6th Grade Winter Break Tutorials Integer Operations

Integer Operations

Review how to add, subtract, multiply, and divide integers.

Adding Integers

When you add inverses, they always cancel eachother out so you get zero.

Fill in the Blank

What is the inverse of -8?

Fill in the Blank

What is 4 + (-4) =

Adding Two Negative Numbers

• Add them and keep the sign

Multiple Choice

What is-3 + (-10)

• 13

• -13

• 7

• -7

Fill in the Blank

-8 + ? = -14

Fill in the Blank

9 + ? = 0

Adding Integers with DIFFERENT SIGNS

• Subtract them
• Keep the sign of the LARGER NUMBER (absolute value)

Fill in the Blank

-5 + 9 Will this answer be positive or negative?

Fill in the Blank

Which number has the larger absolute value? -12 + 8

Multiple Choice

Solve -13 + 3

• -10

• 10

• 16

• -16

Fill in the Blank

Solve 12 + (-3)

Subtracting Integers

• Keep, Change, Change
• Add the Opposite

Fill in the Blank

5 - (-4) Which number do you keep the same?

Open Ended

5 - (-4) What do you do to the subtraction sign? How would you rewrite this problem?

Open Ended

Solve -7 - 8 after you Keep, Change, Change

Multiple Choice

-9 - (-2) Which of the following is correct after you keep, change, change?

• 9 + 2

• -9 + 2

• -9 + (-2)

Multiplying and Dividing Integers

• Same Signs= Positive Answer
• Different Signs= Negative Answer

Fill in the Blank

-9 x 8 Will the answer be positive or negative?

Multiple Select

Select ALL of the answers that are NEGATIVE

• -5 x 6

• -21/-3

• 8 x (-12)

• -4/2

Fill in the Blank

Solve -8/8

Integer Operations

Pay extra attention to the operating sign.

Adding Integers

• If the signs are the SAME, ADD and KEEP the same sign. Ex: -13 + -27 = -40

• If the signs are DIFFERENT, SUBTRACT and use the sign of the STRONGER number. Ex: -24 + 5 = -19

Multiple Choice

-9 + (-8) = x

• x = 1

• x = -1

• x = 17

• x = -17

Multiple Choice

-15 + (-13) = x

• x = 28

• x = -18

• x = -28

• x = -12

Multiple Choice

It is a cold winter day in Virginia, the temperature when I woke up this morning was

 $-9\degree.$  At noon, the temperature increased by  $8\degree$ .  What was the temperature at noon? 

•  $-1\degree$  

•  $-4\degree$  

•  $4\degree$  

•  $12\degree$  

Subtracting Integers

• Rewrite as an addition problem.

• ADD the OPPOSITE

• Ex: 5 - (-2) becomes 5 + (+2) = 7

Multiple Choice

Rewrite -9 - (-3) using "add the opposite" strategy.

• -9 + 3

• 9 + (-3)

• 9 - (-3)

• 9 + 3

Multiple Choice

Evaluate: 7 - (-5) = x

• x = -2

• x = 2

• x = -12

• x = 12

Multiple Choice

Evaluate: -6 - (-22) = x

• x = 16

• x = -16

• x = 28

• x = -28

Poll

How do you feel about adding and subtracting integers?

• Awesome! I got it!!

• I'm at 75% or higher.

• I'm between 50% and 75%.

• I totally don't get it and need help.

Multiplying and dividing Integers

• Same sign, POSITIVE answer.

• Different sign, NEGATIVE answer.

• Don't forget to multiply or divide. :-)

Multiple Choice

 $\frac{2}{2}$  

Evaluate:

• 1

• 2

• 0

• 4

Multiple Choice

Evaluate:  $-11\ \cdot\ 3=$  x

• x = 33

• x = -33

• x = -14

• x = -8

Multiple Choice

Evaluate: (+7) (7) = x

• x = 14

• x = 0

• x = -49

• x = 49

Multiple Choice

 $-99\ \div\ \left(-11\right)\ =x$  

Evaluate:

• x = 9

• x = -9

• x = 110

• x = -110

Multiple Choice

You take 6 steps forward and 8 steps back. How many steps have you taken?

• 2

• -2

• 14

• -14

Multiple Choice

During the hot summer months, the height of the water in my pool decreases by 4 inches each week. What is the change in height over a six week period?

• 24 inches

• 10 inches

• -24 inches

• -10 inches

Multiple Choice

Last night, the temperature changed at a rate of -3 F per hour.  How long did it take for the temperature to change -33 F?

