Transcript positive.

Learning Target:
I can…
Solve problems involving integers and
absolute value
Definition
Integers: the set of positive whole numbers,
their opposites, and zero
(…-3, -2, -1, 0, 1, 2, 3…)
Real life example:
If it is 10 degrees below zero, it is -10°
20 Feet below sea level = -20
Representing Integers
Gain of 5 yards
Loss of 6 yards
A profit of $18
A decrease of 14 cents
Use your number line to help you!
-8
-7
-6
-5
-4 -3
Negative Integers
-2
-1
0
1
2
3
4
5
6
7
Positive Integers
8
Examples
1. Put the following integers in order from
least to greatest:
-4, 8, -2, -6, 3
-6, -4, -2, 3, 8
2. Put the following integers in order from
greatest to least:
-2, 0, 7, -1, -5
-5, -2, -1, 0, 7
Comparing Integers
Fill in the blank with greater than (>) or less
than (<).
1. -10
4
2. 3
-9
3. -15
-20
4. -1
0
5. -2
-4
OAA Practice
The table below shows the low temperatures of four cities on one winter night.
Low Temperatures of Four Cities One Night
City
Boston
Lowell
Springfield
Worcester
Temperature
3°F
0°F
-8°F
-5°F
Which city had the lowest temperature that night?
A. Boston
B. Lowell
C. Springfield
D. Worcester
Review - Practice
1. Put the following numbers in order:
-2, 3, 0, 6, -5
2. Fill in the correct sign for the following:
(>, <, or =)
3
-4
-1
1
0
-3
Brainpop
Review – Least to Greatest
-8
-7
-6
-5
-4 -3
-2
-1
0
1
2
Negative Integers
1)
-6, 4, -12, 0, 5
2)
-3, 1, 9, -2, -8
3
4
5
6
7
Positive Integers
8
Absolute Value:
The distance of a number to zero
Example:
│6│ = 6
│-6│ = 6
Absolute value is always positive!
You try it!
Find the absolute values!
│-9│ =
│10│=
Quick Check
Compare the numbers │-9│
a.
b.
c.
d.
≥
<
>
=
│5│
Compare the numbers │18│
a.
b.
c.
d.
≥
<
>
=
│-19│
Absolute Values: Evaluating Expressions
1)
|18| ÷ 2 × |–3| = ______
2)
|–3| + 10 = ______
3)
(12 + |–8|) ÷ |–5 |
= ______
4)
|–16| – |–16|
= ______
Ordering with Absolute Value
When you order integers, make sure you put
the number back in its ORIGINAL form when
put into order.
1) -2, │-3│, 0, │-4│, -5
2) │-7│, -3, │-3│, -9, -1
Adding
Exit Question
Fill in the blanks with >, <, or =
1. 6
│-6│
2. │-5│
4
3. │3│
2
4. │-3│
│2 + 1│
Learning Target:
I can…
Solve problems involving integers and
absolute value
Homework?
Summer Assignment?
Parent Signature?
Team Points…
Dividers:
1. Notes 2. HW/CW 3. Weekly Reviews
4. Quizzes
5. Tests
Absolute Value Review
Definition?
The distance of a number to zero
│2│ =
│-2 │ =
-│-2 │ =
-│2 │ =
Clicker Practice
1)
│13│+ │-5│ =
2)
-│-5│ =
3)
│2│ + │-2│ =
4)
-│10│ + │10│ =
Additive Inverse
What you add to a number to get zero.
Examples:
-5 + ____ = 0
13 + ____ = 0
12 + (-12) = ____
1) -7 + _____ = 0
2)
15 + ______ = 0
3) _____ + (-5) = 0
4) 13 + (-13) = _____
Real Life Examples
Opposites combine to make zero
Example 1:
A deposit of $50 combined with a ____________ of $_____
Example 2:
A gain of 5 yards after a ________ of ______ yards.
Clicker Word Problems
1) Which statement best describes a situation in which
opposite quantities combine to make zero?
A. Shawna made 8 cups of soup and divided the soup
into 8 containers.
B. Melanie deposited $10 in her savings account and
then withdrew $10 from the account.
C. Peter scored 2 goals in the first period of a hockey
game and 2 goals in the second period.
D. Marcos missed 4 questions on a test in which each
question was worth 4 points.
2) Which statement best describes a situation
in which opposite quantities combine to make
zero?
