Week 10 -Integers

Week 10 -Integers

Review of Adding and Subtracting & Introduction to multiplying and dividing.

Lesson 1

Review of Adding Integers

Adding Integers

Three Methods

Using Integer Tiles

Use integer tiles to evaluate 4 + (-3)

• First term is 4. Draw 4 shaded tiles.

• The second term is -3. Draw three unshaded tiles. Count the Zero Pairs.

• One positive tile remains. 

Adding Integers using a number line. Use a number line to solve 4 + (-5)

• Draw a number line. Place the pencil at the value of the FIRST term.

• Move the pencil the number of places indicated by the value of the second term. The answer is where the pencil stops.

Using Calculations - Two Rules to Follow

• Rule 1 - If the signs the same on the integers, add the values and keep the same sign.

• Rule 2 - If the signs are different, subtract the smaller value from the larger value. Place the sign of the larger value in front.

Poll

How do you feel about adding integers?

• GREAT!

• Okay

• Meh....

• Need to work on it some more

Multiple Choice

Which addition problem matches the numberline?

• -13 + -4

• -4 + -9

• -9 + -4

• -13 + 13

Multiple Choice

3 + -7

• 10
• 4
• -10
• -4

Multiple Choice

-2 + 4 

• -2
• 2
• 0
• -4

Multiple Choice

What do you do when you are adding integers with different signs? 

• (-) and keep sign of smaller number
• (-) and keep sign of larger number
• (+) and keep sign of smaller number number
• (+) and keep sign of larger number 

Multiple Choice

-9 + (-5)

• -14

• 14

• -4

• 4

Multiple Choice

Which addition expression matches the problem shown on the number line?

• 3 + -4
• -4 + 3
• 7 + -4
• -4 + 7

Multiple Choice

Which integer is the opposite of -8?

• 8
• -8
• 81

Multiple Choice

Which integer is the opposite of 12?

• 21
• 12
• -12

Multiple Choice

(-12) + 7

• 5
• -5
• 19
• -19

Multiple Choice

(-10) + (-7)

• -17
• 17
• 3
• -3

Lesson 2

Review of Subtracting Integers

Poll

How comfortable I am with subtracting integers.

• Easy!

• A bit challenging but okay.

• I need more practice.

• HELP!

Subtracting Integers

• Three Methods

Using integer tiles. Solve (+4) - (+3)

• Draw 4 shaded tiles to represent +4

• Subtract the number of tiles equal to the second term.

• Second term is +3 so take away 3 tiles.

• (+4) - (+3) = (+1)

Using Number Lines. Solve (+4) - (+3)

• Place pencil on the second term. (+3)

• Move the pencil to the point representing the first term. (+4)

• Determine the length and direction of the movement.

• 
  

USING CALCULATIONS. Solve (+4) - (+2)

• KEEP - CHANGE - CHANGE RULE

• Keep the first number the same. Keep (+4)

• Change subtraction to addition. +

• Change second vale. (+2) becomes (-2)

Multiple Choice

During the week Jimmy spent $45 eating out, gained $55 mowing lawns and spent $15 on gas. What was Jimmy's change in dollars at the end of the week?

• $5
• - $5
• - $15
• $15

Multiple Choice

The football team gained 8 yards on the first play. Lost 6 yards on the next. Gained 3 yards on the third play and lost 12 yards on their final play. What was their final change in yardage after the four plays?

• 7
• -7
• 29
• -13

Multiple Choice

I had $-25 in my account.  I deposited $70 into my account.  How much money do I have now?

• $105
• $-45
• $45
• -$105

Multiple Choice

The temperature on a cold winter day starts out at 10 degrees, but it drops rapidly 24 degrees due to a strong cold front moving in.  What is the current temperature?

• 14
• 34
• -14
• -34

Multiple Choice

19 - (-19)

• 0
• 36
• 26
• 38

Multiple Choice

-7 - 2

• -9
• 9
• 5
• -5

Multiple Choice

How would -9 -(-5) look like as an addition problem?

• -9 + (-5)
• 9 + 5
• -9 + 5
• 9 + (-5)

Multiple Choice

 $2-3$  

•  $5$  

•  $-5$  

•  $1$  

•  $-1$  

Multiple Choice

 $-2-8$  

•  $-10$  

•  $-6$  

•  $10$  

•  $6$  

Multiple Choice

 $-7-5$  

•  $-2$  

•  $-12$  

•  $2$  

•  $-2$  

Multiple Choice

 $-3-\left(-2\right)$  

•  $1$  

•  $-1$  

•  $5$  

•  $-5$  

Multiple Choice

What do you do when you are adding integers with different signs? 

