© 21st Century Math Projects

© 21st Century Math Projects
Project Title : CSI Algebra: Factoring & Quadratic Functions
Standard Focus: Patterns, Function and
Algebra
Time Range : 1-3 Days
Supplies : Pencil and Paper
Topics of Focus :
-
Factoring trinomials including GCF and Distributive Property
-
Quadratic Formula
-
Graphing and interpreting parabolic graphs
This particular was mapped to elements of the curriculum in Glencoe Algebra 1 Chapter 9 & 10
and can be used as an enrichment or review activity.
Seeing Structure
in Expressions
Creating
Equations
Reasoning with
Equations and
Inequalities
Reasoning with
Equations and
Inequalities
ASSE
3a. Factor a quadratic expression to reveal the zeros of the function it
defines.
3. Represent constraints by equations or inequalities, and by systems of
Aequations and/or inequalities, and interpret solutions as viable or nonviable
CED
options in a modeling context.
AREI
4. Solve quadratic equations in one variable.
AREI
4b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square
roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the quadratic
formula gives complex solutions and write them as a ± bi for real numbers a
and b.
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.
*Extensions
© 21st Century Math Projects
CSI Algebra: Factoring &
Quadratic Functions
Detectives,
We can literally count the seconds until the Mathemagicians deploy their world conquering device. For
their last crime spree, an associate by the name of Calcuu Paraboloid has terrorized the United States.
Based on our intel, we believe Calcuu Paraboloid is the leader of the evil genius terrorist group.
Investigators suspect that the world conquering device intends to vaporize calculators everywhere!
From Wall St. to Walmart, the world would have to relearn how to do basic arithmetic operations. In
other words, it’s the end of the world.
As the Mathemagicians have done time and time again, they
have scattered six mathematical puzzles and a cryptic text
message that must be solved. After solving the puzzles, you
can decode the message which will lead to Calcuu’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 geometry spatial sense can crack some
codes that have puzzled the detectives on the case so far.
Your job is to bring Calcuu Paraboloid to justice and save the planet. You need to be prepared to state
your case and demonstrate your understanding of the following skills that Calcuu is known to use in the
notes.
-
Factoring trinomials including GCF and Distributive Property
-
Quadratic Formula
-
Graphing and interpreting parabolic graphs
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. We are counting on you. 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 Calcuu Paraboloid?
Name: George
Name: Tecumseh
Occupation: Executive
Occupation: Chief
Favorite Number : 1
Favorite Number:
-900
Name: Tom
Name: Ben
Occupation: Writer
Occupation:
Inventor
Favorite Number: -74
Favorite Number:
1776
Name:
Pocahontas
Occupation:
Translator
Name: Betsy
Occupation: Seamstress
Favorite Number:
630
Favorite Number:
42
© 21st Century Math Projects
Scene #1
Yellowstone National Park –- Wyoming, USA
A ranger was stunned to discover the famed petrified forest completely uprooted. Investigators
suspect Calcuu Paraboloid excavated an entire allosaurus skeleton. In the dirt, they found this note.
Land of the free? Home of the brave? We’ll see how you hold up after we flip the switch on our world
conquering device. All electronic calculation devices will be one big cloud of poof. Go find your abacus
and pull off your socks because you don’t have a chance at solving my puzzles.
Find the GCF of these three monomials. The coefficient of the monomial is equal to s.
792x9y13z4
1056x4yz5
220x12y6z2
s=________
Scene #2
Silicon Valley –- California, USA
The top secret headquarters of Google was infiltrated in the afternoon by a person dressed up like
Elmo from Sesame Street. The person took sixteen prototype Google Gadgets. Based on the lost
resources, it’s quite possible Google was preparing to conquer the world on their own.
You Americans seem to spend a lot time on your phone throwing birds at pigs. Well here you go…
Graph the path of the three projectile
birds (you may need to make tables). The
birds are launched from (0,0) and the pig
sits on (4,0).
y = -2x²+8x
y = -x²+7x
y = 4x–x²
How many birds hit the pig?
Zero One Two Three
b = 0 i = 1 r = 2 d = -4
© 21st Century Math Projects
Scene #3
Hollywood Hills –- California, USA
Security officials were called to a number of celebrity homes. It seems that Calcuu Paraboloid stole
their luxury countertops. Based on the positioning of the mayonnaise jars, Paraboloid may have
also made a sandwich at each house.
Party like a rockstar! I just robbed the six most important people in America according to TMZ! I left
them each with a factoring question.