A. Angie had 100 sheets of paper and divided them
evenly into 5 folders.
B. Mandy deposited $200 in her savings account and
then added $200 her following pay period.
C. Paul and Josie are on a team together. Paul scored
5 points on his turn and Josie lost 5 points on her
turn.
D. Mario bought 2 sodas, which cost $2 each.
3) Steve was golfing at Quail Hollow Resort.
After the first nine holes, Steve was 3 under
par. After the back nine, he had a score that
was even to par. How many over par was
he on the back nine?
A. -3
B. 3
C. 0
D. 6
Monica budgeted $235 for “back to school”
stuff. She went school shopping with her
mom and spent $130 on clothes and $105
on supplies. Is this an example of the
additive inverse?
A. Yes
B. No
http://nlvm.usu.edu/
https://www.youtube.com/watch?v=31Q2_ETqxzc
Learning Target:
I can…
Add integers using counters and number
lines
Any Number Plus Its Opposite Equals?
ZERO!
This is called the ADDITIVE INVERSE!
Real Life Additive Inverses
For example, a hydrogen atom has 0 charge
because its two constituents are oppositely
charged.
(a single positively charged proton and a
single negatively charged electron)
Using A Number Line
Step 1: Plot your __________________________
number.
Step 2: If adding a positive number, move
_________________. If adding a negative
number, move __________________.
Step 3: Record your answer.
1)
2 + (-4) =
2)
-1 + (-2) =
3) -7 + 5 =
4) -3 + 4 + (-9) =
Using Counters
Step 1: Assign one color to be ______________________
and one color to be
____________________.
Step 2: Lay out counters to represent each of the numbers
in the expression
Step 3: Cancel out any ________________________
__________________ (1 positive and
together).
1 negative
1. -8 + 4 =
2.
5 + (-12) =
3. -1 + (-9) =
4)
-5 + (-4) + 9 =
5.
8 + (-2) + (-3)
6. -4 + (-2) + (-1)
Part B. Complete with your partner
Exit Question
Draw out the question and find the sum
below:
-5 + 3 =
Learning Target:
I can…
Solve word problems involving integers
REVIEW
Which number line models the
problem -3 + 2?
│3 + -4│
When you can’t use the number line
Step 1: Ask yourself if the signs are same
or different
Step 2: If they are the same: ADD, if they
are different: SUBTRACT
Step 3: Decide whether your answer will be
negative or positive
Example
1) -99 + 18 =
2) -10 + (-48) =
Quick Check!
3) -45 + 8 =
4) -13 + -43 =
5) 87 + -11 =
Multiple Numbers
1)
-5 + 17 + (-20) + 36 + (-13)
You try!
2)
-97 + (-65) + 15 + (-4)
3)
67 + (-54) + 90 + (-35) + 47
Word Problems (Key Words)
Positive
Negative
Adding Integers Word Problems
Key Words
Below sea level
Below 0
Rise
Drop
Spend
Earn
Adding Integer Word Problems
1. During the football game, Justin caught
three passes. One was for a touchdown and
went 52 yards. The other was for a first
down and was for 17 yards. The other was
on a screen pass that did not work so well
and ended up a gain of -10 yards. What was
the total yardage gained by Justin on the
pass plays?
2. It was a very freaky weather day. The
temperature started out at -9°C in the
morning and rose 15° by noon. It stayed at
that temperature for six hours and then
dropped 8°C. What was the temperature at
6 p.m.?
Integers Word Problems
3. You owe $225 on your credit card. You
make a $55 payment and then purchase
$87 worth of clothes at Macy’s. What is the
integer that represents the balance owed on
the credit card?
4. A monkey sits on a limb that is 15 ft
below sea level. He swings up 10 ft, climbs
up 6 ft more then jumps down 13 ft. How far
below the ground is the monkey now?
5. Mary has $267 in her checking account.
She writes checks for $33, $65, and $112.
What is the balance in her account now?
6. A submarine dove 836 ft. It rose at a rate
of 22 ft per minute. What was the depth of
the submarine after 4 minutes?
Exit
Find the sum without using a calculator,
number line, or tiles.
