Transcript 2nd Period Math

nd
2
Period Math
Monday: Bell Work
The boiling point of water is 212 degrees Fahrenheit (°F).
Propane boils at about –44 °F. How
much hotter is the boiling point of water than that of
propane?
1) draw the problem out- be sure to correctly label it
2) write the correct equation
3) solve
1. Critique
What does this
word mean to
you?
Examples…
This word actually
means…..
a detailed analysis and
assessment of something:
evaluate (a theory or practice)
in a detailed and analytical way.
Explain how
you would use
this word in
math.
Essential Question
Scientific Notation
Adding and Subtracting
Here are the steps to adding or subtracting numbers in scientific
notation :
1. Determine the number by which to increase the smaller
exponent by so it is equal to the larger exponent.
2. Increase the smaller exponent by this number and move the
decimal point of the number with the smaller exponent to the
left the same number of places. (i.e. divide by the appropriate
power of 10 .)
3. Add or subtract the new coefficients.
4. If the answer is not in scientific notation (i.e. if the coefficient
is not between 1 and 10 ) convert it to scientific notation
Example 1: 2.456×105 +6.0034×108 = ?
8 - 5 = 3. The smaller exponent must be increased by 3.
2.456×105 = 0.002456×108
0.002456×108 +6.0034×108 = 6.005856×108
6.005856×108 is in scientific notation.
Multiplication
To multiply two or more numbers in scientific
notation:
1. multiply the coefficients
2. Add the exponents.
Division
To divide two or more numbers in scientific
notation:
1. Divide the coefficients
2. Subtract the exponent of the denominator
from the exponent of the numerator. ( The
first exponent from the second)
Try These: Exit Ticket
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1. (3 x 103) + (2 x 103)
2. (2 x 10-7 m) + (3 x 10-7 m)
3. (8 x 10-8 m2) – (3 x 10-8 m2)
4. (3.8 x 10-7 m2) – (2.8 x 10-7 m2)
5. (5.0 mm) + (2 x 10-4 m)
6. (6.2 km) – (3 x 102 m)
7. (2 x 105 m)(3 x 106 m)
8. (5 x 10-4 m)(4 x 10-2 m)
9. (1.50 x 10-7 m)(2.50 x 1015 m)
10. (9 x 108 kg)/(3 x l04 m2)
11. (2.4 x 105 kg)(3 x 104 m) / (4 x 10-2 s2)
Tuesday: Bell Work
The moon experiences many extremes in temperature
because it has no atmosphere. For example, on the
side of the moon that the sun is shining on, the
temperature can reach 260 °F. On the dark side of
the moon, it gets as cold as –280 °F. How much is
the drop in temperature from day to night?
1) draw the problem out- be sure to correctly label it
2) write the correct equation
3) solve
2. Precision
What does this
word mean to
you?
Examples…
This word actually
means…..
the degree to which
the correctness of a
quantity is expressed.
Explain how
you would use
this word in
math.
Essential Question
Calculator Practice
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1. (3 x 103) + (2 x 105)
2. (2 x 107 ) + (3 x 109)
3. (8 x 108) – (3 x 106)
4. (3.8 x 107) – (2.8 x 1013)
5. (5.0) + (2 x 104)
6. (6.2) – (3 x 102)
7. (2 x 105)(3 x 1024)
8. (5 x 104)(4 x 1015)
9. (1.50 x 107)/(2.50 x 1011)
10. (9 x 108)/(3 x l04)
11. (2.4 x 105)(3 x 104) / (4 x 107)
Word Problems
• http://www.regentsprep.org/regents/math/al
gebra/AO2/PracScientific.htm
Exit Ticket
• Talk with your partner about why it is
important to write in scientific notation.
• Create examples of when you could use
scientific notation in your everyday life.
Wednesday: Bell Work
*HW in basket
On a recent glider flight, Lucy took a tow to 3000
feet above ground level. She found a good thermal
and climbed 1800 feet. Then she hit big sink and lost
2200 feet. What was her altitude at that point?
1) draw the problem out- be sure to correctly label it
2) write the correct equation
3) solve
3. Transform
What does this
word mean to
you?
Examples…
This word actually
means…..
to simplify or solve a
mathematical problem
Explain how
you would use
this word in
math.
Lesson
solve real-world problems using rational
numbers in any form, including those
problems involving multiple steps?
Exponents
Exponents
The exponent of a number says how many times to use the
number in a multiplication.
In 82 the "2" says to use 8 twice in a multiplication,
So 82 = 8 × 8 = 64
In words: 82 could be called "8 to the power 2" or "8 to the
second power", or simply "8 squared"
Exponents
Example: 53 = 5 × 5 × 5 = 125
In words: 53 could be called "5 to the third power", "5 to
the power 3" or simply "5 cubed"
Example: 24 = 2 × 2 × 2 × 2 = 16
In words: 24 could be called "2 to the fourth power" or "2
to the power 4" or simply "2 to the 4th"
Why use exponents???