Jennifer
Will
Oprah
Lopez
Smith
Winfrey
15xy – 30y
x2 – 8x + 7
x2 – 9x + 14
Justin
Lady
Chuck
Bieber
Gaga
Norris
x2 + 11x – 26
4x2 – 25x + 6
5x2 – 6x – 8
Which four celebrities have (x-2) as one of their factors?
b = -2
u = -4
s = -7
a=-9
r = -18
© 21st Century Math Projects
Scene #4
St. Louis Arch -- Missouri, USA
Missourians were baffled when they woke up to find that their famous St. Louis arch was stolen
during the night. Witnesses saw a helicopter carrying an arch away, but assumed it was just some
other arch.
Calcuu Paraboloid -- the New Spirit of St. Louis. This arch will be the perfect fit for the top of our
world conquering device.
The shape of the Gateway Arch in St. Louis,
Missouri resembles a parabola with the
equation h = -0.00635x2 +4.0005x – 0.07875,
where h is the height in feet and x is the
distance from one base in feet.
What is the distance from one base of the
arch to the other? This answer to the nearest
foot is equal to u.
u = ______
Scene #5
Cowboy Stadium –- Texas, USA
Calcuu Paraboloid carved a hole through the roof of the largest dome stadium in the world, the home
of the Dallas Cowboys. He escaped with their jumbotron, which happens to be the largest HD screen
ever built.
Everything is bigger in Texas. Too bad that doesn’t mean they’ll win a playoff game or beat the
Giants. After we conquer the world, we’re going to build our own football field. Help us out…
In the NFL, a football field is 200 feet longer than it is wide, and the area of the field is 57,600 ft2.
What is the width of the field? W will be equal to the width.
(Before you mess this up, the field is not 100 yards long. You must include the lengths of the endzones.)
(And hey wait a second! Before you mess it up now, notice the problem is in FEET)
w will be equal to the width
of the field.
w = ______
© 21st Century Math Projects
Scene #6
Kennedy Space Center –- Florida, USA
NASA was rocked when the entire facility was hit with a bioweapon. Calcuu Paraboloid used the
opportunity to steal a space shuttle. Presumably, this is the final piece of his world conquering
device. The final note was left on the stall of a NASA restroom. The final text message followed.
Before you know it, the Mathemagicians are finally going to conquer the world! For my last puzzle,
a Mars Rover baseball toss problem!
(Vertical Motion Equations: The height H of an object t seconds after it is propelled upward with
an initial velocity v represented by H = -½ gt2 + vt + h, where g is the gravitational pull and h
is the initial height.)
Suppose a NASA rover on Mars, throws a baseball upward with an initial velocity of 10 meters per
second, letting go of the ball 2 meters above the ground. Since the gravity stuff works different on
Mars it will take longer for the ball to land. How much longer will the ball stay in the air on
Mars? The answer to this question rounded to the nearest tenth is equal to A.
Acceleration due to gravity
Vertical Motion Equation
When does the baseball hit the
ground?
9.8 m/s2
3.7 m/s2
A = ______
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Tick, tock, tick, tock.
(u  s  A)(r  b)
(
) (rAw  rs  u)  (s  7r)
uw
© 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 Calcuu Paraboloid?
Name: George
Name: Tecumseh
Occupation: Executive
Occupation: Chief
Favorite Number : 1
Favorite Number:
-900
Name: Tom
Name: Ben
Occupation: Writer
Occupation:
Inventor
Favorite Number: -74
Favorite Number:
1776
Name:
Pocahontas
Occupation:
Translator
Name: Betsy
Occupation: Seamstress
Favorite Number:
630
Favorite Number:
42
© 21st Century Math Projects
Scene #1
Yellowstone National Park –- Wyoming, USA
A ranger was stunned to discover the famed petrified forest completely uprooted. Investigators
suspect Calcuu Paraboloid excavated an entire allosaurus skeleton. In the dirt, they found this note.
Land of the free? Home of the brave? We’ll see how you hold up after we flip the switch on our world
conquering device. All electronic calculation devices will be one big cloud of poof. Go find your abacus
and pull off your socks because you don’t have a chance at solving my puzzles.
Find the GCF of these three monomials. The coefficient of the monomial is equal to s.
792x9y13z4
1056x4yz5
220x12y6z2
44x4yz2
s=________ 44
Scene #2
Silicon Valley –- California, USA
The top secret headquarters of Google was infiltrated in the afternoon by a person dressed up like
Elmo from Sesame Street. The person took sixteen prototype Google Gadgets. Based on the lost
resources, it’s quite possible Google was developing to conquer the world on their own.
