2-1 Integers Pg.76. Essential Question When would you need to use negative integers in the real...

2-1 Integers

Pg.76

Essential Question When would you need to use negative

integers in the real world?

Definitions integers- the set of whole numbers and

their opposites (positive or negative) opposite- two numbers that are an equal

distance from zero on a number line absolute value- the distance of a

number from zero on a number line; shown by l l

INTRODUCTION TO INTEGERS Integers are positive and negative numbers.

…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …

Each negative number is paired with a positive number the same distance from 0 on a number line. These numbers are called opposites.

-3 -2 -1 20 1 3

IntegersNumbers to the left of zero

are less than zero.Numbers to the right of zero are more than zero.

The numbers –1, -2, -3 are called negative integers. The number negative 3 is written –3.

The numbers 1, 2, 3 are called positive integers. The number positive 4 is written +4 or 4.

Zero is neither negative nor positive.

Negative numbers are used to…

1.2.3.

The answers are on the next 3 slides

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

0102030

-10-20-30-40-50

Negative Numbers Are Used to Show Debt

Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5.000 to show they still owe the bank.

Hint If you don’t see a negative

or positive sign in front of a number it is positive.

9 = 9+

•The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. •Zero is its own opposite.

1 2 3 4 5 • •

–5–4–3–2–1 0

–4 and 4 are opposites

–4 4

Opposite Example 1

Graph the integer 7 and its opposite on a number line.

Opposite Example 2

1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

7 units 7 units

1 2 3 4 5 6 7 8 9 -9–8 –7–6–5–4 –3–2 –1 0

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

Graph the integer and its opposite on a number line.

Opposite Examples 3&4

Absolute Value Video Clip (1:30)

Write down 1 fact from the clip about absolute value.

http://player.discoveryeducation.com/index.cfm?guidAssetId=EE3ED6D0-96E6-4FF7-8D82-3FCD782528EB&blnFromSearch=1&productcode=US

The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.

Reading Math

Use a number line to find each absolute value.

Absolute Value Example 1

|8|

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

8 units

8 is 8 units from 0, so |8| = 8.

Absolute Value Example 2

Use a number line to find each absolute value.

|–12|

–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

–12 is 12 units from 0, so |–12| = 12.

12 units

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

2

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

7

Absolute Value Examples 3 & 4

•Integers increase in value as you move to the right along a number line.

•They decrease in value as you move to the left.

The symbol < means “is less than,” and the symbol > means “is greater than.”

Remember!

You can compare and order integers by graphing them on a number line.

Compare the integers. Use < or >.

Comparing Example 1

-4 is farther to the right than -11, so -4 > -11.

-4 -11>

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Use a number line to order the integers from least to greatest.

Comparing Example 2

–3, 6, –5, 2, 0, –8

The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0

-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4

›

‹

Comparing Examples 3&4

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

Comparing Example 5

Work Session-Together Showing off Integer WS Meaning of Integer WS

Comparing and Ordering Sort

Number Line WS

Work Session-With your Partner

Work Session- On your own

Closing When would you use negative numbers in

the real world?

Do the numbers increase or decrease as you move to the left of zero?

< means:

> means:

Homework

13.3 WS Comparing and Ordering Integers

Role of IntegersVideo Clip

Write down 3 facts about integers from the clip. 1. 2. 3.

http://player.discoveryeducation.com/index.cfm?guidAssetId=E2DCB058-17F3-41C9-A4C8-B08D1D2AACB8&blnFromSearch=1&productcode=US

HomeworkWorkbook pg. 13All problems

Work Session Textbook Pg. 78 16-38 even only GRADED