• 11 hours

• -11 hours

• 36 hours

• -36 hours

Multiple Choice

During a 12 hour period, the temperature dropped 48 degrees F. How many degrees did the temperature drop each hour?

• $4\degree F$

• $-4\degree F$

• $56\degree F$

• $-56\degree F$

Open Ended

Overall, how do you feel about operations with integers? Write in a complete sentence, your strengths and weaknesses with integers.

Modeling Integer Operations

​Adding Integers

​Adding integers on the number line.

• ​The bottom arrow is the first number.

• ​The top arrow is the second number.

• ​It ends on the sum.

• ​The arrows are straight lines.

• ​This model represents

-4 + (-2) = -6

Multiple Choice

Look at the number line.

• –2 + 4 =  –2
• –2 + (–4) =  –6
• 4 + (–6) =  –2
• 4 + (–2) =  6

Multiple Choice

• 7 + 10 = 3
• -7 + 10 = 3
• -7 - 10 = 3
• -7 + 3 = 10

Multiplying Integers

Multiplying integers on the number line.

• ​The arrows are curves or groups of arrows

• ​Count number of arrows. That will be the first number.

• ​The length of the arrow is the second number.

• ​It ends on the answer.

• ​This model represents

2(-3) = -6

Multiple Choice

• 4 x 4 = 16
• -4 x (-4) = -16
• -4 x (-4) = 16
• 4 x (-4) = -16

Multiple Choice

• 5 × 2 = 10
• -5 × 2 = 10
• 5 × (-2) = -10
• -5 × (-2) = -10

​Adding Integers Part 2

• Sometimes on adding integers there is only one arrow.

• ​The first number is where the arrow starts.

• ​The length of the arrow is the second number.

• ​The sum is where it stops.

• ​Pay attention to the direction of the arrows!

• ​This model represents

3 + (-5) = -2

Multiple Choice

Which equation matches the number line model?

• -1 + (-6) = -7

• -1 + 6 = 5

• 1 + (-6) = -5

• 1 + 6 = 7

Multiple Choice

Which equation matches the number line model?

• 3 + (-6) = -3

• -3 + (-6) = -9

• -3 + 6 = 3

• 3 + 6 = 9

Multiple Choice

Which equation is represented by the model?

• 8 + (-5) = 3
• -8 + 5 = -3
• 8 + 5 = 13
• -8 + (-5) = -13

Multiple Choice

Which equation is represented by the model?

• 9 + 4 = 13
• 9 + (-4) = 5
• -9 + 4 = -5
• -9 + (-4) = -13

Multiple Choice

• -5 + 3 = -2
• 5 + (-3) = 2
• 5 + 3 = 8
• -5 + (-3) = -8

Multiple Choice

Choose the equation that best represents the model.

• 2 + (–6) =  –4
• 0 – 6 = –6
• –6 + 8 = 2
• 8 + (–6) = 2

Multiple Choice

• -5 - 4 = -1
• -5 + 1 = -1
• -5 + 4 = -1
• 5 + (-4) = 1

Multiple Choice

• -7 - 4 = -28
• 7 x 4 = 28
• 7 x (-4) = -28
• -7 x (-4) = -28

Integer Operations

Today, we are reviewing how to add, subtract, multiply and divide integers.

Adding Integers

• When you are adding two positive integers there is an increase in value

• When you are adding a positive and a negative integer there is a decrease in value

• When you are adding a negative and a positive integer there is an increase in value

• When you are adding two negative integers there is a decrease in value

Examples:

(+2) + (+10) = +12

(+5) + (-2) = +3

(-3) + (+6) = +3

(-5) + (-6) = -11

Multiple Choice

(+4) + (+2)

• -6

• +6

• 2

• -2

Multiple Choice

(+5) + (-2)

• +3

• +7

• -7

• -3

Multiple Choice

(-4) + (+5)

• -9

• -1

• +9

• +1

Multiple Choice

(-4) + (-6)

• -10

• +2

• -2

• +10

Subtracting Integers

• When you are subtracting two positive integers there is a decrease in value

• When you are subtracting a positive and a negative integer there is an increase in value

• When you are subtracting a negative and a positive integer there is a decrease in value

• When you are subtracting two negative integers there is an increase in value

Examples:

(+2) - (+10) = -8

(+5) - (-2) = +7

(-3) - (+6) = -9

(-5) - (-6) = +1

Multiple Choice

(+5) - (+3)

