Course Description
Presents topics in mathematical reasoning and problem solving; numeration systems; numbers; arithmetic
operations on numbers; number theory; fractions, decimals and percents; and proportional reasoning.
Prerequisite: Satisfaction of the University’s proficiency requirements for mathematics
Credit Hours: 3
General Course Purpose
This is the first of two courses that focus on developing the mathematical understanding of students who are
preparing to be licensed as Elementary Teachers.
Upon the successful completion of this course, students will satisfy these objectives:
Course Objectives
(1.) Problem Solving
(a.) Explain the four-step problem solving process.
(b.) Solve problems using problem-solving strategies.
(c.) Apply deductive reasoning in arguments.
(d.) Apply inductive reasoning in arguments.
(e.) Determine patterns in objects as applicable.
(f.) Determine the nth term of certain sequences.
(2.) Numbers and Numeration Systems
(a.) Discuss the origin of numbers.
(b.) Classify numbers.
(c.) Define the different types of numbers.
(d.) Discuss the different numeration systems including the Hindu-Arabic system.
(e.) Order numbers.
(f.) Perform basic arithmetic operations (addition, subtraction, multiplication, and division) on numbers.
(g.) Discuss the inverse relationship between addition and subtraction.
(h.) Discuss the inverse relationship between multiplication and division.
(i.) Explain the models used to develop the algorithms for addition and subtraction.
(j.) Explain the models used to develop the algorithms for multiplication and division.
(k.) Discuss number bases.
(l.) Solve applied problems on numbers.
(3.) Number Theory
(a.) Discuss the concepts of: Divisibility, Factors, and Multiples.
(b.) State the divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, and 11.
(c.) State the Fundamental Theorem of Arithmetic.
(d.) Determine the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two or more whole
numbers using several methods.
(e.) Factorize whole numbers.
(f.) Discuss the Euclidean Algorithm as regards the greatest common divisor.
(g.) Solve applied problems involving GCD and LCM.
(4.) Integers
(a.) Represent integers on a number line.
(b.) Explain models for the arithmetic operations on integers.
(c.) Perform basic arithmetic operations (addition, subtraction, multiplication, and division) on integers.
(d.) Discuss the properties of the arithmetic operations on integers.
(e.) Discuss the Division Algorithm.
(f.) Perform the order of operations on integers.
(5.) Rational Numbers and Proportional Reasoning
(a.) State the different representations for rational numbers.
(b.) Order rational numbers.
(c.) Perform basic arithmetic operations (addition, subtraction, multiplication, and division) on rational
numbers.
(d.) Discuss the properties of the arithmetic operations on rational numbers.
(e.) Extend the discussion of Exponents to include negative integers.
(f.) Compare ratios and rational numbers.
(g.) Discuss the concept of Proportions and their properties.
(h.) Discuss the concept of Scaling.
(6.) Rational Numbers as Decimals and Percent
(a.) Discuss the topic of Decimals.
(b.) Discuss the topic of Fractions.
(c.) Discuss the topic of Percent.
(d.) Develop efficient algorithms for decimal operations using concrete models, drawings, and strategies.
(e.) Write exponential and scientific notation for decimals.
(f.) Convert between fractions, decimals, and percents
(fraction to decimal, decimal to fraction, fraction to percent, percent to fraction, decimal to percent,
percent to decimal).
(g.) Solve percent problems using proportional relationships.
(h.) Solve applied problems on fractions, decimals, and percents.
This week we will focus on...
Week 1 Learning Objectives:
Upon completion of this week, students will:
(1.) Explain the four-step problem solving process.
(2.) Solve problems using problem-solving strategies.
(3.) Apply deductive reasoning in arguments.
(4.) Apply inductive reasoning in arguments.
(5.) Determine patterns in objects as applicable.
(6.) Determine the nth term of certain sequences.
This week we will focus on...
Week 2 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the origin of numbers.
(2.) Classify numbers.
(3.) Define the different types of numbers.
(4.) Discuss the different numeration systems including the Hindu-Arabic system.
(5.) Order numbers.
(6.) Add whole numbers expressed in several numeration systems.
This week we will focus on...
Week 3 Learning Objectives:
Upon completion of this week, students will:
(1.) Add whole numbers expressed in several numeration systems.
(2.) Subtract whole numbers expressed in several numeration systems.
