standard focus number sense and operations time range 1 -3

© 21st Century Math Projects

Crime Scene Decoders: Exponents, Roots & Scientific Notation

Standard Focus: Number Sense and Operations Time Range : 1-3 Days

Supplies : Pencil and Paper

Topics of Focus :

- Evaluating Exponential Expressions

- Square Root Approximations

- Scientific Notation

- Compound Interest

- Perfect Squares and Perfect Cubes

The Number System

6.NS 6c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Expressions and Equations

6.EE 1. Write and evaluate numerical expressions involving whole-number exponents.


6.EE 2d. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).


8.EE 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions.


8.EE

4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

Procedures:

A.) Student will be given the letter from Chief Harris, the possible suspects, and crime scene puzzles.

B.) Students will work in pairs or individually to solve the crime.

C.) Students will determine which suspect should be arrested.

D.) Students will create a portfolio of evidence proving that they have arrested the right person and will demonstrate their understanding of their mathematical content present in the problem.

*E.) Students can present their evidence to the class as an oral presentation.


CSD: The eviDenCe

name:_______________________________

1.

Clue

___________ 2.

Clue

___________ 3.

Clue

___________


4.

Clue

___________ 5.

Clue

___________ 6.

Clue

___________ CrypTiC TexT meSSage

SuSpeCT

___________


Crime Scene Decoders Pre-Algebra: Exponents, Roots & Scientific Notation Detectives,

Check your Twitter because the international evil genius terrorist group the Mathemagicians are causing havoc on yet another world region. It seems they are making progress in their plans to build a world conquering device despite our best efforts to apprehend their cronies. East Asia is the victim of the latest string of heists at the hands of a henchman (or henchwoman), Dr. Evil Powers. One thing is sure, Dr. Evil Powers is definitely some kind of henchperson.

As has become the calling card of the Mathemagicians they have left behind a trail of notes with a cryptic text message. The text message when substituted correctly will calculate to Dr. Powers’s favorite number. So far there are six suspects that police have questioned. It is hoped that someone with a relatively strong number sense and spatial reasoning can crack some codes that have puzzled the detectives on the case so far.

Your job is to bring Dr. Evil Powers to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Dr. Powers is known to use in the notes.

- Evaluating Exponential Expressions

- Square Root Approximations

- Scientific Notation

- Compound Interest

- Perfect Squares and Perfect Cubes

Be sure to include:

- Other examples of the concepts

- Definitions

- Any other relevant information.

This is not a time to be sloppy. The slightest miscalculation or illegible footnote could result in a not guilty verdict. Oh, did I mention that use of a calculator might prematurely set off his world conquering device? Good luck to you, gumshoe.

Chief Harris


Who is Dr. Evil Powers?

Name: Bao

Occupation: Biologist

Favorite Number:

7.8 x 105

Name: Pete

Occupation: Musician

Favorite Number:

2.3 x 1011

Name: Trish

Occupation: Fashion Designer

Favorite Number:

-1.6 x 109

Name: Aminata

Occupation: Religious Studies Professor

Favorite Number: 80

Name: Ken

Occupation: Butcher

Favorite Number:

9.1 x 1024

Name: Maribel

Occupation: Elementary School Teacher

Favorite Number: 0


Scene #1 Shinjuku Gyoen National Garden -- Tokyo, Japan

Dr. Evil Powers dug up an entire grove of plum trees. It is unclear if the plum trees factor into the World Conquering Device or if Dr. Powers just likes to eat them.

Here we are in the land of the rising sun. I soon shall make the sun set everywhere with the World Conquering Device that will – conquer the world. Ain’t that groovy? That is unless you pay me [Places pinkie to the mouth] 1.0 x 1043 dollars. Muahahahahahahahahahahaha… ha.

Sort the numbers into three groups (perfect squares, perfect cubes or leftovers). Oh wait, they are Kanji numerals and you’ have to translate them first!

十六八四十二

二十十五十九九二十七

Find the sum of the leftovers to get your first clue (equal to a) a =_______

Scene #2 Government House –- Bangkok, Thailand

Posing as an tourist, Dr. Powers snuck away from a tour group and stole a set of antique gold swords.

Let’s play my #2’s favorite game! Find a Country’s Gross Domestic Product in Standard Notation! Which is the largest? Finish before I send in my sharks with laser beams attached to their heads.

