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Standard Focus: Patterns, Algebra & Functions Time Range : 1-3 Days
Topics of Focus :
- Multiplying and Dividing Rational Expressions
- Solving Equations with Rational Functions
- Simplifying Complex Fractions
- Asymptotes
- Graphing Rational Functions
Quantities N-Q 1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
Creating Equations
A-CED 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.
Creating Equations
A-CED 2. Create equations in two or more variables to represent relationships between quantities; graph equations on axes with labels and scales.
Reasoning with Equations and
Inequalities A-REI
2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Interpreting Functions
F-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand and using technology for more complicated cases.β
Interpreting Functions
F-IF 7d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Procedures:
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.
*Extensions.) Students can present their evidence to the class as an oral presentation.
Crime Scene Decoders Algebra 2 & Pre-Calc: Rational Functions
Detectives,
The boys and girls have once again come out to play. This time, the international evil genius terrorist group the Mathemagicians are running amok over Central America. Although we have apprehended a number of their associates, we have yet to recover any pieces of their ill-conceived world conquering device that they soon may deploy to β conquer the world. From the intelligence we have gathered, the anonymous henchman βAsymptote Swaggsterβ 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 Swaggsterβs 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 Asymptote Swaggster to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Asymptote Swaggster is known to use in the notes.
- Multiplying and Dividing Rational Expressions
- Solving Equations with Rational Functions
- Simplifying Complex Fractions
- Asymptotes
- Graphing Rational Functions
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.
Scene #1 Television Manufacturer β- JuΓ‘rez, Mexico Asymptote Swaggster broke into an international TV manufacturer and the inventory of unused cathode ray tubes was stolen. Investigators found this note in the parking lot.
Hello all! Itβs Swaggster here and Iβm gonna perplex you with puzzles. While Iβm stealing stuff Iβm going to look for some rational mathematics. Just like this one I pulled off the CEOβs desk.
Giga Electronica Proposal: Add computer manufacturing to business. Build 650 computers as trial run.
Estimated Start-Up (Fixed) Costs: 250,000 pesos
Itemized Cost: each computer from scratch is 2,000 pesos.
After a campus tour, Swaggster snuck away from the tour group and into the Department of Engineering. From there, they discovered the laser cutter was taken.
While I robbed the local college, I peeked in a math class. I canβt help myself.
Isabella and Santiago graph functions on a calculator. Isabella graphs ππππ+ππππ
and Santiago graphs + ππππ . They both have vertical asymptotes at x
= 0 and horizontal asymptotes at y = 6. They are confused. What is the correct explanation?
They have the same asymptotes , but are different functions
They have the same asymptotes because theyβre the same function They are incorrect
Conservationists were stunned to find out that the large stucco mask of Temple 33 was taken. It is unclear to investigators how the mask may be used in the World Conquering Device.
The Mayan could build cities with rocks, mud and their hands. Can you solve five rational function questions in a row? I have my doubts.
What are the correct horizontal and vertical asymptotes of z(x)
Horizontal at y = 0 Vertical at x = -8, x = 0, x = 2 e =3 Horizontal at y = 0 Vertical at x = -2, x = 0, x = 4 i =3 Horizontal at y = 1 Vertical at x = -4, x = 0, x = 8 r =3
One of the nicest hospitals in Central America, Hospital CIMA was broken into last night and their radiology equipment was stolen. Later, nurses found this note from Asymptote Swaggster.
The Doctor is in! The Dr. of Swagg, that is. While robbing the hospital, I decided to impersonate an Anesthesiologist for a few hours. I had to administer some anesthesia, did I mess up?
Anesthesiology Report
Local anesthesia was administered to the patient at 1:58 prior to surgery.
The concentration of the drug in the bloodstream (in mg/L) is modeled by the
function where t is minutes since receiving the drug: πΆπΆ(π‘π‘) = 8ππ0.3ππ2+4.1
Note: When the concentration drops below 0.1 mg/L the patient may become conscious. They
will need the additional anesthesia administered one half hour prior to reaching this level.
The surgery expects to last 6 hours. Based on this information, when would I need to administer more anesthesia?
