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Course Design for Principles of Mathematics I

4. Understand number theory
Learning objectives

What you will learn as you master the competency:
a. Understand and apply divisibility theorems.
b. Demonstrate the divisibility tests for 2,3,4,5,6,7,8,9,10.
c. De termine whether a number is prime or composite.
d. Determine all the factors of a given number.
e. Write the prime factorization of a given number.
f. Determine the greatest common factor and the least common multiple of two numbers .
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams.
on a two hour cumulative exam.
Your performance will be successful when:
you can understand and can apply divisibility theorems.
you can demonstrate the divisibility tests for 2,3,4,5,6,7,8,9,10.
you can determine whether a number is prime or composite
you can determine all the factors of a given number.
you can write the prime factorization of a given number.
you can determine the greatest common factor and the least common multiple of two numbers.

5. Understand the set of Integers.
Learning objectives

What you will learn as you master the competency:
a. Explain the rules for addition and subtraction of integers using a variety of applications
b. Illustrate the rules for addition and subtraction of integers using a number line and colored
counters.
c. Explain the rules for multiplication and division of integers by establishing a pattern, and using a
variety of applications.
d. Extend the properties of Whole Numbers to the Integers.
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams.
on a two hour cumulative exam.
Your performance will be successful when:
you can explain the rules for addition and subtraction of integers using a variety of applications.
you can illustrate the rules for addition and subtraction of integers using a number line and colored
counters.
you can explain the rules for multiplications and division of integers by establishing a pattern, and
using a variety of applications.
you can extend the properties of Whole Numbers to the Integers.

6. Understand the set of Rational Numbers
Learning objectives

What you will learn as you master the competency:
a. Demonstrate four meanings of an elementary fraction.
b. Use two methods for verifying the equivalence of two fractions
c. Explain the rules for adding and subtracting fractions.
d. Use fraction bars to illustrate the rules for adding and subtracting fractions.
e. Explain the rules for multiplying and dividing fractions.
f. Illustrate the rules for multiplying and dividing fractions using a variety of methods.
g. Extend the properties of the Integers to the Rational Numbers.
h. Discuss strategies for mental computation and estimation of Rational Number operations .
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams.
on a two hour cumulative exam.
Your performance will be successful when:
you can demonstrate four meanings of an elementary fraction.
you can use two methods for verifying the equivalence of tow fractions.
you can explain the rules for adding and subtracting fractions.
you can use fraction bars to illustrate the rules for adding and subtracting fractions.
you can explain the rules for multiplying and dividing fractions.
you can illustrate the rules for multiplying and dividing fractions using a variety of methods.
you can extend the properties of the Integers to the Rational Numbers.
you can discuss strategies for mental computation and estimation of Real Number operations.

7. Understand the Real Number System
Learning objectives

What you will learn as you master the competency:
a. Explain the meaning of decimal numbers using place value models
b. Explain the rules for adding, subtracting, multiplying, and dividing decimal numbers.
c. Solve problems using ratios and proportions .
d. Convert between percents, fractions and decimals.
e. Solve percent problems.
f. Identify the major subsets of the Real Numbers.
g. Discuss the properties of Real Number operations.
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams
on a two hour cumulative exam.
Your performance will be successful when:
you can explain the meaning of decimal numbers using place value models.
you can explain the rules for adding, subtracting, multiplying, and dividing decimal numbers.
you can solve problems using ratios and proportions.
you can convert between percents, fractions, and decimals.
you can solve percent problems.
you can identify the major subsets of the Real Numbers.
you can discuss the properties of Real Number operations.

Types of Instruction
Classroom Presentation

Grading Information
Grading Rationale

Each instructor has the flexibility to develop evaluative procedures within the fol lowing parameters .
1. Written Exams must re present at least 60% of the final course grade.
2. Final Exam must represent at least 20% of the final course grade.
3. The Post Test is to be embedded in the final exam and must represent at least 10% of the final
course grade.
4. Other Activities may represent at most 10% of the final course grade.

Grading Scale

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