Download unit 1: number sense - Warren County Schools

UNIT 2: INTEGER OPERATIONS
I Can …
 Order integers on a number line
 Add integers and solving problems involving integers.
 Subtract integers and solve problems involving subtraction
 Multiply and divide positive and negative numbers
 Solve addition and subtraction equations
 Solve multiplication and division equations
 Solve inequalities with integers
 Solve problems written in exponential form
 Apply the properties of exponents to solve problems
 Solve problems involving scientific notation
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
Vocabulary
*Positive & Negative Numbers in real life
Integer---
Example
*Write an integer to represent
10 below zero
A gain of $2.00 per share
Positive Number -Example
Graph the #’s on a number line(2, -3, 4, 0 4, 3, -2)
---------------------------------------
Negative Number -Example
Compare the numbers using an inequality
sign (< or >)
-5______ 0 6______-2 -4_______-3
Absolute Value -Example
Order from least to greatest
5, 3, 0, 6, -2, -4, 1, -1
Evaluate the expressions on the board
NAME THREE METHODS TO ADD
INTEGERS:
1.
2.
3.
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
Notes and Examples
Adding Integers with a number line
DRAW A NUMBER LINE TO ADD
(-6) + 2
Vocabulary
Opposites –
Example
(-3) + 7
(-3) + (-2)
Adding Integers with ALIKE signs
I need to _____________ the integers like
Normal and ____________ the sign.
Examples
Additive Inverse Property –
Example
ADDING THREE OR MORE INTEGERS
Group the ___________ together and
Group the ___________ together
Examples:
Adding Integers with UNLIKE signs
I need to ______________ the integers
And take the sign of the _____________
Looking numbers.
Examples
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
Vocabulary
Subtracting Integers
Modeling
Opposite –
Try these examples:
6–7
-17 – 18
21 - ( -24)
-36 – 47
4 - l-6l
-13 - (-25)
What do you notice about
3 – 5 and 3 + (-5)
-25 – 15
Subtraction is the same as _____________
The opposite.
Word Problems
If the overnight temperature was - 14
degrees but rose to 8 degrees during
the day, what was the difference in the
daytime and night time temperatures?
Rules—learn this chant
Same
Change
Opposite
Examples
9 - 12
7 - (-15)
-6 - 8
2–6
3–8
-30 - (-20)
The boiling point of water is 212
degrees while -460 degrees is its
absolute lowest temperature. Find the
difference between the boiling point
and the absolute lowest temp.
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
Vocabulary
The WEMS football team did not have a very
good first half against Moss. On the first 4
plays of the game, WEMS lost 5 yards a
play. How could we write an expression to
represent five yards lost for 4 plays?
Dividing integers – the rules are the same
+ * + = __________
+ * - = __________
Look at the pattern on the board
What rule do we discover?
- * + = __________
A POSITIVE integer multiplied by a
POSITIVE integer results in a
_____________ product.
- * - = __________
Examples
 2
A POSITIVE integer multiplied by a
NEGATIVE integer results in a
______________ product.
-4  (-2)
5/(-1)
A NEGATIVE integer multiplied by a
NEGATIVE integer results in a
________________ product.
Multiplying and Dividing Integers
Examples from class
-4(-3)
2(-9)
6(4)
-5(-8)
-20(2)
-3(2)
(-3)²
-36  9
8/(-2)
10  (-5)
-15/(-3)
-100/(-50)
ALGEBRAIC EXPRESSSIONS!
Use all of our rules or strategies to evaluate these
algebraic expressions if a = -3 and b = -5
-2a - b
a + 2b
5a - b
(-5)²
What about 3 or more integers?
4 • (-3) • (-2)
-2 • (-3) • 6
-2(3)(-9)
-1(-9)(-4)
(-2)³
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UNIT 2: INTEGER OPERATIONS
INTEGERS IN THE REAL WORLD!!!
Vocabulary
At the WEMS football game versus
Moss, the 5 plays resulted in the
following yards, a loss of 5, a gain of
10, a loss of 15, a loss of 5, and a
gain of 5 yards. What is the mean
yards of the five plays?
Mean–
Example
Chris Allen reported that the
temperature is dropping at a rate of 5° per hour. At this rate, how long
will it take the temperture to drop by
-25°?
At a golf match, the scores for the top
five players were 6 below par, 4 below
par, par, one above par, and 5 above
par. What was the mean score for the
five players
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
Vocabulary
You checked your bank statement today and it
had a negative balance of $5.00. Yesterday,
you had taken out $20.00. What type of
equation would represent the amount that your
account began with?
Write and solve your own equations
If you decrease a number by 20, the result is
-14
the sum of n and 25 equals -18
Refresher -- how do
we solve these equations?
if you decrease a number by 8 the result is -14
Isolate the _________________ by
“____________” the operations.
Addition Equations with Integers
w + (-4) = -5
s + (-3) = -8
the sum of a number and 40 is 9
Solving division and multiplication equations
with integers
8g = -32
-35 = -7r
6a = -42
-2 + n = -6
Subtraction equations with integers
x - 8 = -3
y-2=5
b - 4 = -10
n - 5 = -6
n = -12
2
x =4
-5
t = -8
-6
7 = p - 12
-8 = d - 11
A scuba diver can dive at a rate of -10 feet per
minute. If the diver is at a depth of -60 feet,
how many minutes has he been diving? Write
and solve an equation.
r - 20 = -4
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
Vocabulary
To keep ice cream from melting, the
temperature of the freezer must be no
more than 32 degrees.
