Adding Integers Welcome to the world of integers

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. “Left Arrow” “Home” “Right Arrow”

What are Integers? • Integers are just whole numbers ü Numbers like 1 or 2 ü Even like 2, 153 • Integers can be negative ü Like -3 or -5 ü Even -3, 403, 69 • Integers are not decimals or fractions ü Not 4. 5 or 2. 1320421 ü Not 1/2 or 3/4 • Not negative decimals or fractions ü Not -2. 3 or -98. 576 ü 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 Counters 2. ) Temperature 3. ) 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

Great Job! Next Question 2. ) How much is represented in the picture? a. ) 6 b. ) 5 c. ) -5 d. ) -3

Oops… Let’s review Think of each Green Chip as positive 1 1 = 3

Awesome! Next question… 3. ) How much is left? a. ) One Green + = b. ) Two Greens c. ) Two Reds d. ) Nothing!

Oops… Let’s review Each red cancels out a green. Only one green is left + =

Nice! Last question… 4. ) What is the sum? + a. ) 3 b. ) 9 = c. ) -9 d. ) -3

Oops… Let’s review Remember… 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. o 100 C 0 o. C -30 o. C

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

So here we are. It’s 63 o. F outside. The high temperature is supposed to be 80 o. F. How many degrees is it supposed to rise today? a. ) 34 o b. ) -17 o c. ) 17 o d. ) 27 o

Not quite… Remember that the temperature today will get hotter. Which way will thermometer go? a. ) It will rise b. ) It will fall

Let’s review… • We can use subtraction to get the o answer. If it’s 50 outside and it’s going o to be 80. Here’s what we’d do. 80 50 30

Let’s try it with negatives o • Let’s say it’s -23 below zero. If the o temperature rises 10 , how cold will it o be? 33 a. ) b. ) -13 o c. ) -23 o -33 o

Nope. Let’s review • Remember, thermometer rises when the temperature goes up, even if we start in the negatives. • HINT: Take a look at the amount of RED inside thermometer.

Nice try, but no… • Remember, we’re only rising the o temperature 10. It looks like you o raised the temperature 57 !

Great! Let’s try another. o • Let’s say it’s 32. If the temperature falls o 12 , how cold will it be? a. ) 32 o 44 b. ) o c. ) 20 o 83 o

Not quite… Remember that the temperature today will get colder. The thermometer will fall.

One more… • Let’s say the temperature starts off o today at 12. A cold front is expected o to drop the temperature 20. What will the temperature be after the cold front passes? a. ) 32 o b. ) -8 o c. ) 8 o d. ) -20 o

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 negative positive

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 = ? negative positive

No, that’s not it… but why? Addition: Face Positive Subtraction: 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 = ? Backward 4 Way to walk

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. BEWARE, BEWARE 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