21 st Century Math Projects

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2 Project Title : CSI Geometry: Proportions & Similarity Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Ratios and Scale Factors - Similar Polygons - Parts of Similar Polygons This particular was mapped to the proportions curriculum of most geometry textbooks and can be used as an enrichment or review activity. Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships 6.RP 6.RP 7.RP 7.RP 7.RP 7.RP 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 2. Recognize and represent proportional relationships between quantities. 2a. Decide whether two quantities are in a proportional relationship, 2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 2c. Represent proportional relationships by equations. Geometry 7.G 1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Similarity, Right Triangles, and Trigonometry Procedures: G- SRT 5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

3 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

4 CSI Geometry: Proportions & Similarity Detectives, As you know, we are after a group of international evil geniuses, the Mathemagicians. Our evidence indicates they have plans to build a world conquering device to conquer the world. It seems that one of the anonymous henchmen, the Moose Jaw Bandit, has committed a string of robberies all over Canada. We fear this is another step in the Mathemagician s attempt to build a world conquering device. Fortunately, the Mathemagicians are arrogant about their work and have a reputation for leaving behind a trail of notes and a sending a cryptic text message. The text message when substituted correctly will calculate to the Moose Jaw 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 Moose Jaw is known to use in the notes. - Ratios and Scale Factors - Similar Polygons - Parts of Similar Polygons 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

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 The Moose Jaw Bandit? Name: Doyle Occupation: Landscaper Favorite Number: -6,821 Name: Tripiti Occupation: Pet Store Owner Favorite Number: 7.5 Name: Trish Occupation: Factory Supervisor Favorite Number: 184 Name: Sam Occupation: Recruiter Favorite Number: -90 Name: Cesar Occupation: Insurance Claims Adjuster Favorite Number: 1,431 Name: Charlie Occupation: Historian Favorite Number: -153

8 Scene #1 CN Tower - Toronto, Ontario The Moose Jaw Bandit broke into the CN Tower and stole their supply of incandescent light bulbs that were once used to light the entire building at night. How these bulbs factor into the World Conquering Device is unknown at this time. On my path to conquering the world, I wanted to enjoy some of the great Canadian sites, eh. Up first is the Western Hemisphere s tallest tower. Watch out for the falling ice! If a 6 foot tall man casts at 2 foot shadow and at the exact same time, the CN Tower casts a shadow of 605 feet, how tall is the tower? This height will be equal to h. h= Scene #2 RCMP Heritage Center - Regina, Saskatchewan Disguised as cartoon character, Dudley Do-Right, the Moose Jaw Bandit broke into the museum of the Royal Canadian Mounted Police and stole cases of medals, badges and stuffed animals. The Mounties always get their man. Too bad you can t get me or your next clue! You might be surprised, but I m kind of a nerd about my action figures. They have to be in perfect proportion. Are these figures similar? Do the action figures have the same scale factor? What is it? Not similar figures Both similar, but not the same scale factor In scale, 15 : 2 In scale, 3 : 40

9 Scene #3 Giant Mine -- Yellowknife, Northwest Territories In the night, the Moose Jaw Bandit invaded a mine and left with 40 pounds of gold and tungsten. When I go see Grandma Bandit in Yellowknife, it is quite a trek on the MacKenzie Hwy. Use the scale to estimate the length of the trip. Which estimate is the most possible? (This leads to the clue) 1,910 km 2,250 km 2,520 km 2,840 km =

10 Scene #4 Canadian Rockies - Vancouver, British Columbia A rare Kwakwaka'wakw house pole of the indigenous people was taken from display in a local museum. In the snow, the Moose Jaw Bandit drew this puzzle. I wonder if you know how to measure indirectly with poles? If I shoot a laser from point A, that brushes the top of point B and hits the peak of Mount Robson (the highest in the Canadian Rockies) at point C. With the given measurements calculate the elevation of the mountain. The answer is equal to e. e = Scene #5 Calgary Stampede - Calgary, Alberta Before the bareback bronco competition, riders discovered that six bulls were bullnapped from their pens. Inside, investigators found this note. Looks like I m going to need to swap some of my American dollars to Canadian if I m going to get tickets to the rodeo. If you can calculate an exchange rate, you re on your way to a clue. Exchange Ratio: I exchanged 100 US Dollars for Canadian dollars. I spent 50 Canadian dollars on a ticket to the rodeo and 10 for parking. I converted the rest back to US Dollars, how much will I have? $38.14 $38.92

11 Scene #6 Molson Centre -- Montreal, Quebec The Moose Jaw Bandit broke into the home of the Montreal Canadiens. A Guy LaFleur game used jersey was taken. It is unclear if it factors into the World Conquering Device or if the Bandit is just a fan. Oh, Canada. It s been fun, but I couldn t take this trip and not stop for some hockey. In fact, I m going to build my own rink to perfect scale to the NHL! Determine the unknown variables: (b, p, t, v, w, x and z) Cross the numbers off the Bench. You will be left with two numbers. Add them together and you will be on your way to your last clue. The Bench v 9 0 1/ Do the remaining numbers add to 9 or 80? a = 9 c = 80 CRYPTIC PUZZLE SOLVER TEXT MESSAGE Take care now, bye bye then. Moose Jaw [C A N A D A] (E (H 7))