If the COEFFICIENTS are
NEGATIVE!!!!!!
How do we write that as an inequality?
WARNING:
Suppose the current temperature of the
freezer is -10 degrees. How many
degrees can the temperature rise to keep
the ice cream from melting? Write an
inequality to represent this situation.
Solving addition and subtraction
inequalities
When multiply or divide BY a
NEGATIVE number,
you must FLIP the sign
-4x < 16
-2r  -10
r < -3
-3
w>5
-4
-5m  -25
a  -2
-10
Solve just like equations
y+7 1
h - 2 < -1
x + 2 < -4
p - 4  -2
r + 3  -5
j - 5  -2
Solving inequalities by Multiplying and
Dividing with Integers
7h < 63
9r  -45
2m  -4
x >6
2
r < -4
3
w  -3
5
Using inequalities
A local weather forecast stated that it
would be 12°F tonight and at least
10° colder the next night. Write an
inequality to show how cold it will be?
The temperature at ten oclock was
-5 degrees. The temperature at 2
o'clock was at least 20 degrees
below the temperature at ten.
Write an inequality to represent
the possible temperature
at two.
Notice that the _______________ ARE
ALL ______________!
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Notes and Examples
What are exponents?
What do they mean?
Vocabulary
Base --
Rewrite using exponents
Example
3(3)(3)(3)(3)
4x4x4
10 x 10
8x8x8x8
Rewrite without exponents in as a product
N5
63
34
26
Exponent --
Example
Power –
Example
Rewrite using exponents
a•a•a•a
a•a•b•b•b
a•b•b•b•c•c
More Examples
Complete this pattern
10³ =
10³
10² =
101
8²
100
10-1
10-2
Any exponent of 0 has a product of _______
Negative exponents can be written as one
divided by the number to the nth power
2°
54
2²•5²
3-3
5°
6°
3-1
4-2
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UNIT 2: INTEGER OPERATIONS
Section Title: _________________________________________________
I CAN…
Simplify these fractions
Notes and Examples
Can you rewrite these expression using
exponents?
4(4)(4)(4)(4)
4(4)(4)
7(7)(7)(7)
2(2)(2)(2)(2)(2)(2)
2(2)
4(4)
3(3)(3)(3)(3)(3)
Rule: To _____________ powers with
the same___________, keep the
_______ and ______________________.
2(2)(2)
If 4(4)(4) = 4³,
then what do you think about 4 * 4²
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If 3(3)(3)(3)(3)(3) = 3 ,
then what do you think about 3² * 3
So here is our rule when multiplying
exponents
To ______________ powers with the
same ________, keep the __________
and ________________________.
example: 5² * 5³ = 5
16 * 16³ = 16
Your turn
6
6²
12³
12²
8
8³
There are about 10 molecules in a cubic
meter of air at sea level, but one 10
molecules at the altitude of 33 km.
How many more molecules are there at
sea level than at 33 km?
a² * a² = a
3² * 4² = ?
Your turn
8 * 8²
2² * 2
10 * 10³
A light-year is the distance that light
travels in one year. A light year is 10
centimeteres. To convert this number
to kilometers, you must divide it by 10
. How many kilometers is a light year?
r³ * r
10
The weight of the planet Mars is 8
tons. The weight of Venus is 8 tons.
How many more tons is Mars, than
Venus?
A rectangle has a side of 15² inches and
another side of 15³ inches. What is the
area of the rectangle written with one
base?
More Complex
8 x 10
4 x 10
3x5
2x5
The population of the United States is 3
x 10 and the population of the world is 7
x 10 . How many times larger is the
population of the world than the
population of the United States?
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UNIT 2: INTEGER OPERATIONS
Section Title:____________________________________________________________
I CAN…
Notes
Vocabulary
Why do we use scientific notation?
Scientific Notation—
Writing Numbers in STANDARD FORM
(________________________________)
5.34 x 10³
the exponent is 3, so you move the decimal
3 places in a positive direction
WORD PROBLEMS
The distance from Earth to the new nonplanet Pluto is 4,280,000,000 miles. Write
this number in scientific notation
Try these
7.42 x 10²
.
A googol is a number written as a 1
followed by 100 zeros. Write a googol n
scientific notation.
6.1 x 105
3.7456 x 104
The smallest unit of time is the
yoctosecond, which equals
0.000000000000000000000001 second.
Write this number in scientific notation.
6.2897 x 106
What if the power is a negative number?
2.3 x 10-2
AN OXYGEN ATOM HAS A MASS OF 2.66
X 10-23 GRAM. WRITE THIS NUMBER
IN STANDARD FORM.
3.68 x 10-4
6 x 10-7
11.2 x 10-3
Writing numbers in scientific notation
Step one -- move the decimal to a point that
makes the number greater than or equal to
____________, but less than ________
Step two -- count how many places you
moved the decimal
37.5
0.00876
3, 725, 000
0.114
4,999,999,999
0.000316
14,140,000
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JUMPSTARTS UNIT 2
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