TCAP REVIEW WEEK 3
SPIs 2.1, 2.2, 2.3, 2.4, 1.1. 1.2, 1.3
Do Now – (√16), (-1 x -1), (√169)

1.
2.
3.
Please pick up your guided notes, take out your tracker, and
respond to the following SILENTLY & INDEPENDENTLY:
Which point on the number line best represents the value of
3π?
Which point on the number best represents -16 ?
7
Consider the three numbers: 2.82427…, π, √7. Order them
from least to greatest.
Weekly Agenda
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

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Monday – Numbers on a Number Line, Rational
and Irrational Numbers, Computing Numbers in
Scientific Notation
Tuesday – Numbers on a Number Line, Rational
and Irrational Numbers, Word Problems with
Scientific Notation
Wednesday – Reading Graphs, d=rt, Cost per Unit
Thursday – Jeopardy Review
Friday – Quiz
Today’s Objective
SWBAT identify a number
as rational or irrational
and compute numbers in
scientific notation.
Homework - Worksheet
Rational and Irrational Numbers

Rational Numbers
 Numbers
that can be converted into a fraction.
 Examples: perfect squares, terminating decimals,
repeating decimals, etc.
 √25,

0.5, 0.33333…., 8
Irrational Numbers
 Numbers
that can’t be converted into a fraction.
 Examples: non-repeating continuous decimals,
imperfect squares.
 0.6512389640752….,
√112, π
Rational and Irrational Numbers

Identify as rational or irrational:

√3

24.5%

3/11

0.491739109334…

√49

√47

2½

0.666666666…

3.14

π

(√4)2


100
25
8p
10
Scientific Notation

A way of writing really large or really small numbers easily.

Always written as a number of 1 or greater, but less than 10
(factor 1) and a power of 10 (factor 2).




Example: 6.4 x 108
Numbers with positive exponents are greater than 1.
Numbers with negative exponents are less than 1.
Shortcut when computing numbers in scientific notation:


When multiplying, multiply factor ones, keep the power of 10,
add exponents.
When dividing, divide factor ones, keep the power of 10,
subtract exponents.
Scientific Notation


Watch as I walk through this one.
Example 1: Solve. (2.7 x 102) x (3.2 x 104)
Scientific Notation

Watch as I walk through this one.

Example 2: Solve. (8.4 x 103) ÷ (2.1 x 10-4)
Scientific Notation


Watch as I walk through this one.
Example 3: Solve. (2 ´10-3 )(3 ´10 7 )
(2 ´10-8 )
Scientific Notation


Work on this one on your own.
Example 4: Solve. (5.8 x 10-5) x (2.9 x 1010)
Scientific Notation


Work on this one on your own.
Example 5: Solve. (5.6 ´1012 )
(10.5 ´10 5 )
Scientific Notation


Work on this on eon your own.
Example 6: Solve. (9 ´1013 )(6 ´108 )
(3.5´10 -4 )
Whiteboard Practice




Each person has their own whiteboard.
You will have 40 seconds to solve each problem.
Keep the answer hidden so no one steals your
answer!
There will be a prize for the person who answers
the most questions correctly!
Scientific Notation

(9 x 10-10) (4 x 104)
Scientific Notation
-7
(5.6 ´10 )(3.6 ´10 )
4
(5 ´10 )
14
Scientific Notation
(3.4 X 106) ÷ (2 X 108)
Scientific Notation

(1.8 x 106) (7.5 x 10-2)
Scientific Notation

a)
b)
c)
d)
Which one of these expressions correctly identifies
the quotient of these two numbers
(7.9 x 10-2) ÷ (9.5 x 10-4)?
(7.9 x 9.5) x 10(-2+-4)
(7.9 x 9.5) x 10(-2--4)
(7.9 ÷ 9.5) x 10(-2+-4)
(7.9 ÷ 9.5) x 10(-2--4)
Scientific Notation

(4.8 X 10-5) ÷ (3.2 X 10-6)
Scientific Notation
(6.4 ´10 5 )(2.9 ´1012 )
(9.8 ´10 5 )
Scientific Notation

(3.4 X 104) (2.1 X 103
Scientific Notation

(10.5 X 1020) ÷ ( 1.2 X 10-14)
Scientific Notation
-10
(8 ´10 )(4 ´10 )
9
(8 ´10 )
5
Scientific Notation

