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)

Please pick up your guided notes, take out your tracker, and respond to the following SILENTLY & INDEPENDENTLY:

1. Which point on the number line best represents the value of 3π?

2. Which point on the number best represents -1 ?

3. Consider the three numbers: 2.82427…, π, √7. Order them from least to greatest.

Weekly Agenda

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 ObjectiveSWBAT 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 2 ½ 0.666666666… 3.14 π (√4)2

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.

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.

Scientific Notation

Work on this on eon your own. Example 6: Solve.

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

Scientific Notation

(3.4 X 106) ÷ (2 X 108)

Scientific Notation

(1.8 x 106) (7.5 x 10-2)

Scientific Notation

Which one of these expressions correctly identifies the quotient of these two numbers(7.9 x 10-2) ÷ (9.5 x 10-4)?

a) (7.9 x 9.5) x 10(-2+-4)

b) (7.9 x 9.5) x 10(-2--4)

c) (7.9 ÷ 9.5) x 10(-2+-4)

d) (7.9 ÷ 9.5) x 10(-2--4)

Scientific Notation

(4.8 X 10-5) ÷ (3.2 X 10-6)

Scientific Notation

Scientific Notation

(3.4 X 104) (2.1 X 103

Scientific Notation

(10.5 X 1020) ÷ ( 1.2 X 10-14)

Scientific Notation

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

Which expression correctly indicates the product of these two numbers:

4.5x108 & 1.2 x 103

a) (4.5 ÷ 1.2) x 10(8-3)

b) (4.5 x 1.2) x 10(8x3)

c) (4.5 x 1.2) x 10(8÷3)

d) (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

Scientific Notation

Scientific Notation

(4.5 X 10-5) (5.2 X 10-6)

Scientific Notation

Scientific Notation

(7.3 x 108) (5.8 x 10-10)

Scientific Notation

(9.45 x 1010) ÷(1.5 x 106)

Scientific Notation

Scientific Notation

Scientific Notation

(9.3 X 1024) ( 5 X 10-13)

Scientific Notation

Which expression correctly indicates the product of these two numbers:

2.4x10-8 & 6.7 x 105

a) (2.4 x 6.7) x 10(-8x5)

b) (2.4 x 6.7) x 10(-8+5)

c) (2.4 x 6.7) x 10(-8÷5)

d) (2.4 ÷ 6.7) x 10(-8-5)

Scientific Notation

Scientific Notation

(4.2 x 10-8) ÷(1.68 x 10-2)

Scientific Notation

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. Which point on the number line represents -1.88?

2. Order the following numbers from least to greatest: (-1/9), √5, -0.8, 3.5

3. 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 smaller the exponent, the smaller

the number. If the exponents are the same, compare the

factor ones.

The larger the exponent, the larger the number. If 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.

How much more money did Jay-Z make over Yo Gotti?

Artist 2010 Income

Jay-Z 2.56 x 107

Yo Gotti 5.1 x 106

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. One microgram is equal to 1x10-6 gram. If the mass of a substance is 8x109 micrograms, what is its mass in grams?

2. If a penny is 0.4 x 103 inches thick, how thick are 6 pennies?

3. 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. 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?

2. 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

3. True or False: The temperature of NYC steadily increased over time?

Today’s ObjectiveSWBAT 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!