Transcript What is an integer?

What is an integer?
Integers
 Integers: all positive and negative whole numbers and 0
 Opposites: integers that are the same distance from
zero on a number line
Comparing Integers: The greatest number is the
one furthest to the right on the number line.
 Which is greater -7 or -2?
Greater Than
(Increasing)
Less Than
(Decreasing)
-8
-6
-4
-2
0
2
Comparing Integers
 Which is greater -5 or -10?
 Which is greater 2 or 5?
 Which is greater -3 or 7?
Comparing Integers Card Game
 You will play the game with a partner.
 Each person will receive 20 cards and each pair
will get a page to record the results
 Each person will flip over the top card at the
same time and the person with the highest
integer wins!
 Record the numbers and a greater than or less
than symbol on your page
Warm-Up
 Use the data set to answer the following
questions: 6, 5, 14, 9, 7, 12, 17
 What is the median?
 What is the mean?
 What is the mode?
What are some real world examples of
positive and negative integers?
Positive Integers
Negative Integers
 a bank deposit
 a bank withdrawal
 an elevation above sea
 an elevation below sea
level
 a rise in temperature
level
 a drop in temperature
What does zero represent?
 A bank deposit or withdrawal
 Having no money in your bank account
 An elevation above or below sea level
 Being at sea level
 A rise or drop in temperature
 No change in temperature
Think Fast!
 Which point represents -7?
 What integer is represented by point D?
 Which 2 points represent opposites?
A
B
 
-10
D
E
 

C
-5
0
5
Absolute Value
 The absolute value of a number is its distance from
zero.
 Distance is always positive!!
 Absolute value is represented by 2 lines surrounding
the number.
-2 = 2
-2 and 2 are
both a distance
of 2 units from
zero!
2 = 2
Magnitude
 You can use absolute value to describe the magnitude
of a situation.
 Hannah wrote a check for more money than she has in
her bank account. The balance in her account is now
-$60. How much money does Hannah owe the bank?
-60
Hannah owes the bank $60.
Less than or greater than
 A team of mountaineers climbed to the summit of Mt.
Everest. The temperature at the summit is less than -15°F.
Describe how many degrees Fahrenheit below zero the
temperature is.
 How could you graph the temperature it could have been at the
summit on a number line?

-20
-15
-10
-5
Example
Lori’s checking account has a balance of less than -$200.
Which of the following statements is true about how
much money Lorraine owes the bank?
A. She owes exactly $200.
B. She owes exactly -$200.
C. She owes less than $200.
D. She owes more than $200.
Warm-Up
 There are 15 students in a math class and 6 of the students
are boys. What is the ratio of boys to girls in simplest form?
 Abigail is going shopping this weekend because Target is
having a 30% off sale. She is buying a pair of sunglasses that
cost $14. How much will she have to pay?
 Write down the following definitions
 Bivariate Data: data for two variables or two types of related
data; example: ice cream sales versus the temperature of the
day. The two sets of data are ice cream sales and temperature.
 Univariate Data: just one set of data; example: temperature
The Opposite of…
 If you see a number written like, -(-5) that means the
opposite of -5 which would be 5.
 The same if true with an absolute value sign.
- -2 = -2
 What does –(-56) equal?
 What does -|5| equal?
Rational Numbers
 Rational Number: a number that can be expressed as the
ratio of two integers in the form a/b where b is not equal to
zero.
 Rational numbers can be positive or negative.
 Integers, fractions, mixed numbers, percents, terminating
decimals, and repeating decimals
 http://www.brainpop.com/math/numbersandoperations/rati
onalandirrationalnumbers/
Plotting Rational Numbers
 Plot the rational numbers ⅗ and -⅖ on a number line.
1. What intervals do you need to use on your number line?
2. Plot your points
0
What do the points represent?
A
-1
B
C
D
0
 What value does each of the points represent?
1
More Practice
B
A
-2
-1
C
0
1
 What are the intervals of this number line?
 What values do the points represent?
2
Warm-Up
 The trip costs at least $200. Write an inequality to represent the
situation.
 What is the surface area of the following shape? Use the formula
SA = 2(wl) + 2(hl) + 2(hw)
Quick Review!
 Convert Fraction to Decimal: Top dog goes in the
house (divide)
 What is ⅘ as a decimal?
 Convert percent to decimal: move the decimal to the
left 2 times!
 What is 25% as a decimal?
Which of these rational numbers is the
greatest?
Ordering Rational Numbers
 Khan Academy:
http://www.youtube.com/watch?v=VZOHWaw5dqM&edufil
ter=fU9N1e_9JCp4rAvc4PaVkQ
 To put rational numbers in order, you need to plot them on
a number line!
 Or you can turn your numbers into decimals because they
are the easiest to compare.
 Put these numbers in order from least to greatest:
0.5, ¾, -1½, |0.8|
 Correct order: -1½, 0.5, ¾, |0.8|
Example
 #8 on your packet!
 Put the following numbers in order
from least to greatest:
-3⅓, 3.3, -3¾, 3.5
Warm-Up
 Mary is 3 years more than 5 times as old as Paula. If p
represents Paula’s age, write an expression to represent
Mary’s age.
 Mrs. Perry hires a landscaper that charges 15 dollars per hour.
The landscaper says that the total charge for the work Mrs.
Perry wants done will cost at least 120 dollars. Write an
inequality for the situation where h represents the number of
hours worked.
Warm-Up
 What is the area of a triangle with a base of
5.3 m and a height of 2.5 m?
 What is the volume of a block that is 5 meters
long, 3 meters wide, and 2 meters high?
 What is the height of a triangle that has an
area of 120 square feet and a base of 12 feet?
Coordinate
Plane
(-,+)
(+,+)
Quadrant
Quadrant
II
I
(-,-)
(+,-)
Quadrant
Quadrant
III
IV
When plotting points, x is first and y is second. (x,y)
Plotting Coordinates
 http://www.khanacademy.org/partner-content/pixar/pixar-
planes/v/the-coordinate-plane
 http://www.brainpop.com/math/geometryandmeasurement/
coordinateplane/
Plot the coordinates on the coordinate plane.
(-4 , 5)
(-3, -2)
(2, 1)
(6, -3)
Reflections
 Reflection: When a point is flipped over the x or y axis.
 If a point (x,y) is reflected across the x-axis, the sign of
the y-coordinate changes.
 (x , y)  (x, -y)
 If a point (x,y) is reflected across the y-axis, the sign of
the x-coordinate changes.
 (x , y)  (-x, y)
 If a point (x,y) is reflected across both axes, the sign of
both its coordinates changes.
 (x , y)  (-x, -y)
Reflect the
point (4,5)
across the
x-axis.
Reflect the
point (-2,3)
across the
y-axis.
CRCT Review
 What is the surface area of the rectangular prism?
SA = 2(wl) + 2(hl) + 2(hw)
 What is the surface area of a rectangular prism
with a width of 7 cm, a height of 4 cm, and a
length of 8 cm?