Goal of the Lesson
We want to make students understand the value of astronomical numbers and how we could use them.
Objectives
Students will be able to understand and use astronomical numbers and they should also be able to perform the most basic operations with them. Students will write explaining their answers.
Background Information
It is estimated that the Universe as we know it now is about 16 billion years old. It is also estimated that the Earth and the Solar System are about 4.6 billion years old. The explosion of a super nova created the Solar System, with the Sun, the planets, the asteroids, comets, moons and everything else in it. The Earth has been around for about 4.6 billion years. We have been part of these processes since the beginning of time. magnetic charges, atoms, molecules, simple life forms are our humble beginnings.
There is a time when we, as human beings, start to differentiate ourselves from other life forms. This is the time of culture. This is the time when we could say that the dust from the hypothetical explosion of the super nova begins to think about itself. The Universe thinks about itself. We are, in this sense, the consciousness of the Universe. This is one of the reasons why we have chosen to write and work with astronomical numbers. Again, it is estimated that the history of humankind, the time that humans have been recording and scratching on rocks and bones events of the past, is about 200,000 years. If this is true, then, how could we visualize the difference between 4.6 billion years and 200,000 years? The use of astronomical numbers in the context of the historical statement of humans and the age of the Earth is of interest to the student. We want to make students understand the value of astronomical numbers and how we could use them to get to a higher understanding of ourselves.
Students will be able to distinguish the difference between a common number such as 200,000 and 4,600,000,000. If students are able to visualize this difference, then, they would be able to visualize the number 16,000.000.000. Further, students will conduct experiments of measurement of time with the help of manipulatives (color yarn).
200,000 vs. 4,600,000,000
How would students manage to understand these numbers and their relationships? Our answer is in the method: students actually have to see the difference visually in order for them to grasp what would otherwise be an incomprehensible number.
Materials
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-yarn of various colors
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-scissors
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-calculator
Procedure
Teacher will ask students about their age. Students in the fifth grade are generally 10 to 11 years of age. What does it mean to be 50 years of age? 70? 100? 10,000?
What kind of numerical system do we use? Did we always use this system? The advantages of the use of the decimal system could be seen in the technology that we have been able to amass. One reflects the other. The decimal system allows us and afford us a tremendous flexibility in the construction of systems and in problem solving, in the production of food as well as in traveling. The decimal system is really the mathematics of one for all practical purposes.
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Let’s explain this realization. Students are going to use a piece of string the size of a thumb to be 200,000. All thumbs are about one inch (about 2.5 cm). We estimate this. We round it. Then they are going to measure 5 of these pieces to build 1,000,000. Now, with this piece they will measure ten times this 1,000,000 piece to get 10,000,000. These numbers are years. They represent years of life of the Earth. Going forward with our measuring we take this last piece and measure it ten times with the result of 100,000,000 years. The age of the Earth will be 46 times the length of this string. We actually did this exercise and students were going around the hallways in the school getting everyone’s attention and curiosity.
I am sure that this is one of the ways to really make students grasp the difference between 200,000 and 4,600,000,000.
_____ ~ 200,000 years
_____ _____ _____ _____ _____ ~ 1,000,000 years
_____ _____ _____ _____ _____ x 10 ~ 10,000,000 years
(_____ _____ _____ _____ _____ x 10) 46 ~ 4.6 billion years.
The next step is the scaling of the Milky Way and the actual construction of a model of it. The structure in already in place. We built a model of the Milky Way with the help of our art teacher, Mr. Leger. Students and teachers worked together to place it in the lobby of the school, next to the Solar System. The Earth is less than a microscopic speck within another microscopic speck—the Solar System.
Because of the work that has been done during this year two teachers have been awarded with some money to actually construct a telescope in the school. The telescope is called The Cold Springs Telescope honoring the institution giving the resources for the telescope.
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