(9 x 10-11) ÷(2.4 x 108)
Scientific Notation

(6.4 x 10-3) (3.5 x 10-2)
Scientific Notation

(3.24 x 10-4) ÷(8.1 x 10-7)
Scientific Notation

(7.3 x 108) (5.8 x 10-10)
Scientific Notation

a)
b)
c)
d)
Which expression correctly indicates the product of
these two numbers:
4.5x108
&
1.2 x 103
(4.5 ÷ 1.2) x 10(8-3)
(4.5 x 1.2) x 10(8x3)
(4.5 x 1.2) x 10(8÷3)
(4.5 x 1.2) x 10(8+3)
Scientific Notation

(1.26 x 10-12) (4.78 x 10-13)
Scientific Notation

4.64 x 10-4) ÷(2.9 x 10-6)
Scientific Notation

(3.7x 105) ÷ (2.9 x 1011)
Scientific Notation
(7 ´10-12 )(1´10 6 )
(14 ´10-8 )
Scientific Notation
(6 ´10 )(2 ´10 )
(4 ´1010 )
4
7
Scientific Notation

(4.5 X 10-5) (5.2 X 10-6)
Scientific Notation
-7
(9 ´10 )(4 ´10 )
4
(6 ´10 )
14
Scientific Notation

(7.3 x 108) (5.8 x 10-10)
Scientific Notation

(9.45 x 1010) ÷(1.5 x 106)
Scientific Notation
-9
(5 ´10 )(6 ´10 )
5
(3 ´10 )
7
Scientific Notation
(4.8 ´10 8 )(3.9 ´10 4 )
(7 ´10 3 )
Scientific Notation

(9.3 X 1024) ( 5 X 10-13)
Scientific Notation

a)
b)
c)
d)
Which expression correctly indicates the product of
these two numbers:
2.4x10-8 &
6.7 x 105
(2.4 x 6.7) x 10(-8x5)
(2.4 x 6.7) x 10(-8+5)
(2.4 x 6.7) x 10(-8÷5)
(2.4 ÷ 6.7) x 10(-8-5)
Scientific Notation
-7
(2.7 ´10 )(5.2 ´10 )
-8
(2 ´10 )
12
Scientific Notation

(4.2 x 10-8) ÷(1.68 x 10-2)
Scientific Notation
-17
-10
(5 ´10 )(4 ´10 )
5
(2 ´10 )
Scientific Notation

(3.2 x 107) (1.75 x 10-10)
Scientific Notation

(5.4 x 105) (4.6 x 103)
Do Now – (2 x 2), (½ x 4), (18 – 5)
1.
2.
3.
Which point on the number line represents -1.88?
Order the following numbers from least to
greatest: (-1/9), √5, -0.8, 3.5
Solve.
(3.7x 105) ÷ (2.9 x 1011)
Today’s Objective
SWBAT solve order numbers
from least to greatest in
scientific notation and solve
word problems involving
numbers in scientific
notation.
Homework Worksheet
Ordering Numbers in Scientific
Notation

Things to remember when ordering numbers in
scientific notation:
 The
 If
 The
 If
smaller the exponent, the smaller the number.
the exponents are the same, compare the factor ones.
larger the exponent, the larger the number.
the exponents are the same, compare the factor ones.
Ordering Numbers in Scientific
Notation


Watch as I walk through this one.
Example 1: Order the following numbers from least
to greatest:
3.72 x104
.46 x105
4.2x108
82x105
Ordering Numbers in Scientific
Notation


Watch as I walk through this one.
Example 2: Order the following numbers from least
to greatest:
4.56x10-3
45.1x10-2
4.56x10-5
72x10-4
Ordering Numbers in Scientific
Notation


Work on this one with your partner.
Example 3: The table lists the total value of music
shipments for four years. List the years from least to
greatest dollar amount.
Year
Music Shipments ($)
1
1.22 x 1010
2
1.12 x 1010
3
9.87 x 109
4
7.99 x 109
Ordering Numbers in Scientific
Notation


Work on this one with your partner.
Example 4: The following diameters are shown for
different types of cells. Order these from greatest
to least.
Cell Type
Diameter
Fungi
4.6 x 10-5
Bacteria
2.5 x 10-3
Cat
5.2 x 10-4
Human
4.9 x 10-3
Scientific Notation Word Problems