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 The Moose Jaw Bandit? Name: Doyle Occupation: Landscaper Favorite Number: -6,821 Name: Tripiti Occupation: Pet Store Owner Favorite Number: 7.5 Name: Trish Occupation: Factory Supervisor Favorite Number: 184 Name: Sam Occupation: Recruiter Favorite Number: -90 Name: Cesar Occupation: Insurance Claims Adjuster Favorite Number: 1,431 Name: Charlie Occupation: Historian Favorite Number: -153

14 Scene #1 CN Tower - Toronto, Ontario The Moose Jaw Bandit broke into the CN Tower and stole their supply of incendescent light bulbs that were once used to light the entire building at night. How these bulbs factor into the World Conquering Device is unknown at this time. On my path to conquering the world, I wanted to enjoy some of the great Canadian sites, eh. Up first is the Western Hemisphere s tallest tower. Watch out for the falling ice! If a 6 foot tall man casts at 2 foot shadow and at the exact same time, the CN Tower casts a shadow of 605 feet, how tall is the tower? This height will be equal to h. h= 1,815 Scene #2 RCMP Heritage Center - Regina, Saskatchewan Disguised as cartoon character, Dudley Do-Right, the Moose Jaw Bandit broke into the museum of the Royal Canadian Mounted Police and stole cases of medals, badges and stuffed animals. The Mounties always get their man. Too bad you can t get me or you next clue! You might be surprised, but I m kind of a nerd about my action figures. They have to be in perfect proportion. Are these figures similar? Do the action figures have the same scale factor? What is it? Not similar figures Both similar, but not the same scale factor In scale, 15 : 2 In scale, 3 : 40

15 Scene #3 Giant Mine -- Yellowknife, Northwest Territories In the night, the Moose Jaw Bandit invaded a mine and left with 40 pounds of gold and tungsten. When I go see Grandma Bandit in Yellowknife, it is quite a trek on the MacKenzie Hwy. Use the scale to estimate the length of the trip. Which estimate is the most possible? (This leads to the clue) 1,910 km 2,250 km 2,520 km 2,840 km =

16 Scene #4 Canadian Rockies - Vancouver, British Columbia A rare Kwakwaka'wakw house pole of the indigenous people was taken from display in a local museum. In the snow, the Moose Jaw Bandit drew this puzzle. I wonder if you know how to measure indirectly with poles? If I shoot a laser from point A, that brushes the top of point B and hits the peak of Mount Robson (the highest in the Canadian Rockies) at point C. With the given measurements calculate the elevation of the mountain. The answer is equal to e. e = 12,972 feet Scene #5 Calgary Stampede - Calgary, Alberta Before the bareback bronco competition, riders discovered that six bulls were bullnapped from their pens. Inside, investigators found this note. Looks like I m going to need to swap some of my American dollars to Canadian if I m going to get tickets to the rodeo. If you can calculate an exchange rate, you re on your way to a clue. Exchange Ratio: I exchanged 100 US Dollars for Canadian dollars. I spent 50 Canadian dollars on a ticket to the rodeo and 10 for parking. I converted the rest back to US Dollars, how much will I have? 97 CAD 60 CAD = 37 and $38.14 $38.92 convert back. $38.14

17 Scene #6 Molson Centre -- Montreal, Quebec The Moose Jaw Bandit broke into the home of the Montreal Canadiens. A Guy LaFleur game used jersey was taken. It is unclear if it factors into the World Conquering Device or if the Bandit is just a fan. Oh, Canada. It s been fun, but I couldn t take this trip and not stop for some hockey. In fact, I m going to build my own rink to perfect scale to the NHL! Determine the unknown variables: (b, d, p, t, w, x and z) Cross the numbers off the Bench. You will be left with two numbers. Add them together and you will be on your way to your last clue. The Bench 9 0 1/ Do the remaining numbers add to 9 or 80? a = 9 c = 80 CRYPTIC PUZZLE SOLVER TEXT MESSAGE Take care now, bye bye then. Moose Jaw [C A N A D A] (E (H 7))

18 From Puzzle 1: h= 1,815 From Puzzle 2: d = 3/40 From Puzzle 3: a = ½ From Puzzle 4: e =12,972 feet From Puzzle 5: n = 38 From Puzzle 6: c = 80 [C A N A D A] (E (H 7)) [80 1/2 38 1/2 3/40 1/2] (12,972 ((1815) 7)) [ /40 1/2] (12,972 ((1815) 7)) [760 3/40 1/2] (267) [57 1/2] (267) [114] (267) = -153