21 st Century Math Projects

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2 Project Title : CSI Geometry: Circles Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Circumference, Radius, Diameter and Chords - Angles and Arcs - Tangents - Equations of Circles This particular was mapped to the circle curriculum of most geometry textbooks and can be used as an enrichment or review activity. Geometry 7.G Geometry 7.G 4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Circles Circles Procedures: G-C G-C 2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 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.

3 CSI Geometry: Circles Detectives, A thief, working under the alias Radii Montague, has caused a ruckus all throughout the United Kingdom. It is believed that Radii 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, a trail of notes and a cryptic text message were left behind. Our intel believes that the text message will calculate to Radii s favorite number. So far there are six suspects that police have questioned. It is hoped that someone with relatively strong geometry and reasoning skills can crack the codes that have puzzled the detectives on the case so far. 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 Radii is known to use in the notes. - Circumference, Radius, Diameter and Chords - Angles and Arcs - Tangents - Equations of Circles Be sure to include: - Other examples of the concepts - Definitions - Any other relevant information. Keep in mind, 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

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

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

6 Who is Radii Montague? Name: Ben Occupation: Inventor Favorite Number: -209 Name: Victoria Occupation: Princess Favorite Number: 183 Name: Adrianna Occupation: Hostess Favorite Number: 231 Name: Roanoke Occupation: Farmer Favorite Number: 187 Name: George Occupation: General Favorite Number: 1 Name: Bella Occupation: Stock Broker Favorite Number: -26

7 Scene #1 The London Eye - London, England Radii Montague snuck past security for the supersized Ferris Wheel and apparent stole three of the gondolas! How these factor into the World Conquering Device is unclear at this time. Friends, Romans, Countrymen, lend me your eyes! You shalt become frustrated by my mathematical riddles! Suppose you take two full trips around the London Eye, how many meters will you travel? Round to the nearest tenth of a meter and match your answer for the first clue. Length Clue m L = m U = m N =754 Scene #2 The Rose Bowl - Hampshire, England We suspect that Radii went to the famed cricket pitch and stole the bats and wickets from storage. All the world s a stage, and all the men and women merely players. And one man in his time plays many parts one such part is thy Crop Circle Maker! England is the home of the Crop Circle! Which AY is longer? That tis the question. Don t trust thy diagrams. (Choose the clue of the Crop Circle with the longer AY) Diameters: ʘA = 16 ʘB = 24, and ʘC = 12 XZ = 20 U= 21 K = 11

8 Scene #3 Winchester Castle -- Winchester, England A castle curator was astonished that the entire collection of catapults and battle axes were taken. Valiant, I honor you; but as you are ambitious, I ll give you more challenging circle problems. To be a true Knight, one must draw a circle with secants and tangents where the x calculates to the secret code 13. Find out who are the real Knights of the Round Table(that has Secants & Tangents!) Sir Lancelot Sir Galahad Sir Gawain X = X = X = Sir Robin Sir Bedivere How many knights know the secret code? X = X = 2 D = 2 3 K = 3 4 L = 4 5 U = 5 =

9 Scene #4 Stonehenge - Wiltshire, England Radii is suspected to have brought in construction trucks to dig massive holes around Stonehenge. It is believed he escaped with a family of underground aliens. To build a design out of 25 ton stone boulders, or not to build: that is the question. Build I shall! I started my own henge of stones, but tis lots of work. I have already gone 15 meters! How many more meters shall I need to go? Round your answer to the nearest meter. (This answer will be equal to k) K = Scene #5 Big Ben - London, England Radii Montague apperently broke into Big Ben late at night and stole the Great Bell and some 19 th century gears. Come what come may, time and the hour runs through the roughest of geometry assignments! Find the minor arcs ( bigger? ) of the two clock faces. Which is Changing of the Guard Tea Time The measure of the longer minor arc will be equal to o. o = = =

10 Scene #6 Westminster Station -- London, England After hours, Radii Montague broke into Westminster Abbey and stole the Issac Newton sculpture. He boarded a train on the Tube and took off! Later investigators received a text. Good Night, Good night! Parting is such sweet sorrow. I shall say good night til it be morrow or til the Mathemagicians blow up the Universe! MIND THE GAPS! Draw the 4 circles below ʘE: Center at (7, 7), r = 3 ʘF: A circle with a diameter at endpoints (-1, -2) and (-1, -10) ʘG: (x + 4) 2 + (y 4) 2 = 25 ʘH: (x 5) 2 + (y + 1) 2 4 = 0 How many trains did not get circled? (Find the answer and the clue) L = 0 U = 1 N = 2 D = 3 CRYPTIC PUZZLE SOLVER TEXT MESSAGE Radii, Radii, o wherefore art thou Radii? L + O N + D O + N U + K

11 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.

