Launching Into Expressions and Equations

Mission To MarsMission To Mars

For decades, high-tech robotic spacecraft have been able to successfully land on the surface of Mars to collect data. But no human has yet set foot on the red planet. Many mysteries remain. In this mission, you will embark upon the first human voyage to Mars, which requires a lot of planning, time, and effort. Grab a pencil and paper for calculations, and use your skills in expressions and equations to find the answers to prepare for this exciting journey!

1 of 5
Launch From Earth
It costs about $450 million to launch a shuttle into space. How much money does it cost to launch n spacecraft? Write an expression.
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Answer: 450,000,000n
Hint: What operation can you use to show that it costs an equal amount for each space shuttle to be launched?
Or
2 of 5
Determine Trip Time to Mars

Since Earth and Mars move in different orbits around the sun, the distance between the two planets is always changing! When your spacecraft leaves Earth, your flight to Mars will have to cover a distance of 162,000,000 miles. On average, your spacecraft can fly at a speed of 36,000 miles per hour.

Which equation should you write to determine how long your trip to Mars will take? Note: t represents time in hours.

  1. 162,000,000 – 36,000 = t
  2. 36,000t = 162,000,000
  3. 162,000,000t = 36,000
  4. t = 162,000,000 x 36,000
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Check your calculations and try again.
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Answer: B
Hint: What algebraic expression describes how many miles you can fly in a certain number of hours? Set this expression equal to the total distance of the flight.
3 of 5
Food Rationing

Your spacecraft is holding 8 people, including you. Your spacecraft has enough food such that each crew member can eat 2,500 calories per day for the entire length of the 187.5-day trip to Mars. The spacecraft also carries c calories of extra food in case of emergency.

There is a total of 4,687,500 calories worth of food on board. Which equation should you write to determine how many extra calories of food, c, are on the spacecraft in case of emergency?

  1. 4,687,500 = 8 x 2,500 x 187.5 + c
  2. 2,500c x 187.5 x 8 = 4,687,500
  3. 8 x 2,500 x 187.5 = c
  4. 4,687,500 = 8 x 2,500 x 187.5 - c
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Check your calculations and try again.
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Answer: A
Hint: The extra food is a fixed amount that stays the same no matter how long the trip lasts. The food stocked for daily consumption depends on the number of people eating, the number of days in the trip, and the number of calories each person eats.
4 of 5
Oxygen on Mars

Your spacecraft is carrying MOXIE, a machine built to convert carbon dioxide from the atmosphere surrounding Mars into oxygen. You will test MOXIE on Mars to see if it is successful. MOXIE will produce about 20 grams of oxygen every hour, and it will run all day.

You know that a space suit's primary oxygen tanks hold 0.55 kilograms of oxygen. Considering the amount of oxygen MOXIE produces per day, by what percentage must this amount increase in order to fill a space suit's tanks in a single day?

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Check your calculations and try again.
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Answer: 15%
Hint:

To find how much oxygen MOXIE will produce in one day, multiply the amount it will produce in 1 hour by 24 hours.

To find percent increase, find the difference of the two amounts of oxygen, and divide it by the amount of oxygen MOXIE produces each day.

Explanation:

Steps:

0.55 kilograms = 550 grams in the suit tanks

20 grams x 24 hours = 480 grams produced by MOXIE

(550 - 480)/480 is about 0.15, or 15%

Or
5 of 5
Landing on Mars

Temperatures on Earth can range from –126 degrees Fahrenheit at the poles to 136 degrees Fahrenheit at the equator. When you land on the equator of Mars, it is about 70 degrees Fahrenheit, the warmest it ever gets on Mars. NASA has collected data indicating that when you travel to the south pole of Mars, it might be as low as –225 degrees Fahrenheit.

So your space suit will have to be prepared for a greater range of temperatures on Mars than on Earth. Identify how many more degrees larger the range of temperatures is on Mars than on Earth with one of the following equations:

  1. |[70 + (–225)] + [136 + (–126)]| = |–140| = 140 degrees
  2. [136 – (–126)] + [70 – (–225)] = 557 degrees
  3. [70 – (–225)] – [136 – (–126)] = 33 degrees
  4. [136 + 70] – [(–225) + (–126)] = 557 degrees
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: C
Hint: Find the temperature range on each planet. Subtract the lesser range from the greater range to find the difference of the two ranges.
Congratulations! You've Succeeded in Your Mission!
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Bonus Mission Task: Think It Through
Re-write the expression to include units of measure. Simplify the expression. How can this be used to check your answer?

Bonus Mission Task: Think It Through

($450,000,000 / 1 spacecraft) x n spacecraft. This simplifies to $450,000,000n, because the spacecraft in the numerator and denominator cancel out. This helps you check your answer because, in your answer, you are looking for a dollar amount.
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Bonus Mission Task: Think It Through
Your colleague says that to determine the length of your trip, you should divide the left side of the equation by 36,000 to isolate the variable. Then, you should multiply the right side of the equation by 36,000 because division and multiplication are inverse operations. Do you agree with your colleague's thinking? Why or why not?

Bonus Mission Task: Think It Through

Your colleague's process is incorrect. Although the first step of dividing the left-hand side to isolate the variable is correct, the right-hand side should also be divided (not multiplied) by 36,000. To keep both sides of the equation equal, the same operation must be performed on both sides.

Note: Solving for t, t = 187.5 days

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Bonus Mission Task: Think It Through

Use the equation 4,687,500 = 8 x 2,500 x 187.5 + c to determine how many extra calories of food is on the spacecraft.

Imagine the amount of extra calories of food stocked on the spacecraft before launch remains constant.

If the spacecraft could hold 10 people, how many calories of food would the spacecraft need to hold? If the spacecraft could hold 12 people, how many calories of food would the spacecraft need to hold?

Does this equation describe a proportional relationship? How do you know?

In your opinion, if the spacecraft holds more people, should the amount of extra food decrease, increase, or stay the same? Why?

Bonus Mission Task: Think It Through

c = 937,500

For 10 people, the amount of calories would be 5,625,000.

For 12 people, the amount of calories would be 6,562,500.

This equation does not describe a proportional relationship. If it were proportional, then c would have to equal 0. Also, if you were to graph the relationship, the line would not pass through the coordinates (0,0). (Other answers that appropriately address the question can be accepted as well.)

Answers may vary for the final question.

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Bonus Mission Task: Think It Through

Rewrite the expression to include units of measure. Simplify the expression. How can this be used to check your answer?

Bonus Mission Task: Think It Through

(20 grams/hour) x 24 hours simplifies to 480 grams because the hours in the numerator and denominator cancel out. This helps you check your answer because, in your answer, you are looking for a quantity in grams.

0.55 kilograms x (1,000 grams/kilogram) simplifies to 550 grams because the kilograms in the numerator and denominator cancel out.

(550 grams – 480 grams)/480 grams simplifies to about 0.15 because the grams in the numerator and denominator cancel out.

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Bonus Mission Task: Think It Through
In this Misson to Mars, when and how did you model with mathematics? When and how did you use precision? When did you notice mathematical structure? Why are these important skills?

Bonus Mission Task: Think It Through

Students model with mathematics each time they write an equation that represents a real-world problem. They use precision when they manipulate units and perform operations on numbers. They can find mathematical structure when they notice patterns. In question 1, for example, students might notice that 1 spacecraft launched costs $450 million, 2 spacecraft launched costs $900 million, 3 spacecraft launched cost $1350 million, etc. Noticing this pattern might help students understand which equation would best represent the problem situation.
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