21 st Century Math Projects

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2 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 Seeing Structure in Expressions Reasoning with Equations and Inequalities Interpreting Functions Expressing Geometric Properties with Equations Expressing Geometric Properties with Equations Procedures: N-Q A-SSE A-REI F-IF G-GPE G-GPE 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. 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity. 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. 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 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. 3. (+) Derive the equations of ellipses and hyperbolas given foci and directrices. 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

3 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

4 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

5 CSI: The Evidence Name: 1. Clue 2. Clue 3. Clue

6 4. Clue 5. Clue 6. Clue Cryptic Text Message Suspect

7 Who is Two-Scoops N.A. Waffle? Name: Pete Occupation: Musician Favorite Number: Name: Pat Occupation: Seamstress Favorite Number: x 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

8 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. Outside Rainbow F(x) = -x x 3500 Inside Rainbow G(x) = -x x 4150 The difference in the maximum heights (rounded to the nearest meter) of the rainbows will be your next clue (equal to U) U =

9 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

10 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? a = 64 r = 729 i = 256 s = 225 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: Two Hints 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. 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 =

11 Scene #6 The State Hermitage Museum St. Petersburg, Russia Last night, a curator was stunned to discover an entire room of 18 th 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... Kremlin Lynx Ushanka a = 88 i = 99 s = 101 CRYPTIC PUZZLE SOLVER TEXT MESSAGE From Russia, R + U S S i A + With Love, Two-Scoops N.A. Waffle

12 Thank you for being my Math Friend! If you liked this 21 st Century Math Project You might like others. (Click the logo) Math it Up. Boomdiggy.

13 Who is Two-Scoops N.A. Waffle? Name: Pete Occupation: Musician Favorite Number: Name: Pat Occupation: Seamstress Favorite Number: x 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

14 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. Outside Rainbow F(x) = -x x 3500 = -(x-90) Inside Rainbow G(x) = -x x 4150 = -(x-80) The difference in the maximum heights (rounded to the nearest meter) of the rainbows will be your next clue (equal to U) U = 2350

15 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

16 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? a = 64 r = 729 i = 256 s = 225 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: Two Hints 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. 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 = and b = 3303 c = so = Round your answer to the nearest kilometer. It will be equal to = _5245

17 Scene #6 The State Hermitage Museum St. Petersburg, Russia Last night, a curator was stunned to discover an entire room of 18 th 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... Kremlin Lynx Ushanka a = 88 i = 99 s = 101 CRYPTIC PUZZLE SOLVER TEXT MESSAGE From Russia, R + U S S i A + With Love, Two-Scoops N.A. Waffle

18 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) = 2365