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


 Clifford Harmon
 2 years ago
 Views:
Transcription
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 56 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 makeup of your class, different methods work. Highachieving classes will eat it up and beg for more class time or beg to take it home. Lowerachieving 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, Decimalfractionpercent 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 : 13 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 realworld 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 realworld 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 ninjalike 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 fivestar 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 threecourse meal. In all there was one familysized 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 mostprized 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 twofifths 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 : 13 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 realworld 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 (ñqñ)^(g/p)  (SQRT(AW))  3Qñ rofl Guapo Too Slick Arcsin
18 Unit 3: CSI Algebra: Solving Equations Standard Focus : Patterns Algebra and Functions Time Range : 13 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 AlJabr 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 AlJabr to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that AlJabr 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 AlJabr? 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 AlJabr softly repelled into the heavily alarmed security system. AlJabr 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 AlJabr 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 AlJabr 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 AlJabr 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 swaggrific 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, AlJabr went outside, ate a picnic lunch, and climbed the Sphinx. Our research team suspects, AlJabr 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 twothird, 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, AlJabr 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 AlJabr
25 Unit 4: CSI Algebra: Relations, Functions & Patterns Standard Focus : Patterns Algebra and Functions, Geometry and Spatial Sense Time Range : 13 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 FIF FIF FIF FIF 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 FBF 1. Write a function that describes a relationship between two quantities. Building Functions FBF 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 FBF 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 : 13 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 FIF G GPE G GPE SID 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 manhours 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 fortyfive 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 : 13 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 realworld 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 illconceived 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 fullsized 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 bearhide 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 fortyfive 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 VikeTalk 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 : 13 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 realworld 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 brandspanking 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 : 13 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 realworld problems. 4. Use variables to represent quantities in a realworld 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 breakin at a lab that specializes in mathematical, microorigami 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 Honganji  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(x2) = 4(x 23) 4 xy(y+x) = x(y 27)+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 24x  5 (x 5 y 2 z) (x 3 y 2 z) 4x 5 (x5)(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 : 13 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 ASSE ACED AREI AREI 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 (x2) as one of their factors? b = 2 u = 4 s = 7 a =  9 r = 18
The program also provides supplemental modules on topics in geometry and probability and statistics.
Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationPowerTeaching i3: Algebra I Mathematics
PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and
More informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
More informationInfinite Algebra 1 supports the teaching of the Common Core State Standards listed below.
Infinite Algebra 1 Kuta Software LLC Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below. High School
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More informationMTH124: Honors Algebra I
MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,
More informationCopyrighted Material. Chapter 1 DEGREE OF A CURVE
Chapter 1 DEGREE OF A CURVE Road Map The idea of degree is a fundamental concept, which will take us several chapters to explore in depth. We begin by explaining what an algebraic curve is, and offer two
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationAlgebra 12. A. Identify and translate variables and expressions.
