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Integers & Using

the Number Line. Comparing Rational Numbers. Integers. MCC6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.. MCC6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself , e.g., -(-3) = 3..

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Integers & Using






Presentation on theme: "Integers & Using"— Presentation transcript:

Slide1

Integers & Using the Number Line

Comparing Rational NumbersSlide2

Integers

MCC6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.

MCC6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself , e.g., -(-3) = 3.

MCC6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

- 3

-15

26

16

-7

0Slide3

Integers are defined as the set of whole numbers and their opposites.

Integers include

Positive numbers, also called the counting numbers, (1,2,3,4, . . .)

Their opposites, negative numbers, (-1,-2,-3,. . .)

And zero, which is neither positive nor negative.Slide4

Integers are represented by small slashes on the number lines, and do not include the fractions or decimals (those are in between the slashes). Slide5

Creating a Number Line

Numbers left of 0 are negative.

Numbers right of 0 are positive.Slide6

Reading the Number Line

Numbers get

larger

toward the right.Numbers get

smaller toward the left.

A number line visually shows how numbers are organized from least to greatest.Slide7

Reading the Number Line

Numbers get

smaller

going down.

Numbers get larger going up.

A number line visually shows how numbers are organized from least to greatest.Slide8

Positive

Integers

Depositing money in a checking account

Elevation above sea levelAny temperature above zero

Yardage gained in footballNegative Integers

Withdrawing money from a checking account

An elevation below sea levelBelow zero temperaturesYardage lost in footballSlide9

Now you give examples into your mathberries

.Slide10

Example 1

A sea gull is flying 25 feet above sea level and a shark is swimming 10 feet below sea level.

1) What

elevation does the surface of the water represent?

2) What is the elevation of the bird?3) What is the elevation of the fish?Slide11

What

is the temperature on this thermometer?

What is the temperature on this thermometer

?Slide12

Opposites

Numbers describe their distance from zero.

3 is three spaces from 0 and

-3 is three spaces from 0.

3 and -3 are opposites.Slide13

Opposites

Every number has an opposite.

For every positive number, there is a negative number.

*Zero is its own opposite!Slide14

Using the Number Line

When comparing

numbers

use the number line. The

number on the right is the bigger number. The number on the left is the smaller number.

Ex: -3 is less than -1-3 < -1

(-3 is on the left of -1 on the number line

.)

-3 -1Slide15

Common Misconception with Comparing Numbers

Some students think the

greatest number

is the number closest to zero.

NOPE!  Because that rule is not always true.

-5 -2 0 10-2 is closer to 0 than -5 and is greater than -5… but -2 is

closer to 0 than 10 but

is less than 10.Slide16

Practice

What is the opposite of the following integers?

2,345 -2,345

-16 160 08 -8Using the number line, determine which integer is greater:2 -2 >-5 -7 >

0 3 <0 -8 >Slide17

Signs of Numbers - GPS

means

turn Left or turn Down on the number line.

means turn Right or Up on the number line.

The signs of a number tell which way to go on the number line, like a GPS gives directions!