Country Gross Domestic Product (GDP) In Standard Notation

India 153.8 x 1010

Indonesia 0.0071 x 1014

Nepal 15,108,000 x 103

South Korea 1.007 x 1012

Thailand 0.313 x 1012

(the first letter of the country with the largest GDP) = (Their GDP)

______=______________

Perfect Squares

Perfect Cubes

Leftovers (Neither)


Scene #3 Angkor Wat – Angkor, Cambodia

The famed Hindu turned Buddhist temple was struck as the next victim in the heist. While everything seemed intact, all of the carvings of griffins and unicorns were ripped from the wall.

Here we are with a Shrivatsa ( ) of sorts. It’s kind of like a knot and it might be endless. However, I’ve decided to throw you a bone so that it’s not quite so endless. Solve for x and use this result to work your way to the top to find the answer to an auspicious symbol and your next clue.

Check your work and write your answer for the Shirvatsa on the line below.

=______

Angkor Wat


Scene #4 Bank of Beijing –- Beijing, China

After repelling onto the roof of the bank, Dr. Powers broke into the vault and escaped with over 元1,000,000,000 Chinese Yuan. Somewhere along the line Dr. Powers also ate a sandwich because crumbs were everywhere.

Unlike Americans who spend every quarter that they find in their couch cushions, the average Chinese family saves at least 30% of their money.

Three friends have put money into three different banks. They will keep it there for 5 years. They are debating who will have the most in their account after the 5 years are over. You help decide! You will need the equation…

A = P(1 +r)t where P= principal (starting amount), r= rate (as a decimal) and t= time (in years)

Exim Bank Industrial Bank Shengjing Bank 元15,000 at 3% interest rate

元14,500 at 4% interest


(first letter of bank)=(amount in savings)

______=______ Scene #5 Great Wall of China –- Shanhaiguan, China

With some sort of scientific contraption, Dr. Powers was able to melt down the mortar connected parts of the Great Wall. By helicopter, a ¼ mile pieces of the wall was taken.

The Great Wall of Evil

Myself and my friend Mini-Dr. Evil Powers were going to walk the entire Great Wall of China and then we thought… umm… how ‘bout no…

We decided instead it would be a much better use of our time to create an exponent challenge. The outcome of this expression is approximately the length of the entire wall (in kilometers).

(−2)7 ∙ 33 ∙ (−4)2 ∙ 56 ∙ 11.0424 ∙ 32 ∙ (−5)5

Choose the clue that is the closest to the value of your answer.

e = 8,851.80 km s = 14,713.19 km t = 21,196.18 km


Scene #6 Taj Mahal –- Agra, India Dr. Hiram Powers flew a helicopter over Taj Mahal and stole one of the famed minarets! The following note was dropped from the helicopter.

I’m about to melt the polar ice caps and flood the planet and umm… yeah I’m pretty sure you’re not going to be able to stop me! Muhahaha. But first I had to stop by one of the most perfect marriages between math and art -- the Taj Mahal.

Make a decimal approximation for the expressions and match them to the correct point on the number line.

_____ = _____ _____ _____ _____ 4 5 1 2 3 ____=____

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

It’s a hard knock life with just the 2 of us.

E • A + S – T ÷ • A + S + i ÷ A

Love, Dr. Evil Powers

Decimal Approximation

1. �92

2. 2.52

3. √85

4. √92.5 − 1.682

5. √100 − √4 − 0.2

6 7 8 9

U E A F T I O R S


Kanji Numerals 1 一 2 二 3 三 4 四 5 五 6 六 7 七 8 八 9 九 10 十 11 十一 12 十二 13 十三 14 十四 15 十五 16 十六 17 十七 18 十八 19 十九 20 二十

27 二十七


Who is Dr. Evil Powers?

Name: Bao

Occupation: Biologist

Favorite Number:

7.8 x 105

Name: Pete

Occupation: Musician

Favorite Number:

2.3 x 1010

Name: Trish

Occupation: Fashion

Designer

Favorite Number:

-1.6 x 109

Name: Aminata

Occupation: Religious

Studies Professor

Favorite Number: 80

Name: Ken

Occupation: Butcher

Favorite Number:

9.1 x 1024

Name: Maribel

Occupation: Elementary

School Teacher

Favorite Number: 0


Scene #1 Shinjuku Gyoen National Garden -- Tokyo, Japan

Dr. Evil Powers dug up an entire grove of plum trees. It is unclear if the plum trees factor into

the World Conquering Device or if Dr. Powers just likes to eat them.

Here we are in the land of the rising sun. I soon shall make the sun set

everywhere with the World Conquering Device that will – conquer the world.

Ain’t that groovy? That is unless you pay me [Places pinkie to the mouth]

1.0 x 1043 dollars. Muahahahahahahahahahahaha… ha.

Sort the numbers into three groups (perfect squares, perfect cubes or

leftovers). Oh wait, they are Kanji numerals and you’ have to translate them first!

