21 st Century Math Projects

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2 Project Title : CSI Pre-Algebra: & Inequalities Standard Focus: Number Sense and Operations Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - One-Step and Inequalities - Two-Step - Translating - Solving with Formulas The Number System 6.NS 7a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 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. 2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. 2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 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.

3 Procedures: 7.EE 8.EE 8.EE 8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 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. 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7. Solve linear equations in one variable. 7a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 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: & Inequalities Detectives, The evil genius group, the Mathemagicians, have crossed the Atlantic and are terrorizing Europe. Indications are that they are behind a number of robberies across the continent and they are making progress in the construction of a world conquering device. Notes have been found at each site and have been signed Justice Equilibrator. Through our intelligence we ve determined this individual is a high ranking member of the group. Once again we have received a cryptic text message and we ve been told the result will calculate to Equilibrator s favorite number. Thus far there are six suspects that police have questioned. It is hoped that someone with a relatively strong number sense and spatial reasoning skills can crack some codes that have puzzled the detectives on the case so far. Your job is to bring Justice Equilibrator to justice (umm yeah!) and save the planet. 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 Equilibrator is known to use in his notes. - One-Step and Inequalities - Two-Step - Translating - Solving with Formulas 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 Justice Equilibrator? Name: Ting Fen Occupation: Speech Therapist Favorite Number: -90 Name: Allen Occupation: Artist Favorite Number: 87 Name: Hiram Occupation: Geneticist Favorite Number: 7,153 Name: Brandi Occupation: Real Estate Agent Favorite Number: 10,000 Name: Roanoke Occupation: Farmer Favorite Number: 76 Name: Jessica Occupation: Music Teacher Favorite Number: 14

8 Scene #1 The Louvre - Paris, France Around 2 AM a security guard heard a loud noise and walked outside to find that the famed Glass Pyramid was gone. Written on the ground in chalk was this message I am Justice Equilibrator! Balancing scales and equalizing all inequalities by way of conquering the world! The Louvre is the most famous art museum in the world. Their glass pyramid is one of their greatest features. Work your way to the top of the pyramid to figure out a, but if you make a mistake on the bottom, you will definitely be wrong on the top. a = Scene #2 The Coliseum - Rome, Italy A man in a Super Mario costume broke into the Coliseum after hours and stole three huge stone blocks. It is believed these could be foundational building blocks for the World Conquering Devices. Spartacus is helping two of Rome s most famous Gladiators settle an argument over who has the bigger heart! Help them figure it out! Flamma III + VII = XIX Crixus XVIII IV = L Flamma > Crixus Flamma < Crixus Flamma = Crixus = 4 = -4 p = 0

9 Scene #3 Catacombs -- Underneath Paris, France A tour group came upon a ransacked section of the Catacombs where it appeared many decorations were taken. Carved into the wall, they found this note from Justice Equilibrator. =

10 Scene #4 Eurail Train Station - Prague, Czech Republic During a conductor shift change, Justice Equilibrator stole a train, dropped off all of the passengers in Slovakia and somehow escaped the police. I ve got a need, a need for speed. I don t care where I m going, but I want to ride the train with the fastest average speed. Remember distance equals rate times time (d = rt). Prague Express Destination Distance Time Rate Which is Faster? Amsterdam, Netherlands 713 km 15 hrs e = 713 Cologne, Germany 541 km 10 hrs p = 541 Moscow Russia 1670 km 32 hrs r = 1670 Zagreb, Croatia 495 km 9 hrs u = 490 Choose the clue associated with the fastest train. = Scene #5 Loch Ness Lake - Scotland In broad daylight, a helicopter flown by Justice Equilibrator lifted a humongous object from the lake. It is unclear what the object was, but witnesses say it made a loud, screeching noise. Despite popular belief, investigators have gotten a tip that the Loch Ness Monster is actually being kept as a pet in a Scottish Hotel (rooms numbered -10 to 10). Four specially-trained monster hunters checked different rooms. None of them found Nessie. Through process of elimination, figure out where the Nessie must be hiding. 1) x + 4 < 3 2) x 5 > 1 3) 2x + 3 > 11 4) -3x > -9 Which room must Nessie by hiding in? This letter will be equal to 100. = 100

11 Scene #6 Museum of the Ancient Agora -- Athens, Greece An archivist was surprised to discover that 100 kg of bronze and clay were taken from the museum. Read about my leisure time in Greece with Euclid s great-great-great-great-great-great-greatgreat grandnephew and match them to the correct answers. This will lead to your final clue Euclid spent 14 euros to visit the ancient Agora and now has 29 euros left over. How many euros did he have before the Agora? At the Greek Bowling House, Euclid s score was 73 points higher than President Papoulias. If Euclid bowled a 134, what was the President s score? I led an Acropolis tour group that had 7 more than Euclid s tour group. If my group had 36, how many were in Euclid s group? I bought three boxes of End of the World cards at the Monastiraki Flea Market. I used 54 and had 9 cards leftover. How many cards were in each box? At the Benaki Museum, a plaster bust of the head of Athena was 240 euros. This was 16 euros more than eight times the cost of a Terracotta replica. How much does the Terracotta replica of Athena cost? E - 21 N - 29 S - 28 T - 43 V - 61 = = CRYPTIC PUZZLE SOLVER TEXT MESSAGE I ve tipped the scales! Justice Equilibrator E + U + R 0 + P A

