© 21st Century Math Projects
Project Title : CSI Algebra: Real Numbers Standard Focus : Number, Number Sense, and Operations
Time Range : 1-3 Days Supplies : Pencil and Paper
Topics of Focus : -
Square root approximation
-
Decimal, fraction, percent, conversion
-
Scientific Notation
-
The Real Number System
-
Perfect Squares
This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 2 and can be used as an enrichment or review activity. Expressions and Equations
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).
The Number System
7.NS
2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
The Number System
7.NS
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
The Number System
8.NS
1. Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
The Number System
8.NS
2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).
8.EE
2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Expressions and Equations
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.
© 21st Century Math Projects
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. *Extensions
© 21st Century Math Projects
CSI Algebra: Real Numbers Detectives, A thief, working under the alias Guapo Arcsin, has caused a ruckus all throughout Central America. It is believed that Guapo is a member of the evil genius group, the Mathemagicians. From what the detectives have gathered thus far from the previous thefts, the Mathemagicians are building a world conquering device. Fortunately, Guapo has left behind a trail of notes and a cryptic text message that he has told us will calculate toward his favorite number. Thus far there are six suspects that police have questioned. It is hoped that someone with a relatively strong number sense can crack some codes that have puzzled the detectives on the case so far. Your job is to bring Guapo to justice and save the planet. Since you are being brought in as a specialist you have to have definitive proof in order for any arrest to hold up in court. You need to be prepared to state your case and demonstrate your understanding of the following skills that Guapo is known to use in her/his notes. -
Square root approximation
-
Decimal, fraction, percent, conversion
-
Scientific Notation
-
The Real Number System
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
© 21st Century Math Projects
CSI: The Evidence Name:_______________________________ 1.
Clue ___________ 2.
Clue ___________ 3.
Clue ___________ © 21st Century Math Projects
4.
Clue ___________ 5.
Clue ___________ 6.
Clue ___________ Cryptic Text Message Suspect ___________ © 21st Century Math Projects
Who is Guapo Arcsin? Name: Stillman
Name: Charmelle
Occupation: College Student
Occupation: Mechanical Engineer
Favorite Number: -7
Favorite Number:
Name: Hiram
Name: Logan
Occupation: Doctor
Occupation: Politician
Favorite Number: 6
Favorite Number : 13
Name: Pedro
Name: Eden
Occupation: Fire Fighter
Occupation: Organic Food Grower
Favorite Number: ½
Favorite Number: 0
© 21st Century Math Projects
Scene #1
Machu Picchu - Peru
At about 12:24, Guapo Arcsin broke into the famous Incan ruins and stole an Intihuatana stone. The Intihuatana is a ritual South American stone used to tell time.
Hello Peru Peeps and Police, To let you know upfront, I plan on conquering the world. Okay, now that I have your attention, I figure I’ll give you a fighting chance to stop me. MuHahahahahaha. If found this riddle carved into an Incan temple.
Figure out a number that fits all three of these criteria. 1.
A is a WHOLE NUMBER
2.
A is a two digit perfect square
3.
A > |-7| +
Please be aware I will later send you a CRYPTIC PUZZLE SOLVER TEXT MESSAGE.
A=_______
Sincerely Yours, Guapo Arcsin Scene #2
Mayan Ruins -- Mexico
Four rare, limestone cornerstones were extracted from the ruins of a Mayan ceremonial platform. These stones could perhaps lay the foundation for a devastating world conquering device. My Dearest, Since I haven’t been captured yet, I’ve been thinking about running for Congress! I’ll make the next one an easy one. I have run three different opinion polls.
Which one is the best?
G.
11 out of every 20 voters is expected to vote for me!
ñ.
The percentage of voters that are expected to vote for me is 54%!
P.
There are 240,000 expected to vote, and of these, 130,000 are expected to vote for me!
This letter = -6
______=-6 © 21st Century Math Projects
Scene #3
Andes Mountains -- Colombia
Thursday night, Guapo Arcsin traversed the mountains and shaved two dozen alpacas. While it’s unclear what he plans to do with the wool, there are now many cold and confused alpacas. He carved this note into the mountain. Greetings Police Officer, I see that my first puzzle has befuddled even the best of you. I’ve made the next one even harder. Remember my World Conquering Device will go off at the touch of a calculator.