St. Mary's College High School Algebra 12 The Language of Algebra What is a variable? A. Identify and translate variables and expressions. The following apply to all the skills How is a variable used
More informationAlgebra 1 Course Objectives
Course Objectives The Duke TIP course corresponds to a high school course and is designed for gifted students in grades seven through nine who want to build their algebra skills before taking algebra in
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationThis unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationCOGNITIVE TUTOR ALGEBRA
COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationGeorgia Standards of Excellence Curriculum Map. Mathematics. GSE 8 th Grade
Georgia Standards of Excellence Curriculum Map Mathematics GSE 8 th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. GSE Eighth Grade
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More informationThnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks
Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationDRAFT. Algebra 1 EOC Item Specifications
DRAFT Algebra 1 EOC Item Specifications The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as
More informationSECTION 16 Quadratic Equations and Applications
58 Equations and Inequalities Supply the reasons in the proofs for the theorems stated in Problems 65 and 66. 65. Theorem: The complex numbers are commutative under addition. Proof: Let a bi and c di be
More informationFry Instant Word List
First 100 Instant Words the had out than of by many first and words then water a but them been to not these called in what so who is all some oil you were her sit that we would now it when make find he
More information6 EXTENDING ALGEBRA. 6.0 Introduction. 6.1 The cubic equation. Objectives
6 EXTENDING ALGEBRA Chapter 6 Extending Algebra Objectives After studying this chapter you should understand techniques whereby equations of cubic degree and higher can be solved; be able to factorise
More informationPythagorean Triples. Chapter 2. a 2 + b 2 = c 2
Chapter Pythagorean Triples The Pythagorean Theorem, that beloved formula of all high school geometry students, says that the sum of the squares of the sides of a right triangle equals the square of the
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationVeterans Upward Bound Algebra I Concepts  Honors
Veterans Upward Bound Algebra I Concepts  Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER
More informationFry Instant Words High Frequency Words
Fry Instant Words High Frequency Words The Fry list of 600 words are the most frequently used words for reading and writing. The words are listed in rank order. First Hundred Group 1 Group 2 Group 3 Group
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationReview of Intermediate Algebra Content
Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6
More informationStudents will understand 1. use numerical bases and the laws of exponents
Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationMyMathLab ecourse for Developmental Mathematics
MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and
More informationUtah Core Curriculum for Mathematics
Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More information1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)
More informationMATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring noncourse based remediation in developmental mathematics. This structure will
More informationCommon Core State Standards for Mathematics Accelerated 7th Grade
A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting
More informationIN A SMALL PART OF THE CITY WEST OF
p T h e L a s t L e a f IN A SMALL PART OF THE CITY WEST OF Washington Square, the streets have gone wild. They turn in different directions. They are broken into small pieces called places. One street
More informationFilling in Coordinate Grid Planes
Filling in Coordinate Grid Planes A coordinate grid is a sstem that can be used to write an address for an point within the grid. The grid is formed b two number lines called and that intersect at the
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationMultiplying Polynomials 5
Name: Date: Start Time : End Time : Multiplying Polynomials 5 (WS#A10436) Polynomials are expressions that consist of two or more monomials. Polynomials can be multiplied together using the distributive
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationAnchorage School District/Alaska Sr. High Math Performance Standards Algebra
Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,
More informationSUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills
SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)
More informationSuccessful completion of Math 7 or Algebra Readiness along with teacher recommendation.
MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL:... 811 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION
More informationPythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom
Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives
More information3.4 Complex Zeros and the Fundamental Theorem of Algebra
86 Polynomial Functions.4 Complex Zeros and the Fundamental Theorem of Algebra In Section., we were focused on finding the real zeros of a polynomial function. In this section, we expand our horizons and
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationCopyright (c) 2015 Christopher Small and The Art of Lawyering. All rights reserved.
Copyright (c) 2015 Christopher Small and The Art of Lawyering. All rights reserved. 1 In this special report, I ll be sharing with you the ten biggest mistakes that lawyers make when marketing their law
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationCARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM
GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write
More informationLearning Objectives 9.2. Media Run Times 9.3
Unit 9 Table of Contents Unit 9: Factoring Video Overview Learning Objectives 9.2 Media Run Times 9.3 Instructor Notes 9.4 The Mathematics of Factoring Polynomials Teaching Tips: Conceptual Challenges
More informationMath Matters: Why Do I Need To Know This? 1 Probability and counting Lottery likelihoods
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Four 1 Probability and counting Lottery likelihoods Objective: To demonstrate the
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1100 Overview: This unit models realworld situations by using one and twovariable linear equations. This unit will further expand upon pervious
More informationYOU CAN COUNT ON NUMBER LINES
Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a selfadaptive test, which potentially tests students within four different levels of math including prealgebra, algebra, college algebra, and trigonometry.
