21 st Century Math Projects

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2 Project Title : CSI Pre-Algebra: Fractions Standard Focus: Number Sense and Operations Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Operations with Fractions - Interpreting Fractions from Real World Problems - Common Denominators - Using Fractions in Formulas - Interpreting Circle Graphs The Number System Expressions and Equations Expressions and Equations Expressions and Equations Expressions and Equations Expressions and Equations The Number System The Number System The Number System 6.NS 6.EE 6.EE 6.EE 6.EE 6.EE 7.NS 7.NS 7.NS 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 2. Write, read, and evaluate expressions in which letters stand for numbers. 2a. Write expressions that record operations with numbers and with letters standing for numbers. 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. 1d. Apply properties of operations as strategies to add and subtract rational numbers. 2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 2c. Apply properties of operations as strategies to multiply and divide rational numbers.

3 The Number System Expressions and Equations Procedures: 7.NS 7.EE 3. Solve real-world and mathematical problems involving the four operations with rational numbers. 3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 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 Pre-Algebra: Fractions Detectives, The boys and girls have once again come out to play. This time, the international evil genius terrorist group the Mathemagicians are running amok over Central America. Although we have apprehended a number of their associates, we have yet to recover any pieces of their ill-conceived world conquering device that they soon may deploy to conquer the world. From the intelligence we have gathered, the anonymous henchman the Evil Denominator Monster is the culprit behind these robberies. As with other crimes related to the Mathemagicians, they have left behind a trail of mathematical puzzles and a cryptic text message that needs to be deciphered. When substituted correctly, the text message will calculate to the Monster s favorite number. So far there are six suspects that police have questioned. It is hoped that someone with a relatively strong number sense can crack some codes that have puzzled the detectives on the case so far. Your job is to bring the Evil Denominator Monster to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that the Monster is known to use in the notes. - Operations with Fractions - Interpreting Fractions from Real World Problems - Common Denominators - Using Fractions in Formulas - Interpreting Circle 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. 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 Evil Denominator Monster? Name: Zoey Occupation: Retired Favorite Number: 9 ¾ Name: Austin Occupation: Bank Teller Favorite Number: 18 ½ Name: Donnie Occupation: Warehouse Supervisor Favorite Number: 4/5 Name: Quinn Occupation: Cake Decorator Favorite Number: 17 ¼ Name: Stillman Occupation: ATV Salesman Favorite Number: 999/1000 Name: Batulo Occupation: Blogger Favorite Number: 32/55

8 Scene #1 Tenochtitlan - Mexico City, Mexico The Evil Denominator Monster is suspected to have broken into the famed Aztec city and escaped with five Giant Eagle bags full of gold. Investigators later found this note. = = = = = = The Evil Denominator Monster has come to destroy all whole numbers, integers and decimals. Although I understand these are subsets of fractions, they are not truly fractions! I demand that fractions be used in all walks of life! All fractions. All the time. I have graffitied an ancient Aztec decoration with a fraction puzzle! If you can get to the end of this puzzle you will get your first clue (equal to E). HINT: the answer is a fraction! e = Scene #2 Caribbean Sea - Belize City, Belize A figure parachuted from an airplane and landed on a yacht in the middle of the Caribbean Sea. All of the passengers were sent to shore in lifeboats, but the yacht was taken. Victims claimed the figure kept yelling that they were the Evil Denominator Monster. Woohoo. It is time for my favorite game: See Real-Life Situations as Fractions Game. In the Caribbean Sea, there are 15 yachts, 32 sailboats, and 8 trawlers. What fraction of the boats are sailboats? On the coast of Belize, there are 4,200 butterflies. 800 are orange, 200 are purple, 400 are yellow and the rest are blue. What fraction of the butterflies are blue? Which fraction is larger? The fraction of Sailboat is larger The fraction of butterflies is larger m = 1/2 c = 1/2

9 Scene #3 Tikal National Park Tikal, Guatemala The local conservationists were stunned to find out that the large stucco mask of Temple 33 was taken. It is unclear to investigators how the mask may be used in the World Conquering Device. The Mayans seem to have forgotten fractions in their number system. Of course the Evil Denominator Monster can take care of that! Use the common dominators from the Bank to solve these expressions. Cross them out as you go. The sum of the leftovers is equal to A= 16 C = 18 M = 20 R = 26 =

10 Scene #4 Afinity de Mexico - Ciudad, Mexico A shoe factory specializing in lightweight footwear was broken into last night and their entire inventory of rubber was taken. Custodians later found this note in the restroom. Three friends are going to the store for the latest, greatest athletic shoe (so they can run from the Evil Denominator Monster). The good news is the Mexico produces a lot of great footwear. The bad news is that there are only 2 pairs left and they have three pairs of feet. And worse news They have to use fractions to figure out their shoe size. Use the equation to determine the correct shoe size for each person. (shoe size) = (foot length in cm) Shoe Store Inventory Foot Length: 25 cm Foot Length: 30 cm Foot Length: 27 cm 5½ 11½ Who will not be able to get shoes? (the first letter of their name) = (their shoe size) = Scene #5 Arena Volcano - San Jose, Costa Rica With a special suit, a number of witnesses watched the Evil Denominator monster repel into the volcano and leave with 20 liters of magma. Hola, cómo estás? Voy a practicar mi español y hacer que realmente confundido! Encontrar las fracciones equivalentes! Qué fracción es permanecer? Será igual a i. i =