You Americans seem to spend a lot time on your phone throwing birds at pigs. Well here you go…
Graph the path of the three projectile
birds (you may need to make tables). The
birds are launched from (0,0) and the pig
sits on (4,0).
y = -2x²+8x
y = -x²+7x
y = 4x–x²
How many birds hit the pig?
Zero One Two Three
b = 0 i = 1 r = 2 d = -4
© 21st Century Math Projects
Scene #3
Hollywood Hills –- California, USA
Security officials were called to a number of celebrity homes. It seems that Calcuu Paraboloid stole
their luxury countertops. Based on the positioning of the mayonnaise jars, Paraboloid may have
also made a sandwich at each house.
Party like a rockstar! I just robbed the six most important people in America according to TMZ! I left
them each with a factoring question.
Jennifer
Will
Oprah
Lopez
Smith
Winfrey
15xy – 30y
x2 – 8x + 7
x2 – 9x + 14
Justin
Lady
Chuck
Bieber
Gaga
Norris
x2 + 11x – 26
4x2 – 25x + 6
5x2 – 6x – 8
Which four celebrities have (x-2) as one of their factors?
b = -2
u = -4
s = -7
a=-9
r = -18
© 21st Century Math Projects
Scene #4
St. Louis Arch -- Missouri, USA
Missourians were baffled when they woke up to find that their famous St. Louis arch was stolen
during the night. Witnesses saw a helicopter carrying an arch away, but assumed it was just some
other arch.
Calcuu Paraboloid -- the New Spirit of St. Louis. This arch will be the perfect fit for the top of our
world conquering device.
The shape of the Gateway Arch in St. Louis,
Missouri resembles a parabola with the
equation h = -0.00635x2 +4.0005x – 0.07875,
where h is the height in feet and x is the
distance from one base in feet.
What is the distance from one base of the
arch to the other? This answer to the nearest
foot is equal to u.
Zeroes: 0.0197 and 629.98. Difference 630
Scene #5
u = ______ 630
Cowboy Stadium –- Texas, USA
Calcuu Paraboloid carved a hole through the roof of the largest dome stadium in the world, the home
of the Dallas Cowboys. He escaped with their jumbotron, which happens to be the largest HD screen
ever built.
Everything is bigger in Texas. Too bad that doesn’t mean they’ll win a playoff game or beat the
Giants. After we conquer the world, we’re going to build our own football field. Help us out…
In the NFL, a football field is 200 feet longer than it is wide, and the area of the field is 57,600 ft2.
What is the width of the field? W will be equal to the width.
(Before you mess this up, the field is not 100 yards long. You must include the lengths of the endzones.)
(And hey wait a second! Before you mess it up now, notice the problem is in FEET)
w will be equal to the width
of the field.
w = 160
© 21st Century Math Projects
Scene #6
Kennedy Space Center –- Florida, USA
NASA was rocked when the entire facility was hit with a bioweapon. Calcuu Paraboloid used the
opportunity to steal a space shuttle. Presumably, this is the final piece of his world conquering
device. The final note was left on the stall of a NASA restroom. The final text message followed.
Before you know it, the Mathemagicians are finally going to conquer the world! For my last puzzle,
a Mars Rover baseball toss problem!
(Vertical Motion Equations: The height H of an object t seconds after it is propelled upward with
an initial velocity v represented by H =- ½ gt2 + vt + h, where g is the gravitational pull and h
is the initial height.)
Suppose a NASA rover on Mars, throws a baseball upward with an initial velocity of 10 meters per
second, letting go of the ball 2 meters above the ground. Since the gravity stuff works different on
Mars it will take longer for the ball to land. How much longer will the ball stay in the air on
Earth? The answer to this question rounded to the nearest tenth is equal to A.
9.8 m/s2
H =- ½ (9.8)t2 + 10t + 2
2.2 seconds
Acceleration due to gravity
Vertical Motion Equation
When does the baseball hit the
ground?
3.7 m/s2
H =- ½ (3.7)t2 + 10t + 2
5.6 seconds
Difference 3.4 seconds
A = ______ 3.4
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Tick, tock, tick, tock.
(u  s  A)(r  b)
(
) (rAw  rs  u)  (s  7r)
uw
© 21st Century Math Projects
S= 44
r = 2 u = 630 w = 160 b = -2 A = 3.4
0 +(2(3.4)(160)+(2)(44)+630)-(44-14)
(1088+88+630)-(30)=1776
© 21st Century Math Projects