Mathematics Department
Course Outline
Ma 508 Professionalized Subject Matter
in Arithmetic
Course
Description: This course offers a
study of procedures in arithmetic. Attention is given to concepts in
manipulative and problem solving areas. Various services for diagnostic and
remedial measures are introduced and evaluated.
Goals of the Course
1.
To provide the
student with mathematical skills needed in the study of algebra.
2.
To provide the
student with an algebraic, numerical and graphical approach to problem solving.
3.
To investigate
and evaluate diagnostic tools used for student evaluation.
4.
To provide the
student with knowledge of technological resources that is available for this
level of student.
5.
To expose the
student to a variety of problem solving techniques.
Instructional Procedures
1.
Classroom
Lecture.
2.
Group Projects.
3.
Calculator and
Computer Projects.
4.
Class Project or
Presentation.
Course Content
1. Whole Numbers
A.
Place Value and
Names for Numbers
B.
Properties and
Facts of Addition
C.
Addition with
Whole Numbers and Perimeter
D.
Rounding Numbers,
Estimating Answers, and Displaying Information
E.
Subtraction with
Whole Numbers
F.
Properties and
Facts of Multiplication
G.
The Distributive
Property and Multiplication with Whole Numbers
H.
Division with
Whole Numbers
I.
Exponents and
Order of Operations
J.
Area and Volume
2. Introduction to Algebra
A.
Positive and
Negative Numbers
B.
Addition with
Negative Numbers
C.
Subtraction with
Negative Numbers
D.
Multiplication
with Negative Numbers
E.
Division with
Negative Numbers
F.
Simplifying Algebraic
Expressions
G.
Multiplication
Properties of Exponents
H.
Adding and
Subtracting Polynomials
I.
Multiplying
Polynomials: An Introduction
3. Fractions and Mixed
Numbers
A.
The Meaning and
Properties of Fractions
B.
Prime Numbers,
Factors, and Reducing to Lowest Terms
C.
Multiplication
with Fractions, and the Area of a Triangle
D.
Divisions with
Fractions
E.
Addition and
Subtraction of Fractions
F.
Mixed Number
Notation
G.
Multiplication
and Division with Mixed Numbers
H.
Addition and
Subtraction with Mixed Numbers
I.
Combinations of
Operation, and Complex Fractions
4. Solving Equations
A.
Distributive
Property and Algebraic Expressions
B.
Addition Property
of Equality
C.
Multiplication
Property of Equality
D.
Linear Equations
in One Variable
E.
Applications
F.
Evaluating
Formulas
G.
Paired Data and
Equations in Two Variables
H.
Rectangular
coordinate System
I.
Graphing Straight
Lines
5. Decimals
A.
Decimal Notation
and Place Value
B.
Addition and
Subtraction with Decimals
C.
Multiplication
with Decimals, Circumference and Area of a circle
D.
Division with
Decimals
E.
Fractions and Decimals,
and the Volume of a Sphere
F.
Equations
containing Decimals
G.
Square Roots and
the Pythagorean Theorem
H.
Simplifying
Square Roots
I.
Adding and
Subtracting Square Roots
6. Ratio, Proportion and Unit
Analysis
A.
Ratios
B.
Unit Analysis 1:
Length
C.
Unit Analysis 2: Area
and Volume
D.
Weight
E.
Converting
between the Two Measurement System
F.
Proportions
7. Percent
A.
Percents,
Decimals, and Fractions
B.
Basic Percent
Problems
C.
General
Applications of Percent
D.
Sales Tax and
Commission
E.
Percent Increase
or Decrease and Discount
F.
Interest
Evaluation Measures
Determining Students’ Grades
1.
Two hourly exams 50%
2.
Final Exam 25%
3.
Projects 25%
Bibliography
A. Required Text
Carpenter, Thomas P.,
Elizabeth Fennema, Megan Loef
Franke, Linda Levi and, Susan Empson,
Children’s Mathematics: Cognitively Guided Instruction, Heinemann
Publishers, Portsmouth, NH, 1999.
Fosnot, Catherine Twomey, and Maarten Dolk, Young
Mathematicians at Work: Constructing Multiplication and Division, Heinemann
Publishers,
Fosnot, Catherine Twomey, and Maarten Dolk, Young
Mathematicians at Work: Constructing Fractions, Decimals, and Percents,
Heinemann Publishers,
Required
Calculator: TI83 or equivalent graphing calculator.
B. Additional Required
Curriculum
and Evaluation Standards for School Mathematics, National Council of Teachers of Mathematics, NCTM,
C. Supporting Bibliography
Bach, Daniel, and Patricia Leitner, PreAlgrebra:
Mathematics for a Variable World, Houghton Mifflin Publishers,
Bennett, Jeffrey, and William
Briggs, Using and Understanding Mathematics: A Quantitative Reasoning
Approach, Addison Wesley Publishers,
Lial, Margaret,
McKeague, Charles, Prealgebra:
Third Edition, PWS Publishing Company,
Shankland,
Sobel, Max, and Evan Maletsky, Teaching
Mathematics: A Sourcebook of Aids, Activities, and Strategies: Third Edition,
Allyn & Bacon Publishing Company,
Van Dyke, James, James Rogers,
and Holli Adams, Fundamentals of Mathematics:
Seventh Edition,
Whimbey, Arthur, and Jack Lochhead, Developing
Mathematical Skills, McGraw Hill Publishers,
D. Relevant Periodical
Resources
Mathematics Teacher, National Council of Teachers of Mathematics,
Mathematics in the Middle School, National Council of Teachers of Mathematics,
Teaching Children Mathematics, National Council of Teachers of Mathematics,
Mathematics Magazine, Mathematics Association of
E. Relevant Software
TI-83 Graphing Calculator
Guidebook,
Best,
George, Best Grapher 4.0, Houghton Mifflin
Publisher,
Converge, Version 4.5, Soft Warehouse Inc.,
Derive: A Mathematical
Assistant, Version 2.56, Soft
Warehouse Inc.,
Geometers
Sketchpad, Key Curriculum Press,
Hubbard, Elaine, and Ronald Robinson,
The Computer Tutor for Elementary and
Intermediate Algebra, Houghton Mifflin Publishers,