11 Scene #6 Panama Canal Zone - Ancón, Panama The Evil Denominator Monster is suspected to have taken the locks for the Panama Canal rendering it useless. Birds carried the following note to investigators. You are running out of time. Soon, the entire internet will begin to display all numbers in fraction form. Next I ll be going after the words Not counting Mexico (which accounts for over 70% of the population of Central America) how are the rest of the people distributed? The Estimated Total Population of these 7 Countries in 2012 was: 42,688,190 people Population in Central America (without Mexico) Costa Rica, 11/100 Nicaragua, 13/100 Panama, 2/25 Belize, 1/100 Guatemala, 1/3 Which of these two numbers are smaller? El Salvador, 7/50 Honduras, 1/5 The difference between the population of El Salvador and Costa Rica. The difference between the population of Nicaragua and Panama. a = 1/4 m = 3/4 CRYPTIC PUZZLE SOLVER TEXT MESSAGE 5 out of 4 people can t do fractions. C A M E R i C + A The Evil Denominator Monster

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 Evil Denominator Monster? Name: Zoey Occupation: Retired Favorite Number: 9 ¾ Name: Austin Occupation: Bank Teller Favorite Number: 18 ½ Name: Donnie Occupation: Warehouse Supervisor Favorite Number: 4/5 Name: Quinn Occupation: Cake Decorator Favorite Number: 17 ¼ Name: Stillman Occupation: ATV Salesman Favorite Number: 999/1000 Name: Batulo Occupation: Blogger Favorite Number: 32/55

14 Scene #1 Tenochtitlan - Mexico City, Mexico The Evil Denominator Monster is suspected to have broken into the famed Aztec city and escaped with five Giant Eagle bags full of gold. Investigators later found this note. = = = = = = The Evil Denominator Monster has come to destroy all whole numbers, integers and decimals. Although I understand these are subsets of fractions, they are not truly fractions! I demand that fractions be used in all walks of life! All fractions. All the time. I have graffitied an ancient Aztec decoration with a fraction puzzle! If you can get to the end of this puzzle you will get your first clue (equal to E). Hint: the answer is a fraction! e = 2/3 Scene #2 Caribbean Sea - Belize City, Belize A figure parachuted from an airplane and landed on a yacht in the middle of the Caribbean Sea. All of the passengers were sent to shore in lifeboats, but the yacht was taken. Victims claimed the figure kept claiming that they were the Evil Denominator Monster. Woohoo. It is time for my favorite game: See Real-Life Situations as Fractions Game. In the Caribbean Sea, there are 15 yachts, 32 sailboats, and 8 trawlers. What fraction of the boats are sailboats? 32/ /4200 On the coast of Belize, there are 4,200 butterflies. 800 are orange, 200 are purple, 400 are yellow and the rest are blue. What fraction of the butterflies are blue? Which fraction is larger? The fraction of Sailboat is larger The fraction of butterflies is larger m = 1/2 c = 1/2

15 Scene #3 Tikal National Park Tikal, Guatemala The local conservationists were stunned to find out that the large stucco mask of Temple 33 was taken. It is unclear to investigators how the mask may be used in the World Conquering Device. The Mayans seem to have forgotten fractions in their number system. Of course the Evil Denominator Monster can take care of that! Use common dominators from the bank to solve these expressions. Is the sum of the leftovers? A= 16 C = 18 M = 20 R = 26 =

16 Scene #4 Afinity de Mexico - Ciudad, Mexico A shoe factory specializing in lightweight footwear was broken into last night and their entire inventory of rubber was taken. Custodians later found this note in the restroom. Three friends are going to the store for the latest, greatest athletic shoe (so they can run away faster from the Evil Denominator Monster). The good news is the Mexico produces a lot of great footwear. The bad news is that there are only 2 pairs left and they have three pairs of feet. The worst news? They have to use fractions to figure out their shoe size. Use the equation to determine the correct shoe size for each person. shoe size = (foot length in cm) Shoe Store Inventory Foot Length: 25 cm 5.5 Foot Length: 30 cm 11.5 Foot Length: 27 cm ½ 11½ Who will not get shoes? (the first letter of their name) = (their shoe size) R = 8.5 Scene #5 Arena Volcano - San Jose, Costa Rica With a special suit, a number of witnesses watched the Evil Denominator monster repel into the volcano and leave with 20 liters of magma. Hola, cómo estás? Voy a practicar mi español y hacer que realmente confundido! Encontrar las fracciones equivalentes! Qué fracción es permanecer? Será igual a i. i =

17 Scene #6 Panama Canal Zone - Ancón, Panama The Evil Denominator Monster is suspected to have taken the locks for the Panama Canal rendering it useless. Birds carried the following note to investigators. You are running out of time. Soon, the entire internet will begin to display all numbers in fraction form. Next I ll be going after the words Not counting Mexico (which accounts for over 70% of the population of Central America) how are the rest of the people distributed. The Estimated Total Population of these 7 Countries in 2012 was: 42,688,190 people Costa Rica, 11/100 Nicaragua, 13/100 Panama, 2/25 Belize, 1/100 Guatemala, 1/3 Which of these two numbers are smaller? El Salvador, 7/50 Honduras, 1/5 The difference between the population of El Salvador and Costa Rica. The difference between the population of Nicaragua and Panama = 1,280, = 2,134,409.5 a = 1/4 m = 3/4 CRYPTIC PUZZLE SOLVER TEXT MESSAGE 5 out of 4 people can t do fractions. C A M E R i C + A The Evil Denominator Monster

18 From Puzzle 1: e = 2/3 From Puzzle 2: c = 1/2 From Puzzle 3: M = 20 From Puzzle 4: R = 8 ½ From Puzzle 5: i = From Puzzle 6: a = 1/4 C A M E R i C + A 1/2 1/4 20 2/3 8 ½ 1/2 + 1/4 = 17 ¼