Introduction
ARGH! 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
Optional section for part one:
2. Before our adventure, we will review systems of equations and systems of inequalities, if you want.... THIS is optional for you.... or you can use it for review as you seek the treasure. NOTE - IT IS NOT REQUIRED!
Go to www.learnzillion.com and locate the search bar (the magnifying glass)
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.
Extra graphing help: type G7F2RK4 in search box
Use these videos to assist you as needed.
PART TWO (this part is NOT optional):
Okay, let's move on to our challenge.
To find our locations, we will first solve systems of equations to find the coordinates. Solve at least one with each method (and you may pick how to solve the other three! Show all work on your paper!)
Once you've solved all 6 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. And, you will then create your own system of inequalities that highlights the region which contains the treasure! Happy hunting and creating!
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: To find our second location, we will solve the following system of equations. You may use your calculator, if needed.
-x+y = -82
.5x+ y = 14
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: To find our fourth location, we will solve the following system of equations. You may use your calculator, if needed.
4x+y = 28
y=-7x-50
Location 5: to find our fifth location, we will solve the following system of equations. You may use your calculator, if needed.
y= -2x+8
-x+y = 65
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. 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!
Now, you need to be creative. If you were going to "make things easier" for the next pirate, you might create a system of linear inequalities that pinpoints the region in which your solution lies. Create your system of inequalities then graph this system of inequalities and see if your coordinate lies in the appropriate region as defined by this system of inequalities. Provide this system of inequalities for me along with the solution.
(If it helps, you can use www.desmos.com to assist you. You can type in the coordinates of all solutions and then build your inequality system to house the one coordinate you need. Basically, you want two inequalities. And you want your solution to the inequality system to have the coordinate of the treasure inside of it! It is easier to draw the lines then create the equations.... and if you need help creating the inequalities, watch this video.
How to write an equation from a graph: Go to www.learnzillion.com and Type 2XS2AC3 in the search box. (This could prove most helpful when you create your own system.)
If you do this, you still need to graph your system by hand to turn in.)
Extra points - if you can provide a handdrawn "map" that includes the locations, their coordinates and an X where the treasure is located, you will recieve 3 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 solved location one (5 points)
- Correctly solved location two (5 points)
- Correctly solved location three (5 points)
- Correctly solved location four (5 points)
- Correctly solved location five (5 points)
- Correctly solved location 6 (5 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) (6 points)
- Location of treasure located with google maps (2 points)
- Correctly created inequality and graph (6 points)
- Correctly created inequality two and graph (6 points)
- Correctly solved inequality system (6 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
3. The system of inequalities you developed and its corresponding graph
3. Your artistic map (optional for extra points)