# Mathematics

**Part 1**- Whole Numbers
- Lesson 1: Introduction to Whole Numbers
- Lesson 2: Adding Whole Numbers and Perimter
- Lesson 3: Subtraction of Whole Numbers
- Lesson 4: Rounding and Estimating
- Lesson 5: Multiplication of Whole Numbers and Area
- Lesson 6: Dividing Whole Numbers
- Lesson 7: Exponents and Order of Operations
- Lesson 8: Introduction to Variables, Algebraic Expressions and Equations
- Module 1: Vocabulary Review & Puzzle

- Integers and Inroduction to Solving Equations
- Solving Equations and Problem Solving
- Fractions
- Decimals
- Ratio, Proportion and Percent
- Geometry
**Part 2**- Problem-Solving and Inequalities
- Measurement
- Graphing and Systems of Equations
- Data Analysis / Probability / Statistics

## Lesson 1: Introduction to Whole Numbers

### We Need Numbers!

What do you think is the first number we ever learned? We learn about numbers when we need them.

Download: Practice Worksheet

### Natural Numbers

Name of Set | Symbol | Example |
---|---|---|

Natural or Counting Numbers | N | {1,2,3,...} |

To count we need the set of Natural or counting numbers. The { } are called braces they are one form of grouping symbols, here they indicate a set, the set of natural numbers. The ... tells us that set goes on forever with that pattern. To get from one number to the next we add 1. The smallest Natural number is 1 there is no largest natural number. What numbers are not included in this set?

### The Need for Other Numbers

Fill in the blak to make a true statement:

8 + ___ = 8

We then went to school and as early as first grade we were given a question like this. This is really the first step to algebra solving for the unknown, using common sense. Why is it hard to do this problem? This is when math anxiety occurs. There is no natural number that solves this. We now have the need for other numbers. What number do we need?

### Whole Numbers

Set of Numbers | Symbol | Example |
---|---|---|

Whole | W | {0,1,2,3,...} |

If we add 0 to the set of Natural numbers we get a new set called the whole numbers. Notice when you say the word "whole" your lips make a 0. COOL!

### Summary of the Sets of Numbers

Sets of Numbers | Symbol | Example |
---|---|---|

Natural or Counting Numbers | N | {1,2,3,...} |

Whole Numbers | W | {0,1,2,...} |

Let's summarize the sets of numbers we have already talked about. Are there any other types of numbers that you know? Right now we don't need those "other numbers".

### Example

Please do these problems on the worksheet you printed out for this section.

Given the numbers 245 and 542, answer the following:

- Are the numbers natural, whole, neither, or both? Explain.
- Write the numbers in words.
- True or False: 245 = 542

### Place Value Chart

A place value system means every digit in a number will take on a different value based on where it is in a number. The 5 has a place value of hundreds making it worth 500. Every group of three digits is called a period. Four periods are shown above.

### Place Value Chart

Even though the number 245 is made with the same digits as 542, it is much smaller. In 245 the 2 is in the hundreds place, and the 5 is in the ones place making it 5 (5 ones is equal to 5).

### Place Value Chart

This is standard form for the given number. How can we write this number in words? Where do the commas go?

### Reading and Writing Whole Numbers

**Writing Whole Numbers in Words:**

We put commas in the words in the same place they would be in the number. Hyphens are used for two digit numbers.

**Reading Whole Numbers:**

We read the numbers formed by the left period and then say the name of that period. Then we read the name of the next number and read the name of that period. We continue until all periods are read. The name of the units period is not said.

Commas go after every three digits (period) counting from right to left.

### Example

7,093,400,451 = Seven billion, ninety-three million, four hundred thousand, four hundred fifty-one.

Count 3 digits from right to left then place a comma. Notice no "and" and only commas to match the commas in the number.

### Examples

For each number below:

- Separate the digits into periods using commas.
- Name the place value for the digit 2 in each number.
- Write the number in words.

- 21365764
- 900205000

Do these problems on your worksheet.

### Examples

Write the following number in standard form:

- Twenty thousand, five.
- Eight million, eight thousand, eight hundred thirty-eight.

What do we mean by standard form? Do this problem on your worksheet.

### Expanded Form

**Expanded Form** of a number shows each digit and its place value.

Standard Form | Expanded Form |
---|---|

6,789 | 6,000 + 700 + 80 + 9 |

Notice if you write the digit and follow it with the same number of 0's as you have digits left, you will get the right place.

### Example

Express 2,340,078 in expanded form.

Notice we disregard the zeros in the given number.

### How Do These Numbers Compare?

5 and 5

2 and 5

Write the statements can you make to compare each pair of numbers on your worksheet.

### Comparison Symbols

The word "is" is really important.

Equality Symbol | Meaning |
---|---|

= | is equal to |

Inequality Symbol | Meaning |

≠ | is not equal to |

> | is greater than |

< | is less than |

≥ | is greater than or equal to |

≤ | is less than or equal to |

### The Real Number Line

As you move from left to right on the number line the numbers get bigger.

2 is less than 5, because 2 is to the left of 5.

2 < 5

The real number line called the number line is a visual representation of the sets of numbers.

### Examples

Insert all comparison symbols that will make a true statement:

- 0 ___ 12
- 406 ___ 400
- 50 ___ 50

On your worksheet include all comparison symbols that would make a true statement.

### Understanding Tables

Given in the table below are the candidates in a local election and the number of votes that each candidate obtained. Answer the questions that follow.

Candidates | Number of Votes |
---|---|

Mr. Olsen | 2,078 |

Ms. Li | 3,760 |

Mr. Barone | 2,780 |

Mrs. Vaporis | 3,706 |

Tables are a good way to organize information; they help us answer questions about the data.

### Questions About the Table

Answer the questions on your worksheet.

- Fill in the blank with either expanded form or standard form to make a true statement:

The number of votes in column 2 are given in _____ _____. - What is the place value of the 8 in the number of votes received by Mr. Olsen?
- Write in words the number of votes received by Ms. Li.
- Write the number of votes received by Mr. Barone in expanded form.
- Who won the election?

Download: Practice Worksheet Answer Key