# Math 3041 – Introduction to Mathematics I

Arithmetic and Algebra for Elementary Teachers

## Course Objectives

After Math 3041 students are expected to:

1. have achieved competency in the fundamental mathematical concepts necessary for the teaching of mathematics up to the sixth grade.
2. have become familiar with the main definitions, concepts, results and methods of proof relating to each part of the syllabus.
3. be able to quote the definitions and results, and to reproduce the proofs of some key results.
4. be able to solve problems relating to the material covered and present the solutions in a good mathematical style.

## Catalog Description

Concepts of Arithmetic and Algebra Three credits. Three hours of lecture per week. Prerequisite: For Elementary School Teachers.

Algebraic properties of the integers, the natural numbers and rational numbers. The decimal number system. Ordering of numbers. The number line. Solution of simple equations and inequalities. Measurement and approximation. Divisibility rules. Maximum common divisor and minimum common multiple. Percentages, ratio and proportion. Word problems. Graphs. Correspondences. The real numbers.

## Syllabus

1. Course Introduction
2. Numeration, Place Value and Arithmetic Operations
1. Roman numerals
2. Place value
3. Expanded form of a number
4. The four arithmetic operations for whole numbers
5. Interpretations for subtraction: Part-whole, Take-away, Comparison
6. Definition of division and the Quotient-Remainder Theorem
7. Interpretations for division: Partitive, Measurement
8. Basic properties of operations: commutative, associative, distributive properties, additive identity, multiplicative identity
3. Mental Math and Word Problems
1. Mental Math
2. Word Problems
3. The Art of Word Problems
4. Algorithms
2. A Subtraction Algorithm
3. A Multiplication Algorithm.
4. Long Division by 1-digit Numbers
5. Estimation
6. Completing the Long Division Algorithm
5. Prealgebra
1. Letters and Expressions
2. Identities, Properties, Rules
3. Exponents
6. Factors, Primes, and Proofs
1. Definitions, Explanations and Proofs
2. Divisibility Tests
3. Primes and the Fundamental Theorem of Arithmetic
4. More on Primes
5. Greatest Common Factors and Least Common Multiples
7. Fractions
1. Equal division of a segment by ruler and compass
2. A definition of the concept of fraction
3. Representations of fractions
4. Equivalence of fractions. The cancellation law
5. Ordering fractions
6. Addition and subtraction of fractions
7. Bar diagrams illustrating addition and subtraction of fractions
8. Multiplication and division of fractions
9. Area models of fractions
8. Ratios, Percentages, and Rates
1. Ratios and Proportions
2. Changing Ratios and Percentages
3. Solving Percent Problems by the Unitary Method
4. Rates, Speed, and Dimensional Analysis
9. Negative Numbers and Integers
1. Negative Numbers
2. Arithmetic with Integers
3. Integers as a Step Towards Algebra
10. Decimals, Rational and Real Numbers
1. Decimals
2. Rational Numbers and Decimals.
3. Real Numbers and Decimals

### Texts

1. Thomas Parker and Scott Baldridge, Elementary Mathematics for Teachers, Sefton-Ash Publishing, 2004.
2. Singapore Primary Mathematics 3A, 4A, 5A, and 6A Textbooks. Primary Mathematics 5A Workbook. (http://www.singaporemath.com)
3. Mario L. Rodríguez Barrios, Matemática para Maestros, Editora Centenario, 2001. (ISBN 1-8817736-21-0). Distribuidora: Los Hermanos López Inc, Río Piedras, Puerto Rico)
4. Philip Pennance, Mathematics Standards of Puerto Rico: Analysis and Recommendations.

## Bibliography

A list of texts and references for this course can be found in the Education Page.

## Evaluation

Based on Homework and up to 4 exams.
Scale:

A: 90-100;     B: 80-89;    C: 65-79;   D: 50-64;   F: < 50.