CSI: Algebra. Second Edition ebook. 21 st Century Math Projects

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1 CSI: Algebra Second Edition ebook

2 What the heck did I just buy? CSI: Algebra is a collection of nine different algebraically inspired mathematical puzzles with a little international pizazz. The nine puzzles intend to target specific Algebra 1 units and add a little flair to the ordinary challenge question. I mapped the puzzles to the curriculum in the widely used Glencoe Algebra 1, although in my experience most Algebra 1 books line up pretty much the same. Each puzzle has 6 scenes which will uncover a mystery variable. These six mystery variables will be used to decode a cryptic text message and if everything is correct, the result will match one of the six suspects. Why in the world would I use this? Based on the experience in my own classroom, students are actively engaged in the puzzle solving element in my CSI assignments. Top students brighten up because it is something different and hard to motivate students will pick the pencil to give it a crack. These assignments are designed to be mathfirst projects. By that I mean, the Algebra 1 skill is explicitly what the students are doing, the rest works as window dressing. In my career, I ve found most math projects I ve attempted from books are typically not mathematically rigorous enough and the math concept I intended to teach was lost. In my experience, students will complete interesting assignments and I ve put a lot of sweat into making each of these puzzles interesting and fun. Okay but how would I use these? These assignments work best as a unit review (maybe replacing the 45 th consecutive Jeopardy! game *guilty hand raise*). Typically they work best in partners or teams. Students can divide responsibilities and check answers. I have also effectively used these for standardized test prep for remedial students. These are hard! Depending on the puzzle, that is a true statement. Some puzzles may depend on students doing 5-6 problems correct in a row. Lots of word problems. By design, I use a variety of levels of problems to keep a variety of learners engaged and challenged. Help and hint, as you desire. I suggest that you be very mindful about how you give these assignments. This is not a good idea to assign only for homework. Students will likely ask questions and need a little guidance. Depending on the make-up of your class, different methods work. High-achieving classes will eat it up and beg for more class time or beg to take it home. Lower-achieving classes may need more than a couple of hints to keep the energy from stalling. All answers are provided in the Answer Guide. How long should these take? I d estimate it takes most student teams between minutes to complete the puzzle. Some more, some less. It depends on their level. It may work best strewn across two days. Or you may give some helpful hints before assigning the rest for homework. If you want the students to present their findings to the class (maybe you don t give away the answer yet), then you can add an extra day or two. Have fun. Enjoy. Math it up.

3 CSI: Algebra Quick Start Guide Unit Topic World Region Quick Print Page #s Variables & Expressions Australia p (Mapped to Glencoe Ch 1) Order of Operations, Translating Verbal and Algebraic Expressions, Open Sentences, Distributing, Combining Like Terms Real Numbers Latin America p (Mapped to Glencoe Ch 2) Square root approximation, Decimal-fraction-percent conversion, Scientific Notation, The Real Number System, Perfect Squares Solving Equations Middle East p (Mapped to Glencoe Ch 3) Translating Verbal & Algebraic Equations, Solving different equation types, Using Formulas Relations & Functions Europe p (Mapped to Glencoe Ch 4) Coordinate Planes, Domain & Range, Inverses, Patterns & Arithmetic Sequences Lines China p (Mapped to Glencoe Ch 5) Slope & Rates of Change, Calculating, graphing and interpreting lines, Parallel and Perpendicular lines Inequalities & Absolute Value Scandinavia p (Mapped to Glencoe Ch 6) Solving & Graphing Inequalities, Compound Inequalities, Solving Absolute Value Equations Systems of Equations Africa p (Mapped to Glencoe Ch 7) Solving Systems with Elimination, Substitution and Graphing, Graphing Systems of Inequalities Polynomials Japan p (Mapped to Glencoe Ch 8) Operations on Monomials, Operations with Polynomials, Scientific Notation Factoring & Quadratics United States p (Mapped to elements Glencoe Ch 9 & 10) Factoring (GCF, Distributive Property, trinomials), Quadratic Formula, Graphing and interpreting parabolic graphs App. CSI: Evidence Worksheet Student Handout p

4 Unit 1 : CSI Algebra: Variables and Expressions Standard Focus : Number, Number Sense, and Operations Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Order of Operations - Translating Verbal and Algebraic Expressions - Open Sentences - Distributing - Combining Like Terms This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 1 and can be used as an enrichment or review activity. Expressions and Equations Expressions and Equations Expressions and Equations Expressions and Equations Expressions and Equations Procedures: 6.EE 6.EE 6.EE 6.EE 7.EE 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. 2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 2d. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 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. 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

5 CSI Algebra: Variables & Expressions 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, Otto Pemdas, has committed a string of robberies all over Australia. 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 cryptic text message. The text message when substituted correctly will calculate to the Otto 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 Otto Pemdas to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Otto is known to use in the notes. - Order of Operations - Translating Verbal and Algebraic Expressions - Open Sentences - Distribution - Combining Like Terms 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

6 Who is Otto Pemdas? Name: Bianca Occupation: Baker Favorite Number: 3 Name: Randal Occupation: Dentist Favorite Number: -8 Name: Donnie Occupation: Factory Supervisor Favorite Number: 62 Name: Sue Occupation: Corrections Officer Favorite Number: 44 Name: Alex Occupation: Politician Favorite Number: 98 Name: Stu Occupation: Chef Favorite Number: 24

7 Scene #1 Sydney Opera House -- New South Wales Last night, Otto Pemdas broke into the Opera House and stole three parabolic shell ribs from the unique roof. Since he moves at ninja-like speed, the security cameras missed everything, but he left this note. G Day Police Officers of Australia, To let you know upfront, the Mathemagicians plan on conquering the world. Okay, now that I have your attention, I figure I ll give you a fighting chance to stop us. MuHahahahahaha. x = # of sides on a triangle y = # of femurs an average man has z = # of syllables in integration Start Here W = 2x 2 yz A = 4x z + wx E = a +(b + w) x + (y z) B = (x 2 +z 2 ) a + w - yz E = Scene #2 The Dingo Steakhouse - Western Australia At a five-star restaurant just outside of Perth, a waitress stumbled upon this note on the back of the receipt. It was later discovered that the restaurant s signature sauce was missing. To celebrate our thefts, I took the whole Pemdas family out for a native three-course meal. In all there was one family-sized BBQ Shrimp that cost $40, 5 grilled kangaroo legs that cost $18.50 each, 2 alligator burgers that cost $24 a piece, 7 drinks that cost $2.50 each, and 7 quadruple chocolate pavlova at $11.49 a pop. For their wonderful service, I ve tipped the waiter $0.57 AUD! I paid with a recently stolen $300 AUD. How much change did I get? This answer will be equal to $. $ =

