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

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 = 105.7 ft2 P = 60 ft A = 31.5 cm2 P = 29 cm A = 47.5 cm2 P =

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

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

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

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 ̶ 12 + 11 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

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.

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

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

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!

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!

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) = _____

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 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 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 OWE 3 BOOKS YOU DECIDE TO PUT THE GREEN ONE BACK

Back to our lesson…

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.

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

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

LET’S PRACTICE 1) 126 2) -70 GET YOUR PENCILS READY!

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

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

– (– 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

– 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

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

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

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

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

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

–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.

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

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

End of PowerPoint