2. Needed Skills p. 30 8 + (-9) = -11 + (-18) = -4 + (-6) = 14 + (-3)= 6 + (-6) = -13 + (-10) = -29 -10 11 0 -23

3. 1.6 “Subtracting” with Integers Adding to Subtract This lesson will be a more simplified version of the text lesson.

4. A New Rule! To subtract an integer, we have to change the problem into an addition problem. We then add the opposite. -12 - 4 This problem is telling us to subtract +4 from -12. (-12) + (-4) We change the subtraction sign to an addition sign and change the next number to its opposite. To subtract an integer, we have to change the problem into an addition problem. We then add the opposite. -12 - 4 This problem is telling us to subtract +4 from -12. (-12) + (-4) We change the subtraction sign to an addition sign and change the next number to its opposite. Yes…I know

5. We now have an addition problem. We use the integer addition rules to finish it. Solve: -16 -12 + (-4) = Original problem: -12 - 4 = Don’t overthink this. Learn the process. Copy, change to +, change to opposite, This process will be streamlined after the class has shown mastery and before we combine terms in algebraic expressions……wait for it….work the process.

6. When we were combining integers with addition rules, it was easy to demonstrate the process through the use of models and stories. The “subtraction” process, however, is not clarified by this. The use of opposites, and changing signs to opposites leads us to believe we would be right where we started….. That is not always the case. So..learn the process. Copy, change to +, write the opposite. You are a machine…. You are an integer machine…. Copy, rewrite, solve….

7. Original problem: 4 - (-4) = Original problem: 6 - 8 = Original problem: -2 - 12 = Original problem: -10 - 8 = Rewrite: 4 + 4 = -2 Rewrite: 6 + (-8) = Rewrite: -2 + -12 = Rewrite: -10 + (-8) = 8 It is a little tricky when the second number is +. Remember, no sign means +. -14 -18 You are a machine…. You are an integer machine…. Copy, rewrite, solve….

8. Original problem: -15 - (-15) = Original problem: 12 - (-15) = Rewrite: 12 + 15 = Rewrite: -15 + 15 = 27 0 You are a machine…. You are an integer machine…. Copy, rewrite, solve…. There is NEVER a short cut for this one.

9. Evaluating Expressions Write, substitute, and solve. n = 4 -12 - n3 - n n - (-8) -12 - (4) -12 + (-4) = -16 3 - (4) 3 + (- 4) = - 1 (4) - (-8) (4) + 8 = 12 You are an integer machine…. Copy, SUBSTITUTE, rewrite, solve….

10. As you complete your work… Notice what we did NOT do……. We did NOT cross out a - sign to make an + - This is not acceptable. Show all steps and follow the process!! Notice what we did NOT do……. We did NOT cross out a - sign to make an + - This is not acceptable. Show all steps and follow the process!! a – b = a + (-b) a – (-b) = a + b Key Concept p. 31

11. Applying the Skill In January, 1916, the temperature in Browning, Montana, dropped 100 degrees overnight. The initial temperature was 44 0 F. What was the final temperature? Original temperature drops 100 = final temp 44 – 100 = final temp 44 + (- 100 ) = -56 degrees

12. The lowest temperature ever recorded on the moon was about -170 0 C. The lowest temperature ever recorded in Antarctica was -89 0 C. Find the difference in the two. -170 0 - ( -89 0 ) = difference -170 0 + ( 89 0 ) = -81 degrees C

13. Review and Practice -10 - 5 = 12 - (-2)= 12 + 2 = 14 -10 + (-5) = -15 -15 - (-6) + 12 = -15 + 6 + 12 = 14 - 15 = -10 + (-8) = -18 -10 - 8 = 14 + (-15)= -1 -20 + 2 + (-8) = -20 - (-2) - 8 = 3-28 + 2 = -26

14. Putting it all together... The – sign is a signal to change/change!!!! -4 + 12 – 18 = -4 + 12 + (-18) = -6 + -8 - (-10) = -6 + -8 + 10 = -14 + 10 = -4 8 + 12 – 16 - (-2) + 4 + (-10) - 11 = -22 + 12 = -10 8 + 12 + (-16) + 2 + 4 + (-10) + (-11) = 8 + 12 + 2 + 4 + (-16) + (-10) + (-11) = 26 + (-37) = - 11

15. Magic Squares Your notes have a section on Magic Squares….we will do this tomorrow. Today and tonight are for drill and practice….practice……practice…..practice. You are a machine…. You are an integer machine….

16. What did we accomplish? We have added another integer rule to our list of processes. We have evaluated integer expressions and applied this to word problems. 15 + (-3) + (12) – (-3) + |-4| - |-6| 15 + (-3) + (12) + (3) + (4) – (6) 15 + (-3) + (12) + (3) + (4) + (-6) 34 + (-9) 25

18. 5 -9 ? ? ? -3?-7 Magic Squares All diagonal, vertical, and horizontal sums must be equal. The sum we need is -3. 1 3 7 -5

19. 6 43 205 -3-6 Find the Magic Square Sum. Try to find the missing values within your group. SUM????? 6 9 -4 -2 1 7 8 p. 34 #80

20. What have we done? We have continued to work with integer rules as we work towards perfection of the process.