1) -13 + (-12) =
2) 10 + (-15) =
3) 29 + (-9) =
Learning Target:
I can…
Subtract integers without a calculator
Review – Adding Integers
The temperature is -4°F in Alaska on a day in
January. If it is 8°F warmer here, what is the
temperature here?
a. 12°F
b. 4°F
c. 5°F
d. -12°F
The Golden Gales football team loses 2
yards on the first down. On the
second down, they gain 5. What is
their net yardage gained?
a. 7 yards
b. 3 yards
c. -7 yards
d. -3 yards
A number plus its opposite
Review
The answer to -10 + 5 will be:
a. Negative
b. Positive
c. Zero
The answer to -11 + (-6) will be:
a. Negative
b. Positive
c. Zero
And again!
Adding and SUBTRACTING Integers
Brainpop
Subtracting Integers
To subtract integers, say “cha-ching!”
Step 1: Change subtraction to addition
Step 2: Change the second number to its
opposite
Step 3: Add
Example 1
4 – (-7) =
4 + (+7) =
= 11
Example 2:
-7 – 2 =
Cha-ching!
-7 + -2 =
= -9
Example 3
6 – 10 =
Example 4
4)
-7 – 4
Examples
5)
3 – (-9)
6)
2 – 10
7)
-4 – (-6)
8)
-9 – 1
Word Problem
1) On back
2) On back
The highest point in the United
States is Mount McKinley at 20,320
feet above sea level. The lowest
elevation in the country is Badwater
Basin at 280 feet below sea level.
What is the difference between
these two elevations?
3) On Back
4) On Back
Discuss - Extended Response
Example
Alberto subtracts
different negative
integers from 13.
Show three different
examples of what
Alberto does. Explain
what happens when
you subtract different
negative integers
from 13.
EXIT
1) 16 – (-1) =
2) -5 – 1 =
3) -3 – (-2) =
Exit
What is 14 – (-8)?
Learning Target:
I can…
Solve word problems involving the adding
and subtracting of integers
Review
Remember cha-ching!
Review!
Kelly has $40 in her account. If she
withdraws $30, then deposits $50, how
much does she have in her account now?
And again!
Ohio State gains 7 yards in the first down. If
they lose 10 yards on the second down,
and gain 6 yards on the third, what is their
net yardage for this series of plays?
In January, the temperature hit a low of 2°F. The next day, it got 3 degrees
colder! What expression could be
used to show the temperature on the
second day?
a. -2 – (-3) = 1°
b. -2 + (-3) = -5°
c. -2 + 3 = 1°
d. -2 – 3 = -1°
Word Problems
Stacey is a cliff diver. She starts 90 feet above
the water, dives and falls to 25 feet below the
water. Write an expression to find the total
distance Stacey traveled.
Exit
Mount Graf is located 1,547 feet above sea
level. Lake Graf is 120 feet below sea level.
What is the difference in altitude between
the two locations?
Learning Target:
I can…
Multiply integers without a calculator
Review Adding and Subtracting
Integers
To add ask yourself:
Signs same or different?
Should I add or subtract?
Will the answer be negative or positive?
To subtract:
Cha-Ching!
Change the subtraction to addition and the
second number to its opposite
Examples
-85 – (-13) =
-14 + (-5) =
-8 – 13 =
-23 + 5 =
13 – (-14) =
Multiplying Integers Using Counters
Multiplication is really repeated addition.
2 · 3 means 2 sets of 3
2 · -3 means 2 sets of -3
-2 · -3 means the opposite of 2 sets of -3
You Try!
1) 3 · (-1)
2) 5 · (-2)
3) -3 · (-4)
4) -2 · (4)
You Try!
1) -3 · (-2)
2) -3 · (2)
3) -4 · (-4)
4) (-3)²
Multiplying Integers Rules
1. Positive x positive = positive
example: 2 x 3 = 6
2. Positive x negative = negative
example: 2 x -3 = -6
3. Negative x positive = negative
example: -2 x 3 = -6
4. Negative x negative = positive
example: -2 x -3 = 6
Why?
1. 2 x 3 means two groups of 3, which is
6
2. 2 x -3 means two groups of negative
three, which is -6
3. -2 x 3 means the opposite of two
groups of 3 or -6
4. -2 x -3 means the opposite of 2
groups of -3, which is 6
You try! No calculators!
-4 ∙ 2 =
-5 ∙ -3 =
2 ∙ -3 =
You try!