1.)
Q is a RATIONAL NUMBER
Q=_______ 2.)
Give up yet? Your Friend, Guapo Arcsin
3.)
Scene #4
Panama Canal -- Panama
An oiler tanker ship was reported missing from the canal. Apparently the captain decided to go ashore to eat a sandwich and was shocked to find this note in place of his boat. To Whom It May Concern, I’m sure you are thoroughly confused by now. Hopefully you don’t arrest the wrong person! 1.
A = the denominator of 125/1000 when it is written in lowest terms.
2.
B = the number of minutes in a day divided by 360.
3.
√
4.
Mystery Letter = Approximation of √
4
A
G
5
Mystery Letter = 32
Q
on the number line.
W
6
ñ
Y
7
B
______= 32 © 21st Century Math Projects
Scene #5
St. Cecilia Acatitlan -- Mexico
An unknown amount of rubble and multiple Aztec jade masks depicting various gods were stolen. Guapo has successfully robbed the Aztec, Incans, and Mayans. It’s unknown what he’s capable of…he must be stopped quick. What’s Good, I’m getting bored. I decided to make some of my own wall art. Which point most accurately represents √
C
L
A
10
U
C
?
L
U
12
11
S 13
Which point most accurately represents √ your previous answer.
(HINT: C=3, A=1, L=12 etc.)
M
3
? Use
A
4
T
5
H
6
Which point most accurately represents √
Q
U
A
-1
?
D
R
A
0
T
I
C 2
1
Which point most accurately represents √
P -3
ñ
Q
?
G -2
W
-1
S 0
Round your last answer to the nearest integer and you might have figured out me out.
Final Letter = Rounded Answer
____ =____
We will be deploying our device soon. Good luck. Happy Holidays, Guapo Arcsin © 21st Century Math Projects
Scene #6
Museo Nacional de Antropologia – Mexico City
Three rare, blind Egyptian six legged mice were stolen from the National Museum of Anthropology. We suspect Guapo Arcsin will be using their abnormal DNA as part of his World Conquering Device. Hola, Como estas? Muy bien gracias. I’m liking this Spanishness! I want to play some futbol! Elegir la respuesta con los números en orden de menor a mayor.
½ ½ ½
ñ = El numéro de letras en la palabra es la respuesta.
ñ =____
Adios Amigos, Señor Guapo Arcsin
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
omg u arent gonna figure this out my num is perfect (ñ-Qñ)^(G/P) - (SQRT(A-W)) - 3Qñ
rofl Guapo Too Slick Arcsin © 21st Century Math Projects
Thank you for being my Math Friend! If you liked this
21st Century Math Project You might like others.
(Click the logo)
Math it Up. Boomdiggy.
© 21st Century Math Projects
Who is Guapo Arcsin? Name: Stillman
Name: Charmelle
Occupation: College Student
Occupation: Mechanical Engineer
Favorite Number: -7
Favorite Number:
Name: Hiram
Name: Logan
Occupation: Doctor
Occupation: Politician
Favorite Number: 6
Favorite Number : 13
Name: Pedro
Name: Eden
Occupation: Fire Fighter
Occupation: Organic Food Grower
Favorite Number: ½
Favorite Number: 0
© 21st Century Math Projects
Scene #1
Machu Picchu - Peru
At about 12:24, Guapo Arcsin broke into the famous Incan ruins and stole an Intihuatana stone. The Intihuatana is a ritual South American stone used to tell time.
Hello Peru Peeps and Police, To let you know upfront, I plan on conquering the world. Okay, now that I have your attention, I figure I’ll give you a fighting chance to stop me. MuHahahahahaha. If found this riddle carved into an Incan temple.
Figure out a number that fits all three of these criteria. 1.
A is a WHOLE NUMBER {0,1,2,3,4…}
2.
A is a two digit perfect square {16, 25, 36,…}
3.
A > |-7| +
A > 7 +64 … A>71 …
A must be 81 to fulfill the two prior conditions . A=81 Will be used in the text message.
Please be aware I will later send you a CRYPTIC PUZZLE SOLVER TEXT MESSAGE.
