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Lesson Plan 3: Ratios, Proportions, and Cross-multiplication

During space shuttle missions astronauts sometimes have to perform extravehicular activities (EVAs), also called spacewalks. They do EVAs to develop techniques, test procedures, and capture satellites for repair. NASA has to closely monitor the vital signs of astronauts during an EVA to make sure the astronauts don’t use up their oxygen supplies too quickly.

In this activity your students will use cross-multiplication to find the unknown respiration rate per minute of an astronaut during several EVA tasks. They will use this same mathematical process to find missing values in proportions during the mission.


60 minutes


cross-multiplication: the process of multiplying the numerator of one ratio by the denominator of the other ratio in a proportion; the cross-products of two equal ratios are always equal. You can use cross-multiplication to find a missing value in a proportion.

proportion: a pair of equal ratios.

rate: a comparison of two quantities with different units of measure.

ratio: a comparison of two quantities, often written as a fraction.


NCTM Standards for Mathematics
Grades 6-8; Number and Operations Standard

Understand numbers, ways of representing numbers, relationships among numbers, and number systems:

  • Work flexibly with fractions, decimals, and percentages to solve problems.
  • Understand and use ratios and proportions to represent quantitative relationships.


  • Copies of Student Worksheet: Ratios, Proportions, and Cross-multiplication for each student
  • Pencils

Teacher Preparation

  1. Make copies of student worksheets.

  2. Gather calculators (optional) if you will allow students to use them for this activity or for the mission.


  1. Decide how you want the students to work on the activity. You may choose to have the students work individually or in cooperative groups. Another option would be to assign this activity for homework and review the answers together in class.
  2. Discuss all vocabulary in the lesson, including ratio, rate, proportion, and cross-multiplication.
  3. Preview the activity with the students. Read the student version of the instructions out loud in class. Allow time for questions and discussion.
  4. Make sure that your students understand the relevance of this activity to their mission work. During the Satellite Rescue live simulation, students will use proportions to calculate the heart rates, respiration rates, and oxygen usage of the astronauts.

Discussion Tips
Students must be able to use cross-multiplication to problem solve during the mission. Make sure you allow enough time for student questions and to check for student understanding.

Special Comments
You may want to use this lesson to assess student skill with math application. Even if a student is not a particularly strong math student, he/she can sometimes do well when the math is tied to a mission scenario.

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