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Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to “Did either of these sets of measurements determine one unique triangle? How do you know?” In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing.
If time allows, display these prompts for feedback:
Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words that they got from their partners in order to make their next draft stronger and clearer.
If the optional blackline master was used, ask students:
If not mentioned by students, explain to students that the top left and bottom left configurations result in the same triangle, because in both cases the
Arrange students in groups of 2. Tell students that they should attempt to create a triangle with the given specifications. If they can create one, they should attempt to either create at least one more or justify to themselves why there is only one. If they cannot create any, they should show some valid attempts to include as many pieces as they can and be ready to explain why they cannot include the remaining conditions.
Give students 5 minutes of quiet work time, followed by time to discuss with a partner the triangles that they individually made. Follow with a whole-class discussion. Provide access to geometry toolkits and compasses.
Draw as many different triangles as you can with each of these sets of measurements:
One angle measures
One angle measures
Did either of these sets of measurements determine one unique triangle? How do you know?
If students struggle to get started, remind them of Lin’s technique of using the protractor and a ruler to make an angle that can move along a line.
Select students to share their drawings and display them for all to see. Ask students:
Consider displaying the applet for all to see while discussing the last questions:
Some students may draw two different orientations of the same triangle for the first set of conditions, with the
If students struggle to create more than one triangle from the first set of conditions, prompt them to write down the order they already used for their measurements and then to brainstorm other possible orders they could use.