Adding Integers

1. 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”

2. Integers are just whole numbers Numbers like 1 or 2 Even like 2,153 Integers can be negative Like -3 or -5 Even -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 What are Integers?

3. 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?

4. Adding Integers First start by choosing a method to learn how to add integers: 1.) Color Counters 2.) Temperature 3.) Hiker

5. Adding with Color Counters • Think of each Green Chip as positive 1 • Think of each Red Chip as negative 1 1 -1

6. 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) = +

7. 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! = +

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

9. Now, replace your chips with numbers. = + 4 -3 = 1 +

10. How about this one? Can you predict what’s left over? = +

11. Now, replace your chips with numbers. = + -5 3 = -2 +

12. Now it’s your turn. 1.) Which color chip represents NEGATIVE one? a.) b.)

13. Oops… Let’s review • Think of each Green Chip as positive 1 • Think of each Red Chip as negative 1 1 -1

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

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

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

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

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

19. Oops… Let’s review -2 -5 3 Remember… replace your chips with numbers. = +

20. Great Job! • Click the Right button to try adding integers using temperature, or click on the Home button to return to the Main Menu

21. Adding Integers with Temperature • This time we’re going to look at a vertical number line.

22. We all know that a thermometer has lower numbers at the bottom, and higher numbers at the top. 100oC 0oC -30oC

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

24. So here we are. It’s 63oFoutside. 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

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

26. 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. 80 50 30

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

28. 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.

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

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

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

32. 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

33. Oops… not quite • Remember that the temperature should be less after the cold front passes.

34. Almost… but no • Your calculation is close, but think to yourself… is the answer going to be positive, or negative?

35. Whoa! dude! Not even close… • That’s too cold! You calculated as if the starting temperature was zero.

36. 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

37. Adding Integers with a Hiker • Imagine you are a hiker standing on a number line.

38. The 3 Things you NEED to know • The Starting Number • The Direction to face • How much to Walk

39. Starting Point • The first number in an addition problem is your starting point • This is where you, the hiker, will stand Example

40. 3 + -4 = ? Starting Point

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

42. 3 + -4 = ? Direction to Face negative positive

43. Where to Walk • The last number tells us how many spaces to walk • Positive: Walk Forwards • Negative: Walk Backwards Example

44. 3 + -4 = ? Way to walk Backward 4

45. Last Step • Literally… where did you end up on the number line? • This is your final answer Example

46. 3 + -4 = -1 Ending Point

47. Now you give it a try… 1. Given this equation, which hiker is in the correct starting place? -5 + 6 = ?

48. No, that’s not it… 3 + -4 = ? Starting Point

49. Very Good! Next. Using the same equation, which direction should you face? -5 + 6 = ? negative positive

50. 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