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=DxC
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!