8 Scene #3 Great Barrier Reef -- Queensland A cruise ship captain was stunned to find the following note plastered to the inside of his personal bathroom. A few guests believed they saw a stealth helicopter drop in during the middle of the night. G Dafternoon Mate! When everyone was asleep, I stole a dolphin right out of the reef. It was pretty easy too. Just for kicks, this might help you find me. Find the solution set of each of the five problems using the replacement set: Flipper = {-40, -13.5, -5, 0, ½, 5, 300} 1.) x = ) x 2 = ) x < ) x = (9 23 ) (6 4) 5.) 10 x < 7 Take a good long look at the solution sets there s an unused object in the set Flipper. F is this number. F = Scene #4 Aboriginal Museum in the Outback - South Australia The curator of an Aboriginal Museum was stunned to find one of the most-prized hollowed log coffins was stolen. The log coffin, of a noted Aboriginal poet, supposedly has mystical powers. The Outback sure is beautiful in the spring. Aboriginal villages, marvelous rock painting, cacti, and stealing more stuff. Here s a little map puzzle of my journey. Oh, g = -1 miles and h = 4 miles. If you find the total distance of the path, you ll find its magic number. $ = 51 miles ɸ = 53 miles E = 55 = 57 miles

9 Scene #5 Melbourne Cricket Ground -- Victoria After the Aussie Rules Football match between rivals the Demons and Eagles, a security officer discovered the world s oldest football was stolen from the museum. While it s unsure how Otto plans to use it, the football was made out of an inflated pig bladder. Later he found this note. FUMBLE. You shoulda been watching your ball. The coach has drawn up a complicated play. I m not even sure he knows what it is. MYSTERY EXPRESSION GAME!!!!! i. Twice x Answer I: ii. 9 less than the Answer I Answer II: iii. The sum of Answer II and the product of 5 and t Answer III: iv. Answer III decreased by two-fifths the cube of another number Answer IV: v. Half of Answer IV Answer V: ANSWER V is E (9 2x + 5t) 2 5 n3 2 ɸ (2x 9 5t) 2 5 n3 2 $ (9 2x + 5t) n3 (2x 9 + 5t) 2 5 n3 2 The correct answer = -2 = -2

10 Scene #6 Television Studio - New South Wales After a Bindi Irwin television taping, this note was found outside the studio. Otto is suspected of stealing a number of Bindi Irwin DVDs. It s unclear whether the DVDs are related to the world conquering device or if Otto is just a big Bindi Irwin fan. G Daft night. I guess you aren t hot on my trail as it seems I can enjoy a really great television taping of The Bindi Show without worry. I had some extra time for this puzzle. I m sure you won t figure it out. What is V? V = 36a (a c) 24c(2a 3c) + 2a( -2( 3a +c)) v = So you were actually able to distribute and combine like terms. Whoopdidoo. Too bad that doesn t tell you the value of V. Here s the values for a and c -- I even did it for you. UNLESS I M LYING = = 7 is an example of the associative property 3 + (1+5) = (3+1) +5 = 9 is an example of the commutative property So a = 7 and c = 9 HAHAHAHAHA see I just gave you to values! Or did I? MUHAHAHAHA. Better figure it out quick before you plug them in to find V. I d surely hate if you did it wrong. CRYPTIC PUZZLE SOLVER TEXT MESSAGE lol c if u can solve this. u need sum variables. ($ + ɸ + V) + FE$ L8r, Otto Pemdas

11 Unit 2 : CSI Algebra: Real Numbers Standard Focus : Number, Number Sense, and Operations Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Square root approximation - Decimal, fraction, percent, conversion - Scientific Notation - The Real Number System - Perfect Squares This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 2 and can be used as an enrichment or review activity. Expressions and Equations The Number System The Number System The Number System The Number System Expressions and Equations 6.EE 7.NS 7.NS 8.NS 8.NS 8.EE 2d. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 3. Solve real-world and mathematical problems involving the four operations with rational numbers. 1. Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). 2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.

12 CSI Algebra: Real Numbers Detectives, A thief, working under the alias Guapo Arcsin, has caused a ruckus all throughout Central America. It is believed that Guapo 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, Guapo has left behind a trail of notes and a cryptic text message that he has told us will calculate toward his favorite number. Thus 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 Guapo to justice 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 Guapo is known to use in her/his notes. - Square root approximation - Decimal, fraction, percent, conversion - Scientific Notation - The Real Number System 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

13 Who is Guapo Arcsin? Name: Stillman Occupation: College Student Name: Charmelle Occupation: Mechanical Engineer Favorite Number: -7 Favorite Number: Name: Hiram Name: Logan Occupation: Doctor Favorite Number: 6 Occupation: Politician Favorite Number : 13 Name: Pedro Occupation: Fire Fighter Favorite Number: ½ Name: Eden Occupation: Organic Food Grower Favorite Number: 0

14 Scene #1 Machu Picchu - Peru At about 12:24, Guapo Arcsin broke into the famous Incan ruins and stole an Intihuatana stone. The Intihuatana is a ritual South American stone used to tell time. Hello Peru Peeps and Police, To let you know upfront, I plan on conquering the world. Okay, now that I have your attention, I figure I ll give you a fighting chance to stop me. MuHahahahahaha. If found this riddle carved into an Incan temple. Figure out a number that fits all three of these criteria. 1. A is a WHOLE NUMBER 2. A is a two digit perfect square 3. A > Please be aware I will later send you a CRYPTIC PUZZLE SOLVER TEXT MESSAGE. Sincerely Yours, Guapo Arcsin A= Scene #2 Mayan Ruins -- Mexico Four rare, limestone cornerstones were extracted from the ruins of a Mayan ceremonial platform. These stones could perhaps lay the foundation for a devastating world conquering device. My Dearest, Since I haven t been captured yet, I ve been thinking about running for Congress! I ll make the next one an easy one. I have run three different opinion polls. Which one is the best? G. 11 out of every 20 voters is expected to vote for me! ñ. The percentage of voters that are expected to vote for me is 54%! P. There are 240,000 expected to vote, and of these, 130,000 are expected to vote for me! This letter = -6 =-6

15 Scene #3 Andes Mountains -- Colombia Thursday night, Guapo Arcsin traversed the mountains and shaved two dozen alpacas. While it s unclear what he plans to do with the wool, there are now many cold and confused alpacas. He carved this note into the mountain. Greetings Police Officer, I see that my first puzzle has befuddled even the best of you. I ve made the next one even harder. Remember my World Conquering Device will go off at the touch of a calculator. 1.) Q is a RATIONAL NUMBER 2.) x = ( ) + ( ) ( ) Q= Give up yet? Your Friend, 3.) 60 x = Q Guapo Arcsin Scene #4 Panama Canal -- Panama An oiler tanker ship was reported missing from the canal. Apparently the captain decided to go ashore to eat a sandwich and was shocked to find this note in place of his boat. To Whom It May Concern, I m sure you are thoroughly confused by now. Hopefully you don t arrest the wrong person! 1. A = the denominator of 125/1000 when it is written in lowest terms. 2. B = the number of minutes in a day divided by AB 4. Mystery Letter = Approximation of AB on the number line. A G Q W ñ Y B Mystery Letter = 32 = 32

