The purpose of this Warm-up is for students to use structure to reason about equivalent equations. In this unit, students will write equations to represent how angles are related to each other, and this Warm-up helps prepare for that work.
All of the given statements could be true so students may be quick to say each of them must be true. Ask these students if there is a case in which that particular statement would not be true for possible values for a and b.
Arrange students in groups of 2.
Ask students, “If we know for sure that a+b=180, what are some possible values of a and b?” Give students 30 seconds of quiet think time, and then ask several students to share their responses. Some examples are a=90 and b=90, a=0 and b=180, and a=10 and b=170. Tell students that in this activity, we know for sure that a+b=180, but we don’t know the exact values of a and b.
Give students 2 minutes of quiet work time followed by 1 minute to discuss their responses with a partner. Follow with a whole-class discussion.
If a+b=180 is true, which statements also must be true?
a=180−b
a−180=b
360=2a+2b
a=90 and b=90
Invite students to share their reasoning for each statement. If students disagree, allow students to discuss until they come to an agreement. Consider asking some of the following questions while students discuss:
If students claim that a−180=b or a=90 and b=90 must be true, explain that this may be true, but does not have to be true. Invite them to discuss this idea and think of examples where a+b=180 but their statement is not true.
If students claim that a−180=b cannot be true, ask them to consider what would happen if one of the values is 0.
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The purpose of this Warm-up is for students to use structure to reason about equivalent equations. In this unit, students will write equations to represent how angles are related to each other, and this Warm-up helps prepare for that work.
All of the given statements could be true so students may be quick to say each of them must be true. Ask these students if there is a case in which that particular statement would not be true for possible values for a and b.
Arrange students in groups of 2.
Ask students, “If we know for sure that a+b=180, what are some possible values of a and b?” Give students 30 seconds of quiet think time, and then ask several students to share their responses. Some examples are a=90 and b=90, a=0 and b=180, and a=10 and b=170. Tell students that in this activity, we know for sure that a+b=180, but we don’t know the exact values of a and b.
Give students 2 minutes of quiet work time followed by 1 minute to discuss their responses with a partner. Follow with a whole-class discussion.
If a+b=180 is true, which statements also must be true?
a=180−b
a−180=b
360=2a+2b
a=90 and b=90
Invite students to share their reasoning for each statement. If students disagree, allow students to discuss until they come to an agreement. Consider asking some of the following questions while students discuss:
If students claim that a−180=b or a=90 and b=90 must be true, explain that this may be true, but does not have to be true. Invite them to discuss this idea and think of examples where a+b=180 but their statement is not true.
If students claim that a−180=b cannot be true, ask them to consider what would happen if one of the values is 0.