Week 13 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the topic of Probability.
(2.) Discuss the applications of probability in several disciplines.
(3.) Discuss the types of events.
(4.) Determine the probability of an event.
(5.) Apply the rules of probability.
(6.) Solve applied problems involving probability.
This week we will focus on...
Week 14 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the basic concepts used in Combinatorics.
(2.) State the Fundamental Counting Principle.
(3.) Determine the number of ways two tasks can be done consecutively.
(4.) Determine the number of ways multiple tasks can be done successively.
(5.) Determine the number of permutations of items.
(6.) Determine the number of permutations of duplicate items.
(7.) Determine the number of permutations of total items taking some items at a time.
(8.) Determine the number of combinations of total items taking some items at a time.
(9.) Apply the rules of probability in combinatorics.
(10.) Solve applied problems involving combinatorics.
This week we will focus on...
Week 15 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concept of Congruency.
(2.) Explain geometric constructions leading to the SSS, SAS, ASA, AAS, and HL congruence properties.
(3.) Discuss the concept of Similarity.
(4.) Determine if two triangles are congruent.
(5.) Determine if two figures are similar.
(6.) State the theorems for determining similarity for triangles.
(7.) Solve problems involving congruent triangles.
(8.) Solve problems involving similar figures.