Integer Operations

​MGSE6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

What are integers?

• Include all Whole Number and their OPPOSITES

• Integers DO NOT include fractions, or decimals

What are opposites?

The opposite number, is a number that is the same distant from zero on the number line in the opposite direction.

Zero is neither positive or negative and does not have an opposite.

Multiple Choice

What is the opposite of 6

• 
  

  $$\frac{1}{6}$$

• 0

• -6

• 6

Multiple Select

What numbers are integers?

• 5

• 2.5

• $$-\frac{1}{9}$$

• 2,301

• -12

Multiple Choice

an $8o dollar withdrawl

• 80

• -80

• +80

Multiple Choice

a flight overbooked by 4    passengers

• 4

• -4

Multiple Choice

draining 15 gallons of water     from a fish tank

• 15

• -15

• 10

• -10

Absolute Value

• The distance a value is from zero

• Distance cannot be negative

• If you walk forward 3 steps or you walked backward 3 steps, you still covered the same amount of ground

Multiple Choice

Is the absolute value of a number ever negative?

• yes

• no

• sometimes

Multiple Choice

How would you represent the absolute value of -23?

• $$\left|-23\right|=-23$$

• $$\left|-23\right|=0$$

• $$\left|-23\right|=23$$

• $$\left|-23\right|=\left|23\right|$$

Multiplying & Dividing Integers

Match

Match the following

Find the product or quotient

• 9 x -4

• -12

• -15(-3)

• -23

• -36 $$\div$$  3

-36

2(-6)

45

-92 4

-12

• -36

• 2(-6)

• 45

• -92 $$\div$$  4

• -12

Poll

$$positive\ \times\ negative\ =$$  

• Negative

• Positive

Multiple Choice

(-) $$\div$$  (-)

• +

• -

Multiple Choice

If the product of multiplying two numbers was POSITIVE, what does that mean about the two numbers?

• They had the same signs

• They had different signs

• Not enough info to tell

Multiple Choice

$$\frac{0}{-6}$$ =

• 0

• Undefined

• OK

• NO

Multiple Choice

Now try with more than two numbers. Take them two at a time. Will the answer be negative or positive??

(-2)(3)(-2)

• Negative

• Positive

Multiple Choice

(-1)(-3)(-5)=?

• -15

• 15

• -16

• 16

Multiple Choice

(-2)(-1)(-3)(-2)=?

• 12

• -12

• 8

• -8

Multiple Choice

Multiply

(5) • (–9) • (–2)

• 90

• -45

• -90

• 47

Match

Find Each sum or difference

• -23 +12

• -17

• 6+(-4)

• -11+(-6)

• -4 -(-16)

-11

-2-15

2

-17

12

• -11

• -2-15

• 2

• -17

• 12

Multiple Choice

-23 + 11

• -12

• 12

• 34

• -34

​MGSE6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., −(−3) = 3, and that 0 is its own opposite.

Adding integers rules

• Same sign, add and keep the sign.

• Different sign? Subtract and keep the sign of the # that is larger.

Multiple Choice

5+(-5)

• 5

• -5

• 0

• 10

Subtracting integers rules

• Keep the first number.

• Change subtraction to addition.

• Change the sign of the last #

• Then follow the addition rules

Multiple Choice

33 + (-38)

• -5

• 5

• 71

• -71

Multiple Choice

What are the rules for subtracting integers?

• Change to multiplication and use the opposite of the second number.

• Keep the first #. Change subtraction sign to addition and Change the last number into its opposite.

• Keep the opposite of both numbers and then change it to add.

• Subtract like normal and keep the larger sign.

Multiple Choice

16 - (-9) 

• -7

• 11

• 15

• 25

​Integers in Context

Multiple Choice

At 2pm, the temperature was 15 degrees. By midnight, the temperature dropped by 30 degrees. What is the temperature at midnight?

• 45 degrees
• -45 degrees
• 15 degrees
• -15 degrees

Multiple Choice

The first play of a football game resulted in a loss of 12 yards.  Then a penalty resulted in another loss of 5 yards.  What is the total loss or gain?

• a gain of 7 yards
• a loss of 7 yards
• a gain of 17 yards 
• a loss of 17 yards

Multiple Choice

The temperature on Sunday was -15^o C.  The temperature on Monday was 12 degrees less than the temperature on Sunday.  What was the temperature on Monday? 

• -27^o C
• 27^o C
• -3^o C
• 3^o C

Multiple Choice

A submarine was located 800 feet below sea level. If it ascends (rises) 350 feet, what is its new position?

• 450

• -450

• 1150

• -1150

Key Vocabulary

-Words like "increased", "more", "raised", "up", "gained" and "deposit" tells you that you probably have to add or multiply integers.

-However, words like "down", "lowered", "decreased", "less", and "withdraw" implies that you must divide or subtract.

Multiple Choice

A drought can cause the level of the local water supply to drop by a few inches each week. Suppose the level of the water supply drops 2 inches each week. How much will it change in 4 weeks?

• -16 inches

• -8 inches

• -2 inches

Multiple Choice

At 7:00PM the temperature was 40 degrees F. If the temperature dropped steadily at a rate of 6 degrees per hour, what was the temperature at 11:00 PM?

• 46 degrees

• -22 degrees

• -16 degrees

• 16 degrees

Multiple Choice

A football team lost 5 yards on 4 consecutive plays. What is the total change in yards from where the team started?

• 9 yards

• 20 yards

• -20 yards

• -1 yards

Multiple Choice

9. As a cold front passed through Lodi, the temperature changed steadily over 6 hours. Altogether it changed -18 degrees. What was the change in temperature each hour for the 6 hours?

• -18 ÷ 6 = -3 degrees

• 18 ÷ 6 = 3 degrees

Video Response

Tell me what you learned about integers. Your video must be at least 15 seconds. Use complete sentences.

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