Adding Integers

Welcome to the world of integers! You are about to investigate 3 different ways to add integers. Use the “Left Arrow” to go back one page. Use the “Right Arrow” to go forward one page. Use the “Home” to go to the main menu.

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What are Integers?

• Integers are just whole numbersNumbers like 1 or

2Even like 2,153

• Integers can be negativeLike -3 or -5Even -3,403,69

• Integers are not decimals or fractions Not 4.5 or 2.1320421 Not 1/2 or 3/4

• Not negative decimals or fractions Not -2.3 or -98.576 Not -4/5 or -5/8

When are Integers Used?

• We use integers when we deal with temperature. Especially when it’s really cold.

• We use integers when we use dollars. Have you ever “owed” anyone money before?

• We will use integers a lot when we deal with algebra and graphing. They help us navigate when we are on a grid.

• A lot of computer software use integers in their programming. Ever thought about being a video game designer?

Adding Integers

First start by choosing a method to learn how to add integers:

1.) Color Counters2.) Temperature3.) Hiker

Adding with Color Counters

• Think of each Green Chip as positive 1• Think of each Red Chip as negative 1

1 -1

Each red chip cancels out a green chip– Think of it like money. A green chip is

money you earn (like allowance) and a red chip is money you spend (on Doritos)

+ = Nothin’ (You spent all your money on Doritos)

This goes for each chip. If we have 8 greens and 8 reds, each red still cancels out a green.

+ =Still Nothing

Now you spent all 8 dollars you had on Doritos!

Now if we have 4 green chips, and 3 red, we have a green left over.

+ =

Now, replace your chips with numbers.

+ =

+ =4 -3 1

How about this one? Can you predict what’s left over?

+ =

Now, replace your chips with numbers.

+ =

+ =-5 3 -2

Now it’s your turn.

1.) Which color chip represents NEGATIVE one?

a.) b.)

Oops… Let’s review

• Think of each Green Chip as positive 1• Think of each Red Chip as negative 1

1 -1

a.) 6 b.) 5

c.) -5 d.) -3

Great Job! Next Question

2.) How much is represented in the picture?

Oops… Let’s review

Think of each Green Chip as positive 1

1

1 1= 3

a.) One Green

b.) Two Greens

c.) Two Reds

d.) Nothing!

Awesome! Next question…

3.) How much is left?

+ =

Oops… Let’s review

+ =

Each red cancels out a green.Only one green is left

a.) 3

b.) 9

c.) -9

d.) -3

Nice! Last question…

4.) What is the sum?

+ =

Oops… Let’s reviewRemember… replace your chips with numbers.

+ =-5 3 -2

Great Job!

• Click the Right button to try adding integers using temperature, or click on the Home button to return to the Main Menu

Adding Integers with Temperature

• This time we’re going to look at a vertical number line.

We all know that a thermometer has lower numbers at the bottom, and higher numbers at the top.

100oC

0oC

-30oC

When we are adding integers, think of positive numbers going up and negative numbers going down.

PO

SIT

IVE

NE

GA

TIV

E

So here we are. It’s 63oF outside. The high temperature is supposed to be 80oF. How many degrees is it supposed to rise today?

a.) 34o b.) -17o

c.) 17o d.) 27o

Not quite…

Remember that the temperature today will get hotter. Which way will the thermometer go?

a.) It will rise b.) It will fall

Let’s review…• We can use subtraction to get the

answer. If it’s 50o outside and it’s going to be 80o. Here’s what we’d do.

805030

Let’s try it with negatives

• Let’s say it’s -23o below zero. If the temperature rises 10o, how cold will it be?

-23o

a.) b.)

c.)

-13o

33o

-33o

Nope. Let’s review

• Remember, the thermometer rises when the temperature goes up, even if we start in the negatives.

• HINT: Take a look at the amount of RED inside the thermometer.

Nice try, but no…

• Remember, we’re only rising the temperature 10o. It looks like you raised the temperature 57o!

Great! Let’s try another.

• Let’s say it’s 32o. If the temperature falls 12o, how cold will it be?

32o

a.) b.)

c.)

20o

83o

44o

Not quite…

Remember that the temperature today will get colder. The thermometer will fall.

One more…• Let’s say the temperature starts

off today at 12o. A cold front is expected to drop the temperature 20o. What will the temperature be after the cold front passes?

a.) 32o b.) -8o

c.) 8o d.) -20o

Oops… not quite

• Remember that the temperature should be less after the cold front passes.

Almost… but no

• Your calculation is close, but think to yourself… is the answer going to be positive, or negative?

Whoa! dude! Not even close…

• That’s too cold! You calculated as if the starting temperature was zero.

Way to go!

• Click on the Right button to try learning integers with a hiker.

• Click on the Home button to return to the menu

Adding Integers with a Hiker

• Imagine you are a hiker standing on a number line.

The 3 Things you NEED to know

• The Starting Number• The Direction to face• How much to Walk

Starting Point• The first number in an addition

problem is your starting point• This is where you, the hiker, will stand

Example

3 + -4 = ?

Starting Point

Direction to Face

• The operation symbol tells us which direction to face. – Addition: Face Positive– Subtraction: Face Negative

Example

3 + -4 = ?

Direction to Face

positivenegative

Where to Walk

• The last number tells us how many spaces to walk– Positive: Walk Forwards– Negative: Walk Backwards

Example

3 + -4 = ?

Way to walk

Backward 4

Last Step

• Literally… where did you end up on the number line?– This is your final answer

Example

3 + -4 = -1

Ending Point

Now you give it a try…

1. Given this equation, which hiker is in the correct starting place?

-5 + 6 = ?

No, that’s not it…

3 + -4 = ?Starting Point

Very Good!Next. Using the same equation, which direction should you face?

-5 + 6 = ?

positivenegative

No, that’s not it… but why?

Addition: Face PositiveSubtraction: Face Negative

Hint: Look to see if there is a plus sign or a minus sign between numbers

Yes! Good One!

What should the hiker do next?a.) move forward 6 spaces

b.) move backwards 6 spaces

c.) move backwards 5 spaces

No he shouldn’t…

Remember:

3 + -4 = ?Way to walk

Backward 4

You’re on a roll now…

…but where should the hiker end up?

Not there…

Remember, we moved forwards 6 spaces.

Precisely…

You seem to have mastered the hiker’s movements. Try the problem on the next page to see if you can visualize all three steps to get the right answer.

BEWAREBEWARE, if you answer incorrectly you will be directed to the beginning slide.

Final Question

6 + -9 = ?

a.) 15 b.) -3

c.) 3 d.) -15

Congratulations

You did it! You have now completed this portion. Click on the right button to end your journey, or click on the Home button to return to the Main Menu