Fundamentals of Math I (1350) and Fundamentals of Math II (1351)

Major Learning Objectives
Essential Competencies
Upon completion of MATH 1350 and 1351, the student will be able to demonstrate:
1.Competence in applying both inductive and deductive methods of reasoning.
2.Competence in using set notation and identifying the union and intersection of sets.
3.Competence in identifying functions and relations and their graphs.
4.Competence in using various numerical representations of the
number system, including different bases and scientific notation.
5.Competence in solving problems using properties of the whole numbers.
6.Competence in solving problems using the properties of the integers and ordering the integers.
7.Competence in applying the rules of number theory to the integers.
8.Competence in solving problems using the properties of the rational numbers.
9.Competence in solving problems using the properties of the real numbers.
10.Competence in solving geometry problems involving area, volume, constructions and congruence, parallel and perpendicular lines and translations, and the metric system.
11.Competence in organizing and representing statistical data, measuring central tendencies, and solving problems involving permutations and combinations.
12.Competence in computing slope and distance, and then using this knowledge to write the equations of lines.

After studying the material presented in the text(s), lecture, laboratory, computer tutorials, and other resources, the student should be able to complete all behavioral/learning objectives listed below with a minimum competency of 70%.
Page 7 of 16.
Math 1350
1.Given a sequence of numbers, complete the missing terms of the sequence and write the formula defining the sequence.
2.Identify the three types of valid arguments and draw Venn diagrams representing them.
3.Given true premises, supply a conclusion implied by the premises and identify if the argument is valid or invalid.
4.Identify the strategies for solving problems and use them to solve problems.
5.Given a set, identify the elements of the set and use proper set notation to name the set.
6.List the elements of the well-defined set using set-builder notation.
7.Define and apply the following: set union, set intersection, set complement, empty set, subset, and proper subset. Draw Venn diagrams to represent each.
8.Define and apply the Cartesian product (cross product).
9.Prove with sets and with Venn diagrams the properties of set union and set intersection.
10.Define and identify a relation and a function, and distinguish between the two.
11.Identify the domain and range of a relation and a function.
12.Define the reflexive, symmetric and transitive properties, and given a relation, discuss whether the relation is reflexive, symmetric or transitive.
13.Define an equivalence relation, and discuss whether a relation is an equivalence relation.
14.Determine the cardinality of a set.
15.Given two sets, determine whether the sets can be paired in a one-to-one correspondence.
16.Describe the features, advantages and disadvantages of the early systems of numeration.
17.Given a Hindu-Arabic numeral, write the number in each of the early numeration systems. Write numerals from other systems into a Hindu-Arabic numeral.
18.Define exponent and apply the properties of exponents when solving problems.
19.Write a number in scientific notation, in standard form and expanded form.
20.Correctly read and write numbers in the Hindu-Arabic numeration system.
21.Define “number system” and use the roster method to define the set of whole numbers.
22.Define “addition” of whole numbers, and correctly identify the addends and the sum.
23.Apply the following properties of whole numbers: the closure property, the commutative property, the associative property, the identity property, and model or prove these properties given sets A, B, and C.
24.Define “multiplication” of whole numbers and correctly identify the factors and the product.
25.Define “subtraction” of whole numbers and correctly identify the minuend, subtrahend, and the difference.
26.Define “division” of whole numbers and correctly identify the dividend, divisor, quotient, and the remainder.
27.Define “algorithm” and use the Division Algorithm to find the quotient and the remainder.
28.Convert numbers in other bases to base ten and numbers in base ten to other bases.
29.Add, subtract, multiply and divide in other bases.
30.Use the roster method to identify the set of integers.
31.Apply the properties of integers when solving problems.
32.Add, subtract, multiply and divide integers, and use models to demonstrate the answer.
33.Apply the properties of inequalities for integers.
34.State the “Law of Trichotomy” for integers.
35.Define “absolute value” and use the definition to describe distance on a number line.
36.For two integers, define “a divides b.”
37.State the divisibility rules and use them to determine factors of a given number.
38.Use the Sieve of Eratosthenes to find the prime numbers between 1 – 100.
39.State the Fundamental Theorem of Arithmetic and use it to give the prime factorization of any integer.
40.Given two numbers, find the greatest common factor (GCD) and the least common multiple (LCM) using prime factorization. Use Euclid’s Method to find the GCD of two integers.
41.Perform operations in clock arithmetic or modular arithmetic.

