Download Notes Packet for Positive/Negative Number and Adding Integers

Notes Packet for Positive/Negative Number and Adding Integers
Negative numbers
Positive numbers
Number line counts up from zero going right. Number line counts down from zero going
__left___.
Numbers to the right of 0 are _positive__; Numbers to the left of 0 on the number line are
_negative__, zero is neither _positive__or __negative_____.
Mark the following numbers on the number line above:
7, -2.5, ½ , -9.5
Two numbers that are the same distance from zero but in opposite directions are called
opposites.
Example: -6 and +6 are opposites, + 3.5 and -3.5 are opposites.
Name a pair of opposites: _______________
Opposite numbers have the same _value_____, just opposite _signs____. The sum of any
number and its opposite is _zero_____. Example: 6 + (-6) = 0
Work:
-8 + 8 = ______
4 + (-4) = ______
-0.3 + 0.3 = ______
The _sign____ of a number refers to whether it is positive _ or _negative______ (“+” or “-“).
The sign____ of 32 is “+” or positive______. The sign or -5 is “-“ or _negative______.
What is the sign of?:
-5 ____
7 _____
3 ____
-4.2 ____
|-10| = 10
|8| = 8
Absolute Value_ is the distance a number is from zero. Absolute value is always a
_positive_________ number. Specify absolute value by putting number between 2
_vertical________ bars. Absolute value of x is shown as |x|. Think of it as “How much is it
worth?” (The $20 dollars you owe someone is worth the same amount as the $20 in your piggy
bank.) or “What is the distance?” (If you are two floors below ground, you are the same distance
from ground level as if you are two floors above ground.)
What is the absolute value of the following:
|-7| = _____
|9| = _____
|-6.5| = _____
|4.2| = ______
If someone is standing at -9 on the number line and they walk to 6 on the number line, how far
did they travel? |-9| + |6| = 9 + 6 =15
If someone is standing at -4 on the number line and they walk to 9 on the number line, how far
did they travel?
|-4| + |9| = _______
INTEGERS
Integers are whole numbers (positive, negative, zero). Fractions, mixed numbers and decimals
are not integers. Note to the wise: BE ABLE TO DEFINE AN INTEGER!
The numbers on a telephone keypad are integers. The number of kids in each class in the school
is an integer.
Circle the integers:
9
-7
6.3
-4.5
3½
0
274
-1
75.2
Comparing Integers
Less
Greater
Integers that are farther to the right on the number line are greater than those to their left.
A positive integer is always greater than a negative integer (1 > -100)
The farther to the left a negative integer is from zero, the smaller its value (-1 > -100).
Fill in the blank with > or < to make the statement true:
9 ___ 11
5 ___ 4
-3 ___ 7
-5 ___ -9
20 ___ -25
3 ___ -7
-4 ___ -3
1 ___ -100
Adding Integers
You can show the sum of two integers by using arrows on a number line. When we add
a positive number, we move right on the number line. When we add a negative number
we move left on the number line. Careful: This is different than adding absolute value.
Here the sign gives us direction, left or right.
Adding two positive integers:
Find the sum of (+5) and (+3). Starting at zero, first move 5 units to the right, then 3
units to the right.
+5
+3
Therefore (+5) + (+3) = (+8). (Remember, positive integers are most often written
without positive signs: 5 + 3 = 8. The sum of two positive integers is positive.
Students, please use a straight edge to draw your arrows.
Show on the number line below the sum of (+2) and (+4), then write out the number
sentence:
_________ + ________ = ________
Adding two negative integers:
Find the sum of (-5) and (-3). Starting at 0, first move 5 units to the left, then 3 units to
the left.
-3
-5
Therefore, (-5) + (-3) = -8. You can add two negative integers, but because you are
moving in the opposite direction, the sum is negative. The sum of two negative integers
is negative.
Show on the number line the sum of (-4) and (-2), then write out the number sentence.
________ + _______ = _______
Adding a positive integer and a negative integer:
Add (+7) and (-4). Step 1) move 7 units to the right. Step 2) move 4 units to the left.
Step 2) -4
Step 1)
+7
Therefore (+7) + (-4) = ____.
Add (-10) + (+8):
Step 2) +8
Step 1)
-10
Therefore, (-10) + (+8) = _____
Add (+5) and (-7):
-7
+5
Therefore, (+5) + (-7) = ____
Add (-3) + (+9):
+9
-3
Therefore (-3) + (+9) = ______
Add on the following number line (-4) + (5), then write the number sentence:
_______ + _______ = ________
Remember we said before that a number and its opposite add up to zero. When you add a
positive integer with a negative integer, which ever number is smaller in absolute value cancels
out that same number from the number of greater absolute value. That is, when we add (-4) +
(5), the 4 negative units cancel out 4 of the positive units, and we are left with (-1).
Please pull out your set of Algebra Tiles. Each yellow square is marked “+1” and represents a
positive 1 integer. Each red square is marked “-1” and represents a negative 1 integer.
If we add (-4) + (5), we lay out 4 red tiles to which we add 5 yellow tiles. Match up each red on
top of a yellow. Each red/yellow pair adds up to zero and can be removed. We are left with one
yellow tile.