16 Scene #5 St. Cecilia Acatitlan -- Mexico An unknown amount of rubble and multiple Aztec jade masks depicting various gods were stolen. Guapo has successfully robbed the Aztec, Incans, and Mayans. It s unknown what he s capable of he must be stopped quick. What s Good, I m getting bored. I decided to make some of my own wall art. Which point most accurately represents 168? C A L C U L U S Which point most accurately represents (number_of_the_letter_in_the_alphabet)? Use your previous answer. (HINT: C=3, A=1, L=12 etc.) 3 M 4 A 5 T 6 H Which point most accurately represents (number_of_the_letter_in_the_alphabet) 6? Q U A D R A T I C Which point most accurately represents (number_of_the_letter_in_the_alphabet) 5? P ñ Q G W S Round your last answer to the nearest integer and you might have figured out me out. Final Letter = Rounded Answer We will be deploying our device soon. Good luck. Happy Holidays, = Guapo Arcsin

17 Scene #6 Museo Nacional de Antropologia Mexico City Three rare, blind Egyptian six legged mice were stolen from the National Museum of Anthropology. We suspect Guapo Arcsin will be using their abnormal DNA as part of his World Conquering Device. Hola, Como estas? Muy bien gracias. I m liking this Spanishness! I want to play some futbol! Elegir la respuesta con los números en orden de menor a mayor. ½ ½ ½ ñ = El numéro de letras en la palabra es la respuesta. Adios Amigos, ñ = Señor Guapo Arcsin CRYPTIC PUZZLE SOLVER TEXT MESSAGE omg u arent gonna figure this out my num is perfect (ñ-qñ)^(g/p) - (SQRT(A-W)) - 3Qñ rofl Guapo Too Slick Arcsin

18 Unit 3: CSI Algebra: Solving Equations Standard Focus : Patterns Algebra and Functions Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Translating Equations - Solving Equations - Using Formulas This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 3 and can be used as an enrichment or review activity. Expressions and Equations Expressions and Equations Expressions and Equations Reasoning with Equations and Inequalities 8.EE 8.EE 8.EE A- REI 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). 7b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

19 CSI Algebra: Solving Equations Detectives, Once again the world has been rocked by a string of high profile robberies. This time it seems the Middle East has been victim of the evil genius group, the Mathemagicians. Notes signed Kareem Al- Jabr have been discovered at each of the robbery sites. Once again a cryptic text message was sent, but requires the puzzles to be cracked. We believe the Mathemagicians have been successfully piecing together a world conquering device. Again we ve been told the result of the cryptic text message will calculate to Al-Jabr s favorite number. Thus 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 Al-Jabr to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Al-Jabr is known to use in the notes. - Translating equations - Solving equations - Using 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

20 Who is Kareem Al-Jabr? Name: Bao Occupation: Insurance Agent Favorite Number: -20 Name: Trish Occupation: Lawyer Favorite Number: 0 Name: Chloe Occupation: High School Teacher Favorite Number: 97 Name: Eugene Occupation: Musician Favorite Number: ¼ Name: Darryl Occupation: Optometrist Favorite Number: 9 Name: Carlo Occupation: Grocer Favorite Number: -210

21 Scene #1 Egyptian Museum -- Cairo In the middle of the night, Kareem Al-Jabr softly repelled into the heavily alarmed security system. Al-Jabr most definitely has soft feet and great swag. He left with hundreds of coins from the ancient world. These coins look really really old. I ll be sellin these on ebay check out my I m about to knock over the home of Algebra! Come enjoy the ride with me? g= Scene #2 National Museum of Iraq Baghdad, Iraq A baked clay tablet with Hammaurabi s Code was found astray this morning. It appears Kareem Al-Jabr was attempting to translate the document. While my Akkadian is a little rusty, my swagg tells me rule 204 says, what you do to one side you better do to the other side. Otherwise your hand will be cut off. i. 3k 5 = 7k 33 ii x = 11.6x 54.8 iii. 8f + 12 = 7f + 9 iv. k+vf = x + V V =

22 Scene #3 Ancient Babylon -- Iraq Etched into the grounds of Babylon, Kareem Al-Jabr left the this note. It s suspected he used Babylonian numerals. I was going to etch this a few spots over, but it seems the US military built a helipad in Babylon. Good thing it s not an ancient civilization that should be cherished forever. Well at least they didn t crush the ground with their tanks. Oh wait, are those tank tracks? See if you can solve this puzzle from the ruins. =

23 Scene #4 The Great Pyramids - Giza, Egypt Kareem Al-Jabr snuck past Pyramid Security at an unspecified time. While we are unsure what he stole, we are in the process of taking inventory of all the mummies. Hmmm so sure the algebra stuff isn t that hard, let see if you can handle some swagg-rific geometry. The volume of the pyramid is 18,069, cubits 3 How tall is it? I ll be a nice person. Here s the formula for the volume of a pyramid: V = (1/3)lwh (Round your answer to the nearest whole number) h= Scene #5 Sphinx - Giza, Egypt We suspect after his robbery at the pyramid, Al-Jabr went outside, ate a picnic lunch, and climbed the Sphinx. Our research team suspects, Al-Jabr stole a limestone fragment of the Sphinx s beard. I so stole a piece of that dude s beard. Check this out, here s some good ol Egyptian math right off the Rhind Papyrus! I stole that too! Problem 44. The sum of A certain quantity p together with its two-third, And its half becomes 234. What is the quantity p? p=

24 Scene #6 Nile River Cruise - Alexandria, Egypt After the pair of robberies at Giza, Al-Jabr hopped on a Nile River cruise. He stole a dangerous amount of shampoo. Livin it up on the Nile. Gotta go get my swaggilicious self on the dance floor. Check out these two receipts I had to pay with Egyptian Pounds after my Swaggcard got denied. What a coincidence? Both receipts totaled to the same amount X. I really wish I knew how much a Du aah cost. They were yummy. œ = CRYPTIC PUZZLE SOLVER TEXT MESSAGE check dis out. You dont got no chance. (h p) (9g + ) + œ (pv)^g Kareem Master of Swagg Al-Jabr

25 Unit 4: CSI Algebra: Relations, Functions & Patterns Standard Focus : Patterns Algebra and Functions, Geometry and Spatial Sense Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Coordinate Planes - Domain & Range - Inverses - Patterns & Arithmetic Sequences This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 4 and can be used as an enrichment or review activity. Functions 8.F Functions 8.F 1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Interpreting Functions Interpreting Functions Interpreting Functions Interpreting Functions F-IF F-IF F-IF F-IF 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Building Functions F-BF 1. Write a function that describes a relationship between two quantities. Building Functions F-BF 4a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Building Functions F-BF 4b. (+) Verify by composition that one function is the inverse of another.

