Introduction
Ahoy matey! Over the next few days, you will be a pirate searching for hidden treasure. You will use the clues in left by highly mathematical pirates to pinpoint the treasure's exact location. Happy hunting!
Task
Your task will be to pinpoint where the buried treasure is. To do this, you will be solving the systems of equations in the Process section. The first part of our process is review, the second part of our process will help us find the buried treasure.
Process
PART ONE:
Make sure you have the worksheet that Mrs. Albertson provided for you.
1. Write your pirate name on the worksheet and your real name underneath
2. Before our adventure, we will review systems of equations and systems of inequalities:
(note - the worksheet questions and answers should be found in the video. Listen carefully! Listen/watch more than once, if needed).
Go to www.learnzillion.com and locate the search bar.
Then, Watch these videos:
Solving a system with substitution: Type 5EX86G9 in the search box
Solving a system with elimination: Type FP6NA6A in the search box
Solving a system with graphing: Type Z4PN3AP in the search box.
Solving a system of inequalities: Type CX78E97 in the search box.
(Optional: extra graphing help: type G7F2RK4 in search box)
Use these videos to assist you in your worksheet answers.
PART TWO:
Okay, now that your memory is refreshed and you have notes to assist you, let's move on to our challenge.
To find our locations, we will first solve systems of equations to find the coordinates. Solve each one however you are comfortable :0)
Your paper provides space for 6 systems. You are only required to solve the three mentioned below. On your paper, write OMIT on the ones that are not available for you to solve.
Once you've solved all 3 of your required systems of equations for your latitude and longitude coordinates, you will plug these into Google maps to find the locations in the world where our buried treasure may be (see bottom of the process for directions).
Location 1:
To find your first location, we will solve the following system of equations. You may use your calculator, if needed.
y = 31 - 6x
y = -3x-23
Location 2: WRITE OMIT!
Location 3:
To find our third location, we will solve the following system of equations. You may use your calculator, if needed.
y = 100x+15
y = 200x-85
Location 4: Write OMIT
Location 5: Write OMIT!
Location 6: to find our final location, we will solve the following system of equations. You may use your calculator, if needed.
x+y = 53
-.25x+y = -7
Copy all the coordiantes in the chart provided. Remember, write OMIT next to the locations that you were not required to do. This will make your life easier.
Now that you have your coordiantes, here comes the fun part. Go to Google Maps, more specifically go to http://www.gps-coordinates.net/. Once at Google Maps, type in the coordinates from your first location (x is your latitude and y is your longitude). Hit enter. Then, zoom out until you can see the country name. Record your country name on the space provided on your worksheet.
The Treasure is located in the only country that is NOT an island. Put a star next to that country on your chart!
To check yourself (and yes, you must check yourself), graph this system of inequalities and see if your coordinate lies in the appropriate region as defined by this system of inequalities. You will turn in your graph of these inequalities and how the coordinate solution on the graph by plotting it inside your system of inequalities solution.
y<x+1
y>1/2x-50
Extra points - if you can provide a hand-drawn "map" that includes the locations, their coordinates and an X where the treasure is located, you will recieve 2 extra points!
Evaluation
This project is worth 60 points.
Here's how the points are broken down:
- Your pirate name (1 point)
- Your regular name (1 point)
- Correctly completed worksheet with videos (15 points)
- Correctly solved location one (4 points)
- Correctly solved location two (4 points)
- Correctly solved location three (4 points)
- Correctly solved location four (4 points)
- Correctly solved location five (4 points)
- Correctly solved location 6 (4 points)
- There are three systems solved three different ways and solved correctly (at least one system solved with graphing; one system solved with elimination; one system solved with substitution) (5 points)
- Location of treasure located with google maps (3 points)
- Correctly graphed first inequality of system (4 points)
- Correctly graphed second inequality of system (4 points)
- Correctly solved inequality system (3 points)
- Extra points - artistic map drawn from information provided (2 points)
Conclusion
Congratulations! You have found the treasure!
Make sure you turn in the following:
1. Your worksheet
2. All work for your systems of equations and inequalities
3. Your artistic map