Exponents make it easier to write and use many
multiplications
Example: 96 is easier to write and read than 9 ×
9×9×9×9×9
Exponents are commonly used by
mathematicians and scientists.
Exponent *special info
Example: 2^4 is the same as 24
2^4 = 2 × 2 × 2 × 2 = 16
** When you have a negative base, you must put it is
parenthesis when using a calculator!
-8 ^ 2 means (-8)^2
You will not get the correct answer if you do not do
this. The calculator doesn't read the – sign and just
adds it to the answer.
Exit / Closure
Solve these 10 scientific notation problems for a
class work grade.
* Place them into the red, yellow, or green tray
based on how well you understand the
concept of scientific notation.
Thursday: Bell Work
One day in July, the temperature at ground level at
the airport was 90°. A pilot reported the
temperature at 10,000 feet was 50°. How much did
the temperature drop per 1000 feet? (Hint: find the
amount of temperature change and set up a
proportion.)
1) draw the problem out- be sure to correctly label it
2) write the correct equation to solve the distance
3) then solve to figure out the change
4. Computation
What does this
word mean to
you?
Examples…
This word actually
means…..
using 4 basic
operations (=, -, x,
÷) to solve a
problem .
Explain how
you would use
this word in
math.
Lesson
... use the commutative and associative
properties to add and/or subtract linear
expressions with rational coefficients?
... use the distributive property to factor
or expand linear expressions with
rational coefficients?
Order of Operations
How Do I Remember Which Order To Do The
Problem?
BODMAS !
B- Brackets first ( includes Parentheses () or Brackets [ ] )
O- Orders (includes Powers and Square Roots, etc.)
DM- Division and Multiplication (left-to-right)
AS- Addition and Subtraction (left-to-right)
Order of Operations
After you have done "B" and
"O", just go from left to
right doing any "D" or "M"
as you find them.
Then go from left to right
doing any "A" or "S" as you
find them.
EXAMPLES
Example: How do you work out 3 + 6 × 2 ?
Multiplication before Addition:
First 6 × 2 = 12
Then 3 + 12 = 15
Create your ice cream cone
3+6x2
3 + 12
15
EXAMPLES
Example: How do you work out (3 + 6) × 2 ?
Brackets first:
First (3 + 6) = 9, then 9 × 2 = 18
(3 + 6) x 2
9x2
18
***Only do one operation per line!!
EXAMPLES
Example: How do you work out 12 / 6 × 3 / 2 ?
Multiplication and Division rank equally, so just go
left to right:
First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3
12 / 6 x 3 / 2
2x3/2
6/2
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EXAMPLES
Oh, yes, and what about 7 + (6 × 25 + 3) ?
7 + (6 × 25 + 3)
7 + (6 × 25 + 3)
7 + (150 + 3)
7 + (153)
7 + 153
160
Start inside Brackets, and then use
“Orders" First
Then Multiply
Then Add
Brackets completed, last operation
is add
DONE !
Order of Operations Reminders
• As the problems become more complicated it is very
important that you do one step at a time!! This will
prevent many mistakes.
• And as always.... YOU MUST SHOW YOUR
WORK!!!
Practice Time!
Practice problems
Exit/ Closure
Solve the following (use an index card)
3.8n + 15 = 30.2
Show your work to justify your answer
Friday: Bell Work
*HW in basket
1. The cells of the bacteria E. Coli can double every 20
minutes. If you begin with a single cell, how many
cells can there be after 4 hours?
2. The population of metropolitan Orlando, Florida,
has doubled about every16 years since 1960. In
2000, the population was 1,644,561. At this
doubling rate, what could the population be in
2048?
5. Additive Inverse
What does this
word mean to
you?
This word actually
means…..
the opposite of a
number (+5, -5).
Examples…
Explain how
you would use
this word in
math.
Lesson
... use the commutative and associative
properties to add and/or subtract linear
expressions with rational coefficients?
... use the distributive property to factor
or expand linear expressions with
rational coefficients?
Scavenger Hunt
• We will now begin our Pirate Treasure Hunt!
Good Luck!
• 3 + (122 + 6) + 52 x 2 + 28 =
Order of Operations
Let's solve problems!!!!
Site 1
Site 2
Order of Operations Check
1) You may write on the paper
2) You MUST show all work
3) A calculator may be used to check your
work...... BUT your work must match your
answer
Exit / Closure
Partner discussion with your neighbor(s)
–
Tell the order of operations and why it is
important to follow them!!