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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)
