Purpose
The purpose of the ENGAGE phase is to activate and assess students’ prior knowledge, raise questions and prompt thinking about the meaning of “big” as a relative, rank-ordered, “eye-ball” estimate of size. The sample optical illusions serve as a brief diagnostic review of students’ understanding of metric measurements and mathematics before using these skills in the EXPLORE phase activity.
Materials
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Music Videos from YouTube:
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One or more of the following books:
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Clement, Rod. (1991). Counting on Frank. Gareth Stevens Publishing Co.
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Schwartz, David M. & Kellogg, Steven (illust.). (1994). How Much is a Million? NY: Lothrop, Lee & Shepard Books/HarperCollins
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Wells, Robert E. (1993). Is a Blue Whale the Biggest Thing There Is? Morton Grove, IL: Albert Whitman and Company.
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Three same-sized photos of the Earth, Moon, and Sun (reproduced from the photographs at the end of the unit)
Activity
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Pose the question: What are the three biggest things you can think of? Have students do an individual Think-Write to generate a list, and then ask them to Pair-Share to generate more ideas. [Students are most likely to mention large living things and nonliving objects on Earth. Note whether any students mention the Earth itself or other astronomical bodies or if their perspective is more Earth-bound. It is also important to note if students confound the idea of linear and cubic (or volume) measures and meanings of the term “big.”]
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Follow the Pair-Share with a whole-class discussion around the following questions:
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How do the things we brainstormed compare in relative size (i.e., big…bigger…biggest)?
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[In attempting to generate a size-sequence list, the teacher is likely to encounter cases where off-scale representations in books have misled students about relative sizes.]
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What sources of information could we use to make a rank-ordered sequence or list?
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[Books, the Internet, direct measurements, measurements of scale models.]
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Use a document camera to share select portions of the text and thought-provoking visuals from any of the trade books cited in the Materials section to get students thinking more about the relative (scale order) size of different objects on Earth. If a document camera is unavailable, the teacher can divide the students into small groups and rotate the titles among them.
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Introduce the Earth, Moon and Sun as examples of objects that are bigger than any objects found on Earth. Display a variety of pictures of these three astronomical bodies from books and/or the Internet as well as physical models. Then raise a question such as the following:
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Do the two-dimensional images and 3D models we use always accurately show the relative (or scale order) size of the different things we brainstormed or these three astronomical objects?
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[The three same-size images of the Earth, Moon and Sun at the end of this activity are provided as an example that visually compelling pictures can “lie”].
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Use one of the music videos listed in the Materials section to provide an aesthetic element to the lesson and to show students Earth-bound images of the Moon (which can be quite deceptive). Then pose the following question for discussion:
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While pictures that are NOT drawn to a common scale can certainly “lie” (or misrepresent reality), do our eyes always correctly estimate the relative size of objects? Hint: Consider the objects silhouetted in the foreground of the moon in the music videos (i.e., actual or perceived distance from the object to viewer matters in our size estimates).
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How can measurements help us determine the relative (and actual) size of things? Assuming that students have previously learned how to measure the circumference and diameter of a circle with a metric ruler and string, challenge them to answer empirically the questions posed in the following optical illusions (Use as an in-class and/or at-home assignment; measuring to the nearest 0.1 cm or mm).
Seeing Is Believing?
Eyes Can Deceive What Metric Measurements Help us to Perceive
Are the two colored lines the same length?
If different, which line (red or blue) is longer?
http://brainden.com/images/helicopters-big.jpg
Which central circle is bigger? The left one or the right one? Are you sure?
http://brainden.com/images/dots-big.gif
Do the two checkered design balls have the same or different length diameters?
http://www.eyewow.com/wp-content/uploads/2011/05/circle-size-illusion.jpg
Can you pick out which of the soldiers is the tallest one?
http://www.123opticalillusions.com/pages/opticalillusions6.php
