© 21st Century Math Projects

© 21st Century Math Projects

Project Title : CSI Algebra 2 / PreCalculus: Conic Sections

Standard Focus: Geometry & Spatial Sense Time Range : 1-3 Days

Supplies : Pencil and Paper

Topics of Focus :

- Equations of Circles, Ellipses, Parabolas & Hyperbolas

- Identifying Conic Sections

- Graphing Conic Sections

This particular unit was mapped to the introductory curriculum of most Algebra 2 & PreCalculus

textbooks and can be used as an enrichment or review activity.

Quantities N-Q

1. Use units as a way to understand problems and to guide the solution of

multi-step problems; choose and interpret units consistently in formulas;

choose and interpret the scale and the origin in graphs and data displays.

Seeing Structure

in Expressions A-SSE

1b. Interpret complicated expressions by viewing one or more of their

parts as a single entity.

Reasoning with

Equations and

Inequalities

A-REI

4a. Use the method of completing the square to transform any quadratic

equation in x into an equation of the form (x – p)2 = q that has the same

solutions. Derive the quadratic formula from this form.

Interpreting

Functions F-IF

7. Graph functions expressed symbolically and show key features of the

graph, by hand in simple cases and using technology for more complicated

cases.★

Expressing

Geometric

Properties with

Equations

G-GPE

1. Derive the equation of a circle of given center and radius using the

Pythagorean Theorem; complete the square to find the center and radius of

a circle given by an equation.

Expressing

Geometric

Properties with

Equations

G-GPE 3. (+) Derive the equations of ellipses and hyperbolas given foci and

directrices.

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

© 21st Century Math Projects

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 2 & Pre-Calc: Conic Sections

Detectives,

As you probably could have guessed, the evil genius terrorist group the Mathemagicians are at it again.

The latest series of heists have brought a dark cloud over Russia. The latest heists are by the hand of

anonymous minion, Two-Scoops N.A. Waffle. Investigators fear that the Mathemagicians are putting

the finishing touches their world conquering device -- to conquer the world.

As has become their trademark, the Mathemagicians 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 Waffle’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 Two-Scoops N.A. Waffle to justice and save the planet. You need to be prepared to

state your case and demonstrate your understanding of the following skills that Waffle is known to use

in the notes.

- Equations of Circles, Ellipses, Parabolas & Hyperbolas

- Identifying Conic Sections

- Graphing Conic Sections

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 Two-Scoops N.A. Waffle?

Name: Pete

Occupation: Musician

Favorite Number:

2.3 x 1010

Name: Pat

Occupation: Seamstress

Favorite Number: 0.02

Name: Chloe

Occupation: High

School Teacher

Favorite Number: 15

Name: Vernon

Occupation: Computer

Programmer

Favorite Number: 1010

Name: Hiram

Occupation: Geneticist

Favorite Number: 2,365

Name: Tripiti

Occupation: Pet Store

Owner

Favorite Number: 16

© 21st Century Math Projects

Scene #1 The Kremlin –- Moscow, Russia Two-Scoops N.A. Waffle snuck into the Kremlin through a chimney and stole a collection of

diamonds from a safe. Written on the Red Square in sidewalk chalk, investigators found this note.

From Russia, with love to all my soon-to-be frustrated math sleuths. Let’s see if you can figure me out.

I stumbled across this Portuguese map

of the Kremlin. Secret jewels are

hidden in the room encircled by all

three of these circles.

I.

II.

III.

Which location holds the jewels?

Armaria a = 1

Catedral do Aracanjo r = 18

Monumento a Lenine s = 19

Scene #2 Mount Elbrus –- Caucasus Mountains, Russia

A park ranger witnessed a person loading up jars of water from a nearby hot spring. Later investigators

found this note written snow.

It’s a DOUBLE RAINBOW! Look at it! It’s like two

rainbows. Even though they are optical illusions,

they are optical illusions of parabolic figures. With

my Google Glasses I was able to take a picture and

model the two rainbows.

