# fairmath™ Educational Resources: Pre-Algebra

The OER has been categorized as either fairmath ™ OA or fairmath™ and others' OS . As the organization grows, so will the curriculum and content. We are currnetly recruiting contributors and editors. We are very low on these resources, therefore if you see anything that needs to be corrected or changed, please contact us.Please read Curriculum and Pedaogy before using the resources.The pedagogy used is very important to insure positive outcomes of the fairmath™ OER. The resources are designed for active students and instructors. The current Pre- Algebra resources are designed as a transition from traditional instruction towards student centered learning.

# fairmath ™ OER

Open access, OA, broad definiton is making information available to all. Open access has many advantages. Open Access develops an acedemic community of sharing and cooperation. Thus Open Acess promotes gowth within those fields that use it. There are diferent types of licensing. We use Creative Commons by-nc-sa. Please reffer to the link http://creativecommons.org/licenses/by-nc/3.0/.

For more information on Creative Common licensing visit http://creativecommons.org/

# Support Resources

Concepts and Skills needed for Algebra

These resources can be used for all ages. These are the important concepts and skills that should be learned before starting the algebra curriculum. Theses resources are alligned with the athematics Common Core State Standards. For more informatio visit this outside link CCSI. They are also alligned with the NCTM standards. For more informatio visit this outside link NCTM.We are currnetly recruiting contributors and editors. We are very low on these resources, therefore if you see anything that needs to be corrected or changed, please contact us.

# The Structure of the texts

The texts are divided into parts. The parts are, the reading and writing of mathematics, concepts through problem solving, notes, mathematical skills practice, and re-enforcement. The sections parallel each other through the lesson plans. The students are not always dong the same thing every day. Even though the texts are wirtten at an 11th or 12th grade reading level. All students can understand the material, becuase the intructor and class work together for comprehension. Students practice reading the text and taking notes directly on the text. These texts should be owned by the student.

## Reading and Writing of Mathematics

Many students are not literate in the language of mathematics and therefore have dificulties. The reading and writitng of mathematics is teaching the very symbolic language of mathematics. These texts cover the syntax and semantics of mathematics. An appropriate literacy level of mathematics can extniguish many arithmetic and algebraic manipulation errors. to structure of text / to top

## Problems Solving for Mathematical Concepts

To be a proficient problem solver one has to practice.
Problem solving skills are not inate, but rather learned. Problems
solvers grow by experienced guidance. Problem solvers do not grow by
being told how to do it. It is best, if they have practice
solving problems by themselves and in groups. Please refer to
the text *'The Three Easy Steps to Problem Solving'* for guidlines of
problem solving. Available on this web site. The problems should be novel to the
students. to structure of
text / to top

## Notes

Notes can be divided into two distinct categories. The first category are the notes given to the student by the texts and instructor. The more important category are the notes generated by the students. The students should be taking notes of their observations and questions. Also the students should be taking notes of the analysis of their errors and successes. Notes are not just read once, but referred to consistenly. to structure of text / to top

## Mathematical Skills

# The Structure of the texts

The texts are divided into parts. The parts are the reading and writing of mathematics, concepts through problem solving, notes, mathematical skills practice, and re- enforcement. These are the arithmetic and underlying mathematical skills needed for the algebra curriculum. Many of the texts appear not to have a lot of skill practice. A closer look will reveal a lot of practice of mathematical skills. For example, a text that is an exploration of a function has more than thirty problems to solve algegraically to compare to the graphed functions.

Many students' mathematical dificulties are that they are not literate in the language of mathematics. The reading and writitng of mathematics is teaching the very symbolic language of mathematics. These texts cover the syntax and semantics of mathematics. An apropriate literacy level of mathematics can extniguish many arithmetic and algebraic manipulation errors. to structure of text / to top

## Problems Solving for Mathematical Concepts

To be a profieccient problem solver one has to practice. Problem solving skills are not inate, but rather learned. Problems solvers grow by experienced guidance. Problem solvers do not grow by being told how to do it. It is best, if they have practice solving problems by themselves and in groups. Please refer to the text 'The Three Easy Steps to Problem Solving' for guidlines of problem solving. The problems should be novel to the students. to structure of text / to top

## Notes

Notes can be divided into two distinct categories. The first category are the notes given to the student by the texts and instructor. The more important category are the notes generated by the student. The student should be taking notes of their observations and questions. Also the student should be taking notes of the analysis of their errors and successes. Notes are not just read once, but refferred to consistenly. to structure of text / to top

## Mathematical Skills

This is the arithmetic and underlying mathematical skills needed for the algebra curriculum. Many of the texts appear not to have a lot of skill practice. A closer look will reveal a lot of practice of mathematical skills. For example a text that is an exploration of a function has more than thirty problems to solve algegraically to compare to the graphed functions. to structure of text / to top

## Re- enforcement

These are the arithmetic and underlying mathematical skills needed for the algebra curriculum. Many of the texts appear not to have a lot of skill practice. A closer look will reveal a lot of practice of mathematical skills. For example, a text that is an exploration of a function has more than thirty problems to solve algegraically to compare to the graphed functions.The mathematical skills and conepts need to be re-visited and used throughout the curriculum to ensure that they are learned and remembered. Careful lesson planning that builds upon the previous will ensure re-enforcement. to structure of text / to top

# List of Links to pdf Files and World Wide Web ADA Browser files.

## Fairmath™ is currently working on distributing an ADA compliant browser files distribution. We will also distribute PDF files for print.

