This Warm-up prompts students to compare four equations that may arise while using the Pythagorean Theorem. It gives students a reason to use language precisely (MP6) and it gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the equations in comparison to one another.
Arrange students in groups of 2–4. Display the equations for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three equations that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Which three go together? Why do they go together?
A
52=32+b2
B
52−32=b2
C
32+52=b2
D
32+42=52
Sample responses:
A, B, and C go together because:
A, B, and D go together because:
A, C, and D go together because:
B, C, and D go together because:
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use, such as "variable" or "term," and to clarify their reasoning as needed. Consider asking:
“How do you know . . . ?”
“What do you mean by . . . ?”
“Can you say that in another way?”
If time allows, invite 2–3 students to share what they notice all of the equations have in common (they all have three terms, all terms are a value squared). The purpose of this concluding share out is to reinforce that all 4 equations show the relationship between three squared values but with different orderings. Paying attention to order while using the Pythagorean Theorem is a focus of later activities.
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This Warm-up prompts students to compare four equations that may arise while using the Pythagorean Theorem. It gives students a reason to use language precisely (MP6) and it gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the equations in comparison to one another.
Arrange students in groups of 2–4. Display the equations for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three equations that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Which three go together? Why do they go together?
A
52=32+b2
B
52−32=b2
C
32+52=b2
D
32+42=52
Sample responses:
A, B, and C go together because:
A, B, and D go together because:
A, C, and D go together because:
B, C, and D go together because:
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use, such as "variable" or "term," and to clarify their reasoning as needed. Consider asking:
“How do you know . . . ?”
“What do you mean by . . . ?”
“Can you say that in another way?”
If time allows, invite 2–3 students to share what they notice all of the equations have in common (they all have three terms, all terms are a value squared). The purpose of this concluding share out is to reinforce that all 4 equations show the relationship between three squared values but with different orderings. Paying attention to order while using the Pythagorean Theorem is a focus of later activities.