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A.1 Foundations of Algebra
by Brian McLogan
# A.1 Foundations of Algebra

## A.15Translating Expressions

### A.1520 Essential questions and definitions

### A.1511Addition

### A.1512 Division

### A.1513 Two operations

### A.1514 Why do we need to know this

### A.15116 Subtraction

### A.1517 Multiplication

### A.1518 Translating Expressions to sentences

### A.1519 I still don't get it

## A.11Concept Videos need to
be added later in the year

### A.11124 What is a constant?

### A.11125 What is a coefficient?

### A.11126 What are like terms?

## A.13Classifying Real Numbers

### A.134 Square Roots

### A.131Classifying

### A.133 Graphing and Ordering

## A.16 Operations with real numbers

### A.167 Essential questions and definitions

### A.161 Adding real numbers

### A.162 Subtracting real numbers

### A.163 Multiplying real numbers

### Why do we have to know this

### A.164 Dividing

### A.166 I still don't get it

## A.12Properties of real numbers

### A.1108 What are Equivalent Expressions

### A.122 What is the associative
property of addition and
multiplication

### A.1105 What is the
Commutative Property of
Multiplication

### A.1104 What is the
Commutative Property of
Addition

### A.12003 What is the zero
property of multiplication

### A.11122 What is the
multiplication property of -1

### A.1106 What is the Identity
Property of Addition

### A.1107 What is the Identity
Property of Multiplication

### A.123Why do we need to know this?

### A.125 Essential Questions and Definitions?

## 1.4 Distributive Property

### Essential questions

### A.141Simplifying expressions
using distributive property

### A.142 Rewriting fraction expressions

### A.143 Simplifying with negative one

### A.144 Combining like terms

### Why do I need to know this

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http://www.freemathvideos.com In this video series explain the properties of real numbers. When working with numbers in mathematics it is very important to understand the properties of real numbers because knowing the properties tells us what we are allowed to do with certain numbers and why. When mathematics gets more difficult these properties remain true and become a foundation of how to solve and simplify in mathematics. Tags: properties, real, numbers, how to, what is, why, what, learn

http://www.freemathvideos.com Definitions are very important to your understanding of why and how we use mathematical processes. Without understanding what a process or certain terms mean it is very hard to understand how or why to do something. That is why I want to spend some time explaining to you these processes or definitions. Please understand that these videos are my interpretation and that there may be other ways of explaining or describing the same information.

A.1111 What is an algebraic expression?

A.11123 What is a term?

A.1113 What is a variable?

http://www.freemathvideos.com In this video series I will show you how to translate sentences into algebraic expressions We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, more than, sum, increased by, more than, the total

A.15111 More Than

A.15112 Sum

A.15113 Increased By

A.15114 More Than

A.15115 The Total

http://www.freemathvideos.com In this video series I will show you how to translate sentences into algebraic expressions We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, division, quotient, divided by

A.15121 Translating using quotient

A.15122 Translating using divided by

http://www.freemathvideos.com In this video series I will show you how to translate sentences into algebraic expressions We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, two, operations

A.15133 Translating more than one operation ex1

A.15135 Translating more than one operation ex2

A.15134 Translating more than one operation ex3

A.15136 Translating more than one operation ex 4

recorded

http://www.freemathvideos.com In this video series I will show you how to translate sentences into algebraic expressions We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, subtraction, minus, less than, difference

A.115161 Translating using minus

A.115162 Translating using less than

A.115163 Translating using the difference

http://www.freemathvideos.com In this video series I will show you how to translate sentences into algebraic expressions. We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, multiplication, product, times, double, twice,

A.15171 Translating using product

A.15172 Translating using times

A.15173 Translating using double and twice

recorded http://www.freemathvideos.com In this video series I show you how to translate an algebraic expression into an algebraic sentence. We do this by understanding how each operation can be expressed as a word and writing the expression out in a sentence. Tags: translating, expression, sentence, operations, add, subtract, multiply, divide, how to, write, learn

not discussed till later iin the year recorded; linked

recorded; linked not discussed till later

recorded; linked not discussed till ater

http://www.freemathvideos.com In this video series we explore square roots. We look to understand what are the parts of a square root, how to simplify, approximate and evaluate square roots. Understanding square roots are very important to understanding our number system and knowing how to use the properties of numbers.

A.1102 What is the definition of a square root?

A.1103 What is a radical?

A.1103 What is a radicand?

A.11121 What is a perfect Square?

A.1341Simplify perfect square roots

A.1342 Approximating square roots

A.1343 Evaluating square roots of rational numbers

A.1344 Why: do I need to know this?

Is every number under a radical sign an irrational number?

What is the difference between finding the square root of a perfect square and the square root of a non perfect square

A.1321 What is the difference between a perfect square and a number that is not one?

http://www.freemathvideos.com In this video series I show you how to classify numbers. In our classification of numbers there are five categories. Whole, irrational, rational, integers and natural numbers. We will learn how to classify a number and explain what are the properties of each category. Tags: classify, classifying, numbers, real, imaginary, whole, irrational, rational integer, natural, how to, learn

A.132 Essential Questions:, A.1312 What are Whole Numbers, A.1315 What are Irrational Numbers, A.1314 What are Rational Numbers, A.1313 What are Integers, A.1311What are Natural Numbers, What is the preferred form to write numbers so that they may be compared

A.1316 Classifying mulitple real numbers

A.1317 Why do we have to know this?

http://www.freemathvideos.com In this video series I show you how to graph and order numbers. It is important when graphing and ordering numbers that we have all of our numbers simplified and written in the same form. We then can arrange the numbers from least to greatest and plot them on a x-axis graph. Tags: graph, order, numbers, irrational, real, rational, how to, least, greatest

A.1110 What is an inequality

A.1331 Graph and order from least to greatest ex1

A.1332 ex 2

A.1333 ex 3

http://www.freemathvideos.com Definitions are very important to your understanding of why and how we use mathematical processes. Without understanding what a process or certain terms mean it is very hard to understand how or why to do something. That is why I want to spend some time explaining to you these processes or definitions. Please understand that these videos are my interpretation and that there may be other ways of explaining or describing the same information.