十六16 8 八四4 10 十 2 二

20 二十 15 十五 19 十九 9 九 27 二十七

Find the sum of the leftovers to get your first clue (equal to a) a =_______66

Scene #2 Government House –- Bangkok, Thailand

Posing as an tourist, Dr. Powers snuck away from a tour group and stole a set of antique gold swords.

Let’s play my #2’s favorite game! Find a Country’s Gross Domestic Product in Standard Notation!

Which is the largest? Finish before I send in my sharks with laser beams attached to their heads.

Country Gross Domestic Product (GDP) In Standard Notation

India 153.8 x 1010 1,538,000,000,000

Indonesia 0.0071 x 1014 710,000,000,000

Nepal 15,108,000 x 103 15,108,000,000

South Korea 1.007 x 1012 1,007,000,000,000

Thailand 0.313 x 1012 313,000,000,000

(the first letter of the country with the largest GDP) = (Their GDP)

i______=______1,538,000,000,000

Perfect Squares

16, 4, 9

Perfect Cubes

8, 27

Leftovers (Neither)

10, 2, 20, 15, 19


Scene #3 Angkor Wat – Angkor, Cambodia

The famed Hindu turned Buddhist temple was struck as the next victim in the heist. While everything

seemed intact, all of the carvings of griffins and unicorns were ripped from the wall.

Here we are with a Shrivatsa of sorts. It’s kind of like a knot and it might be endless. However, I’ve

decided to throw you a bone so that it’s not quite so endless. Solve for x and use this result to work

your way to the top to find the answer to an auspicious symbol and your next clue.

Check your work and write your answer for the Shirvatsa on the line below.

=______260

Angkor Wat


Scene #4 Bank of Beijing –- Beijing, China

After repelling onto the roof of the bank, Dr. Powers broke into the vault and escaped with 元

1,000,000,000 Chinese Yuan. Somewhere along the line Dr. Powers also ate a sandwich because

crumbs were everywhere.

Unlike Americans who spend every quarter that they find in their couch

cushions, the average Chinese family saves at least 30% of their money.

Three cousins have put money into three different banks. They will keep it

there for 5 years. They are arguing who will have the most in their account

after the 5 years are over. You will need the equation…

A = P(1 +r)t where P = principal (starting amount), r = rate (as a decimal) and t = time (years)

Exim Bank Industrial Bank Shengjing Bank

元15,000 at 3% interest rate

17389.11


17641.47


17,867.94

(first letter of bank)=(amount in savings)

s______=______17,867.94

Scene #5 Great Wall of China –- Shanhaiguan, China

With some sort of scientific contraption, Dr. Powers was able to melt down the mortar connected parts

of the Great Wall. By helicopter, a ¼ mile pieces of the wall was taken.

The Great Wall of Evil

Myself and my friend Mini-Dr. Evil Powers were going to walk

the entire Great Wall of China and then we thought… umm…

how ‘bout no…

We decided instead it would be a much better use of our time to

create an exponent challenge. The outcome of this expression is

approximately the length of the entire wall (in kilometers).

Choose the clue that is the closest to the value of your answer.

e = 8,851.80 km s = 14,713.19 km t = 21,196.18 km


Scene #6 Taj Mahal –- Agra, India Dr. Hiram Powers flew a helicopter over Taj Mahal and stole one of the famed minarets! The

following note was dropped from the helicopter.

I’m about to melt the polar ice caps and flood the planet and

umm… yeah I’m pretty sure you’re not going to be able to

stop me! Muhahaha. But first I had to stop by one of the most

perfect collaborations between math and art -- the Taj Mahal.

Make a decimal approximation for

the expressions and match them to

the correct point on the number line.

___e__ = __f___ _o____ __u___ _r____

e____=____4

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

It’s a hard knock life with just the 2 of us.

E • A + S – T ÷ • A + S + i ÷ A

~Dr. Evil Powers

Decimal

Approximation

1. √ 9 -> o

2. 6.25 -> U

3. √ 9.22 ->R

4. √ 6.80 -> E

5. √ √ 7.8 -> F

6 7 8 9

U E A F T I O R S


From Puzzle 1: a =66

From Puzzle 2: I = 1,538,000,000,000

From Puzzle 3: = 260 From Puzzle 4: s=17,867.94

From Puzzle 5: t = 21,196.18

From Puzzle 6: e = 4

E • A + S – T ÷ • A + S + i ÷ A

4 • 66 + 17867.94 – 21196.18 ÷ 260 • 66

+ 17867.94 + 15380000000000 ÷ 66 =

2.33 x 1011

standard focus number sense and operations time range 1 -3

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