Example 5: In 2006, Blue Ridge Parkway was
visited by about 1.9 x 107 people. That same year,
Great Smoky Mountains National Park was visited
by about 9.3 x 106 people. How many more
people visited Blue Ridge Parkway than Great
Smoky Mountains National Park in 2006?
Scientific Notation Word Problems

Example 6: In 2006, the US had a Gross Domestic
Product (GDP) of 1.313 x 1013. The United
Kingdom had a GDP of 1.93 x 1012. What were
the combined GDPs of the US and the UK in 2006?
Scientific Notation Word Problems

Example 7: One cell has a diameter of 4.5 x 10-6.
If there are 20 cells growing in a lab, what is their
combined diameters?
Scientific Notation Word Problems

Example 8: The average distance from Earth to the
Sun is 1.46 x 108 kilometers. The average distance
from Earth to the Moon is 3.84 x 105 kilometers.
About many more times as great is the distance
from Earth to the Sun than to the Moon?
Word Problem Investigation





A problem will come up on the board.
Individually, each of you will have 35 seconds to
read the problem and determine what operation
will be necessary to solve.
After the 35 seconds is up, you will have 1 minute to
determine the answer to the problem with your
group.
One group member will write the answer on the
group whiteboard to be checked.
The group with the most points will win a prize!
Problem 1

About 8.73 x 108 people in the world speak
Chinese. About 3.22 x 108 speak Spanish. In
scientific notation, how many more people speak
Chinese than Spanish?
Problem 2

Great Lake Superior covers an area of 3.17 x 104
square miles. The smallest Great Lake, Ontario,
covers an area of 7.34 x 103 square miles. About
how many times as great is the area covered by
Lake Superior than Lake Ontario?
Problem 3


The income following incomes are recorded for
music artists in 2010.
Artist
2010 Income
Jay-Z
2.56 x 107
Yo Gotti
5.1 x 106
How much more money did Jay-Z make over Yo
Gotti?
Problem 4

The table below shows the approximate tons of
cars exported from Germany to the US over
time. Order the amount of cars over the years
from least to greatest.
Year
Tons of Cars
2007
7.2 x 105
2008
8.31 x 106
2009
5.9 x 107
2010
3.76 x 106
Problem 5

The distance between Memphis and Sand Francisco
is 1.2 x 103 miles. The distance between Memphis
and Nashville is 2.5 x 102. How much further is San
Francisco than Nashville from Memphis?
Problem 6

The largest planet in our solar system is Jupiter with
a diameter of about 1.43 x 105 kilometers. The
smallest planet in our solar system is Mercury with a
diameter of about 4.9 x 103 kilometers. About how
many times greater is the diameter of Jupiter than
the diameter of Mercury?
Problem 7

In 2006, China had 1.311 x108 internet users. That
same year, Japan had 9.09 x 107 internet users.
How many internet users did the two countries have
combined?
Problem 8

The table below shows the thickness in inches
for the following types of paper. List the paper
types in order from the least thick to most thick.
Paper Type
Thickness
Cardstock
3.348 x 10-2
Printer paper
1.898 x 10-3
Construction paper
3.684 x 10-3
Poster paper
1.024 x 10-2
Problem 9

With nearly 3.0 x 108 books, the Library of
Congress is the largest library in the US. The
University of Tennessee has about 2.97 x 107 books
in its library. How many more books does the
Library of Congress have than the University of
Tennessee?
Problem 10

In 2010, USA had 2.31 x105 IPhone users. That
same year, Europe had 1.49 x 104 IPhone users.
How many IPhone users did the USA and Europe
have combined?
Do Now – (⅛ x 32), (⅓ x 9), (⅙ x
78)
1.
2.
3.
One microgram is equal to 1x10-6 gram. If the mass
of a substance is 8x109 micrograms, what is its mass
in grams?
If a penny is 0.4 x 103 inches thick, how thick are 6
pennies?
Which graph best represents the relationship the
flow of water during a shower?
Today’s Objective
SWBAT solve cost per
unit and distance,
rate, and time
problems.
Homework - Worksheet
Cost per Unit