(-4) + (5) = (1).
Use tiles to work out the following problems:
(-8) + (6) = ____
(7) + (-3) = ______
(10) + (-6) = ______
(-2) + (5) = ____
(2) + (6) = ______
(1) + (-3) = ______
(-3) + (-4) = ______
(9) + (-7) = _______
What is the rule for adding a positive integer with a negative integer?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
____________________________
Stations Packet
Station 1: Computers set to this website:
http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html. Works like Algebra Tiles.
Follow “Instructions in upper right hand corner.”
Work 4 problems. Write them here.
_______ + ________ = ________
_______ + ________ = ________
_______ + ________ = ________
_______ + ________ = ________
Station 2: Money Station: Banker steps you through income and payment steps. What
is your financial situation along the way? Write out the math sentences and solve.
You start with $50 savings. Good for you.
___________
You dogsit for a week and get paid $100. Cool! Feeling rich!
___________
Your balance:
Your balance:
Got to have that $200 itouch. Mom charges it. You pay her what you have now and owe
her the rest.
Your balance:
___________
You broke your sister’s itouch. Mom says you must pay for it. Your balance:
___________
You babysit every Friday and Saturday night for a month and make $300. Your balance
after paying mom what you owe her: ______
Station 3:Thermometer: Large wooden, standing thermometer with Start Temperature
Clip and End Temperature Clip. Be careful to use the right temperature scale!
1) One cold morning in DC, the temperature is -6°C, but rises by 18°C to get to the
afternoon high. What is the afternoon high temperature? Mark start and end temperatures
on the thermometer and write out the number sentence:
(-6) + (18) = _____
2) One afternoon in NYC, it is a lovely 68° F when a cold front moves through and
drops the temperature 30°F. What does the temperature get down to? Mark start and end
temperatures on the thermometer and write out the number sentence:
(68) + ____ = _____
3) One day in January in the Mojave Desert, the temperature reaches 18°C during the
day but drops to -6°C that night. How much of a drop is that? Mark start and end
temperatures on the thermometer and write out the number sentence:
______ + ______ = ______
4) The low temperature in Fairbanks, AL in January 2010 was -41° F recorded on
January 12th. The high temperature for that month was 58° F higher than the low and
was recorded on January 7th. What was the high temperature for that month in
Fairbanks? Mark start and end temperatures on the thermometer and write out the
number sentence:
______ + ______ = ______
Station 4) Elevation: Large standing poster with picture of a mountain next to the ocean
(Sierra Nevada Mountains next to the Mediterranean Ocean in Spain—from high
elevations, look across the Mediterranean to Africa). One the side there is a ruler
marking the elevation (11,000 ft. to the top of Mt. Mulhacen, sea –level and the depth of
the Mediterranean (average 5000 ft).
Use Start Clip and End Clip to mark the problems. Write out the math sentences and
solve.
How much of an elevation change is there from the bottom of the Mediterranean to the
top of Mulhacen? (-5000’) + _____ = (11,000’)
How much of a drop is there between the mid-way station on Mulhacen (marked on
poster) and the submarine in the ocean (also marked on poster)?
_____ + (-____) = _____
A drop of 7000’ from the summit of Mulhacen gets you to what station?
_________
_______ + (-7000) = _______
How far is the seagull above the octopus on the poster?
______ + _____ = ______
Station 5: Laptop playing scene from movie Stand and Deliver where new teacher,
Jamie Escalante, teaches bright, but previously under-taught student how to add positive
and negative numbers by envisioning digging holes in the sand. “Fill up the holes,” he
tells him. Students watch scene then use Duplo board filled completely with one layer of
duplos to represent untouched sand (zero). Student takes away duplos (buckets of sand)
to represent negative numbers, and then fills them in by adding duplos (buckets of sand)
representing positive numbers.
Start with 3 Duplos removed from the board. Add 5 Duplos first filling in the holes.
(-3) + 5 = ______
Now add (-8) Duplos. _____ + (-8) = _____
Add 10 Duplos :
______ + ______ = ______
Homework: Addition of Integers (Positive and Negative)
Define an
Integer:_______________________________________________________
_____________________________________________________________
_____________________________________________________________
_________________
Fill in the blanks with < or > to make the number sentence true:
1) -100 ____ 1
2) 70 ____ -75
3)
-3 ____ 2
4)
5 ____ -4
Complete the number sentence to make it true.
5) (-7) + (7) = ______
6)
(-3) + (4) = ______
7)
(9) + (-15) = ______
8) (6) + (12) = ______
9) (-7) + (-4) = ______
10)
(-20) + (11) = ______
Complete the following word problems. You will be given one point for a
drawing showing the problem, one point for a correct math sentence, and
one point for the correct answer.
11)
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The
Dead Sea, the lowest elevation, is 1,312 feet below sea level. What vertical distance
would be traveled going between these two elevations?
12) In Buffalo, New York, the temperature was -14°F in the morning. If the temperature
dropped 7°F, what is the temperature now?
13) A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its
new position?
14) If I am $570 in debt, but I get paid $1000 by my employer and pay off my debt, how
much money will I have left? (Picture can just be a number line).