Dilations on a Graph
This 3 Act Task turns the act of zooming in and out of an image on a phone camera into a dilations puzzle. The puzzle is designed to help students develop an awareness of the proportionality that exists among the distance from a set center, a given magnification, and the size of an image, and to prime them for further exploration of the effects of centers of dilations and scale factors on a dilated image.
Before presenting the Act 1 video, ask students to consider the following questions as they watch:
“What do you notice? What do you wonder?”
“Is there anything that sticks out?”
“Is there anything that reminds you of something else?”
“What are you curious to know?”
Present the Act 1 video.
After presenting the Act 1 video, allow students to share their initial thoughts.
Replay the Act 1 video and continue with the following questions:
“What do you think is the solution to the puzzle?”
“Are there any predictions you’d automatically rule out? Why or why not?”
“What additional information would help you make a more confident prediction?”
After allowing students to share their initial predictions, proceed to Act 2.
Before presenting the Act 2 video, ask students to be on the lookout for new information that will help them refine their predictions.
Present the Act 2 video.
After presenting the Act 2 video, prompt students to consider the following questions:
“How does this new information affect your initial prediction?”
“Are there any changes you’d like to make? Why or why not?”
Give students time to finalize their predictions.
Continue with the following questions:
“What is your final prediction?”
“What is the reasoning behind your prediction?”
“How does your prediction and reasoning compare to others in the class?”
After allowing students to share their final predictions, proceed to Act 3.
Illuminating Teacher Moves
Before presenting the Act 3 video, celebrate the process! 🥳
Remind students that regardless of whether or not their prediction turns out to be correct, everyone has already successfully completed the activity by putting their existing knowledge to work and engaging in critical thinking.
Present the Act 3 video.
After presenting the Act 3 video, take some time to validate students’ reactions.
Irrespective of whether or not their prediction is correct, students may experience a variety of emotions including, but not limited to:
Encouragement, joy, curiosity, excitement
Discouragement, frustration, confusion, and apathy
Take some time to reflect on who your students are and how you can leverage their unique personalities to guide their emotions to a place of awareness and appreciation for the learning that is taking place.
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