26 CSI Algebra: Relations, Functions & Patterns Detectives, The evil genius group, the Mathemagicians, have taken a European vacation. 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 The Diophantus of the Opera. 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 the Diophantus 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 the Diophantus of the Opera to justice 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 the Diophantus is known to use in the notes. - Coordinate Planes - Domain & Range - Patterns & Arithmetic Sequences 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

27 Who is the Diophantus of the Opera? Name: Hailey Occupation: Panini Maker Favorite Number : 99 Name: Vernon Occupation: Network Administrator Favorite Number : -10 Name: Jeff Occupation: Blogger Favorite Number: π Name: Owen Occupation: Graphic Designer Favorite Number : 1 Name: Jessica Occupation: Musician Favorite Number: φ Name: Rishi Occupation: App Developer Favorite Number: 19

28 Scene #1 Descartes Home -- Ville de Descartes, France Yesterday the Diophantus of the Opera broke into the childhood home of esteemed geometer, René Descartes. The owners woke up to find the lucky straightedge of Descartes was missing. René Descartes worked awfully hard creating his Cartesian Coordinate System, but it strikes me as a little too trivial for our grand premiere. The Diophantus of the Opera is here inside your mind, but how about later? 47 o N 5 o E Here are the directions to my odyssey. The name of the final destination will be equal to From my starting point (the star), I m going 5 o N and 7 o E. I am in 2. Then 8 o S. I am in 3. Then I m gracefully traveling 5 o S and 10 o E. I am in 4. Finally, 14 o N and 24 o W to my final destination = -8

29 Scene #2 Eiffel Tower - Paris, France It is suspected that the Diophantus of the Opera broke into the Eiffel Tower, climbed to the top and proceeded to drop euro coins. A figure was seen taking measurements and investigators later found this note. Although most of the great French mathematicians were not around to see it, I m sure they would have loved to have thrown coins from atop the Eiffel Tower. The distance the coin will fall is 4.9 meters the first second, 14.7 meters the next second and so on in an arithmetic sequence. If the coin continues to fall at this rate, how many meters will it fall during the 8 th second? t (seconds) meters fallen during that second e You might like this equation... a n = a 1 + (n 1)d e= Scene #3 Remains of the Berlin Wall, Germany It is believe that after his raid in France, the Diophantus hitchhiked to Germany. Our researchers seems chunks of the mortar from the remains of the Berlin Wall was chiseled away and stolen. Brava, Brava, Bravissima. I seem to have reached the Point of No Return. Is this yours? f(x) = 3x - 2 g(x) = x 2 4 q(x) = PHANTOMx P = f(2) + 4 H= 2[g(3)] A= f(0) + 5 N= g(-2) + 3 T= 5[f(4)] 49 O= -3[g(1) + 9] M= f(1) + g(1) q(x) = 6480? X=

30 Scene #4 Aristotle University of Thessaloniki -- Greece A Greek manuscript filled with philosophical writings was found on a table next to a dozen empty cans of Mountain Dew. Investigators believe the Diophantus was attempting to translate the document. My sweet Christine, tis best if we can improve our relations. Remember that relations may take many different forms and look different ways -- masks of a sort. Unfortunately only one of our famous Greek friends could translate their relation correctly every time. Who s right? R = {(1, 4), (-2, 5), (5, 5), (2, 3), (-1, -1)} Greek Mathematician Domain & Range Aristotle x = 10 D: {-2, -1, 1, 2, 5} R: {-1, 3, 4, 5} Table, Mapping Relation, or Graph Is it a Function? Yes Inverse {(4,1), (2, -5), (5, 5), (3, 2), (-1, -1)} Euclid e = -5 D: {-2, -1, 1, 2, 5} R: {-1, 3, 4, 5} Yes {(4,1), (5, -2), (5, 5), (3, 2), (-1, -1)} Plato u = -4 D: {-2, -1, 1, 3, 5} R: {-1, 2, 4, 5} Yes {(4,1), (5, -2), (5, 5), (3, 2), (-1, -1)} Ptolemy ω = 0 D: {-2, -1, 1, 2, 5} R: {-1, 3, 4, 5} Yes {(4,1), (5, -2), (5, 5), (3, 2), (-1, -1)} Pythagoras k = 20 D: {-2, -1, 1, 2, 5} R: {-1, 3, 4, 5} No {(4,1), (5, -2), (5, 5), (3, 2), (-1, -1)} Who s right? =

31 Scene #5 Stonehenge -- England The curators of the mysterious ruins found that a mythic satchel was missing. They believe the contents are jewels from a departed alien life form. This could potentially be the fuel for a world conquering device. Atop one of the mammoth stones, investigators found nearly a hundred half eaten apple cores and this note written with sidewalk chalk. The final act is near. I thought it d be best to honor the locals by paying respects to their most significant mathematical figure Isaac Newton. I toyed with some different apple tossing strategies to inspire the genius I ll soon need to complete this world conquering device. I leave you with my last puzzle. A bit of calculus. Here are the models for my two different apple tosses. Complete the tables. Graph them. f(t) = 2t g(t) = t 2 If you shade the region between the intersection points of the two functions, which shape will be drawn? This is the final piece of the puzzle. y= 9 z= 9 e= 9 x= 9

32 Scene #6 Gondola Dock -- Venice, Italy A pair of gondoliers came upon a surprise when thet found the following carved in the floor of their boats. Soon after, they discovered some famous Fibonacci mystical artwork was missing. Later, investigators were sent a cryptic text message. Blaise Pascal and Fibonnacci join together for a duet aria for the ages. Who will steal the stage? The Triangle or the Golden Spiral? D A + B + C +D = Z Z = CRYPTIC PUZZLE SOLVER TEXT MESSAGE It s golden! Good luck cracking this code. ~The Diophantus of the Opera e z UK y ( UK)( x)

33 Unit 5: CSI Algebra: Lines Standard Focus : Patterns, Functions and Algebra Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Slope - Calculating, graphing and interpreting lines - Parallel and Perpendicular lines This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 5 and can be used as an enrichment or review activity. Functions 8.F Functions 8.F 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models Interpreting Functions Expressing Geometric Properties with Equations Expressing Geometric Properties with Equations Interpreting Categorical and Quantitative Data F-IF G- GPE G- GPE S-ID 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 6c. Fit a linear function for a scatter plot that suggests a linear association.