More Than 2 Numbers
-7 · (-5) · (-4) = _________
-1(9)(-5) = _________
-3(5 · 2) · -2 = ______________
More than 2 Numbers
1. When multiplying an EVEN number of
negatives, and zero is not present, the
product will be
___________________________________
2. When multiplying an ODD number of
negatives, and zero is not present, the
product will be
___________________________________
Practice Again
(-1)(-7) ∙ -4 =
-3 ∙ 4 ∙ -2 =
(7)(-2)(2) =
EXIT
-3 ∙ 4 ∙ -2 =
Exponents
(-2)²
-2²
(-2)³
(-2)⁴
Exit
1) -3 ∙ 1 ∙ -7 =
2) (-3)²
3) -3²
Learning Target:
I can…
Divide integers without a calculator
Review - Multiplication
(-5)²
-5²
(-5)³
Counters - Discuss
When we divide a positive and a positive the
quotient is positive.
When we divide a positive and a negative (in
either order), the quotient is negative.
When we divide a negative and a negative,
the quotient is positive.
Examples
-4/2 = __________
-15 ÷ -3 = _____________
-27/9 = ____________
You try! No calculators!
50/(-10) =
(-144) ÷ (-12) =
(-33) ÷ (-11) =
Order of Operations
P
E
MD
AS
1)
-45 ÷ (-5) + 7
2)
-3 – 12 ÷ (-3)
3)
2  (5) (20)
2  (3)
4)
 3(4) (20)
 5  (3)
Word Problem
The table below shows the number of points
scored in the first ten minutes of Jeopardy.
Find the mean number of points scored.
Person
James
Jenny
Howard
Arie
Points
-100
300
-500
200
The West Side Dolphins football team gained
8 yards, then gained 4 yards, then lost 4 yards,
then gained 15 yards, then gained 3 yards,
then gained zero yards, then lost 2 yards,
then gained 8 yards. How many yards did the
Dolphins gain or lose on average per play?
EXIT
EXIT
A negative number multiplied by a negative
number will result in a product that is
__________________.
Real-Life Integer Problems
Learning Target:
I can…
Solve real life integer problems
Addition/Subtraction
A submarine was situated 800
feet below sea level. If it
ascends 250 feet, what is its
new position?
The lowest point of the St. Lawrence River is
294 feet below sea level. The top of Mt.
Jacques Cartier is 1,277 feet above sea
level. How many feet higher is the top of
Mt. Jacques Cartier than the lowest point
of St. Lawrence River?
Word Problems
Ohio State gains 7 yards in the first down. If
they lose 10 yards on the second down,
and gain 6 yards on the third, what is their
net yardage for this series of plays?
Multiplication/Division
A failing company lost $200 for 5 months
straight. What is their net profit?
Expression
(-200)(5)
a. -$200
b. -$1000
c. $1000
d. -$205
Ten people went to dinner. As a group, they
spent $120. If they are going to split it
equally, how much will each person owe?
A little bit tougher…
Jack just got his license. In his bank
account, he currently has $2000. He paid
$500 as a down payment on a car. He
also plans on spending $50 a month in
gas. How much will he have left in his
bank account after 1 year?
Justin gets $100 a week from his job.
He puts half in his savings account and half in his
checking account. If he spends $20 a month all from
his checking account, how much will he have left in
each account after 1 year?
Exit
Which expression could be used to show that Jan
spent $20 every week for 3 weeks and then
earned $50 at the end of the month?
a. 20 x 3 + 50
b. (-20 x 3) + 50
c. 20 + 3 – 50
d. (20 x 3) - 50
Stations!
Learning Target:
I can…
Review for my integers quiz
Exit
James subtracts different negative integers
from 10. Show an example of what James
does. Is the answer always positive, always
negative, or always 0?
Exit
On four consecutive days Arnold has the
following transactions: Monday, he
deposited $20.00, Tuesday he withdrew
$5.00, Wednesday he deposited $10.00
and Thursday he withdrew $25.00. Write
a number phrase for this situation and
solve.
Review (answer numerically)
(6)(-7) =
(-60) ÷ (-12) =
Learning Target:
I can…
Do well on my integers quiz
BONUS MATH
1. Addition
-9 + 1
-9 + -1
2. Subtraction
-9 – 1
-9 – (-1)
9 – (-1)
3. Multiplication
-3 · 2
-3 · -2
4. Division
-45 ÷ (-5)
-45 ÷ (5)
-(-3)
│-9│ =
-│-9│=
Exit
Simplify the following expression:
-│-9 + 3 – 1│=