# A.1 Foundations of Algebra

by Brian McLogan
# 1. A.15Translating Expressions

## 1.1. A.1520 Essential questions and definitions

### 1.1.1. A.1111 What is an algebraic expression?

### 1.1.2. A.11123 What is a term?

### 1.1.3. A.1113 What is a variable?

## 1.2. A.1511Addition

### 1.2.1. A.15111 More Than

### 1.2.2. A.15112 Sum

### 1.2.3. A.15113 Increased By

### 1.2.4. A.15114 More Than

### 1.2.5. A.15115 The Total

## 1.3. A.1512 Division

### 1.3.1. A.15121 Translating using quotient

### 1.3.2. A.15122 Translating using divided by

## 1.4. A.1513 Two operations

### 1.4.1. A.15133 Translating more than one operation ex1

### 1.4.2. A.15135 Translating more than one operation ex2

### 1.4.3. A.15134 Translating more than one operation ex3

### 1.4.4. A.15136 Translating more than one operation ex 4

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

## 1.6. A.15116 Subtraction

### 1.6.1. A.115161 Translating using minus

### 1.6.2. A.115162 Translating using less than

### 1.6.3. A.115163 Translating using the difference

## 1.7. A.1517 Multiplication

### 1.7.1. A.15171 Translating using product

### 1.7.2. A.15172 Translating using times

### 1.7.3. A.15173 Translating using double and twice

## 1.8. A.1518 Translating Expressions to sentences

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

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

## 2.1. A.11124 What is a constant?

## 2.2. A.11125 What is a coefficient?

## 2.3. A.11126 What are like terms?

# 3. A.13Classifying Real Numbers

## 3.1. A.134 Square Roots

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

### 3.1.2. A.1103 What is a radical?

### 3.1.3. A.1103 What is a radicand?

### 3.1.4. A.11121 What is a perfect Square?

### 3.1.5. A.1341Simplify perfect square roots

### 3.1.6. A.1342 Approximating square roots

### 3.1.7. A.1343 Evaluating square roots of rational numbers

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

### 3.1.9. Is every number under a radical sign an irrational number?

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

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

## 3.2. A.131Classifying

### 3.2.1. A.132 Essential Questions:

3.2.1.1. A.1312 What are Whole Numbers

3.2.1.2. A.1315 What are Irrational Numbers

3.2.1.3. A.1314 What are Rational Numbers

3.2.1.4. A.1313 What are Integers

3.2.1.5. A.1311What are Natural Numbers

3.2.1.6. What is the preferred form to write numbers so that they may be compared

### 3.2.2. A.1316 Classifying mulitple real numbers

### 3.2.3. A.1317 Why do we have to know this?

## 3.3. A.133 Graphing and Ordering

### 3.3.1. A.1110 What is an inequality

### 3.3.2. A.1331 Graph and order from least to greatest ex1

### 3.3.3. A.1332 ex 2

### 3.3.4. A.1333 ex 3

# 4. A.16 Operations with real numbers

## 4.1. A.167 Essential questions and definitions

### 4.1.1. A.1119 What are multiplicative inverses?

### 4.1.2. A.1117 What are additive inverses?

### 4.1.3. A.11123 What is the reciprocal

## 4.2. A.161 Adding real numbers

### 4.2.1. A.1611Positive to a positive

### 4.2.2. A.1612Positive to a negative

### 4.2.3. A.1613 negative to a positive

### 4.2.4. A.1614 negative to a negative

### 4.2.5. A.1615 Adding decimals

### 4.2.6. A.1616 Adding Fractions

## 4.3. A.162 Subtracting real numbers

### 4.3.1. A.16121 Subtracting positive from a positive

### 4.3.2. A.16122 Subtracting negative from a positive

### 4.3.3. A.16123 Subtracting a positive from a negative

### 4.3.4. A.16124 Subtracting a negative from a negative

### 4.3.5. A.16125 Subtracting decimals

### 4.3.6. A.16126 Subtracting fractions

## 4.4. A.163 Multiplying real numbers

### 4.4.1. A.1631 Multiplying positive numbers

### 4.4.2. A.1632 Multiplying negative numbers

### 4.4.3. A.1633 Mulitplying positive and negative numbers

## 4.5. Why do we have to know this

## 4.6. A.164 Dividing

### 4.6.1. A.1641 Dividing positive numbers

### 4.6.2. A.1642 Dividing negative numbers

### 4.6.3. A.1643 Dividing positive and negative numbers

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

# 5. A.12Properties of real numbers

## 5.1. A.1108 What are Equivalent Expressions

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

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

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

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

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

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

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

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

## 5.10. A.125 Essential Questions and Definitions?

### 5.10.1. A.1251 Why are the associative and communative properties useful

### 5.10.2. Essential Question How do the rules for finding the sign of a product compare to the rules of the quotient

5.10.2.1. What two ways can we find the sum and difference of two methods

# 6. 1.4 Distributive Property

## 6.1. Essential questions

### 6.1.1. A.11127 What is the distributive property?

## 6.2. A.141Simplifying expressions using distributive property

### 6.2.1. A.1411

### 6.2.2. A.1412

### 6.2.3. A.1413

### 6.2.4. A.1414

### 6.2.5. A.1415

### 6.2.6. A.1416

## 6.3. A.142 Rewriting fraction expressions

### 6.3.1. A.1421

## 6.4. A.143 Simplifying with negative one

### 6.4.1. A.1431

### 6.4.2. A.1432

### 6.4.3. A.1433

### 6.4.4. A.1434

## 6.5. A.144 Combining like terms

### 6.5.1. A.1441 Using distributive property

6.5.1.1. A.14411

6.5.1.2. A.14412

### 6.5.2. A.1442 By adding and subtracting

6.5.2.1. A.14422

6.5.2.2. A.14421

### 6.5.3. A.1443 Multiple terms

6.5.3.1. A.14431

6.5.3.2. A.14432

6.5.3.3. A.14433

6.5.3.4. A.14434

## 6.6. Why do I need to know this