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.

- 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.
- Establish Classroom Norms. Discussion around norms for working together and doing math. (i.e. How to have a discussion, how to justify answers, etc.)
- 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
- 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.

- 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.

- Teacher Talking Points:

- 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.

- 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.

- 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