Since these texts are written at a high level, one can make the necessary changes to best suit the students' age level. The accompanying "Read Me" files are intended for instructors. The following are pdf format files that can be downloaded from any computer to be viewed, saved, or printed. The pdf files can also be used to be printed and bound as texts.

# The 'Three Easy' Steps of Problem Solving

Notes for Problem Solving

There are more than three steps. And if it was easy, it would not be a problem. These notes are meant to be written on and deciphered. These notes are meant as a reference and guide to problem solving.

"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.."

- Chinese Proverb

## Problem Solve 3 Steps

# Classification Patterns Cards

Calssification and Pattern Problems

Classification, sets, and finding patterns are fundemental skills of mathematics. Other objects can be used instead of cards.

# Classification Patterns Cards Read Me

# Classification Patterns Cards

# Binary and Unary Operations and Syntax of Real Numbers

Mathematics Grammar and Basic Dictionary.

These notes are meant to be written on and deciphered. These notes are meant as a reference. Not all the information would be used for one course.

# Binary Unary Operations Syntax Real

# Additive and Multiplicative Inverses

Practice and re- enforcement

The excercises help the students with determining inverse additives and multplitcatives. The excercises also re- enforce the Algebraic Porperties of the multplicative and additive identities.

# Inverse add mult Read Me

# Inverse add mult

# Categories of Numbers

Venn Daigram of Number Sets

These notes are meant to be written on and deciphered. These notes are meant as a reference.

# Venn Diagtam Of Number Sets

# Base Ten

Notes on Base Ten Dictionary.

These notes are meant to be written on and deciphered. These notes are meant as a reference.

# Base Ten

# Base Two

Notes on Base Two Dictionary.

With the advent of computers and digital information in our daily lives, knowing base two has become a life skill. These notes are meant to be written on and deciphered. These notes are meant as a reference.

# Base Two

# Finger Abacus

Calculations and Base Ten

The Finger Abacus can be used for any age group that has not used it for awhile. It re-enforces base ten, syntax of place holders, and modulas. It is a good way to re visit arithematic skills in a new way.

# Finger Abacus Read Me

# Finger Abacus

# Multiplication Area Model

Patterns and properties of Multiplication

The Multiplication Area Model Excercises re-enforces the concept of multiplication and explores number theory.

# Area Model Multiplication Read Me

# Area Model Multiplication

# FTA Axiom

Notes and Problems on the Fundematntal Theorem of Arithmetic

FTA, the Fundemental Theorem of Arithmetic, is a fundemental concept for arithmetic, factors, alegebra, and number theory. The FTA problem is the exploration of prime factorization.

# FTA Read Me

# FTA Axiom

# Combine Like Terms

and Simplyfication of Addition

Combine Like Terms is the starting place for simplifying expressions and equations.# Combining Like Terms Read Me

# Combining Like Terms

# Ratios as Fractions

Notes and Excercises for fractions.

Ratios as Fractions is an introduction to ratios expressed as fractions. Multiple representations of values, preferred representations, and the trivial factor of one is explored.

# Ratios as Fractions Read Me

# Ratios as Fractions

# Ratios as Precentages

Notes and Excercises for Percentages.

Ratios as Percentages is an introduction to ratios expressed as percentages. Multiple representations of percentages, preferred representations, and the trivial factor of one is explored. The complement of a percentage is also defined. It is best to introduce Ratios as Fractions first.

# Ratios as Percentages Read Me

# Ratios as Percentages

# Read and Write Graphs

Graphing Literacy Excercises

Graphing is an important life skill. Much of the information we recieve is in the form of some type of graphic representation. Students need to be literate in graphs before exploring functions.

# Graphing Read Write Read Me

# Graphing Read Write

# Graphing Read Write big

# Graphing Read Write 1

# Graphing Read Write 2

# Read and Write Mathematics

Mathematics Literacy Excercises

Many students have a difficulties with mathematics not because they do not understand the concepts but are impeded by a lack of profficiency in the language of mathematics. Mathematics is a highly symbolic and abstract language. These excercises will help with semantics and syntax of mathematics.

# Read Write Mathematics Read Me

# Read Write Mathematics 1

# Read Write Mathematics 2

# Units and Unit Conversion

Fraction Arithmetic

This text contains more practice with fractions and proportions. and various types of unit conversion.

# Units Combine and Conversion Read Me

# Units Combine

# Units Conversion 1

# Units Conversion 2

# Units Conversion 3

# Powers and Its Inverse

Rational Powers

The following set of exercises is to help the student undersand rational powers their inverse. The set also re- enforces the Law of Expontents.

# Power Fast Multiplication Read Me

# Power Fast Multiplication

# Power Fast Multiplication Expanded

# Inverse Powers Read Me

# Inverse Powers

# Contribute

Support with OER and other resources

Help contribute to projects and the distribution of resources. Without contributions F.E.R.M.A.T. cannot grow and learn. We need all kinds of help with the front side and back side of F.E.R.M.A.T. top

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