Nonadjacent Angles

5 min

Teacher Prep
Setup
Groups of 2. 2 minutes quiet work time followed by partner and whole-class discussions.

Narrative

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 aa and bb

Launch

Arrange students in groups of 2.

Ask students, “If we know for sure that a+b=180a+b=180, what are some possible values of aa and bb?” Give students 30 seconds of quiet think time, and then ask several students to share their responses. Some examples are a=90a=90 and b=90b=90, a=0a=0 and b=180b=180, and a=10a=10 and b=170b=170. Tell students that in this activity, we know for sure that a+b=180a+b=180, but we don’t know the exact values of aa and bb.

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.

Student Task

If a+b=180a+b=180 is true, which statements also must be true?

a=180ba=180-b

a180=ba-180=b

360=2a+2b360=2a+2b

a=90a=90 and b=90b=90

Sample Response

a=180ba=180-b and 360=2a+2b360=2a+2b
Activity Synthesis (Teacher Notes)

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:

  • “Do you have an example that might support this statement being true (or untrue)?”
  • “What evidence do you have to support that statement being true (or untrue)?”
  • “What other values of aa and bb might work?”
  • “What was done to the equation to make the statement true (or untrue)?” 

If students claim that a180=ba-180=b or a=90a=90 and b=90b=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=180a+b=180 but their statement is not true.

If students claim that  a180=ba-180=b cannot be true, ask them to consider what would happen if one of the values is 0.

Standards
Addressing
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
  • 7.EE.A·Use properties of operations to generate equivalent expressions.

10 min

15 min