1. AddingIntegers

2. In the integer models we drew, we saw that putting together (+) integers does not automatically mean they are going to add up. -5 -4 -3 -2 -1 0 1 2 3 4 5

3. When positive integers are put together with positive integers, the numbers appear to add up to a bunch of positive integers. -5 -4 -3 -2 -1 0 1 2 3 4 5 2 + 3 = 5

4. When negative integers are put together with negative integers, the numbers appear to add up to a bunch of negative integers. -5 -4 -3 -2 -1 0 1 2 3 4 5 -3 + -1 = -4

5. BUT, when negative integers are put together with positive integers, the numbers appear to subtract and the answer takes the sign of the integer you have the most of. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 + 7 = 2 more positives than negatives, so answer is positive

6. The ADD sign between two integers simply means to put the integers together! The ADD sign between two integers simply means to put the integers together! Examples: Examples: 1. r = 23 + 34 2. s = -9 + -6 3. - 4 + (-3) = q 4. + 7 + + 11 = t IF THE SIGNS ARE THE SAME IF THE SIGNS ARE THE SAME The integers add up Sign of the big number! r = 57 s = -15 -7 = q +18 = t COPY

7. The ADD sign still means to put the integers together! The ADD sign still means to put the integers together! Examples Examples 1. f = (-17) + 20 2. m = 52 + (-60) 3. 6 + (-3) = s 4. g = 3 + (-8) IF THE SIGNS ARE DIFFERENT: IF THE SIGNS ARE DIFFERENT: The integers subtract Take the sign of the big number! f = 3 m = -8 3 = s g = -5 COPY

8. More examples 1. m = -10 + 8 m = -2 2. d = 7 + 20 d = 27 3. w = -4 + (-3) w = -7 4. b = 5 + (-2) b = 3 5. d = - 5 + + 5 d = 0 Put together Put together Put together Put together Put together

9. Integers Operations with a -

10. Integers with a - To solve integer problems with a -, add the opposite of the second integer (the subtrahend). The subtrahend is the integer being subtracted. Examples: +8 − +3 = +8 + ¯3 = +5 +9 − ¯5 = +9 + +5 = +14 ¯8 − +3 = ¯8 + ¯3 = ¯11 ¯7 − ¯2 = ¯7 + +2 = ¯5 ¯4 − ¯4 = ¯4 + +4 = 0

11. Now let’s talk about 0. Zero subtracted from any integer is that integer. Example: 9 − 0 = 9 + 9 − 0 = + 9 ¯6 − = ¯6 ¯6 − 0 = ¯6

12. Integer Rules When you see a subtract sign you will add the opposite of the second integer. When you see a subtract sign you will add the opposite of the second integer. Same signs – add and keep that sign Same signs – add and keep that sign ex: 5 – -8 = 5 + 8 = 13 ex: -5 – 8 = - 5 + -8 = - 13 Different signs – subtract and use the larger Different signs – subtract and use the larger number’s sign number’s sign ex: -8 – -5 = - 8 + 5 = - 3 ex: 8 – 3 = 8 + - 3 = 5

13. Now let’s practice 1. -10 - -4 = 2. -4 - -9 = 3. +2 - +9 = 4. +6 - +7 = 5. -14 - -15 = 6. -10 - -14 = 7. -4 - +5 = 8. +6 - -3 = 9. -10 - -8 = 10. -16 - -6 = -6 +5 -7 +1 +4 -9 +9 -2 -10

15. In a 3 rd grade classroom, the teacher decided to pair her students with a partner to work on a class project. The first 2 students she paired up were Claire and Pedro. Little did she know that the two students would develop a negative attitude about working together. Claire wanted to work with her girlfriends and Pedro wanted to work with his buddies. He’s got coodies!

16. Next she paired up Esmerelda and Janine. The two girls were so excited. They displayed a positive attitude and jumped for joy at the announcement of their names. Girl power! You go girl.

17. The teacher then grouped Cole and Shawn. They too were so excited about being paired up that their positive attitude shown through. Cool dude!!! Awesome!

18. If the girls in this story were represented by a (+) and the boys were represented by a (-) Then when combining a (+) and a (-), the result would be a ____________. When combining a (+) and a (+) or a (-)and a (-), the result would be a ____________.

19. Let’s Review x= negative attitude x = positive attitude x

20. Grouping positive (+) and negative (-) numbers by multiplying or dividing, is like grouping boys (-) and girls (+) in a 3 rd grade classroom.

21. -6 x +8 = ____-36 ÷ +3 = _____ -7 x -5 = ____+56 ÷ -8 = _____ +9 x +9 = ____-48 ÷ -12 =_____ +11 x -6 = ____+24 ÷ +6 = _____ Yuk! Ugh! Dude No way Girl power Male bonding Oh no! Girls rule

22. 1.-6 (9) = 2.12 x -3 = 3.3 × (-4) = 4.-16 ÷ ( -4) = 5.-24 x 3 = 6. -14 (-8) = 7. 12 ÷ -6 = 8. 81 ÷ (-9) = 9.-24 (8) = 10.-64 ÷ 8 = -54 -36 -12 4 -72 112 -2 -9 -192 -8 Now let’s see what you can do! Work with your partner

23. Warm-up 1)How many milliliters of soda are in a container labeled 2 liters? 2)Greg checks in books at the school library. One day, Greg found the ¼ of the books returned were overdue. What percent of the books returned that day were overdue?

24. Warm-up 3) Jerome’s scout troop took a 4-day bike trip last summer. On the first day, they rode 52 miles. On the second day, they rode 46 miles. On the third day, they rode 38 miles. On the fourth day, they rode 40 miles. What was the mean distance the scouts rode per day? 4) A bag contains 5 red marbles, 8 blue marbles, 5 white marbles, and 6 yellow marbles. The marbles are all of the same size. If a marble is chosen at random, what is the probability that it will be blue?

25. Warm-up 5) Hector bought 3 chairs for $79.95 each. Which is the best estimate of the total cost of the chairs? 6) Luther is putting new math books on the shelves in the school book room. There are 145 books. Luther can fit 27 books on one shelf. Which is the best estimate of the number of shelves Luther will need for all the books?