Notes

Math 7 – Unit 1: Integers
INTEGERS ON THE NUMBER LINE

OBJECTIVES

Represent positive and negative values.
Locate integers on the number line.
VOCABULARY

infinite increasing or decreasing without end
integer a number belonging to the set made up of the whole numbers and their opposites
natural number a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on
negative number a number that is less than zero
number line a line that graphically represents all numbers
point a dot that marks a location on a graph
positive number a number that is greater than zero
whole number a number belonging to the set made up of zero and the natural numbers
Vocabulocity
Flash Cards
Spelling Bee
Connections
Can you think of any other situations in which you can have a value that is less than zero? Think about temperature. In many places in the world, the temperature gets below zero, or less than zero!
What did Carlton mean when he said that Ondi has "less than no money"? Well, not only does she have zero dollars, but she actually owes a dollar. As soon as she earns a dollar, she'll have to pay it back to Carlton. So right now, Ondi actually has less than zero dollars

Special signs are used to show whether a number is positive or negative. Up until now, the numbers you have worked with had no sign in front of them. That means that they were positive numbers. Positive numbers can either have no sign or a positive sign (+) in front of the digit. But negative numbers must have a negative sign (-) in front of the digit. For example, +3 or 3 can be used to represent "positive three." "Negative three" is represented as -3.

Think about it!
What about the number zero? Is it positive or negative? Actually, it's neither. Zero is the only number that doesn't have a sign.




Words can also be used to show if a number is positive or negative. Phrases like "above zero," "more than zero," or "greater than zero" indicate positive numbers. Phrases such as "below zero" and "less than zero" indicate negative numbers.

Example:
What are some ways to represent the number 4?

Solution:
A digit with no sign represents a positive number. So 4 can also be expressed as +4, positive four, four above zero, four more than zero, or four greater than zero.

The different groups of positive and negative numbers have special names. The counting numbers, like 1, 2, 3, and so on, are called natural numbers. The whole numbers are exactly the same as the natural numbers except that the group also includes zero. You have probably worked a lot with these sets of numbers. Now you'll also be working with the integers. The integers include both the positive counting numbers, the negative numbers, and zero. So numbers like -8, 4, 0, and -2 are all considered integers.

Integers can be represented visually on a number line. A number line is just a graph that is used to represent numbers. Here's an example:



The arrows on each end of the number line mean that this line continues forever in both directions. That's because the set of integers continues forever. It is infinite. Also, notice that numbers to the right of zero are positive and numbers to the left of zero are negative.

Key point!
A number line with no points is like an empty game board. You place a game piece on the board to represent your specific location on the board. On a number line, you place a point to represent the location of a specific number.
Right now, the number line above is empty. No specific integers have been graphed. To graph a specific integer, use a point. A point is a dot on the line that represents the location of a specific number. For example, on the number line below, the point shown represents the number three.



Points on the number line are often labeled using a single letter. For example, in the following number line, point P is located at -2.



Example:
Which point represents the number -1? (Note: Each tick represents 1.)



Solution:
Negative numbers are to the left of zero. Negative one is one place to the left of zero, so B represents -1.

Look at one more example.

Example:


LET'S REVIEW!

Before going on to the practice problems, make sure you understand the main points of this lesson:

Positive numbers are greater than zero. Negative numbers are less than zero.
The set of integers includes the positive counting numbers, the negative numbers, and zero.
Integers can be graphed as points on a number line.