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Introduction
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.
Duration
60 minutes
Vocabulary
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.
Materials
- Copies of Student Worksheet: Ratios,
Proportions, and Cross-multiplication for each
student
- Pencils
Teacher Preparation
-
Make copies of student
worksheets.
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Gather calculators
(optional) if you will allow students to use
them for this activity or for the mission.
Procedure
- 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.
- Discuss all vocabulary in the lesson,
including ratio, rate, proportion, and
cross-multiplication.
- Preview the activity with the
students. Read the student version of the
instructions out loud in class. Allow time for
questions and discussion.
- 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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