12 Who is Radii Montague? Name: Ben Occupation: Inventor Favorite Number: -209 Name: Victoria Occupation: Princess Favorite Number: 183 Name: Adrianna Occupation: Hostess Favorite Number: 231 Name: Roanoke Occupation: Farmer Favorite Number: 187 Name: George Occupation: General Favorite Number: 1 Name: Bella Occupation: Stock Broker Favorite Number: -26

13 Scene #1 The London Eye - London, England Radii Montague snuck past security for the supersized Ferris Wheel and apparent stole three of the gondolas! How these factor into the World Conquering Device is unclear at this time. Friends, Romans, Countrymen, lend me your eyes! You shalt become frustrated by my mathematical riddles! Suppose you take two full trips around the London Eye, how many meters will you travel? Round to the nearest tenth of a meter and match your answer for the first clue. Length Clue m L = m U = m N =754 Scene #2 The Rose Bowl - Hampshire, England We suspect that Radii went to the famed cricket pitch and stole the bats and wickets from storage. All the world s a stage, and all the men and women merely players. And one man in his time plays many parts One such role is thy Crop Circle Maker! Which AY is longer? That tis the question. Don t trust thy diagrams. (Choose the clue of the Crop Circle with the longer AY) Diameters: ʘA = 16 ʘB = 24, and ʘC = 12 XZ = 20 CY = 6 BY = 6 AX = 8, AB = 12, BX = 4 AX + BX + BY = AY;;; = 18 AB + BC + CY = AY CY = 10, BC = 5, AB = 2.5 Total 17.5 U= 21 K = 11

14 Scene #3 Winchester Castle -- Winchester, England A castle curator was astonished that the entire collection of catapults and battle axes were taken. Valiant, I honor you; but as you are ambitious, I ll give you more challenging circle problems. To be a true Knight, one must draw a circle with secants and tangents where the x calculates to the 13. Find the real Knights of the Round Table that has Secants & Tangents! Sir Lancelot Sir Galahad Sir Gawain X = X = X = Sir Robin X = x = 14 in this one! The rest are x = 13 Sir Bedivere X = How many knights know the secret code? 2 D = 2 3 K = 3 4 L = 4 5 U = 5 =

15 Scene #4 Stonehenge - Wiltshire, England Radii is suspected to have brought in construction trucks to dig massive holes around Stonehenge. It is believed he escaped with a family of underground aliens. To build a design out of 25 ton stone boulders, or not to build: that is the question. Build I shall! I started my own henge of stones, but tis lots of work. I have already gone 15 meters! How many more meters shall I need to go? Round your answer to the nearest meter. (This answer will be equal to k) 25/360 = 15 / c -> 25c = 5400, c = 216m is total so 201 meters K = 201 Scene #5 Big Ben - London, England Radii Montague apperent broke into Big Ben after hours and stole the Great Bell and some 19 th century gears. Come what come may, time and the hour runs through the roughest of geometry assignments! Find the minor arcs ( ) of the two clock faces. Which is bigger? Changing of the Guard Tea Time The larger minor arc will be equal to o. o =

16 Scene #6 Westminster Station -- London, England After hours, Radii Montague broke into Westminster Abbey and stole the Issac Newton sculpture. He boarded a train on the Tube and took off! Later investigators received a text. Good Night, Good night! Parting is such sweet sorrow, that I shall say good night till it be morrow. Or til the Mathemagicians blow up the Universe! MIND THE GAPS! Draw the 4 circles below ʘE: Center at (7,7), r = 3 ʘF: A circle with a diameter with endpoints (-1, -2) and (-1, -10) ʘG: (x + 4) 2 + (y 4) 2 = 25 ʘH: (x 5) 2 + (y + 1) 2 4 = 0 How many trains did not get circled? (Find the answer and the clue) L = 0 U = 1 N = 2 D = 3 CRYPTIC PUZZLE SOLVER TEXT MESSAGE Radii, Radii, o wherefore art thou Radii? L + O N + D O + N U + K

17 From Puzzle 1 N =754 From Puzzle 2 U= 21 From Puzzle 3 L = 4 From Puzzle 4 K = 201 From Puzzle 5 o =150 From Puzzle 6 D = 3 L + O N + D O + N U + K = 187