M.A.R.S. Math Tasks

Math Task 1: Measuring the Fuel Cost During the mission you will need to calculate the amount of fuel burned during each leg of your flight path. Your plane starts out with 20 kilograms (kg) of fuel. Your plane burns.02 kg of fuel per kilometer. This is your fuel cost rate.

Fuel Cost Formula You will use the following formula to calculate the amount of fuel used for each leg of the flight path: Fuel Cost = Distance x Fuel Cost Rate OR F = D x C

Example 1 For the first leg of your flight, the distance (D) between site p and site a is 362 kilometers (km). The fuel cost rate (C) is.02 kg/km. Turn to page 2 of your handout. Calculate the fuel cost (F) of flying from site p to site a using the formula. F = D x C

Example 1 (contd) Now that you know the fuel cost of flying from site p to site a, you need to calculate what percentage of your total fuel was used. To calculate what percentage of the fuel tank has been used during this leg of the flight, you will use the following equation: Percentage of Fuel Tank = F x 100% 20 What percentage of your fuel tank did you use? Now try the next example on page 2 of your handout.

Math Task 2: Deciding Which Site to Visit In your mission the best sites to visit are the ones that have the most hematite and will take the least amount of fuel to reach. To see which site is the best, you will be using a graph that compares how much hematite the site contains relative to how much fuel you will need to burn to reach the site. Turn to page 3 of your handout.

Decision-making Graph The x axis is the horizontal axis on the graph. In our graph the x axis represents the amount of fuel that will be used to reach each site (fuel cost). Label the x axis on your graph. The y axis is the vertical axis on the graph. In our graph the y axis represents the amount of hematite at each site (mineral density). Label the y axis on your graph.

Example 1 To choose the first site, you will be given a set of data for the first three sites that are within your range to visit. This data is presented as coordinates (x,y), where x represents the fuel cost and y represents the mineral density. oSite a: (36%, 51%) oSite b: (35%, 62%) oSite c: (41%, 82%) Plot these points on your decision-making graph.

Making Your Decision Use a ruler to draw a line from the origin of the graph (0,0) to each point you have plotted. The line with the greatest slope is usually the best site to visit. The slope is the measure of the steepness of the line. You should choose the site that has the line with the greatest slope. In example 1 which site would be the best site to visit? Now complete example 2 on page 3 of your handout, using the next set of data for sites a, b, and c.

Math Task 3: Calculating the Area of a Site As a science/operations expert, you will need to calculate the area of each site your team chooses to visit. Each site will be in the shape of a triangle, rectangle, circle, or quadrilateral. You will use a formula to find the area of each site to determine if there is enough area to build the Mars base there. We need to find a site with an area of at least 10 km 2 to establish a base. Turn to page 4 of your handout.

Math Task 3 Formulas Area of a triangle = B x H 2 Area of a rectangle = B x H Area of a circle = x r 2 ( = 3.14) Area of a quadrilateral = B x (H 1 + H 2 ) 2

Example 1 Look at the first site picture in your packet on page 4. Decide which formula you should use to calculate the area. Using the formula for the shape you have selected, find the area of the site. What is the total area of the site? Now try example 2 on page 4 of your handout.

Math Task 4: Calculating Mineral Quantity After you determine the area of your site, you need to calculate the total amount of hematite in that area, or the mineral quantity. On your map you will be given the mineral density of hematite located at the site.

The Formula for Calculating Mineral Quantity You will use the following formula to calculate the amount of hematite contained in an area: Mineral quantity = density kg/km 2 x site area in km 2

Example 1 The area of the first site you visited was 4.35 km 2. The mineral density of hematite contained at the site was 50 kg/km 2. Use the formula on page 5 of your packet to calculate the mineral quantity for this site. Now try example 2 in your packet on page 5.

Congratulations! Youve completed the M.A.R.S. math practice. Good luck on mission day!