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Survey of Elementary Mathematics I

I. COURSE DESCRIPTION FROM CATALOG:
Introduction to sets and operations on sets, properties and operations on whole numbers, integers,
rational and real numbers . (Lecture 3, Credit 3)

II. PREREQUISITE(S): Minimum of two years high school algebra and one year of high school geometry.
Admission is restricted to students majoring in Elementary Education.

III. COURSE OBJECTIVE(S):
Build on (not replicate) the competencies gained through the study of two years of high school
algebra and one year of high school geometry. Use mathematics to solve problems and determine if
the solutions are reasonable . Use mathematics to model real world behaviors and apply
mathematical concepts to the solution of real-life problems. Make meaningful connections between
mathematics and other disciplines. Use technology for mathematical reasoning and problem
solving. Apply mathematical and/or basic statistical reasoning to analyze data and graphs.

1. Introduce inductive reasoning and help develop problem solving strategies ;
2. Review elementary set theory and expose the student to elementary logic;
3. Examine and compare different numeration systems;
4. Analyze the different subsets of real numbers (natural numbers, whole numbers, integers, etc.);
5. Promote an understanding of elementary statistics and probability;
6. Review the basics of plane geometry along with some solid geometry;
7. Develop and understanding of constructions, congruence and similarity, and,
8. Cover the basic concepts of measurements and introduce coordinate geometry .

IV. TOPICS TO BE COVERED:
• Introduction to Problem Solving
• Introduction to Set Theory
• Numbers

o Place Value
Decimal system
▪ Other base systems
▪ Counting, comparing, and rounding

o Real numbers
▪ Natural numbers
▪ Whole numbers
▪ Integers
▪ Rational numbers
▪ Irrational Numbers
 

Meaning of fractions (Not necessarily rational numbers)
Equivalent fractions
▪ Comparing fractions
▪ Percents

• Real numbers operations

o Addition and Subtraction
▪ Meaning
▪ Properties of Addition
▪ Addition and subtraction with the decimal system (and other bases)
▪ Addition and subtraction with integers
▪ Addition and subtraction with fractions
▪ Mental Math

o Multiplication
▪ Meaning
▪ Properties of Multiplication
Distributive property (Model pictorially)
▪ Factors and Multiples

Greatest Common Factor and Least Common Multiples
• Prime numbers and prime factorization
• Even and odd
Divisibility tests

Multiplication with the decimal system (and other bases)
▪ Multiplication with integers
▪ Multiplication with fractions
▪ Mental Math

o Division
▪ Meaning
▪ Division with an integer divisor
▪ Division with fractions
▪ Division with a non-integer divisor
▪ Ratio and proportion
▪ Mental Math

V. ADDITIONAL INFORMATION:
These courses may be used to satisfy the minimum general education requirements in mathematics.

VI. POSSIBLE TEXTS AND REFERENCES:
Mathematics for Elementary Teachers, 2nd ed., Beckman
(Topics can be found in Chapters 1-7 and 12.)

VII. ANY TECHNOLOGY THAT MAY BE USED:

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