34 CSI Algebra: Lines Detectives, The sun sets, the winds blow, and the international evil genius terrorist group the Mathemagicians wreak havoc on yet another world region. It seems they are making progress in their plans to build a world conquering device despite our best efforts to apprehend their cronies. China is the victim of the latest string of heists at the hands of a henchman (or henchwoman), Li Squareds. One thing is sure, Li Squareds is definitely some kind of henchperson. As has become the calling card of the Mathemagicians, they have left behind a trail of notes with a cryptic text message. The text message when substituted correctly will calculate to the Li 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 spatial reasoning can crack some codes that have puzzled the detectives on the case so far. Your job is to bring Li Squareds to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Li is known to use in the notes. - Slope & Rates of Change - Calculating, graphing and interpreting lines - Parallel and Perpendicular lines 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

35 Who is Li Squareds? Name: Ken Occupation: Butcher Favorite Number : 7 Name: Tripiti Occupation: Pet Store Owner Favorite Number: 10 Name: Brandi Occupation: Realtor Favorite Number: 13 Name: Pete Occupation: Rock Star / Philanthropist Favorite Number: -19 Name: Dawne Occupation: Archivist Favorite Number: -10 Name: Nash Occupation: Insurance Salesman Favorite Number: 11

36 Scene #1 National Art Museum of China -- 中 国 美 术 馆 Li Squareds broke into the National Art Museum of China and emerged with a ceremonial dragon dance costume. Cameras caught a glimpse of this heist as Li danced out of the museum untouched -- in full dragon gear. Security Guards assumed the night custodians were having a bit of fun. Nǐhǎo dudes, I m honored that your elite team of investigators has decided to waste hundreds of man-hours attempting to crack my uncrackable puzzles. I hope you like change. Rates of change in fact. No place in the world changes as fast as China, and no evil mathematician group increases the rate of change like the Mathemagicians!!1!11! I drew this amazing piece of dragon art out of 18 straight line segments. Find the slope of all 18 segments and add them together. This answer will be equal to 龙. (All Undefined Slopes will count as 0 and all ordered pairs are integer coordinates) (NOTE: Don t count the flaming ball of fire, that s just there to be super cool.) 龙 = Scene #2 Quanjude Restaurant - 全 聚 德 A waitress noticed that eighteen mutated duck legs were stolen. After a thorough investigation, police found pieces of this note in five different fortunate cookies. I just realized that going to China qualifies as roaming on my cell phone plan. I need to get a local cell or I m going to need to sell my car and I really need to stay in touch with the rest of the Mathemagicians. Oh no! More change! Here are my options: Company Unlimited Calls (per month) Texts Mobile 中 国 移 动 通 信 30 RMB.08 RMB/text Unicorn 中 国 联 通 20 RMB.10 RMB/text Telecom 中 国 电 信 10 RMB.12 RMB/text RMB = Renminbi, the official currency of China If I send 1,500 texts per month, which plan is the cheapest? Write equations for each company to find out! The first English letter of the cheapest company will be equal to 2. = 2

37 Scene #3 Beijing West Railway Station -- 北 京 西 客 站 A conductor on a high speed train entered an onboard restroom and imagine his surprise to find the ceiling been dismantled, the wiring in disarray, and a hybrid electric fuel cell missing. Found written on a roll of toilet paper was this note left by Li Squareds. These trains sure go fast. After doing some riding, I built these linear models to estimate their travel time including their station stops. If I m trying to conquer the world quickly, I need the fastest train. Which one is the fastest? (x = hours, y = miles. I m using mph instead of km/h for you silly Americans.) Zhōngguó gāosù tiělù U D T M B y + 12 = 175x y = 31x 186x y = 10 y = 100x -10 (letter of train)=(speed of train) = y 100 = x.15 Scene #4 Yabuli Ski Resort - 亚 布 力 滑 雪 旅 游 度 假 区 A kiloton of pure Mongolian snow was snatched off the top of the highest mountain in the Yabuli Ski Resort. Investigators deciphered this note written in the snow in some sort of liquid. As you can imagine when descending the slopes, I have a need -- a need for speed. Figure out which hill gives me the steepest, dopest, decline. Graph and label them so you don t get confused. Hill M: Travels through points (1, 7) & (6, 4) Hill T: 2x + 6y = 30 Hill U: Travels through the point (6, 1) with a slope of -4/5 (fastest hill)=(its slope) =

38 Scene #5 The Great Wall - 万 里 长 城 Investigators believe forty-five perfectly square limestone bricks were taken from the North Pass in the Great Wall. It is believed these bricks will be foundational pieces in the world conquering device. Lots of interesting landscaping in this country. I m certainly happy to be heading back home with all my goodies, but I ve been inspired to go home and do some yard work. In fact I plan to make the Great Wall of Li Squareds. The big question is where to put it If you want to figure out where I m going to put it, just follow the directions and figure out the equation of the final line. 1. A line parallel to A that travels through the point (5, 1). This line is 2. A line perpendicular to the new line that travels through the point (0, 2). This line is 3. A line perpendicular to the new line that travels through the point (-2, -2). This line is 4. A line parallel to the new line that travels through the point (-1, 1). This line is Find the line and then the next piece of the puzzle. y = ½ x + 1 y = -2x -1 y = -2x + 1 y = ½ x - 1 爱 = ½ 喜 = -2 信 = -2 熊 猫 = ½

39 Scene #6 The Forbidden City -- 故 宫 博 物 院 Inside what is now the modern Palace Museum, curators discovered nine ritual bronze vessels of the Shang and Zhou eras were stolen. These vessels demonstrate the technological sophistication of early metal casting. Li Squareds left this note their place. Change is good. Fast change is better. You should take a look at China s recent Gross Domestic Product. It s on the up and up. Based on the trend line, what is the GDP predicted to be in the year 2018? 有 一 个 愉 快 的 一 天 钱 = CRYPTIC PUZZLE SOLVER TEXT MESSAGE Double check your stroke order when using your Mandarin. Loving Lines. ttyl Li Squareds (M + 喜 )* 钱 + ( 龙 * U )+[( T + M - 喜 )/ 龙 ]

40 Unit 6: CSI Algebra: Inequalities & Absolute Value Standard Focus : Number, Number Sense, and Operations, Patterns, Functions and Algebra Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Solving & Graphing Inequalities - Compound Inequalities - Solving Absolute Value Equations This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 6 and can be used as an enrichment or review activity. The Number System The Number System Expressions and Equations Expressions and Equations Expressions and Equations Creating Equations Creating Equations Creating Equations Reasoning with Equations & Inequalities 6.NS 6.NS 6.EE 6.EE 7.EE A- CED A- CED A- CED A- REI 7. Understand ordering and absolute value of rational numbers. 7a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 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. 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. 4b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

41 CSI Algebra: Inequalities & Absolute Value 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 the formerly safe, docile lands of Scandinavia. 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 Algor Rhythmsson 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 Algor 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 Algor Rhythmsson to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Algor is known to use in the notes. - Solving & Graphing Inequalities - Compound Inequalities - Solving Absolute Value Equations 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

