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Simpsons Sunblocker

The purpose of this activity is to give students an opportunity to explore the concept of geometric proportionality. The essential question in this task is “How do we use math to find the height of things that are difficult to measure?” Since students will be working in teams, this activity helps to establish group norms.

1. Introduce the Essential question “How do we use math to find the height of things that are difficult to measure?”.  Show images of things whose height might be interesting to measure.  Ask students to generate a list of objects whose height might be interesting to measure.
2. Establish Classroom Norms.  Discussion around norms for working together and doing math. (i.e. How to have a discussion, how to justify answers, etc.)
3. Show the Simpson’s clip of Mr. Burns blocking the sun with a circular disk.  State the goal of the day: “Our goal is to help Mr. Burns understand where to place a circular disk in order to block the sun over the town of Springfield.” https://www.101qs.com/2708-simpsons-sunblocker
4. Launch the activity
• Show the contents of the Sunblocker kit: a flashlight, the cut-out sun blockers, a ruler, and the map of the city of San Jose (or a city of your choice).
• Ask several students to help demonstrate the data collection.  One student holds the flashlight, another holds a blocker and another measures.  The fourth records.  Point out that students need to keep the flashlight in the same position at all times, as much as possible, just like the sun is.
• Explicitly call attention to what each member of the group is doing.
• Distribute the Simpsons Sunblocker worksheet.
5. Group Work
• In groups of four, students should repeat the experiment for all  the Sunblockers in their kit. Students should create a table with  the following variables: diameter of the blocking disk and  distance from light source.
• Inform students they will be challenged at the end of the day by being given a disc they have not used. Their goal will be to put the  disc in the best location to block out the sun over San Jose. Note:  Exchange the map in the unit for any location that would be relevant and of interest to the students.
• Teacher Talking Points:
• Precision.  Encourage students to be as precise as possible  in their measurements and in holding the flashlight.
• Noticing. Ask students to share their informal  observations about what they’re noticing.
• Student Challenges & Misconceptions:
• Organization.  Students might not experiment systematically.  They might measure the discs in an order that doesn’t highlight patterns as well as ascending or descending. If they struggle to  see patterns ask students how they could organize their data differently.
6. Formative Assessment
• When groups have completed the table, pass out the next prompt  on a card: “We’ve created a disc that is 15 cm in diameter. Where  should it go? Everybody in your group should be able to explain  your reasoning.”
• Student Conceptions:
• Estimation — Direction. “I know the blocker is going to be  farther away from the light because the disk is bigger.”
• Estimation — Constant Difference. “I know the blocker is going to  be farther away and I used the pattern to count up to where I  thought it would be.”
• Estimation — Interpolation. “San Jose is 18.5 centimeters. The  largest disk is 9.4. This new disk is 15 centimeters so it is going to be really far away from the light source.
• Calculation. The student calculates the constant of  proportionality and uses it to find the new height.
7. Group Work
• As groups find their estimates, the teacher asks a random  member for her answer and her reasoning. (The answer should  be more sophisticated than Estimation — Direction.)
• Teacher passes out the two graphs. The first is to be used for a  sketch. The second is to be used for a more accurate graph. Every  student in the group should make a sketch of the data (rough, no  units, to get a sense of trends) and a graph of the data (precise, using grid paper) and compare with each other. They will explain  to each other in words why they drew it the way they did.
• Teacher Talking Points:
• Methods. Teacher will ask students how they will use their  graph to determine the height of the final sun blocker. Teacher  can ask students, “Can you show me where the final sun blocker  is on your graph?”
• Once students have their answer — both estimated and now tested by graphing — the teacher can test their answer by giving  them the final sunblocker and letting them use it.
• Each group should record how close their answer was from the  actual best placement of the final disk.  (Note: every group may have a different, correct answer,  depending on where they hold the flashlight.) Teacher will offer  extensions as the groups finish. Every group needs to enter their data in a Google Form (or equivalent) so the teacher can pose questions about the class data set the next day.
8. Class Debrief – Headlining. Each group decides on a single “headline,” a major  takeaway or big idea from today. (eg. “Use little data to make  conclusions about big data.”) They write it down and then share  each out to the entire class.

Reference

Licensed under Creative Commons Attribution 3.0 by Dan Meyer, Sarah Kate Selling, Kathy Sun & Jo Boaler