Paper Instructions:

Standards:

  • H HSG-MG.A.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios).  
  •  N-CN.C.9(+), A-REI.D.11, A-APR.B.3, F-IF.C.7c MP.7 Using Structure : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  
  • MII. G-SRT2,3: 2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.  
  • MII.G-GMD.A. Explain volume formulas and use them to solve problems 
  • MII.F.BF Combine standard function types using arithmetic operations. 
  • Driving Question: How can you use your mathematical knowledge to predict what will happen to The Maldives if the world didn’t take sustainability seriously
  • Project Summary:

Scientists believe that the global average temperature will increase by about 2.5 degrees Celsius by 2100. Despite the small change of average temperature, this will cause a rise of sea level and have a bad impact on low islands. Maldives is an example of poor low-lying country which will be hit soon and had hard by the effects of global climate change including sea level rise. The Maldives is located south-southwest of India. It consists of approximately 1190 islands and is the lowest country in the world with a maximum elevation of 2.4 m.  In your project, you will be working together to predict the percentage of Maldives area will be swiped from year 2010 till 2100?

  • Project tasks:

In the following project you will be:

  1. Work on a scale model of The Maldives' to find its map area 
  2. Find dimensions The Maldives as the sea level rises
  3. Use regression to develop a model for predicting the rise of sea level 
  4. Find the Map area of The Maldives' after years of rise in sea level 
  5. Predict the percentage of The Maldives' that will be swiped if global warming was not remedied 

Part 1:

Watch this video (about 4 min) which provides context and human motivation for our work in this project    https://www.youtube.com/watch?v=euGU2AKJhac

What is your first impression?

  1. What is causing the Carteret Islands to become uninhabitable?
  • Name two factors making relocation difficult?

Part 2:

 Since the actual shape of Maldives is complicated, we will use a simple shape to compute and assume that it is good stand-in for the real islands. We will pretend the nation is one triangular prism as pictured below.

Calculate, to the nearest whole number, the map area in Km2?

(Hint: The map area in this project is the area of the rectangles you would see by looking down on the prism from directly above and it is shaded in brown.)

Part 3:

As the sea level rises, the prism gradually

becomes covered with water. The island above the water

is still prism shaped. The  new base B(x)

and the elevation of the new prism x are depicted to the figure shown below.

  1. Give a function B(x) for the width of the base of the prism in km when the elevation of the prism is x in km. (Hint Use similar triangles)
  • The length of the base of the prism never changes. Give a function A(x) for the map area of the prism in Km2 when the elevation of the prism is x km. Recall that map area in this project, we mean the area of the rectangles you would see by looking down on the prism from above
  • In year 2010 the Maldives’ island height is 1.5 m. Give a function E(z) for the elevation of Maldives in km when the sea level is z mm above the 2010 level?

Part 4:

The annual average sea level data from Hulhule Island, Maldives from 1989 to 2013 is given below

Use the table above and Excel spreadsheet to find a trend line (linear) with a zero y-intercept to model the rise in sea level in mm before and after year 2010. Use the variable y to represent the rise in sea level in mm and x to represent the number of years from year 2010? Paste the graph here with the equation of the trend line.

Part 5:

Suppose that  is used to predict the sea level in Maldives t years after 2010 in mm above the 2010 level. The function is consistent with the historical data as show in table in part 4.

Function Inputs (with units) Outputs (with units)
     
     
     
     
     

Fill in the following table:

Part 6:

  1.  Use function composite to write a function  which gives the map area of Maldives t years after 2010 in Km2
  • Use part a) to calculate the map area in year 2100?
  • What percentage of Maldives area will be swiped from year 2010 till 2100?

Rubric

  Criteria Points
  4 3 2 1  
Maths Content   Demonstrates a clear knowledge and application of maths skills Demonstrates a general knowledge and application of maths skills Demonstrates a limited knowledge and application of maths skills Demonstrates little or no knowledge or application of maths skills  
Explanation and work shown Student can explain how to solve, his work is shown clearly Student can explain how to solve but his work isn’t all shown Student can explain only a small part of the work, many steps are missing Student cannot explain any of the work. Work is not shown  
Use of Visuals Clear diagrams and sketches with details Clear diagrams or sketches Inappropriate or unclear diagrams/ sketches No diagrams or sketches  
Use of mathematical terminology Mathematical terminology is prevalent and used correctly Mathematical terminology correctly used Some mathematical terminology is presented, but not correctly used No mathematical terminology is used or attempted  
Accuracy Student’s answer is completely correct Student’s answer is mostly correct Student’s answer is mostly incorrect Student’s answer is completely incorrect  
Quality of work presented Excellent presentation in a neat and organized manner Very good organized presentation Somehow neat presentation The work presented is not neat and lacks organization  
Collaboration and Contribution Routinely provides useful ideas when participating in the group discussion. A definite leader who puts in a lot of effort.   Usually provides useful ideas when participating in the group discussion. A strong group member who tries hard! Sometimes provides useful ideas when participating in the group discussion. A satisfactory group member who does what is required. Rarely provides useful ideas when participating in the group discussion. May refuse to participate.  
Sustainable City Action Plan The students described the problems that will be faced if sustainability was not an important aspect of our future lives, they discussed the Maldives example with details and mathematical justifications The students described the problems that will be faced if sustainability was not an important aspect of our future lives, they discussed the Maldives example but didn’t provide mathematics justifications The students description and justifications were incomplete The action plan failed to mention the effect of not following sustainability aspects  

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