Bell workCronnelly Calculate the area and perimeter of

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

Bell work/Cronnelly Calculate the area and perimeter of each shape below. A = 112. 2 yd 2 P = 49. 4 yd A = 105. 7 ft 2 P = 60 ft A = 47. 5 P = cm 2 A = 31. 5 cm 2 P = 29 cm

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

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

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

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

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 side-by-side equal a positive! positive

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!

IN 6 TH 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 The –(– sort of looks like a big plus sign! That would make -(-3) = 3 -(-12) = _____ it a +3.

DOUBLE NEGATIVES CANCEL TO A POSITIVE Driving You are driving with cruise control set at 65 mph (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 to our lesson…

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

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

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

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

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

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

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

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

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.

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.

Apply rules: – (– 11 ) + (– 6) =

Apply rule Justify 9 + (– 5) =

Apply rule Justify – 8 – (– 6) =

Apply rule Justify 2 – (– 10) =

CLOSURE

End of Power. Point