More informationSouth Carolina College and CareerReady (SCCCR) Algebra 1
South Carolina College and CareerReady (SCCCR) Algebra 1 South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR) Mathematical Process
More informationPearson Algebra 1 Common Core 2015
A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2N1 a, b, c, d, and e Time allotted for this Lesson: 5 hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2N1 a, b, c, d, and e Time allotted for this Lesson: 5 hours Essential Question: LESSON 2 COMPLEX NUMBERS What are complex numbers,
More informationSECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS
(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic
More informationTaylor Polynomials and Taylor Series Math 126
Taylor Polynomials and Taylor Series Math 26 In many problems in science and engineering we have a function f(x) which is too complicated to answer the questions we d like to ask. In this chapter, we will
More informationStudents will be able to simplify and evaluate numerical and variable expressions using appropriate properties and order of operations.
Outcome 1: (Introduction to Algebra) Skills/Content 1. Simplify numerical expressions: a). Use order of operations b). Use exponents Students will be able to simplify and evaluate numerical and variable
More informationTransition To College Mathematics
Transition To College Mathematics In Support of Kentucky s College and Career Readiness Program Northern Kentucky University Kentucky Online Testing (KYOTE) Group Steve Newman Mike Waters Janis Broering
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers
More information1) (3) + (6) = 2) (2) + (5) = 3) (7) + (1) = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = 7) (5)(4) = 8) (3)(6) = 9) (1)(2) =
Extra Practice for Lesson Add or subtract. ) (3) + (6) = 2) (2) + (5) = 3) (7) + () = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = Multiply. 7) (5)(4) = 8) (3)(6) = 9) ()(2) = Division is
More informationTips for Solving Mathematical Problems
Tips for Solving Mathematical Problems Don Byrd Revised late April 2011 The tips below are based primarily on my experience teaching precalculus to highschool students, and to a lesser extent on my other
More informationMath 181 Handout 16. Rich Schwartz. March 9, 2010
Math 8 Handout 6 Rich Schwartz March 9, 200 The purpose of this handout is to describe continued fractions and their connection to hyperbolic geometry. The Gauss Map Given any x (0, ) we define γ(x) =
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationChorus (x2) Chorus (x2)
Inequalities Algebra 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Mr. Queen,
More informationConcept 3: Arithmetic Sequences and Series (as a Bridge to Quadratics)
Concept 3: Arithmetic Sequences and Series (as a Bridge to Quadratics) Common Core Standards: ASSE 3a ACED 1, 2, 3 FIF 3 FBF 1a, 2 FLE 2 Key Vocabulary: Sequence Discrete Linear Function Term Accumulation
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationInstructor Now pick your pencils up and get this important equation in your notes.
Physics 605 Mechanical Energy (Read objectives on screen.) No, I haven t been playing with this toy the whole time you ve been gone, but it is kind of hypnotizing, isn t it? So where were we? Oh yes, we
More informationREVIEW EXERCISES DAVID J LOWRY
REVIEW EXERCISES DAVID J LOWRY Contents 1. Introduction 1 2. Elementary Functions 1 2.1. Factoring and Solving Quadratics 1 2.2. Polynomial Inequalities 3 2.3. Rational Functions 4 2.4. Exponentials and
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationApply and extend previous understandings of arithmetic to algebraic expressions. Draft
6th Grade  Expressions and Equations 1 Standard: 6.EE.1 No Calculator: Write and evaluate numerical expressions involving wholenumber exponents The population of fruit flies increases by a factor of
More informationCurriculum Alignment Project
Curriculum Alignment Project Math Unit Date: Unit Details Title: Solving Linear Equations Level: Developmental Algebra Team Members: Michael Guy Mathematics, Queensborough Community College, CUNY Jonathan
More informationMathematics Curriculum Guide Precalculus 201516. Page 1 of 12
Mathematics Curriculum Guide Precalculus 201516 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing
More informationHigh School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationMath 1. Month Essential Questions Concepts/Skills/Standards Content Assessment Areas of Interaction
Binghamton High School Rev.9/21/05 Math 1 September What is the unknown? Model relationships by using Fundamental skills of 2005 variables as a shorthand way Algebra Why do we use variables? What is a
More information