Fractions, Decimals, and Gravity


Author: Robin A. Ward, California Polytechnic State University-San Luis Obispo


Audience: Grades 5 - 8


Mathematical Topics: fractions and decimals


Rationale: For grades 5 - 8, the NCTM Standards recommend that students should:

  • understand and appreciate the need for numbers beyond the whole numbers;

  • extend their understanding of whole number operations to fractions and decimals;

  • use estimation to check the reasonableness of results;

  • select and use appropriate mental, paper-and-pencil, and calculator methods.

    • The Standardsalso emphasize making links across the curriculum. This activity integrates astronomy and mathematics and provides students practice with performing operations on decimals and fractions.

    In this activity, students will first discuss, with the guidance of the teacher, how a person's weight is directly related to the gravitational force on a planet. Then, students will choose a Space Traveler as a companion and compute how much their guide weighs on various planets, based on each planet's relative surface gravity value (given in decimal form).


    Materials:

    Table showing each planet's relative surface gravity value.
    Worksheet

    Background: Weight refers to how heavy an object is. Mass is the amount of matter contained in an object. Weight encompasses both mass and gravity. Gravity is the force that pulls an object towards the ground. That is, gravity is the magnetic pull from the earth that acts upon all mass. Depending on how strong the gravitational force is determines how much you will weigh. The stronger the gravitational force, the more you will weigh. The weaker the gravitational force, the less you will weigh.

    When an astronaut is in space, he or she experiences weightlessness. Weightlessness occurs because the astronaut is so far away from the earth that he or she is no longer affected by the gravitational pull of the earth. Despite the fact that the astronaut is weightlessness, his or her mass does not change, since the amount of matter in their body has not changed. What only has changed is the gravitational pull on the astronaut which determines the astronaut's weight.

    The gravitational force on Earth is approximately six times greater than on the moon. Thus, if an astronaut were on the moon, he or she would weight six times less than if he or she were on Earth. Thus, if the astronaut weighed 100 pounds on Earth, he or she would only weight one-sixth of that, or approximately 16.7 pounds.

    If this same astronaut were to land on the planet Jupiter, he or she would weigh 234 pounds since the gravitational force on Jupiter is approximately 2.34 times that of the Earth.

    The effects of weightlessness on astronauts are carefully studied by NASA engineers in order to secure astronauts' safety.

    Click here to learn how weight is one of four forces which acts on an airplane.


    The Activity:

  • Provide students with the Table showing each planet's relative surface gravity value in decimal form.

  • Allow students to view the planets as they appear in order from the sun. Pose the following questions and create a discussion: Is there a relationship between the distance a planet is from the sun and its surface gravity? Is there a relationship between the size of a planet and its surface gravity?

    Despite the fact that Jupiter is the largest planet and it has the largest value for surface gravity, a planet's size does not dictate its surface gravity. As a counterexample, notice that Uranus has a larger diameter than the earth's, but Uranus' surface gravity value is smaller than that of the earth. Also, there is no relationship between how far a planet is from the sun and its gravity, since Pluto is the farthest planet from the sun, yet it does not have the smallest (or biggest) value for gravity.

  • Introduce the students to the three Space Travelers who want to help us learn about gravity on other planets:
    • Rocket Man , Three Prong , and Bubble Head.

  • Students will first choose a Space traveler as their guide. Next, the students will predict and then record how much their cosmic friend will weigh on each of the planets, using the worksheet.

  • Students will now compute and record their space traveler's actual weight using the decimal values in the gravity table. Students may be encouraged to use calculators at this time, since the computations may be a bit messy, or, calculators may be used as a means to verify answers.

  • Allow the students to verify their computations by placing the students into 3 groups, one for each Space Traveler. Within each group will be those students who computed the weight for that particular Space Traveler. Allow the students to work collaboratively to check the accuracy of their answers.

  • Next, students will compare their predicted weight values to their computed values. In their journals, students will reflect on their estimation skills in predicting the weights.

  • At this point, the teacher can provide additional practice with decimals by asking the students to re-express the decimal values of gravity as proper or improper fractions.



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    • Funded by the NASA Dryden Flight Research Center


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