Represent Positive and Negative Numbers on the Number Line?

How will we ____, ____ and  ____ negative numbers using a number line?

   introduce    represent    locate

What is a number line?

The number line is a mathematical diagram to represent and locate numbers on a line.  The diagram is a mental model to help visualize number comparisons and arithmetic operations with rational numbers (0, whole numbers,  integers and fractions).

How do you construct a horizontal number line numbered 0 to 10?

1.  Draw a horizontal line, place a point on the line, and label it 0.

2.  To the right of 0 mark 1 and measure (with a ruler or a compass) the segment to the right from 0 to 1 and so define a scale

3.  Use the scale mark off equal segments to the right of 0 and label these points 1, 2, 3, … 10.  (Use a ruler or compass.)

How do you construct a horizontal number line numbered 0 to 10?

1.  Draw a vertical line, place a point on the line, and label it 0.

2.  Above 0 mark 1 and measure (with a ruler or a compass) the segment from 0 to 1 and so define a scale.

3.  Use the scale to mark off equal segments above 0 and label these points 1, 2, 3, … 10.  (Use a ruler or compass.)

What is the starting position on both number lines?

zero

What is the last whole number depicted on both number lines?

10

On a horizontal number line, do the numbers increase or decrease as you move further to the right of zero?

increase

On a horizontal number line, do the numbers increase or decrease as you move further to the left of zero?

decrease

On a vertical number line, do the numbers increase or decrease as you move further above zero?

increase

On a vertical number line, do the numbers increase or decrease as you move further below zero?

decrease

We will introduce “negative numbers” using the whole numbers and fractions we already know.  But why?
Name just three real life situations where we need to use them.

Elevations above or below sea level
Temperatures above or below zero
Debit and credit account deposits and withdrawals

How do we introduce negative numbers on the number line?

We use the concept “opposite of a number”.

Given a nonzero number, a on a number line, the ____ ____ ____ , labeled     −a,     is the number such that:
1)  0 is between a and −a    and
2) the ____ between 0 and a is equal to the distance between 0 and −a.

opposite of a         distance

The opposite of 0 is ____.

0

The set of whole numbers and their opposites, including zero, are called ____

integers

Zero is its own ____.

opposite

The number line diagram shows integers listed in order from least to greatest using ____ spaces.

equal