42 Who is Algor Rhythmsson? Name: Sydney Occupation: CIA Operative Favorite Number : -3 Name: Luigi Occupation: Restaurant Owner Favorite Number:- 1 Name: Murphy Occupation: Adjunct Sculpture Instructor Favorite Number: 1 Name: Waldo Occupation: Police Officer Favorite Number: Name: Dorothy Occupation: Retired Favorite Number: 1/2 Name: Doyle Occupation: Landscaper Favorite Number: 33

43 Scene #1 Haunted House - Stockholm, Sweden Last night, Algor Rhythmsson broke into a spooky old vacant home. Apparently the Swedes have a thing for vampires. Investigators believe some garlic immune vampire blood have tampered with. Young lads, I finished a viewing of Låt den rätte komma in or as you Americans would say Let the Right One In. While you watch Twilight: New Baboon, the Swedes watch GOOD vampire movies. Hopefully your math skills surpass your taste in movies. A vampire is hiding in one of the rooms of this haunted house (numbered -10 to 10). Eight different vampire hunters checked different rooms. None of them found the vampire. Through process of elimination, see if you can figure out where the vampire must be hiding. 1.) v + 2 > 10 2.) 3v < ) v + 5 > 6 4.) 2v < 2 5.) v 3 > 0 6.) v = 5 7.) -3v > 6 8.) v - 5 = -4 V= Scene #2 Sognejord - Norway A large ferry captain noticed a few hundred broken spoons floating in the Sogneford -- the largest fjord in Norway. It turns out that Algor Rhythmsson scrapped layers of snow off of the Jostedalsbreen Europe s -- largest continental glacier. Lots of largeness. Getting visual for a minute. Plot the line 2x + 3y < 9 Which of the following points is in the solution set? (3,1) d = 2 (5, 2) n = 2 (-4, -2) t = 2 (2, 4) v = 2

44 Scene #3 Streets of Malmo -- Sweden A Swedish street food vendor was caught off guard when a person dressed as the lead singer from Abba, stole his special mustard sauce and knocked over his cart. Yes No d = -4 S = 1/3 Scene #4 Kingdom of Crystal - Nybro, Sweden Nineteen candleholders made of world famous Swedish glass were stolen from a safe inside a vault, behind a gate, past a security guard. The glassblower claims these are one of a kind items made from glass extracted after the most powerful lightning strike in Swedish history. Succeeding at impossible security breaches and adding pieces to our World Conquering Device! Yay! I m about to compound your problems with some compound inequalities. Match! 1. 6r > 12 and -2r > r - 1 > 7 or 7r - 3 > 4 3. r - 1 < 2 4. r 2 > 3 One of the answer choice letters should be leftover unless you made a horrific mistake (letter left out)= -11 = -11

45 Scene #5 Viking Ship Museum Oslo Norway It is believed Algor Rhythmsson pulled off a rather unusual heist for his finale. With security guards on patrol, Rhythmsson managed to steal a full-sized Viking longboat from inside a museum. Turns out I ve got some Viking blood in my system. Now I feel like growing a beard and pillaging. Turns out I m closely related to a modern Viking family, the Longswords. They sort of adopted me, here s what we ve been up to. (Be sure to write these as inequalities or I ll blow up the world). 1. The Longswords gave me 85 Viking coins to spend at the local mall (luckily they accept Viking coins). I bought a bear-hide shirt for 25 Viking coins and a seal skin belt for 30. I thought hard about getting a pair of Viking horns, how much did I have left to spend? 2. My adopted father, Papa Longsword, told me that I had to pillage at least forty-five houses before sundown. If I had pillaged thirteen homes before lunch and five after lunch, how many more do I have left to pillage? 3. Mama Longsword made me switch my cell phone company to Vike-Talk Mobile (an international network exclusive to Vikings). I ve been given an allowance of 30 Viking coins a month. If the flat rate is 20 coins and each text message is.25 coins, how many text messages will I be allowed to have each month? 4. I enrolled in an online degree program on University of Phoenix, Viking Studies where my first class is Vikings, Great Vikings, the Greatest People in the History of the World. On my first three tests I scored a 91, 88, and 95. I need an average of 92% to get an A for the class and my last test is today. What score to I need to get for an A? Based on your answers, figure out which of the following statements are true. Yes, 25 IS in the solution set of each answer d = -25 No, 25 IS NOT in the solution set of each answer n = 25

46 Scene #6 Global Warming Institute City - Sodankyla, Finland While researching the effects of global warming on the arctic tundra of northern Finland, geologists noticed that the entire population of lichen was plucked from the marshes. Later they found this note from Algor Rhythmsson. Soon it seems Finland will be completely melted by global warming. One way that we contribute to climate change is by doing things that release CO 2 into the air. CO 2 Emissions per Activity Transportation Emissions (lbs) per Passenger per Mile Average Car 1.10 The Kyoto Protocol is an agreement among nations that sets a target for maximum CO 2 emissions for each nation. The emissions target is pounds per day. Average SUV 1.67 Jet 0.97 Mass Transit (1/4 full) 0.75 Write an inequality and calculate the number of miles you can travel in each mode of transportation and remain below pounds of CO 2. Use the variable Mass Transit (3/4 full) 0.26 m to represent number of miles. Round your answers to the nearest tenth. Average Car Average SUV Jet Mass Transit (1/4 full) Mass Transit (3/4 full) Add up the miles from each of the five problems this is equal to m. m= CRYPTIC PUZZLE SOLVER TEXT MESSAGE Greetings from Norseland. Good luck. Algor Rhythmsson mt mv s ( d) n t

47 Unit 7: CSI Algebra: Systems of Equations Standard Focus : Patterns, Functions & Algebra Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Solving & Graphing Systems of Equations - Systems of Inequalities This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 7 and can be used as an enrichment or review activity. Expressions and Equations Expressions and Equations Expressions and Equations Reasoning with Equations and Inequalities Reasoning with Equations and Inequalities Reasoning with Equations and Inequalities 8.EE 8.EE 8.EE A- REI A- REI A- REI 8a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8c. Solve real-world and mathematical problems leading to two linear equations in two variables. 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

48 CSI Algebra: Systems Detectives, What s another month without a series of high profile robberies at the hands of the Mathemagicians? The evil genius terrorist group has pulled off another elaborate crime spree that has left the continent of Africa in disarray. As the Mathemagicians work to build their world conquering device, our investigators are trying to piece together the thefts by an anonymous associate, Hakuna Math Ata. Cocky as always, the Mathemagicians have left behind a trail of mathematical puzzles and a cryptic text message that must be solved. After solving the puzzles, you can decode the message which will lead to Hakuna 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 Hakuna Math Ata to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Hakuna is known to use in the notes. - Solving Systems with Elimination and Substitution - Graphing Systems of Equations - Solving & Graphing Systems of Inequalities 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