(3.) Solve applied problems involving the addition of numbers.
(4.) Solve applied problems involving the subtraction of numbers.
This week we will focus on...
Week 4 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the inverse relationship between addition and subtraction.
(2.) Explain the models used to develop the algorithms for addition and subtraction.
(3.) Multiply whole numbers expressed in several numeration systems.
(4.) Solve applied problems involving the multiplication of numbers.
This week we will focus on...
Week 5 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the inverse relationship between multiplication and division.
(2.) Explain the models used to develop the algorithms for multiplication and division.
(3.) Divide whole numbers expressed in several numeration systems.
(4.) Solve applied problems involving the division of numbers.
This week we will focus on...
Week 6 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concepts of: Divisibility, Factors, and Multiples.
(2.) State the divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, and 11.
(3.) Solve applied problems involving the divisibility of numbers.
This week we will focus on...
Week 7 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concept of prime numbers.
(2.) Discuss the concept of composite numbers.
(3.) State the Fundamental Theorem of Arithmetic.
(4.) Determine the Greatest Common Divisor (GCD) of two or more whole numbers using several methods.
(5.) Determine the Least Common Multiple (LCM) of two or more whole numbers using several methods.
(6.) Factorize whole numbers.
(7.) Discuss the Euclidean Algorithm as regards the greatest common divisor.
(8.) Solve applied problems involving the Greatest Common Divisor.
(9.) Solve applied problems involving the Least Common Multiple.
This week we will focus on...
Week 8 Learning Objectives:
Upon completion of this week, students will:
(1.) Represent integers on a number line.
(2.) Explain the models for the arithmetic operations (addition and subtraction) on integers.
(3.) Perform basic arithmetic operations on integers.
(4.) Discuss the properties of the arithmetic operations on integers.
(5.) Perform the order of operations on integers.
(6.) Solve applied problems involving the arithmetic operations on integers.
This week we will focus on...
Week 9 Learning Objectives:
Upon completion of this week, students will:
(1.) Explain the models for the arithmetic operations (multiplication and division) on integers.
(2.) Perform the basic arithmetic operations on integers.
(3.) Discuss the properties of the arithmetic operations on integers.
(4.) Perform the order of operations on integers.
(5.) Solve applied problems involving the arithmetic operations on integers.
(6.) Submit your draft on the Number Theory project.
This week we will focus on...
Week 10 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss Rational Numbers.
(2.) State the different representations for rational numbers.
(3.) Order rational numbers.
(4.) Compare ratios and rational numbers.
This week we will focus on...
Week 11 Learning Objectives:
Upon completion of this week, students will:
(1.) Perform basic arithmetic operations (addition, subtraction, multiplication, and division) on rational numbers.
(2.) Discuss the properties of the arithmetic operations on rational numbers.
(3.) Extend the discussion of Exponents to include negative integers.
This week we will focus on...
Week 12 Learning Objectives:
Upon completion of this week, students will:
(1.) Compare ratios and rational numbers.
(2.) Discuss the concept of Proportions and their properties.
(3.) Discuss the concept of Scaling.
(4.) Solve applied problems involving proportions.
This week we will focus on...
Week 13 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the topic of Decimals.
(2.) Perform arithmetic operations on decimals.
(3.) Convert between fractions, decimals, and percents (fraction to decimal, decimal to fraction, fraction to percent, percent to fraction, decimal to percent, percent to decimal).
(4.) Develop efficient algorithms for decimal operations using concrete models, drawings, and strategies.
(5.) Solve applied problems involving decimals.
This week we will focus on...
Week 14 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the concept of exponential/scientific notation.
(2.) Write decimals in standard notation to exponential/scientific notation.
(3.) Write decimals in scientific notation to standard notation.
(4.) Solve applied problems involving scientific notation.
This week we will focus on...
Week 15 Learning Objectives:
Upon completion of this week, students will:
HAPPY THANKSGIVING.
Please complete all outstanding assignments.
This week we will focus on...
Week 16 Learning Objectives:
Upon completion of this week, students will:
(1.) Discuss the topic of Percent.
(2.) Convert between fractions, decimals, and percents (fraction to decimal, decimal to fraction, fraction to percent, percent to fraction, decimal to percent, percent to decimal).
(3.) Solve percent problems using proportional relationships.
(4.) Solve applied problems involving percents.