The difference in the maximum heights (rounded

to the nearest meter) of the rainbows will be your

next clue (equal to U)

U =_____

Outside Rainbow

F(x) = -x2 + 180x – 3500

Inside Rainbow

G(x) = -x2 + 160x – 4150

© 21st Century Math Projects

Scene #3 TatNeft Arena – Kazan, Russia

Waffle broke into the home of the inaugural winners of the Kontinental Hockey League the Ak Bars

Kazan. Equipment managers discover all of their goalie pads were stolen.

,

, ,

Circles

Parabolas

Hyperbolas

put the function on the correct teams)

Circles Parabolas Hyperbolas

A = 1 i = 2 r = 3 s =4

© 21st Century Math Projects

Scene #4 Shukhov Tower –- Polibino, Russia

Police were alarmed to find out that Two-Scoops N.A. Waffle stole the entire Shukhov Tower,

the world’s first hyperboloid structure in the world.

The Russians were building hyperboloid structures, before building hyperboloid

structures was cool. Which hyperbola is the closest to the Shukhov Tower?

Scene #5 Roscosmos Headquarters –- Moscow, Russia

Waffle broke into the famous Russian Space Headquarters and escaped with three authentic astronaut

suits and ten moon rocks. It is unclear to investigators how these thefts will be used in the World

Conquering Device.

There is no way I could steal things all across Russia and not stop by their Space Headquarters.

After stealing an archived notebook from their museum, I found this puzzle for you:

The first satellite to orbit Earth, Sputnik I

(launched by the former Soviet Union in

1957) had an elliptical orbit with the Earth

at one focus. The major and minor axes of

the orbit have lengths of 7325 km and

6606 km respectively. Find the apogee

(greatest distance) from the Earth’s center

of Sputnik’s center.

Two Hints…

1.) The distance from the foci to the center is defined as √

2.) The Apogee is defined as a + c

= _____ Round your answer to the nearest kilometer. It will be equal to

a = 64

r = 729

i = 256

s = 225

© 21st Century Math Projects

Scene #6 The State Hermitage Museum – St. Petersburg, Russia

Last night, a curator was stunned to discover an entire room of 18th Century oil paintings

was taken. It is unclear if these thefts will aid in the World Conquering Device or whether

Two-Scoops N.A. Waffle is just a big fan.

Is it a can or a hat or a wombat? Who knows?! I just started drawing with conic

sections. Soon I will put this work of art on eBay with a Buy It Now price of

$160,000. I’m pretty sure I’ll get it because it is beautiful!

On the left, you’ll find the seven functions that you must sketch to uncover the

clue. Graph them on the same coordinate grid and answer the question…

The art includes something that looks most like a...

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

From Russia,

– R + U – S • S – i • A +

With Love, Two-Scoops N.A. Waffle

1

2

3

4

5

6

7

Kremlin Lynx Ushanka

a = 88 i = 99 s = 101

© 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 Two-Scoops N.A. Waffle?

Name: Pete

Occupation: Musician

Favorite Number:

2.3 x 1010

Name: Pat

Occupation: Seamstress

Favorite Number: 0.02

Name: Chloe

Occupation: High

School Teacher

Favorite Number: 15

Name: Vernon

Occupation: Computer

Programmer

Favorite Number: 1010

Name: Hiram

Occupation: Geneticist

Favorite Number: 2,365

Name: Tripiti

Occupation: Pet Store

Owner

Favorite Number: 16

© 21st Century Math Projects

Scene #1 The Kremlin –- Moscow, Russia Two-Scoops N.A. Waffle snuck into the Kremlin through a chimney and stole a collection of

diamonds from a safe. Written on the Red Square in sidewalk chalk, investigators found this note.

From Russia, with love to all my soon-to-be frustrated math sleuths. Let’s see if you can figure me out.

I stumbled across this Portuguese map

of the Kremlin. Secret jewels are

hidden in the room encircled by all

three of these circles.

I.

II.

III.

Which location holds the jewels?