49 Who is Hakuna Math Ata? Name: Marcy Occupation: Computer Scientist Favorite Number : 1 Name: Bella Occupation: Fashion Designer Favorite Number: -315 Name: Ted Occupation: Mechanical Engineer Favorite Number: i Name: Pat Occupation: ebusiness Entrepreneur Favorite Number: 44 Name: Osbert Occupation: Executive Assistant Favorite Number: 2 Name: Jebediah Wolfhead Occupation: Poet / Scholar Favorite Number: -9

50 Scene #1 Nairobi National Park - Nairobi, Kenya Last night, Hakuna Math Ata snuck into the National Park and left with five baby black rhinos. Investigators believe the baby rhino DNA may be a super serum for the world conquering device. Jambo Westerners! Since I ve been employed to steal a variety of things across Africa, I figure I ll try to enjoy interesting things along the way. No worries, eh? Hakuna Matata as Hakuna Math Ata likes to say. You can try to catch me, but I m gonna throw some algebra systems in your way. Here s your first In the jungle, the mighty jungle, the mommy rhino sleeps tonight. And then I stole her babies. She mad. I leave you with the safari receipts for two families. If you can figure out how much a Child ticket costs, you ll know the answer to the next puzzle. C = Scene #2 Regional Centre for Renewable Energy - Praia, Cape Verde One of the foremost research labs in sustainable energy discovered last night that a prototype for their solar powered monster truck was stolen. In its place, they found this note. Animals live, graze, get turned into hotdogs, cooked, eaten by people who then artificially inseminate more animals -- It s the Circle of Life. We re not going to cook these dogs on a grill or in a pot, but on a solar oven. Let the sun do the work. Solar Oven B: The chef starts her oven at t = 0 and her oven heats an average of 4 degrees per minute. Solar Oven A: The chef started four minutes later and heats an average of 8 degrees per minute. What will the temperature be when the ovens are the same? This temperature will be T. (I d solve it instead of trust a graph). T =

51 Scene #3 Ngorongoro Conservation Area -- Serengeti Plains, Tanzania A park ranger was astonished to find large excavation markings in the famous Ngorongoro Crater, a massive, unflooded volcanic caldera (kind of like a big bowl). Some estimate the crater to be 2 million years old. At this time, investigators are unclear how this factors in the plans of the Mathemagicians. A pair of confused math friends have different pieces to one system of equation, but they re not sure how to find their answer. (1, 3) m = 3 (-4, 0) s = 20 No Solutions u = 21 Infinite Solutions b = 26 It s unclear how the volcanic caldera will factor in the plans of the Mathemagicians, but I love it! I think it can turn some vagabonds into kings! Can you feel the love tonight? Onto our problem Scene #4 Lake Tanganyika - Central Africa A ferry boat captain for the Heart of Peacefulness and Delight cruise line was alarmed when a patron jumped overboard. The figure had stolen a ceremonial African Biombo mask. The staff later found this note in a bed. There s a lost African treasure somewhere around here! Some think it is the riches of a Zulu king hid it during the age of Imperialism. Supposedly it s at one of these six points and it s in the solution to this system of inequalities. I just can t wait to be king! Which of the points is in the solution set?. =-300

52 Scene #5 Namib Desert Namibia This morning it was discovered that thousands of Namib Desert beetles were taken by Hakuna Math Ata. These beetles have developed a unique technique to survive by obtaining water from early morning fogs. It is believed this power may be used in the world conquering device somehow. It s almost getting to the time for the strange old baboon to hold up a brand-spanking new baby lion. That means our story is coming to an end. Match the number of the question to the letter of the answer choice and put them on the row along the bottom = =

53 Scene #6 Mount Kilimanjaro - Tanzania Last night, it s believed Hakuna Math Ata scaled a peak and dug up a field of indigenous African blood lilies. It s suspected the blood lilies have some sort of value to the world conquering device. Carved into the side of the mountain they found this note and were sent a cryptic text message. Simba lives in Kenya and he is applying for a microcredit loan to start a street food business Slimy Yet Satisfying. He is taking out a 48,000 Kenyan Shilling loan (about $570) and will have a 30,000 Kenyan Shilling monthly credit line. Write cost and revenue equations to determine how long it will take Simba to break even. Slimy Yet Satisfying Initial costs 48,000 shillings Projected Monthly Revenue 36,000 shillings Projected Monthly costs 30,000 shillings Cost Equation Revenue Equation The number of months it takes to break even will be equal to S. s= CRYPTIC PUZZLE SOLVER TEXT MESSAGE I m here on Pride Rock. You have an epic coming of age journey ahead. Hakuna Math Ata. c m t s mu b

54 Unit 8: CSI Algebra: Polynomials Standard Focus : Number, Number Sense, and Operations, Measurement Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Multiplying and Dividing Monomials - Scientific Notation - Adding and Subtracting Polynomials - Multiplying Polynomials This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 8 and can be used as an enrichment or review activity. Procedures: Expressions and Equations Expressions and Equations Arithmetic with Polynomials and Rational Expressions 6.EE 7.EE A- APR 2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 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. 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

55 CSI Algebra: Polynomials 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 the Land of the Rising Sun -- Japan. The latest heists are by the hand of anonymous minion, Hideo Nomial. Investigators fear that the Mathemagicians are putting the finishing touches on 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 Hideo 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 Hideo Nomial to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Hideo is known to use in the notes. - Multiplying and Dividing Monomials - Scientific Notation - Adding and Subtracting Polynomials - Multiplying Polynomials 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

56 Who is Hideo Nomial? Name: Tommy Occupation: Game Show Host Favorite Number : 0 Name: HD Occupation: Entertainer Favorite Number: -3.2 x 10 5 Name: Siku Occupation: Game Designer Favorite Number: -74 Name: Esteban Occupation: Professional Ping Pong Player Favorite Number: 6.9 x Name: Roanoke Occupation: Farmer Favorite Number: 1.1 x 10 5 Name: Yamamoto Occupation: Automotive Executive Favorite Number: 3.2 x 10 4

57 Scene #1 Origami Laboratory - Osaka, Japan Late at night there was a break-in at a lab that specializes in mathematical, micro-origami figures. The scientist was devastated to find out his entire Pokemon collection was taken. The sun will soon set on the Land of the Rising Sun. The Mathemagicians will reign! That is unless you can conquer my polynomial puzzles, but I doubt it. Off we go Add the perimeter of this origami crane, match it to the correct answer below and you ll have the first piece of the puzzle. 12x + 17y 12x +14y 14x +12y 17x+12y b = -4 c = -4 d = -4 f = -4 Scene #2 Kantei - Toyko The office of the Japanese Prime Minister was raided and a thousand top secret flash drives were taken from the secret flash drive vault. In the vault, investigators found this note. You shouldn t spend what you don t have and you shouldn t need a Mathemagician to tell you that. If you re not careful, you ll be in worse financial shape than the United States. Let s see if you can handle some scientific notation conversion... In July 2012, the national debt of Japan was about $7.203 x (converted from yen to dollars) and the population was 1.27 x About how much was each Japanese citizen s share of the national debt at that time? Round your total to the nearest dollar and find it below. $52,919 $56,717 $58, 215 $60,420 a = 2.5 x 10 3 b = 2.5 x 10 3 c = 2.5 x 10 3 f = 2.5 x 10 3

