adding integers ppt

Do Now

Complete the Do Now questions 1-5.

Herzog

Lesson 14a

Math Procedures

Monday October 5, 2009

WELCOME TO …

Ms. Herzog’s

IntegersLesson!

What is an integer???

Any whole number. It can be positive or negative.

ANSWER

Adding Integers!

Examples:

2, -5, 245, 0, 9, -1,399

How do we add positive and negative integers?

Think in terms of number chips

Example: We can think of 4 as four positive chips

+4

How do we add positive and negative integers?

Think in terms of number chips

Another example: We can think of -3 as three negative chips

-3

How do we add positive and negative integers?

Think in terms of number chips

Another example: We can think of -8 as eight negative chips

-8

How do we add positive and negative integers?

Think in terms of number chips

Another example: We can think of 6 as six positive chips

+6

Let’s do an example!

Use number chips!

4 + 7

ANSWER+4

+7 11

Let’s do an example!

Use number chips!

-2 + 5

ANSWER

+5 3-2

One negative chip and one positive chip cancel!

Let’s do an example!

Use number chips!

3 + (-5)

ANSWER+3

-2One negative chip and one positive chip cancel!

-5

Let’s do an example!

Use number chips!

-8 + 5

ANSWER

-3One negative chip and one positive chip cancel!

-8+5

Let’s do an example!

Use number chips!

-3 + (-5)

ANSWER

-8There are no chips to cancel!

-5-3

-3 + (-8)

-11ANSWER

-3

-8

Number Chips!

4 + (-5)

-1ANSWERNumber Chips!

+4-5

-3 + 9

6ANSWERNumber Chips!

-3+9

Classwork 14A

• Work on problems 1-10 from the handout

Monday October 5, 2009

Homework: Adding Integers Handout 1-15

HomeworkMath Procedures Herzog

Lesson 14a

Do Now

Complete questions 1-5.

Herzog

Lesson 14b

Math Procedures

Tuesday October 6, 2009

Let’s Continue…

Ms. Herzog’s

IntegersLesson!

•So the chip method works fine for adding and subtracting smaller numbers. (e.g. -4 + 7 = 3)

•What if we need to add larger numbers? (e.g. 65 + (-34))

•Writing out 99 chips would not make sense!

One way to solve these problems:

1. If the numbers you are adding have different signs,

2. Subtract the smaller number from the larger number, then

3. Determine which number is larger

4. The sign (positive or negative) of the answer will be the sign of the larger number

Do the numbers have the same sign?

Yes

Add the numbers together

No

Subtract the smaller number from the larger

number

Is the positive or negative number

larger?

Answer = What sign?

+ is largerFinal answer is

positive

- is larger

Final answer is negative

If the

Beginning Signs are…

Then the

Calculation we do is…

The End Sign of our answer is…

Same AddAdd Same

Different SubtractSubtract The sign of the

Larger number

28 + 631. We are adding and the numbers have the same signs

2. Add:

28 + 63 = 91

ANSWER:

91

(-12) + 341. We are adding and the numbers have different signs

2. Subtract:

34 – 12 = 22

3. 34 is larger than 12

4. Since 34 is larger, and positive, the answer will be positive

ANSWER:

22

24 + (-42)1. We are adding and the numbers have different signs

2. Subtract:

42 – 24 = 18

3. 42 is larger than 24

4. Since 42 is larger, and negative, the answer will be negative

ANSWER:

-18

-64 + 391. We are adding and the numbers have different signs

2. Subtract:

64 – 39 = 25

3. 64 is larger than 39

4. Since 64 is larger, and negative, the answer will be negative

ANSWER:

-25

83 + (-46)1. We are adding and the numbers have different signs

2. Subtract:

83 – 46 = 37

3. 83 is larger than 46

4. Since 83 is larger, and positive, the answer will be positive

ANSWER:

37

57 + (-74)1. We are adding and the numbers have different signs

2. Subtract:

74 – 57 = 17

3. 74 is larger than 57

4. Since 74 is larger, and negative, the answer will be negative

ANSWER:

-17

-132 + 2311. We are adding and the numbers have different signs

2. Subtract:

231 – 132 = 99

3. 231 is larger than 132

4. Since 231 is larger, and positive, the answer will be positive

ANSWER:

99

Classwork 14B

1. 15 + (-7)2. -7 + 153. -10 + (-18)4. -34 + 175. 73 + (-25)6. -45 + (-44)7. 55 + (-75)

8. 99 + (21)9. 82 + (-19)10.(-35) + 1711. 22 + (-111)12. 64 + (-73)13. 254 + (153)14. (-432) + (321)

Homework: Adding Integers Handout 1-15

HomeworkMath Procedures Herzog

Lesson 14b

Tuesday October 6, 2009

Subtracting

IntegersLesson!

Subtracting Integers

Let’s start with signs

What is the sign on:

17

Positive

Subtracting Integers

Let’s start with signs

What is the sign on:

-68

Negative

Subtracting Integers

Let’s start with signs

What is the sign on:

5

Positive

Subtracting Integers

Let’s start with signs

What is the sign on:

-22

Negative

Subtracting Integers

Now let’s work on opposites

What is the opposite of:

12-12

Subtracting Integers

Now let’s work on opposites

What is the opposite of:

-4545

Subtracting Integers

Now let’s work on opposites

What is the opposite of:

-99

Subtracting IntegersTo subtract

integers:

Add the opposite of 11

9 - 11

9 + (-11)

Evaluate using integer addition 9 + (-11)

= -2

Subtracting IntegersTo subtract

integers:

Add the opposite of 8

-6 - 8

-6 + (-8)

Evaluate using integer addition -6 + (-8) =

-14

Subtracting IntegersTo subtract

integers:

Add the opposite of -9

-9 – (-9)

-9 + (9)

Evaluate using integer addition -9 + (9) = 0

Subtracting IntegersTo subtract

integers:

Add the opposite of -1

5 – (-1)

5 + (1)

Evaluate using integer addition 5 + (1) = 6

Subtracting IntegersTo subtract

integers:

Add the opposite of 10

-4 – (10)

-4 + (-10)

Evaluate using integer addition -4 + (-10)

= -14

Subtracting IntegersTo subtract

integers:

Add the opposite of -8

2 – -8

2 + 8

Evaluate using integer addition 2 + 8 = 10

Subtracting IntegersTo subtract

integers:

Add the opposite of -5

-3 – (-5)

-3 + 5

Evaluate using integer addition -3 + 5 = 2

Subtracting IntegersTo subtract

integers:

Add the opposite of 21

12 – 21

12 + (-21)

Evaluate using integer addition 12 + (-21)

= -9

Subtracting IntegersTo subtract

integers:

Add the opposite of 5

and 2

-3 – 5 – 2

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

Evaluate using integer addition = 10

Classwork

1. 18 – (-48)

2. 0 – (-14)

3. 19 – (-10)

4. -20 – 32

5. -1 – (-31)

6. -22 – (-9)

7. 39 – (-13)

8. 2 – (-31)

9. 0 - 14

10.42 – 2711.-43 – 1912.3 – (-18)13. -9 – (-39)14.3 – (-24)15. -47 – 4816.-45 – (-33)17. 2 – (-8)18. -14 – (-50)