• -2

• +8

• +2

• -8

Multiple Choice

(+7) - (-2)

• +9

• +5

• -5

• -9

Multiple Choice

(-6) - (+4)

• +10

• -2

• +2

• -10

Multiple Choice

(-3) - (-4)

• +1

• +7

• -7

• -1

Rules for Multiplying Integers

• When you multiply two numbers with the SAME sign you will get a positive answer

• When you multiply two numbers with DIFFERENT sings you will get a negative answer

Multiple Choice

(-2)(-2)

• -4

• +4

Multiple Choice

(+4)(+6)

• +24

• -24

Multiple Choice

(-5)(2)

• -10

• +10

Rules for Dividing Integers

• The rules for dividing integers are the same as multiplying integers

This graphic is a great tool for helping you to remember the rules when it comes to multiplying and dividing integers.

Multiple Choice

 $10\ \div\ 2$   

• 5

• -5

Multiple Choice

 $-24\ \div\ 6$  

• +4

• -4

Multiple Choice

 $-32\ \div\ 8$  

• -4

• +4

Multiple Choice

 $-72\ \div\ 8$  

• -9

• +9

Integer Operations

Today, we are reviewing how to add, subtract, multiply and divide integers.

Adding Integers

• When you are adding two positive integers there is an increase in value

• When you are adding a positive and a negative integer there is a decrease in value

• When you are adding a negative and a positive integer there is an increase in value

• When you are adding two negative integers there is a decrease in value

Examples:

(+2) + (+10) = +12

(+5) + (-2) = +3

(-3) + (+6) = +3

(-5) + (-6) = -11

Multiple Choice

(+4) + (+2)

• -6

• +6

• 2

• -2

Multiple Choice

(+5) + (-2)

• +3

• +7

• -7

• -3

Multiple Choice

(-4) + (+5)

• -9

• -1

• +9

• +1

Multiple Choice

(-4) + (-6)

• -10

• +2

• -2

• +10

Subtracting Integers

• When you are subtracting two positive integers there is a decrease in value

• When you are subtracting a positive and a negative integer there is an increase in value

• When you are subtracting a negative and a positive integer there is a decrease in value

• When you are subtracting two negative integers there is an increase in value

Examples:

(+2) - (+10) = -8

(+5) - (-2) = +7

(-3) - (+6) = -9

(-5) - (-6) = +1

Multiple Choice

(+5) - (+3)

• -2

• +8

• +2

• -8

Multiple Choice

(+7) - (-2)

• +9

• +5

• -5

• -9

Multiple Choice

(-6) - (+4)

• +10

• -2

• +2

• -10

Multiple Choice

(-3) - (-4)

• +1

• +7

• -7

• -1

Rules for Multiplying Integers

• When you multiply two numbers with the SAME sign you will get a positive answer

• When you multiply two numbers with DIFFERENT sings you will get a negative answer

Multiple Choice

(-2)(-2)

• -4

• +4

Multiple Choice

(+4)(+6)

• +24

• -24

Multiple Choice

(-5)(2)

• -10

• +10

Rules for Dividing Integers

• The rules for dividing integers are the same as multiplying integers

This graphic is a great tool for helping you to remember the rules when it comes to multiplying and dividing integers.

Multiple Choice

 $10\ \div\ 2$   

• 5

• -5

Multiple Choice

 $-24\ \div\ 6$  

• +4

• -4

Multiple Choice

 $-32\ \div\ 8$  

• -4

• +4

Multiple Choice

 $-72\ \div\ 8$  

• -9

• +9

Integer Operations with Word Problems

​

Adding Integers

• SAME SIGNS: Keep the same sign in your answer and ADD

• Ex: 3 + 4 =7

• Ex: (-3) + (-4) = -7

• DIFFERENT SIGNS: Keep the sign of the number with the larger magnitude and SUBTRACT

• Ex: 7 + (-3) = 4

• Ex: (-7) + 3 = -4

Multiple Choice

5 + 4

• 20

• 1

• 9

Multiple Choice

(-9) + 2

• -11

• -7

• -18

• 11

Multiple Choice

5 + (-5)

• 0

• 10

• 1

• -10

Subtracting Integers

• Rewrite any subtraction problem using the rule: "Keep, change, change"

• Ex: 3 - 5 is rewritten as 3 + (-5)

• Then use the addition rule that applies.

