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 (cont’d)

• 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.o Site a: (36%, 51%)o Site b: (35%, 62%)

o Site 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 km2 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 (H1+ H2) 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/km2 x site area in km2

Example 1

• The area of the first site you visited was 4.35 km2.

• The mineral density of hematite contained at the site was 50 kg/km2.

• 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!

You’ve completed the

M.A.R.S. math practice.

Good luck on mission day!