A.1119 What are multiplicative inverses?

A.1117 What are additive inverses?

A.11123 What is the reciprocal

http://www.freemathvideos.com In this video series I show you how to add real numbers. We add positive and negative numbers and explain why and how we get our simplified answer. We will also explore numbers that are represented as fraction and decimals. Tags: adding, add, addition, subtract, subtraction, subtracting, negative, positive, numbers, simplify, decimals, fractions

A.1611Positive to a positive

A.1612Positive to a negative

A.1613 negative to a positive

A.1614 negative to a negative

A.1615 Adding decimals

A.1616 Adding Fractions

http://www.freemathvideos.com In this video series I show you how to subtract real numbers. We subtract positive and negative numbers and explain why and how we get our simplified answer. We will also explore numbers that are represented as fraction and decimals. Tags: subtract, subtracting, subtraction, numbers, expression, how to, simplify, learn

A.16121 Subtracting positive from a positive

A.16122 Subtracting negative from a positive

A.16123 Subtracting a positive from a negative

A.16124 Subtracting a negative from a negative

A.16125 Subtracting decimals

A.16126 Subtracting fractions

http://www.freemathvideos.com In this video series I show you how to multiply real numbers. We multiply positive and negative numbers and explain why and how we get our simplified answer. We will also explore numbers that are represented as fraction and decimals. Tags: multiply, multiplying, multiplication, how to, simplify, numbers, expression, learn

A.1631 Multiplying positive numbers

A.1632 Multiplying negative numbers

A.1633 Mulitplying positive and negative numbers

pg 41 Q39-40,49

http://www.freemathvideos.com In this video series I show you how to divide real numbers. We divide positive and negative numbers and explain why and how we get our simplified answer. We will also explore numbers that are represented as fraction and decimals. Tags: divide, dividing, division, how to, simplify, numbers, expression, learn

A.1641 Dividing positive numbers

A.1642 Dividing negative numbers

A.1643 Dividing positive and negative numbers

http://www.freemathvideos.com In this video series explain the properties of real numbers. When working with numbers in mathematics it is very important to understand the properties of real numbers because knowing the properties tells us what we are allowed to do with certain numbers and why. When mathematics gets more difficult these properties remain true and become a foundation of how to solve and simplify in mathematics. Tags: properties, real, numbers, how to, what is, why, what, learn, addition, multiplication, subtraction

pg 26 recorded; linked

recorded

pg 26 recorded; linked

pg 26 recorded; linked

recorded; linked

recorded; linked

pg 27 recorded; linked

recorded

A.1251 Why are the associative and communative properties useful

Essential Question How do the rules for finding the sign of a product compare to the rules of the quotient, What two ways can we find the sum and difference of two methods

http://www.freemathvideos.com In this video series I will show you how to translate expressions and sentences. We will explore the main keywords that tell us when to apply addition, subtraction, multiplication and division. Tags: translate, translating, sentence, expression, algebraic, numeric, how to, operation, addition, adding, more than, sum, increased by, more than, total

http://www.freemathvideos.com Definitions are very important to your understanding of why and how we use mathematical processes. Without understanding what a process or certain terms mean it is very hard to understand how or why to do something. That is why I want to spend some time explaining to you these processes or definitions. Please understand that these videos are my interpretation and that there may be other ways of explaining or describing the same information.

A.11127 What is the distributive property?

http://www.freemathvideos.com In this video series I will show you how to apply the distributive property to simplify an expression. The distributive property states that whenever you have a number that is multiplied by an expression inside parenthesis that that term is to be multiplied by every term within the parenthesis. Tags: distributive property, distribute, simplify, expression, parenthesis, how to, learn

A.1411

A.1412

A.1413

A.1414

A.1415

A.1416

http://www.freemathvideos.com In this video series I will show you how to rewrite fraction expressions by using the distributive property. This is a common method to help us rewrite fractions as two terms rather than one. Tags: distributive property, fractions, terms, rational, how to, learn.

A.1421

http://www.freemathvideos.com In this video series I will show you how to apply the distributive property when a grouping term is being multiplied by a negative one. We often omit the one when writing and applying the distributive property of negative one because it does not change the absolute value of the number. However we still need to multiply the negative one to every term inside the grouping term. Tags: negative, negative one, distributive property, simplify, grouping term, how to, learn, expression

A.1431

A.1432

A.1433

A.1434

http://www.freemathvideos.com In this video series I will show you how to combine like terms by adding subtracting, multiplying and applying the distributive property. It is important that we only combine like terms that have the same numeric and variable factors. We can only combing like terms once we have applied multiplication and the distributive property. Tags: combining, terms, distributive property, adding, subtracting, how to

A.1441 Using distributive property, A.14411, A.14412

A.1442 By adding and subtracting, A.14422, A.14421

A.1443 Multiple terms, A.14431, A.14432, A.14433, A.14434