Armaria a = 1

Catedral do Aracanjo r = 18

Monumento a Lenine s = 19

Scene #2 Mount Elbrus –- Caucasus Mountains, Russia

A park ranger witnessed a person loading up jars of water from a nearby hot spring. Later investigators

found this note written snow.

It’s a DOUBLE RAINBOW! Look at it! It’s like two

rainbows. Even though they are optical illusions,

they are optical illusions of parabolic figures. With

my Google Glasses I was able to take a picture and

model the two rainbows.

The difference in the maximum heights (rounded

to the nearest meter) of the rainbows will be your

next clue (equal to U)

U =____2350

Outside Rainbow

F(x) = -x2 +180x – 3500 = -(x-90)2 + 4600

Inside Rainbow

G(x) = -x2 +160x – 4150 = -(x-80)2 +2250

© 21st Century Math Projects

Scene #3 TatNeft Arena – Kazan, Russia

Waffle broke into the home of the inaugural winners of the Kontinental Hockey League the Ak Bars

Kazan. Equipment managers discover all of their goalie pads were stolen.

,

, ,

Circles

Parabolas

Hyperbolas

put the function on the correct teams)

Circles Parabolas Hyperbolas

A = 1 i = 2 r = 3 s =4

© 21st Century Math Projects

Scene #4 Shukhov Tower –- Polibino, Russia

Police were alarmed to find out that Two-Scoops N.A. Waffle stole the entire Shukhov Tower,

the world’s first hyperboloid structure in the world.

The Russians were building hyperboloid structures, before building hyperboloid

structures was cool. Which hyperbola is the closest to the Shukhov Tower?

Scene #5 Roscosmos Headquarters –- Moscow, Russia

Waffle broke into the famous Russian Space Headquarters and escaped with three authentic astronaut

suits and ten moon rocks. It is unclear to investigators how these thefts will be used in the World

Conquering Device.

There is no way I could steal things all across Russia and not stop by their Space Headquarters.

After stealing an archived notebook from their museum, I found this puzzle for you:

The first satellite to orbit Earth, Sputnik I

(launched by the former Soviet Union in

1957) had an elliptical orbit with the Earth

at one focus. The major and minor axes of

the orbit have lengths of 7325 km and

6606 km respectively. Find the apogee

(greatest distance) from the Earth’s center

of Sputnik’s center.

Two Hints…

1.) The distance from the foci to the center is defined as √

2.) The Apogee is defined as a + c 2a = 7325 and 2b = 6606 so a = 3662.5 and b = 3303

… c = 1582.43 so 3662.5 + 1582.43 = 5244.93

= _5245 Round your answer to the nearest kilometer. It will be equal to

a = 64

r = 729

i = 256

s = 225

© 21st Century Math Projects

Scene #6 The State Hermitage Museum – St. Petersburg, Russia

Last night, a curator was stunned to discover an entire room of 18th Century oil paintings

was taken. It is unclear if these thefts will aid in the World Conquering Device or whether

Two-Scoops N.A. Waffle is just a big fan.

Is it a can or a hat or a wombat? Who knows?! I just started drawing with conic

sections. Soon I will put this work of art on eBay with a Buy It Now price of

$160,000. I’m pretty sure I’ll get it because it is beautiful!

On the left, you’ll find the seven functions that you must sketch to uncover the

clue. Graph them on the same coordinate grid and answer the question…

The art includes something that looks most like a...

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

From Russia,

– R + U – S • S – i • A +

With Love, Two-Scoops N.A. Waffle

1

2

3

4

5

6

7

Kremlin Lynx Ushanka

a = 88 i = 99 s = 101

© 21st Century Math Projects

From Puzzle 1 r = 18

From Puzzle 2 U =2350

From Puzzle 3 A = 1

From Puzzle 4 i = 256

From Puzzle 5 =5245

From Puzzle 6 s = 101

(STAR) – R + U – S • S – i • A + (STAR)

5245 – 18 + 2350 – 101 • 101 – 256 • 1 + 5245 = 2365