## Course Objectives

After this course students are expected to:

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

## Official

### Sample Exams

- MATH 3041 Exam I Semester 2, 2012
- MATH 3041 Exam II Semester 2, 2012
- MATH 3041 Exam III Semester 2, 2012
- Practice Problems

## Course Notes and Readings

- Course Introduction
- Recomendaciones para Estudiantes Nuevos
- In Praise of Lectures
- Homeworks 1-13
- Relations
- Errata
- Section 1.1 Counting
- Section 1.2 Place Value
- Exercise on the Addition Table
- Section 1.4 Subtraction
- Section 1.5 Multiplication
- Exercise on the Multiplication Table
- Section 1.6 Division
- Section 3.3 Algorithms
- Section 3.4 A Division Algorithm
- Section 3.5 Estimation
- Section 4.1 Prealgebra
- Section 4.3 Divisibility
- Section 5.3 Factors and Prime Numbers
- Exercises on Factors and Primes
- Exercises on prime numbers and the greatest common factor
- Section 6.1 Fractions
- Section 6.1 Partitive and Measure Division
- Notes on the conversion of units
- Solving Algebra and Other Story Problems by Sybilla Beckmann
- Tree of Porphyry
- Some Educational References

## Syllabus

- Course Introduction
- Numeration, Place Value and Arithmetic Operations
- Roman numerals
- Place value
- Expanded form of a number
- The four arithmetic operations for whole numbers
- Interpretations for subtraction: Part-whole, Take-away, Comparison
- Definition of division and the Quotient-Remainder Theorem
- Interpretations for division: Partitive, Measurement
- Basic properties of operations: commutative, associative, distributive properties, additive identity, multiplicative identity

- Mental Math and Word Problems
- Mental Math
- Word Problems
- The Art of Word Problems

- Algorithms
- An Addition Algorithm
- A Subtraction Algorithm
- A Multiplication Algorithm.
- Long Division by 1-digit Numbers
- Estimation
- Completing the Long Division Algorithm

- Prealgebra
- Letters and Expressions
- Identities, Properties, Rules
- Exponents

- Factors, Primes, and Proofs
- Definitions, Explanations and Proofs
- Divisibility Tests
- Primes and the Fundamental Theorem of Arithmetic
- More on Primes
- Greatest Common Factors and Least Common Multiples

- Fractions
- Equal division of a segment by ruler and compass
- A definition of the concept of fraction
- Representations of fractions
- Equivalence of fractions. The cancellation law
- Ordering fractions
- Addition and subtraction of fractions
- Bar diagrams illustrating addition and subtraction of fractions
- Multiplication and division of fractions
- Area models of fractions

- Ratios, Percentages, and Rates
- Ratios and Proportions
- Changing Ratios and Percentages
- Solving Percent Problems by the Unitary Method
- Rates, Speed, and Dimensional Analysis

- Negative Numbers and Integers
- Negative Numbers
- Arithmetic with Integers
- Integers as a Step Towards Algebra

- Decimals, Rational and Real Numbers
- Decimals
- Rational Numbers and Decimals.
- Real Numbers and Decimals

### Texts

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