Math 1351
42.Define a rational number and be able to represent a rational number using manipulatives such as fraction circles, Cuisenaire rods or base ten blocks.
43.Simplify a rational number using the Fundamental Law of Fractions.
44.Add, subtract, multiply and divide rational numbers and be able to
represent the operation using manipulatives.
45.Apply the properties of rational numbers to solve problems or equations.
46.Be able to order the rational numbers and discuss the property of “denseness” of the rational numbers.
47.Calculate the arithmetic mean of two rational numbers.
48.Identify the three types of decimals.
49.Write decimals as fractions in simplest form and write fractions as decimals.
50.Add, subtract, multiply and divide terminating decimals.
51.Convert a repeating decimal o a rational number.
52.Round repeating decimals to a given place value or a given number of significant digits.
53.Solve problems involving ratio and proportion.
54.Define percent and write decimals as percents and percents as decimals.
55.Solve problems involving percents.
56.Prove that a number is “irrational using “proof by contradiction.”
57.Approximate square roots using “Newton’s Method” (”divide and average method”).
58.Discuss the difference between “axiom” or “postulate” and “theorem.”
59.Define basic geometric concepts based on point, line and plane.
60.Define and identify the various types of angles.
61.Define and identify the basic types of arcs.
62.Define and identify the basic types of triangles.
63.Define and identify the basic types of polygons.
64.Define and calculate the complement and supplement of an angle.
65.Discuss the difference between “equal” and “congruent.”
66.Perform the basic compass constructions, constructing figures congruent to the following: a line segment, an angle, constructing a perpendicular and parallel segment.
67.Prove triangles are congruent using the congruence theorems.
68.Identify the types of angles related to parallel lines and apply the theorems to calculate angles related to parallel lines.
69.Identify the basic transformations: reflections, rotations and translations; and given a figure on graph paper, perform a given transformation.
70.Discuss the history of the metric system and the need for standardization of the metric system.
71.Calculate the perimeter and circumference of various polygons.
72.Calculate the area of various plane regions.
73.Identify the five classes of regular polygons.
74.Calculate the volume of various solid regions.
75.Convert from one metric unit to another.
76.Convert from Fahrenheit temperature to Celsius and vice versa.
77.Use the Pythagorean Theorem to find the length of a side of a right triangle.
78.Use the converse of the Pythagorean Theorem to identify the type of triangle: acute, obtuse, or right.
79.Solve problems using similar triangles and indirect measurement.
80.Interpret data from tables, charts and various types of graphs.
81.Given data, draw a table, chart or graph that best represents the data.
82.Calculate the mean, median, mode, range and standard deviation of a set of data.
83.Discuss the distribution of data as following the normal frequency curve or a skewed curve by looking at leaf plots or histograms.
84.Find the probability of a single-stage or multi-stage event.
85.Calculate the odds of occurrence of an event.
86.Apply the definition of mathematical expectation of an event.
87.Apply the Fundamental Counting Principle to calculate probability.
88.Calculate the number of permutations of an event.
89.Calculate the number of combinations of n elements taken r at a time.
90.Label the coordinate plane, including axes, quadrants, and the origin.
91.Graph a linear equation using a table, including the x- and y-intercepts.
92.Define and identify increasing and decreasing functions.
93.Calculate the distance between points on a number line and in the coordinate plane.
94.Given two points calculate the slope of a line containing two given points.
95.Write the equation of a line in standard form given two points.
96.Write the equation of a line in slope-intercept form given two points.
97.Write the equation of a circle given the center and the radius.
98.Given the equation of a circle, identify the center and the radius.

Methods employed will include Lecture/demonstration, discussion, problem solving, analysis, and reading assignments. Homework will be assigned.
Faculty may choose from, but are not limited to, the following methods of instruction:
(1) Lecture
(2) Discussion
(3) Internet
(4) Video
(5) Television
(6) Demonstrations
(7) Field trips
(8) Collaboration
(9) Readings

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities. Faculty may choose from – but are not limited to -- the following methods
•Attendance
•Book reviews
•Class preparedness and participation
•Collaborative learning projects
•Compositions
•Exams/tests/quizzes
•Homework
•Internet
•Journals
•Library assignments
•Readings
•Research papers
•Scientific observations
•Student-teacher conferences
•Written assignments

Letter Grades for the Course will be assigned as follows:
A: 90 < Average < 100
B: 80 < Average < 90
C: 70 < Average < 80
D: 60 < Average < 70
F: 00 < Average < 60