• (-) and keep sign of smaller number
• (-) and keep sign of larger number
• (+) and keep sign of smaller number number
• (+) and keep sign of larger number 

Poll

How I feel about adding and subtracting integers.

• Great!

• Good.

• Meh.

• Can we work on it more?

Lesson 3 - Multiplying Integers

• You already know:

• Integers are the set of positive and negative whole numbers and zero.

Multiplying Integers

• Watch KHAN Academy Video. Posted in Classroom

• 
  

Multiplying Integer Rules

• When multiplying integers with the same sign (Two positives OR Two Negatives) insert a POSITIVE integer sign in front of the product.

• When multiplying integers with the different signs (one positive and one negative), multiply the values and insert a negative integer sign.

 Example (+4) x (+6)

• Calculate the PRODUCT of (+4) and (+6). 4x6 = 24

• Insert a positive integer sign in front of the product. 

Example: (-7)(5)

• Multiply. 7x5=35

• Insert a negative sign.

• (-7)x(5) = (-35)

Multiple Choice

Positive x Negative =

• Positive
• Negative

Multiple Choice

Positive x Positive =

• Positive
• Negative

Multiple Choice

When multiplying or dividing a NEGATIVE and NEGATIVE number your result will be...

• POSITIVE
• NEGATIVE
• DEPENDS ON WHICH NUMBER IS LARGER.

Multiple Choice

-8(0)=

• -8

• 8

• 0

• -0

Multiple Choice

-7(10)=

• 70
• 700
• -70
• -700

Multiple Choice

Which expression DOES NOT have a product of −18?

• −2 ∗ −9
• −6 ∗ 3
• −3 ∗ 6
• −9 ∗ 2

Multiple Choice

The price of jeans was reduced $6 per week for 7 weeks.  By how much did the price of the jeans change over the 7 weeks?

• 42
• -42
• 20
• -20

Multiple Choice

The temperature dropped 3 degrees every hour for six hours.  How much did the temperature drop in all?

• -18
• 9
• 18
• -9

Multiple Choice

(-9)(-8)

• -72
• 72
• 81
• -81

Multiple Choice

If I have a positive multiplied with a positive, what will the answer be?

• Positive 
• Negative 

Multiple Choice

If I have a negative multiplied with a positive, what will the answer be?

• Positive 
• Negative 

Lesson 3 - Dividing Integers

• Two Rules

Rules for dividing integers.

• Rule 1 - when dividing integers with the same sign (two positives or two negatives), divide the integers and place a positive integer sign in front of the QUOTIENT.

• Rule 2 - When dividing integers with different signs (one positive and one negative), divide the integers and place a negative integer sign in front of the QUOTIENT.

Example: 

 $\left(+24\right)\div\left(+6\right)$  

• Divide the value of the integers.

•  $24\div6=4$  

• Insert a (+) sign in front.

• Answer = (+4)

Example: $\left(+28\right)\div\left(-7\right)=$  

• Divide the values of the integers.

•  $28\div7=4$  

• Insert a negative sign in front. 

• Answer is (-4)

Multiple Choice

-30/-10=

• -30
• -3
• 3
• 30

Multiple Choice

-24 ÷ (-8)

• 32
• -3
• -16
• 3

Multiple Choice

-18 ÷ (-2)

• 9
• -9
• -20
• 10

Multiple Choice

-30/-10=

• -30
• -3
• 3
• 30

Multiple Choice

Flora made 3 withdrawals of $75 each from her bank account.
What was the overall change in her account?

• -$225
• $225
• -$25
• $25

Multiple Choice

The football team lost 8 yards on every play for 5 plays. Which integer shows the total number of yards the team has lost? 

• 40
• -40
• 3
• -3

Multiple Choice

If the temperature drops 5 degrees every hour for 9 hours, which integer represents the change in temperature? 

• 14
• -14
• 45
• -45

Multiple Choice

44/-4=

• 11
• -8
• -11
• -1/11

Multiple Choice

When multiplying or dividing a NEGATIVE and POSITIVE number your result will be...

• Positive
• Negative
• Depends on which is bigger.

Multiple Choice

-20/5=

• -4
• 4
• -100
• 100

Multiple Choice

When multiplying or dividing a NEGATIVE and NEGATIVE number your result will be...

• POSITIVE

• NEGATIVE

• DEPENDS ON WHICH NUMBER IS LARGER.

Poll

How do you feel about multiplying and dividing integers?

• Great!

• Okay. I would like more practice.

• Help