# Elementary Mathematics Nayla Corral
Get Started. It's Free Elementary Mathematics ## 1. Solving Multiplication/Division problems

### 1.1. multiplication properties

1.1.1. Identity-When a number is multiplied by 1, the number stays the same.

1.1.2. Zero- when a number is multiplied by 0, the product is 0.

1.1.3. Associative- the way numbers are grouped doesn't matter.

1.1.4. Distributive- Breaking numbers into smaller parts/equations will result in the same product.

### 1.2. Multiplication Algorithms

1.2.1. Standard- Should be the last step students use to solve. no explanation on place values

1.2.2. Expanded Notation- Factors are expanded and then multiplied

1.2.3. Place Value- Factors are seperated into their place values, multiplied then added together.

1.2.4. Lattice

1.2.4.1. Lattice Multiplication Intro: 3 digits times 2 digits

## 2. Problem Solving

### 2.1. Four Step Problem Solving

2.1.1. 1. Understand the problem

2.1.1.1. Ask yourself a couple of questions: Can you restate the problem in your own words? What are you asked to find out and how?

2.1.2. 2. Devise a plan

2.1.2.1. What strategies will you be using? Examples: trial and error, working backwards, creating a diagram

2.1.3. 3. Carry out the plan

2.1.3.1. -Be patient, most problems are not solved quickly or on first attempt. Be persistent and don't be discouraged.

2.1.4. 4. Look back and Reflect

2.2.1. Problem Solving using Polya's Four Steps

## 3. Number System Bases

### 3.1. Base-10

3.1.1. -One unit

3.1.2. Ten units make a ten

3.1.3. ten tens make a hundred

3.1.4. ten hundreds make a thousand

3.1.5. a tenth of a unit is a tenth

3.1.6. a tenth of a tenth is a hundredth

3.1.7. a tenth of a hundredth is a thousandth

3.1.8. What does base 10 mean?

### 3.2. Other number systems

3.2.1. the roman system

3.2.2. binary system (base 2)- used in computing

3.2.3. octal system (base-8)

3.2.5. base-5 and base-12 (indigenous people might use this)

### 3.3. Digits used

3.3.1. base 10- 0,1,2,3,4,5,6,7,8,9

3.3.2. base 2- 0,1

3.3.3. base 3- 0,1,2

3.3.4. base 4- 0,1,3

3.3.5. base 5- 0,1,2,3,4

4.1.1. Identity property- Any number added by zero will stay the same

4.1.1.1. a+0=a

4.1.1.2. 5+0=0

4.1.2. Communitive property- Order in which numbers are added doesn't matter

4.1.2.1. a+b=b+a

4.1.2.2. 4+3=3+4

4.1.3. Associative property- the way numbers are grouped doesn't matter

4.1.3.1. (a+b)+c= a+(b+c)

4.2.1. Standard American Algorithm- Last method students should use. No reference to place value

4.2.2. Partial Sums- No explicit reference to place value. Start right to left

4.2.3. Partial sums with emphasis on place value- There's more of an emphasis on place value. Problems are solved right to left.

4.2.4. Place value explicit- Problems are solved left to right instead of right to left.

4.2.5. expanded notation- Place value is very explicit. addents are expanded into corresponding place values.

4.2.6. lattice method- Place value is emphasized. A box is created to solve the problem.

### 4.3. Subtraction Algorithms

4.3.1. American Standard- No emphasis on place value. Should be the last method used.

4.3.2. European-Mexican- No emphasis on place value. It is solved right to left.

4.3.3. Reverse-Indian-There is no emphasis on place value. Solved left to right.

4.3.4. Left-to-right- Solved left to right. There's more of an emphasis on place value.

4.3.5. Expanded Notation- There's an emphasis in place value. The minuend and subtrahend are expanded and then subtracted.

4.3.6. Integer subtraction- Numbers are subtracted regardless if the difference is negative. then add all integers together to find the difference.