5:48 5:54 6:02
a = 548 i = 554 m = 602
Scene #5 Sinkhole β- Guatemala City, Guatemala
One of the largest sinkholes on record, the Guatemala City Sinkhole was looted last night. It is believed that Asymptote Swaggster stole the underground piping.
Iβve got some bad news. The earth is about to fall out from under you. Luckily, my fortune teller has given me an equation that models its destruction. Graph it!
A figure parachuted from a helicopter and landed on a yacht in the middle of the Caribbean Sea. The passengers were sent to shore in lifeboats, but the yacht was taken. Victims claimed the figure kept yelling βMy name is Asymptote Swaggster! Go tell police! Iβm Swagg!β
Iβm floating off into the sunset on my brand-new stolen yacht. There are a lot of vessels out on the Caribbean. Jet Skis are flying around circles around me and Iβm just waiting for one of them to crash.
The routes of three Jet Skis are modeled by a rational function. Graph the function and determine how many collisions (if any) there will be.
Scene #1 Television Manufacturer β- JuΓ‘rez, Mexico Asymptote Swaggster broke into an international TV manufacturer and the inventory of unused cathode ray tubes was stolen. Investigators found this note in the parking lot.
Hello all! Itβs Swaggster here and Iβm gonna perplex you with puzzles. While Iβm stealing stuff Iβm going to look for some rational mathematics. Just like this one I pulled off the CEOβs desk.
Giga Electronica Proposal: Add computer manufacturing to business. Build 650 computers as trial run.
Estimated Start-Up (Fixed) Costs: 250,000 pesos
Itemized Cost: each computer from scratch is 2,000 pesos.
After a campus tour, Swaggster snuck away from the tour group and into the Department of Engineering. From there they discovered the laser cutter was taken.
While I robbed the local college, I peeked in a math class. I canβt help myself.
Isabella and Santiago graph functions on a calculator. Isabella graphs ππππ+ππππ
and Santiago graphs + ππππ . They both have vertical asymptotes at x
= 0 and horizontal asymptotes at y = 6. They are confused. What is the correct explanation?
They have the same asymptotes , but are different functions
They have the same asymptotes because theyβre the same function They are incorrect
Conservationists were stunned to find out that the large stucco mask of Temple 33 was taken. It is unclear to investigators how the mask may be used in the World Conquering Device.
The Mayan could build cities with rocks, mud and their hands. Can you solve five rational function questions in a row? I have my doubts.
One of the nicest hospitals in Central America, Hospital CIMA was broken into last night and their radiology equipment was stolen. Later, nurses found this note from Asymptote Swaggster.
The Doctor is in! The Dr. of Swagg, that is. While robbing the hospital, I decided to impersonate an Anesthesiologist for a few hours. I had to administer some anesthesia, did I mess up?
Anesthesiology Report
Local anesthesia was administered to the patient at 1:58 prior to surgery.
The concentration of the drug in the bloodstream (in mg/L) is modeled by the
function where t is minutes since receiving the drug: πΆπΆ(π‘π‘) = 8ππ0.3ππ2+4.1
Note: When the concentration drops below 0.1 mg/L the patient may become conscious. They
will need the additional anesthesia administered one half hour prior to reaching this level.
The surgery expects to last 6 hours. Based on this information, when would I need to administer more anesthesia? 266.6 minutes ->4 hr 26 minutes
5:48 5:54 6:02
a = 548 i = 554 m = 602
Scene #5 Sinkhole β- Guatemala City, Guatemala
One of the largest sinkholes on record, the Guatemala City Sinkhole was looted last night. It is believed that Asymptote Swaggster stole the underground piping.
Iβve got some bad news. The earth is about to fall out from under you. Luckily, my fortune teller has given me an equation that models its destruction. Graph it!
A figure parachuted from a helicopter and landed on a yacht in the middle of the Caribbean Sea. The passengers were sent to shore in lifeboats, but the yacht was taken. Victims claimed the figure kept yelling βMy name is Asymptote Swaggster! Go tell police! Iβm Swagg!β
Iβm floating off into the sunset on my brand-new stolen yacht. There are a lot of vessels out on the Caribbean. Jet Skis are flying around circles around me and Iβm just waiting for one of them to crash.
The routes of three Jet Skis are modeled by a rational function. Graph the function and determine how many collisions (if any) there will be.