A=_______81
Sincerely Yours, Scene #2
Mayan Ruins -- Mexico
Four rare, limestone cornerstones were extracted from the ruins of a Mayan ceremonial platform. These stones could perhaps lay the foundation for a devastating world conquering device. My Dearest, Since I haven’t been captured yet, I’ve been thinking about running for Congress! I’ll make the next one an easy one. I have run three different opinion polls.
Which one is the best?
G.
11 out of every 20 voters is expected to vote for me! 55%
ñ.
The percentage of voters that are expected to vote for me is 54%!
P.
There are 240,000 expected to vote, and of these, 130,000 130,000 / 240,000 54.167%
This letter = -6
G
______=-6 © 21st Century Math Projects
Scene #3
Andes Mountains -- Colombia
Thursday night, Guapo Arcsin traversed the mountains and shaved two dozen alpacas. While it’s unclear what he plans to do with the wool, there are now many cold and confused alpacas. He carved this note into the mountain. Q is a fraction
Greetings Police Officer,
X = 4.2/1.4 * 10^5 / 10^3 I see that my first puzzle has befuddled even the best of you. I’ve made the next one even harder. Remember my World Conquering Device will go off at the touch X = 300 of a calculator. 60/300 -> 1/5 = Q , Q goes into the text message
1.)
Q is a RATIONAL NUMBER
Q=_______ 2.)
Give up yet? Your Friend, Guapo Arcsin
3.)
Scene #4
Panama Canal -- Panama
An oiler tanker ship was reported missing from the canal. Apparently the captain decided to go ashore to eat a sandwich and was shocked to find this note in place of his boat. To Whom It May Concern, I’m sure you are thoroughly confused by now. Hopefully you don’t arrest the wrong person! 1.
A = the denominator of 125/1000 when it is written in lowest terms. 1/8 - > x=8
2.
B = the number of minutes in a day divided by 360. 24*60 / 360 = 4
3.
√
4.
Mystery Letter = Approximation of √
4
A
SQRT(8*4) = SQRT(32) = W
G
Mystery Letter = 32
5
Q
on the number line.
W
6 w
ñ
Y
7
B
______= 32 © 21st Century Math Projects
Scene #5
St. Cecilia Acatitlan -- Mexico
An unknown amount of rubble and multiple Aztec jade masks depicting various gods were stolen. Guapo has successfully robbed the Aztec, Incans, and Mayans. It’s unknown what he’s capable of…he must be stopped quick. What’s Good, I’m getting bored. I decided to make some of my own wall art. Which point most accurately represents √
C
L
A
10
U
C
?
L
U
12
11
S
13
Which point most accurately represents √
?
(HINT: C=3, A=1, L=12 etc.) U=21 SQRT(21) = A
M
3
A
4
T
5
H
6
Which point most accurately represents √ SQRT(ABS(1-6)) = SQRT(ABS(-5)) = SQRT(5) = C
Q
U
A
-1
D
R
?
A
0
T
I
C 2
1
Which point most accurately represents √
?
SQRT(3) – 5 = P
P -3
ñ
Q
G -2
W
-1
S 0
Round your last answer to the nearest integer and you might have figured out me out.
Final Letter = Rounded Answer
____ =____
We will be deploying our device soon. Good luck. P=-3 this goes into the text message. © 21st Century Math Projects
Scene #6
Museo Nacional de Antropologia – Mexico City
Three rare, blind Egyptian six legged mice were stolen from the National Museum of Anthropology. We suspect Guapo Arcsin will be using their abnormal DNA as part of his World Conquering Device. Hola, Como estas? Muy bien gracias. I’m liking this Spanishness! I want to play some futbol! Elegir la respuesta con los números en orden de menor a mayor.
½ ½
CORRECT
½
ñ = El numéro de letras en la palabra es la respuesta. Number of letter in word Ñ = 5 Adios Amigos,
ñ =___5
Señor Guapo Arcsin
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
omg u arent gonna figure this out my num is perfect (ñ-Qñ)^(G/P) - (SQRT(A-W)) - 3Qñ (5 – (1/5)(5))^(-6/-3) – SQRT(81-32) – 3(1/5)(5) After simplifying = 6 = Hiram
rofl Guapo Too Slick © 21st Century Math Projects
