# MATH 1350-1351

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

### Math 1350 (and 1351)

**State Approval Code:**2701015619**Semester Credit Hours:**3**Lecture Hours per Week:**3**Contact Hours per Semester:**48

### Catalog Description

**Math 1350**

Concepts of sets, functions, numeration systems, number theory, and properties of natural numbers, integers, rational and real number systems with an emphasis on problem solving and critical thinking. This course is designed specifically for students who seek middle grade (4-8) teacher certification. (2701015619) 3-3-0

**Math 1351**

Concepts of geometry, probability, and statistics, as well as applications of the algebraic properties of real numbers to concepts of measurement with an emphasis of problem solving and critical thinking. This course is designed specifically for students who seek middle grade (4-8) teacher. (2701015619) 3-3-0

### Prerequisites

**1350**--TSIP complete and Math 1314 or permission of instructor.

**1351**– TSIP completed and Math 1350 or Math 1314 or permission of instructor

### Course Curriculum

### Basic Intellectual Compentencies in the Core Curriculum

- Reading
- Writing
- Speaking
- Listening
- Critical thinking
- Computer literacy

### Perspectives in the Core Curriculum

- Establish broad and multiple perspectives on the individual in relationship to the larger society and world in which he/she lives, and to understand the responsibilities of living in a culturally and ethnically diversified world.
- Stimulate a capacity to discuss and reflect upon individual, political, economic, and social aspects of life in order to understand ways in which to be a responsible member of society.
- Recognize the importance of maintaining health and wellness.
- Develop a capacity to use knowledge of how technology and science affect their lives.
- Develop personal values for ethical behavior.
- Develop the ability to make aesthetic judgments.
- Use logical reasoning in problem solving.
- Integrate knowledge and understand the interrelationships of the scholarly disciplines.

### Core Components and Related Exemplary Educational Objectives

### Communication (composition, speech, modern language)

- To participate effectively in groups with emphasis on listening, critical and reflective thinking, and responding.

### Mathematics

- To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
- To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
- To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
- To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize the limitations of mathematical and statistical models.
- To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

### Instructional Goals and Purposes

Panola College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.

### General Course Objectives

1.To apply problem-solving skills through solving application problems.

2.To demonstrate arithmetic and algebraic manipulation skills.

3.To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4.To construct appropriate mathematical models to solve applications.

5.To interpret and apply mathematical concepts.

6.To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems

### Specific Course 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.

### General Description of Each Lecture or Discussion

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 of Instruction/Course Format/Delivery

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

### Assessment

•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

A: 90 < Average < 100

B: 80 < Average < 90

C: 70 < Average < 80

D: 60 < Average < 70

F: 00 < Average < 60