Using Integers to Represent Quantities

By: Lynn Coupal

Content/Rationale

The purpose of this lesson is to show students that there are numbers less than zero (negative numbers) which can be used to represent real-world quantities. For example: When the meteorologist says that the low for the day is 15 below.

Objectives of the Lesson

Upon completion of this lesson, students should be able to:

Define negative numbers, origin, opposite numbers and integers
Construct a vertical and horizontal number line
Explain the difference between positive and negative numbers

Materials/Resources:

Visual vertical number line
Golf Club made out of construction paper
Fun-tac

Instructional Procedure:

Set induction

Does anyone play golf? If so, ask what par is in golf. In golf, par is the score a good play would normally get on a particular hole. *Scores above par are shown with positive numbers, those below par are shown with negative numbers. The more negative a golf score is, the better it is. Most of the numbers you have studied so far have been greater than zero. We are going to explore numbers that are less than zero.

Procedure

Putting up the visual representation of the vertical number line, tell students that a vertical number line can be used to compare heights (above sea level) and depths (below sea level). Referring to the visual representation of the vertical number line, state that positive numbers, such as +200, are greater than zero. Following, state that negative numbers, such as -200, are less than zero. Now, write the definition of Negative numbers - numbers that are less than zero. Proceeding, refer back to the visual representation of the vertical number line and explain that the zero point on a number line is the origin. Write this definition on the board.

At this point, do a couple of examples with the students using a vertical number line.

Example 1:

The greatest recorded altitude (height) of a bird in flight is 37,000 ft. above sea level.
Q. How could we use signs to represent the birds height in flight?
A. Height of bird: +37,000

Example 2:

A turtle once dove (depth) 3,973 ft. below sea level.
Q. How could we use signs to represent the turtle's depth in water?
A. Depth of turtle: -3,973

Now, state that a number line can be drawn horizontally. This number line is used to represent gains and/or losses. As you are drawing this line, state that the farther to the right a number is, the greater it is; the farther to the left it is, the less it is. Again, on this number line, ask students questions regarding previously learned material. For example: Ask students where the origin is located. In addition, point out that the distance between any two numbers is called a unit.

Following, write on the board that ....,-3, -2. -1, 0, +1, +2, +3,.... are integers. Also, write that +1, +2, +3,.... are positive integers and that
-1, -2, -3,.... are negative integers.

Proceeding, state and write on the board that Opposite numbers are numbers that are the same distance from zero. For example: 2 and -2 are both 2 units from zero.

Q: Could anyone give an example of an opposite number?

Example 3 (model):

On seven runs, a football running back gained 6, 2, -4, 0, -2, -1, and 4 yards.
Q: Which numbers are positive? Negative? Which pairs of numbers are opposites?

First of all, explain to students that the first thing they should do is draw a horizontal number line. Does anyone know why I would draw a horizontal number line? (Gains/Losses)
Now, graph each of these points.

<------>

2, 4, 6 are to the right of zero, so they are positive
-4, -2, -1 are to the left of zero, so they are negative
-4 and 4 are opposites; -2 and 2 are opposites

Example 4 (independent):

Q: Which of the numbers, -3, 5, 0, -1, 4, -5 and 3 are positive? Negative? Which pairs of numbers are opposites?

Lastly, tell students that we are going to compare integers using <, >, or =. This will be a brief exercise. Make sure to ask students what < and > symbolizes.

Hand out the worksheet that students will be expected to turn in. If time permits, let them start completing their worksheet.

Closure

What are negative numbers?
What are integers?
What point is the origin located at on any number line?
What is an example of an opposite number?

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