1. Bell work/Cronnelly
Calculate the area and perimeter of each shape below.

2. Bell work/Cronnelly A = 112.2 yd2 P = 49.4 yd A = 105.7 ft2 P = 60 ft
Calculate the area and perimeter of each shape below.
A = ft2
P = 60 ft
A = 31.5 cm2
P = 29 cm
A = 47.5 cm2
P =

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

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

5. The rules for subtracting integers are exactly the same as adding integers except we will add one step in the process.

6. Steps for Adding or Subtracting Integers
Example 1
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.
Solve: ̶ 12 ̶ ( ̶ 11) +
̶ 12 ̶ ( ̶ 11)
Different Signs ̶
Read the steps first. Point out that the –(– almost looks like a plus sign!
Click once to watch Demo. Talk students through the demo as to what is happening. 1
SUBTRACT the numbers.
Give sign of the bigger digit.
̶ 1

7. Let’s justify our answer on a number line
Example 1
Solve: ̶ 12 ̶ ( ̶ 11) = ̶ 1
Yesterday the students learned to model subtraction on a number
line. This demo will reinforce the rule.

8. Let Me Show You Another Example!
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.
Solve: 3 ̶ ( ̶ 4)
Work and explain this problem to the students.
Answer: 3 –(-4) = 7

9. Why do we have to search out the double negatives and change them to a positive?

10. That’s a tough question to explain
That’s a tough question to explain. We did justify that the rule worked by modeling on a number line.
Let me give you a few real-world examples as to why two negatives
side-by-side equal a positive!

11. Double Negatives in Grammar
The “double negatives” cancel each other out…
It is really saying that EVERYBODY likes
Sara Lee.
The two negatives make a positive!
What is this really saying?
Of course we know that this is
poor grammar!

12. In 6th grade you learned about the opposite of an opposite.
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
The –(– sort of looks like a big plus sign!
That would make
it a +3.
This skill was learned in 6th grade.
-(-12) = _____

13. Double negatives cancel to a positive
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 (-10) = 0, or no speed modification thus you are moving at the reference speed of 65 again.

14. Double negatives cancel to a positive
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) = = -2
OWE 3 BOOKS
YOU DECIDE TO PUT THE GREEN ONE BACK

15. Back to our lesson…

16. Let’s look at this subtraction problem.
Example 2
Same Signs…
ADD the numbers.
KEEP the sign.
If there are any double negatives, change them to a positive.
Look at the signs
directly in front of each
number.
Different Signs…
SUBTRACT the numbers.
Give sign of the bigger digit.
Solve: ̶ 9 ̶ 2
No double negatives.
Same Signs.
There are no double negatives.
Tell them double negatives are negative signs side-by-side.
Therefore, this example has no double negatives. 11
ADD the numbers.
̶ 11
KEEP the sign.

17. Let’s justify our answer on a number line
Example 2
Solve: ̶ 9 ̶ 2 = ̶ 11
Chick once to start animation.

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

19. LET’S PRACTICE
1) ) -70
GET YOUR
PENCILS READY!

20. 2 – (– 3) – 6 – (– 2) 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)
Guided Practice -4 You Try 5

21. 15 – 21 – 12 – 10 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
Guided Practice -22 You Try -6

22. – (– 80) – 40 – (– 14) – 7 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
Guided Practice 7 You Try 40

23. – 8 – 2 – (–16) – 6 – (– 3) – 5 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)
Guided Practice -8 You Try 6

24. Last section…
Section 1: Apply the rules for adding or subtracting integers. Section 2: Guided and independent practice. Section 3: Volunteers Needed!

25. Write an equation, and then solve the problem.
Challenge Problem.
Don’t be a chicken!
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.
8 – (-4) = 12 degrees difference

26. Write and equation, then solve.
Challenge Problem.
You can do it!
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.
107 – (-2) = 109 degrees difference

27. Apply rules:
– (– 11 ) + (– 6) =
Answer: 5

28. Apply rule
9 + (– 5) =
Justify
Answer: 4

29. –8 – (– 6) = Apply rule Justify Answer: -2
–8 – (– 6) =
Justify
Answer: -2
When modeling on the number line, please model
as taught in the last lesson. Pencil faces the positives.
If there is a subtract sign in the middle, turn the opposite direction.
Then depending on the sign of the second number
E ither walk forward or backward.

30. Apply rule
2 – (– 10) =
Justify
Answer: 12

31. CLOSURE
Recap the rules with the students. Then move on to classwork.

32. End of PowerPoint