• Ex: 3 - 5 becomes 3 + (-5) = -2

Multiple Choice

Rewrite 9 - (-6) as an addition problem

• 9 + 6

• -9 + 6

• 9 + (-6)

• 9 - (-6)

Multiple Choice

3 - (-7)

• -4

• -10

• 4

• 10

Multiple Choice

-18 - 7

• -25

• -11

• 11

• 25

Multiplying and Dividing Integers

Multiple Choice

 $2\div2$  

• 1

• 0

• 4

Multiple Choice

 $\left(-9\right)\times\left(-3\right)$  

• -11

• -6

• -27

• 27

Multiple Choice

 $\left(-11\right)\times3$  

• -8

• 8

• -33

• 33

Multiple Choice

 $-12\div6$  

• 2

• -2

• 6

• -6

Multiple Choice

 $\left(-30\right)\div\left(-6\right)$  

• -36

• 36

• -5

• 5

Poll

How do you feel about integer operations?

• I still need help

• I could use a little more practice

• I get it

• I'm ready for a challenge

Multiple Choice

The temperature on Sunday was -15^o C. The next day, the temperature went down 12 degrees. What was the temperature the next day?

• -27

• 27

• -3

• 3

Multiple Choice

A submarine was 52 ft. below sea level. It ascended 38 ft. toward the surface. What is the depth of the submarine?

• 90 ft below sea level

• 26 ft below sea level

• 14 ft below sea level

Multiple Choice

On a certain day, the temperature changed at a rate of -2 degrees per hour. How long did it take for the total change in temperature to be -14 degrees?

• 7 hours

• 5 hours

• -7 hours

• -5 hours

Multiple Choice

Lindsay owes 3 people $5 each. Which value shows her total debt?

• $15

• $2

• -$15

• -$8

Integer Operations - STAAR Questions

Mr. Cam's Math Classroom

Multiple Choice

Answer?

• A

• B

• C

• D

Open Ended

What is your answer?

Open Ended

What is your answer?

Open Ended

What is your answer?

Integer Operations Review Part 2

​

Operations with Integers

OBJ: To Multiply, Divide, Add, and Subtract Integers

Adding Integers

If the integers have the same signs, keep the sign and add the numbers.

If the integers have different signs, subtract the numbers and use the sign of the larger absolute value

Multiple Choice

When ADDing two integers with the SAME SIGN...

• Add and keep the same sign.

• Add and change the sign.

• Subtract and keep the same sign.

• Subtract and change the sign.

Multiple Choice

7 + (-13)

• -6

• 6

• -20

• 20

Fill in the Blank

$$24+\left(-24\right)=?$$  

Fill in the Blank

$$3\ -5=?$$  

Fill in the Blank

$$4\ +\ \left(-10\right)=\ ?$$  

Fill in the Blank

$$-7+-2=?$$  

Subtracting Integers

Rewrite the subtraction as addition of the opposite using KEEP - CHANGE - CHANGE then use your addition rules for integers.

Example 1: 3 - (-7) becomes 3 + 7 and 3 + 7 = 10

Example 2: 9 - 4 becomes 9 + (-4) and 9 + (-4) = 5

Multiple Choice

Subtracting a negative is the same thing as...

• Becoming more negative

• Adding a positive

• Becoming 0

• Impossibility

Multiple Choice

3 - 11

• -8

• 8

• -14

• 14

Multiple Choice

A team gains 20 yards.  Then they lose 7 yards.  Find the sum. 

• 13 yards
• 27 yards
• -13 yards 
• -27 yards 

Multiple Choice

Roger owes his mom $5.  He borrows another $6 from her.  How much does Roger owe his mother? 

• $11
• $1
• $6
  $6

Multiple Choice

7 - (-4) =

• 11

• -11

• 3

• -3

Multiple Choice

-1 - 5 =

• 4

• 6

• -6

• -4

Multiplying and Dividing Integers

If the two integers have the same signs, the answer will be positive!

If the two integers have different signs, the answer will be negative!

Multiple Choice

-5 x 9

• -45

• 45

• 4

• yellow

Multiple Choice

4(-6)

• 24

• -24

• -10

• 10

Multiple Choice

-1(-9)

• -9

• 10

• 9

• -10

Multiple Choice

12(-2)

• -24

• 24

• -14

• 14

Multiple Choice

-32 / 8

• 4

• -4

• 256

• -256

Multiple Choice

• 6
• -6
• 7
• -7

Multiple Choice

• 4
• -4
• 64
• -46

Multiple Choice

• -4
• 4
• 16
• -16