Things to remember when determining cost per unit:
 To
determine the cost of an item, divide the cost by the
number of items (units)
 Make sure to determine if the units are sold individually
or in groups.
 If
sold in groups, you may sometimes need to buy more than
you need.
If sold individually, you can buy the exact amount you need.
Cost per Unit


Watch as I walk through this one.
Example 1: A 12 oz. bag of chips costs $1.44.
Given that unit price, how much would a bag of 32
oz chips cost?
Cost per Unit


Watch as I walk through this one.
Example 2: The softball team needs new 25
softballs for practice. They want to save the most
money possible. There are two options. Which
option should they choose and how much money will
they save choosing the cheaper option?
 12
softballs for $33
 10 softballs for $25
Cost per Unit


Work on this one with your partner.
Example 3: What is the best deal?
 10
CDs for $1.20
 $0.8 per CD
 100 CDs for $10
 50 CDs for $4.50.
Cost per Unit




Work on this one with your partner.
Example 4: Ms. Cofer went to the store to buy
maps. The following packages of maps are
available at the store:
3 maps for $24.45 OR 4 maps for $31.00
Ms. Cofer needs to buy 30 maps. How much money
will she save by purchasing maps for the cheapest
total amount?
D = rt

Things to remember when solving distance, rate, and
time problems:
 Rate
always includes a distance and time unit.
 Make sure all units match with rate units (Distances
should be the same and time should be the same. If not,
convert!)
 Identify what the problem is asking for before solving
in order to determine the necessary equation.
 Total distance = add up distances.
 Average rate = total distance/total time.
D = rt


Watch as I walk through this one.
Example 5: On Friday, Dr. Cash traveled 363 miles
from Tiptonvile to Oak Ridge in 7.5 hours. If he
travels at the same rate on Saturday, how far will
he travel in 5 hours?
D = rt


Watch as I walk through this one.
Example 6: A train traveled for ¾ hour at a speed
of 80 miles per hour. It then immediately slowed to
60 miles per hour and traveled at that speed for
the next ¼ hour. What is the total distance the train
traveled during this hour?
D = rt


Work as I walk through this one.
Example 7: : The principal traveled the
following on her way to a conference:
 30
miles at 60 mph
 270 miles at 80 mph
 ½ hour lunch and bathroom break
 550 miles at 50 mph

What was her average speed, including lunch
break?
D = rt


Work on this one with your partner.
Example 8: Tiara is practicing for a swim meet.
Four of his practice results are shown in the table.
For which distance did Tiara swim the fastest?
D = rt


Work on this one with your partner.
Example 9:The volleyball team travels to White
Station MS at 55 mph for ½ hour. On the way
back, they stop at Pizza Hut and travel at 65 mph
for ¾ hour. What is the total distance the team
traveled during this trip?
D = rt


Work on this one with your partner.
Example 10: Beyoncé rode bicycle 2.2 miles up a
hill in 0.2 hour. Then she rode back downhill on the
same path in 0.12 hour. What is her average rate
for the combined trip?
King & Queen of the Class




Each of you will be distributed a worksheet.
On the worksheet is 15 problems.
When directed, you will flip the worksheet over and
begin working.
After 20 minutes, we will grade the problems and
the girl and boy with the most correct answers will
be deemed the Queen & King of the class!
Do Now – (⅓ x 12), (⅕ x 20), (42 + 1)
1.
2.
3.
The head of a pin has a diameter of 1x10-4 meter. A
bacterium has a diameter of 5x10-7 meter. How many
bacteria that size would fit across the diameter of the
pinhead?
There are 2 options for buying class shirts. The 8th grade
needs 375. Which is the best option and how much money
will the school save buying one over the other?
100 shirts for $567 or 30 shirts for $171
True or False: The temperature of NYC
steadily increased over time?
Today’s Objective
SWBAT review for
tomorrow’s quiz via
Jeopardy activity!
Homework - Worksheet
Tomorrow’s Quiz Topics







D = rt
Interpreting graphs
Identifying #s on a # line
Identifying #s as rational or irrational
Computing with scientific notation
Scientific notation word problems
Cost per unit
Do Now – (⅔ x 6), (⅕ x 25), (⅓x
39)



Turn in last night’s homework.
Please clear off your desk of everything except a
pencil, your calculator, and a plain sheet of paper
to cover your quiz.
Wait SILENTLY for further instruction!