1. BELLWORK 1. -32 – (-15) 2. -74 – 56 3. -5 – (-7) 4. -21 – (-32 ) 5. -32 – (-10)

2. LESSON: 3.2.4 SUBTRACTING INTEGERS –12 – (– 11) – 9 – 2

3. Section 1: Apply the rules for adding or subtracting integers. Section 2:Guided and independent practice. Section 3:Volunteers. TODAY…

5. STEPS FOR ADDING OR SUBTRACTING INTEGERS Solve : ̶ 12 ̶ ( ̶ 11) Look at the signs directly in front of each number. Same Signs… ADD the numbers. KEEP the sign. Different Signs… SUBTRACT the numbers. Give sign of the bigger digit. If there are any double negatives, change them to a positive. ̶ 12 ̶ ( ̶ 11) Different Signs ̶ 12 + 11 1 SUBTRACT the numbers. Give sign of the bigger digit. ̶ 1 ̶ 1 + Example 1

6. LET’S JUSTIFY OUR ANSWER ON A NUMBER LINE Solve : ̶ 12 ̶ ( ̶ 11) = ̶ 1 Example 1

7. LET ME SHOW YOU ANOTHER EXAMPLE! Solve : 3 ̶ ( ̶ 4) Look at the signs directly in front of each number. Same Signs… ADD the numbers. KEEP the sign. Different Signs… SUBTRACT the numbers. Give sign of the bigger digit. If there are any double negatives, change them to a positive.

10. DOUBLE NEGATIVES IN GRAMMAR What is this really saying? The “double negatives” cancel each other out… It is really saying that EVERYBODY likes Sara Lee. The two negatives make a positive! Of course we know that this is poor grammar!

11. The opposite of the opposite of a number is the original number. It can be illustrated as follows: -(-a) = a Similar to double negatives in grammar… the double negatives in math also cancel each other out. Example -(-3) = 3 IN 6 TH GRADE YOU LEARNED ABOUT THE OPPOSITE OF AN OPPOSITE. The –(– sort of looks like a big plus sign! That would make it a + 3. -(-12) = _____

12. Driving You are driving with cruise control set at 65mph (in a 65 zone, of course), which we will call your reference speed. You see a sign stating that you are entering a 55 zone so you slow down 10 mph ( -10). After a few miles, a new sign informs you that you are entering a 65 zone again so you resume your original speed, thus removing (subtracting) the -10 mph modification. We thus have 65 -10 - (-10) = 0, or no speed modification thus you are moving at the reference speed of 65 again. DOUBLE NEGATIVES CANCEL TO A POSITIVE

13. Library You borrow 3 books from a library. You thus owe three books (-3). You read one and discover it does not cover what you want, so you return (subtract) it (a borrowed book is a minus, therefore you take away a -1) and thus you have subtracted one book you owe, and now owe only two. And we have: -3 -(-1) = -3 + 1 = -2 DOUBLE NEGATIVES CANCEL TO A POSITIVE OWE 3 BOOKS YOU DECIDE TO PUT THE GREEN ONE BACK

15. LET’S LOOK AT THIS SUBTRACTION PROBLEM. Solve : ̶ 9 ̶ 2 Look at the signs directly in front of each number. Same Signs… ADD the numbers. KEEP the sign. Different Signs… SUBTRACT the numbers. Give sign of the bigger digit. If there are any double negatives, change them to a positive. Same Signs. 11 ADD the numbers. KEEP the sign. ̶ 11 Example 2 No double negatives.

16. LET’S JUSTIFY OUR ANSWER ON A NUMBER LINE Solve : ̶ 9 ̶ 2 = ̶ 11 Example 2

17. MOVING ON… Section 1: Apply the rules for adding or subtracting integers. Section 2:Guided and independent practice. Section 3:Volunteers.

19. Same Signs Add the digits and Keep the sign. Different Signs Subtract the digits and give sign of the bigger digit. Guide Practice #1 You Try #1 – 6 – (– 2) 2 – (– 3)

20. Same Signs Add the digits and Keep the sign. Different Signs Subtract the digits and give sign of the bigger digit. Guide Practice #2 You Try #2 – 12 – 10 15 – 21

21. Same Signs Add the digits and Keep the sign. Different Signs Subtract the digits and give sign of the bigger digit. Guide Practice #3 You Try #3 – (– 14) – 7 – (– 80) – 40

22. Same Signs Add the digits and Keep the sign. Different Signs Subtract the digits and give sign of the bigger digit. Guide Practice #4 You Try #4 – 6 – (– 3) – 5 – 8 – 2 – (–16)

23. LAST SECTION… Section 1: Apply the rules for adding or subtracting integers. Section 2:Guided and independent practice. Section 3:Volunteers Needed!

24. The temperature in Portland, Maine was 8° F at noon. By 10:00 pm the temperature had dropped to – 4° F. Find the change (difference) in the temperatures. Write an equation, and then solve the problem. Challenge Problem. Don’t be a chicken!

25. The record high for Florida is 107°F. The record low temperature is –2°F. What is the difference in temperature between the record high and record low? Write and equation, then solve. Challenge Problem. You can do it!

26. Apply rules: – (– 11 ) + (– 6) =

27. Justify Apply rule 9 + (– 5) =

28. Justify Apply rule –8 – (– 6) =

29. Justify Apply rule 2 – (– 10) =