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 Justice Equilibrator? Name: Ting Fen Occupation: Speech Therapist Favorite Number: -90 Name: Allen Occupation: Artist Favorite Number: 87 Name: Hiram Occupation: Geneticist Favorite Number: 7,153 Name: Brandi Occupation: Real Estate Agent Favorite Number: 10,000 Name: Roanoke Occupation: Farmer Favorite Number: 76 Name: Jessica Occupation: Music Teacher Favorite Number: 14

14 Scene #1 The Louvre - Paris, France Around 2 AM a security guard heard a loud noise and walked outside to find that the famed Glass Pyramid was gone. Written on the ground in chalk was this message I am Justice Equilibrator! Balancing scales and equalizing all inequalities by way of conquering the world! The Louvre is the most famous art museum in the world. Their glass pyramid is one of their greatest features. Work your way to the top of the pyramid to figure out a, but if you make a mistake on the bottom, you will definitely be wrong on the top. a = -13 Scene #2 The Coliseum - Rome, Italy A man in a Super Mario costume broke into the Coliseum after hours and stole three huge stone blocks. It is believed these could be foundational building blocks for the World Conquering Devices. Spartacus is helping two of Rome s most famous Gladiators settle an argument over who has the bigger heart! Help them figure it out! Flamma III + VII = XIX Crixus XVIII IV = L Flamma > Crixus Flamma < Crixus Flamma = Crixus = 4 = -4 p = 0

15 Scene #3 Catacombs -- Underneath Paris, France A tour group came upon a ransacked section of the Catacombs where it appeared many decorations were taken. Carved into the wall, they found this note from Justice Equilibrator. = p = 10

16 Scene #4 Eurail Train Station - Prague, Czech Republic During a conductor shift change, Justice Equilibrator stole a train, dropped off all of the passengers in Slovakia and somehow escaped the police. I ve got a need, a need for speed. I don t care where I m going, but I want to ride the train with the fastest average speed. Remember distance equals rate times time (d = rt). Prague Express Destination Distance Time Rate Which is Faster? Amsterdam, Netherlands 713 km 15 hrs 47.5 e = 713 Cologne, Germany 541 km 10 hrs 54.1 p = 541 Moscow Russia 1670 km 32 hrs r = 1670 Zagreb, Croatia 495 km 9 hrs 55 u = 490 Choose the clue associated with the fastest train. = Scene #5 Loch Ness Lake - Scotland In broad daylight, a helicopter flown by Justice Equilibrator lifted a humongous object from the lake. It is unclear what the object was, but witnesses say it made a loud, screeching noise. Despite popular belief, investigators have gotten a tip that the Lochness Monster is actually being kept as a pet in a Scottish Hotel (rooms numbered -10 to 10). Four specially-trained monster hunters checked different rooms. None of them found Nessie. Through process of elimination, figure out where the Nessie must be hiding. 1) x + 4 < 3 x<1 3) 2x + 3 > 11 x>4 2) x 5 > 1 x>6 4) -3x > -9 x<3 Which room must Nessie by hiding in? This letter will be equal to 100. r= 100

17 Scene #6 Museum of the Ancient Agora -- Athens, Greece An archivist was surprised to discover that 100 kg of bronze and clay were taken from the museum. Read about some of my leisure time in Greece and match them to the correct answers. This will lead to your final clue Euclid spent 14 euros to visit the ancient Agora and now has 29 euros left over. How many euros did he have before the Agora? At the Greek Bowling House, Euclid s score was 73 points higher than President Papoulias. If Euclid bowled a 134, what was the President s score? I led an Acropolis tour group that had 7 more than Euclid s tour group. If my group had 36, how many were in Euclid s group? I bought three boxes of End of the World cards at the Monastiraki Flea Market. I used 54 and had 9 cards leftover. How many cards were in each box? At the Benaki Museum, a plaster bust of the head of Athena was 240 euros. This was 16 euros more than eight times the cost of a Terracotta replica. How much does the Terracotta replica of Athena cost? E - 21 N - 29 S - 28 T - 43 V - 61 = = e = seventeen, e =17 CRYPTIC PUZZLE SOLVER TEXT MESSAGE I ve tipped the scales! Justice Equilibrator E + U + R 0 + P A

18 From Puzzle 1: a = -13 From Puzzle 2: = 4 From Puzzle 3: p = 10 From Puzzle 4: u = 490 From Puzzle 5: r= 100 From Puzzle 6: e=17 E + U + R 0 + P A =87