58 Scene #3 Higashi Hongan-ji -- Kyoto, Japan During the night, a number of healing tea leaves were taken from one of the largest Buddhist temple in Japan. ATV marks on the floor and splatters on the carpet indicate Hideo Monomial was trying to make a fresh batch of tea on the run. Let s use a little area dissection on one of the world s most recognizable flags. Calculate an expression for the area of the white space on the flag and match your answer to the correction option below. (Use 3.14 for π) 4.86x xy 9.14y 2 c = 2 Scene #4 4.86x xy y 2 f = 2 Ryougoku Sumo Hall - Sumida, Tokyo, Japan A locker room attendant noticed a broken window around the belongings of the greatest sumo champs in the country. It is believed, Hideo Nomial stole the mawashis of the ten largest men from the dirty laundry. The attendant later found this note in a soiled mawashi. Large men wear large mawashis. These should make excellent slingshots. See if you can handle a sumo sized chain problem Solve the equations from left to right and hopefully you ll figure out z. 4x(x-2) = 4(x 2-3)- 4 xy(y+x) = x(y 2-7)+x yz(xz x) = xy(z 2 x) 3x z =

59 Scene #5 Geisha Karaoke Restaurant Kyoto, Japan This morning the geishas were alarmed to find out that their trademark face powder and their best karaoke machine were stolen. None of the geishas would give me their memoirs. What s up with that? How many of the outside expressions are the same as this one? This answer is equal to g. (x 2 2x 1) (2x + 4) (2.4*10 3 ) x 2 4x (4.8*10 2 ) (x 2 8x 2) + (4x -3) 2(0.5x 2 2x) 5 x 2-4x - 5 (x 5 y 2 z) (x 3 y 2 z) 4x 5 (x-5)(x+1) g =

60 Scene #6 Underground Ninja Academy - Parts Unknown It is believed that Hideo Nomial, disguised as a pizza delivery man, infiltrated the secret Ninja camp. Nomial left with a cache of ninja stars and nunchucks. Later the ninja sensei found this note and investigators were sent a cryptic text message. Cowabunga dudes, Since I m a diamond class ninja, I need to build my team. One credential I m looking for is a ninja s ability to break down complex polynomials. This is a good indication of their ability to break arms and legs. You might not believe me, but trust me -- I m a diamond class ninja. Choose the ninja who has the most correct answers. Master Mitsubishi b=10 Samurai Nintendo c=10 Sensei Sony g=10 Shogun Toshiba f=10 CRYPTIC PUZZLE SOLVER TEXT MESSAGE It s Hideo Nomial here. Cruising in my Prius. Here s your code If you dare. g f c c ( bz )(d f )

61 Unit 9: CSI Algebra: Factoring & Quadratic Functions Standard Focus : Patterns, Functions, and Algebra Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Factoring trinomials including GCF and Distributive Property - Quadratic Formula - Graphing and interpreting parabolic graphs This particular was mapped to elements of the curriculum in Glencoe Algebra 1 Chapter 9 & 10 and can be used as an enrichment or review activity. Seeing Structure in Expressions Creating Equations Reasoning with Equations and Inequalities Reasoning with Equations and Inequalities A-SSE A-CED A-REI A-REI 3a. Factor a quadratic expression to reveal the zeros of the function it defines. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. 4. Solve quadratic equations in one variable. 4b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

62 CSI Algebra: Factoring & Quadratic Functions Detectives, We can literally count the seconds until the Mathemagicians deploy their world conquering device. For their last crime spree, an associate by the name of Calcuu Paraboloid has terrorized the United States. Based on our intel, we believe Calcuu Paraboloid is the leader of the evil genius terrorist group. Investigators suspect that the world conquering device intends to vaporize calculators everywhere! From Wall St. to Walmart, the world would have to relearn how to do basic arithmetic operations. In other words, it s the end of the world. As the Mathemagicians have done time and time again, they 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 Calcuu 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 Calcuu Paraboloid to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Calcuu is known to use in the notes. - Factoring trinomials including GCF and Distributive Property - Quadratic Formula - Graphing and interpreting parabolic 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. We are counting on you. Good luck to you, gumshoe. Chief Harris

63 Who is Calcuu Paraboloid? Name: George Occupation: Executive Favorite Number : 1 Name: Tecumseh Occupation: Chief Favorite Number: -900 Name: Tom Occupation: Writer Favorite Number: -74 Name: Ben Occupation: Inventor Favorite Number: 1776 Name: Pocahontas Occupation: Translator Favorite Number: 42 Name: Betsy Occupation: Seamstress Favorite Number: 630

64 Scene #1 Yellowstone National Park - Wyoming, USA A ranger was stunned to discover the famed petrified forest completely uprooted. Investigators suspect Calcuu Paraboloid excavated an entire allosaurus skeleton. In the dirt, they found this note. Land of the free? Home of the brave? We ll see how you hold up after we flip the switch on our world conquering device. All electronic calculation devices will be one big cloud of poof. Go find your abacus and pull off your socks because you don t have a chance at solving my puzzles. Find the GCF of these three monomials. The coefficient of the monomial is equal to s. 792x 9 y 13 z x 4 yz 5 220x 12 y 6 z 2 s= Scene #2 Silicon Valley - California, USA The top secret headquarters of Google was infiltrated in the afternoon by a person dressed up like Elmo from Sesame Street. The person took sixteen prototype Google Gadgets. Based on the lost resources, it s quite possible Google was preparing to conquer the world on their own. You Americans seem to spend a lot time on your phone throwing birds at pigs. Well here you go Graph the path of the three projectile birds (you may need to make tables). The birds are launched from (0,0) and the pig sits on (4,0). y = -2x²+8x y = -x²+7x y = 4x x² How many birds hit the pig? Zero One Two Three b = 0 i = 1 r = 2 d = -4

65 Scene #3 Hollywood Hills - California, USA Security officials were called to a number of celebrity homes. It seems that Calcuu Paraboloid stole their luxury countertops. Based on the positioning of the mayonnaise jars, Paraboloid may have also made a sandwich at each house. Party like a rockstar! I just robbed the six most important people in America according to TMZ! I left them each with a factoring question. Jennifer Lopez Will Smith Oprah Winfrey 15xy 30y x 2 8x + 7 x 2 9x + 14 Justin Bieber Lady Gaga Chuck Norris x x 26 4x 2 25x + 6 5x 2 6x 8 Which four celebrities have (x-2) as one of their factors? b = -2 u = -4 s = -7 a = - 9 r = -18

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