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Elementary Math Activities: Solar System

Mathematics is essential to the study of astronomy. Gazing up at the stars, it is difficult to imagine the massive scales of our solar system and the universe beyond, using and comparing numbers; math can be a useful tool in conceptualizing our place in the cosmos. Math projects for kids in astronomy should focus on achieving the educational standards for that group, based on age appropriate state requirements. The Massachusetts state standards are among the highest in the nation, though these exercises can be adapted to your specific state if necessary. Students should be challenged in ways that allow them to use their creativity in practical, interesting ways; math projects in astronomy afford that opportunity.
  1. Grade 1: The Speed of Light

    • The extremes of physics are commonly observed in the study of astronomy. The concept that the speed of light has a finite, observable value may be new to students of this age group. For an exercise in telling time, you could ask the students to interpret the time on a toy clock; once they have given the correct answer, move the minute hand forward 8 minutes and ask for the time change. When they come up with the correct answer, you can use this opportunity to drop this interesting fact about the time it takes for light from the sun to reach the earth: approximately 8 minutes. Describe how this is because of the massive scale of the solar system and the large distance between the sun and our planet. Similarly, you could use the same time-telling exercise to explain to the students that it takes only 1.3 seconds for light reflecting off the moon to reach the earth; use a clock with a large second hand for this activity. Point out the large difference in the travel times of light, and explain that the difference is due to the fact that we are much closer to the moon than we are to the sun.

    Grade 2: Solar System Model

    • For a great hands-on activity that can be done in the classroom, have the students help you build a model solar system that is scaled accurately. This activity will require the students to use standard units of measurement, such as centimeters on a ruler, to properly set up the model system. For instance, if you are building the model in a classroom, you should scale the model so the distance between the sun and Pluto is the maximum diagonal span of the classroom. Starting at this point, instruct the students to place the different model planetary bodies based on the appropriately scaled distances you have calculated beforehand.

    Grade 3: Planetary Comparison

    • Compare the masses of planets in the solar system for an exercise in fractions. For instance, the mass of Jupiter is approximately 32 times greater than the mass of the earth; from this, explain to the students that the earth has a mass of 1/32nd that of Jupiter. Taking it to the next level, the sun's mass is 10,000 times that of Jupiter; therefore, Jupiter is 1/10,000th the mass of the sun! Comparisons of this sort can be made between all planets of the solar system using the mass of the earth as the reference point; help the students calculate unit fractions, or fractions with 1 in the numerator, for simplicity. This exercise will help the students conceptualize the relative mass of planets in the solar system.

    Grade 4: Multi-digit Multiplication

    • Have the students calculate their weight on other planets to become more proficient with multi-digit multiplication and division. For instance, in order to calculate their weight on Jupiter, they would have to multiply their weight in pounds on Earth by 236 because of the stronger gravitational force that one would experience standing on Jupiter's surface. Similarly, students should divide their weight by 15 in order to calculate their weight on Pluto, which has less gravitational force.

    Grade 5: Volume

    • As students prepare to graduate from elementary school, state requirements encourage them to gain experience calculating and conceptualizing volumes. A great science project for fifth graders would be to calculate the volume of the planets and the sun. Not only would this activity satisfy grade specific state requirements, it would give the kids an interesting, practical insight into the scale of planets in our solar system. For instance, the volume of Jupiter is over 1,300 times greater than the volume of Earth, and the sun's volume is 1,000 times greater than Jupiter's and 1,299,400 times greater than Earth's! These scales are massive and hard to comprehend without comparable, Earth-scale volumes to measure up against.

    Additional Activities: The Densities of Planets

    • As a supplement to grade 5 activities, a great project would be to calculate the densities of the different planets. Density is defined as mass divided by volume; the students could practice calculating large density fractions based on their previous calculations of volume. Given the mass of each planet, the students could divide this value by the planet's volume to calculate the density. You may find some of the results surprising. For instance, Saturn is composed mostly of light gas and is therefore not a dense planet; in fact, the density of Saturn is so low that it would float on water. Despite its relatively smaller size, Earth is 8 times denser than Saturn.


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