Solving for Unknown Angles
5 min
Teacher Prep
Setup
Narrative
This Math Talk focuses on line segment measure relationships represented as equations. It encourages students to think about combinations of line segments. As students mentally solve problems, they rely on what they know about how segment lengths relate to each other. The strategies elicited here will be helpful later in the lesson when students explore the relationship of angle measures.
To compare line segment measure relationships, students need to look for and make use of structure (MP7).
In describing their strategies, students need to be precise in their word choice and use of language (MP6).
Launch
Remind students that we refer to a length of a segment by naming its endpoints. For example, AB means the length of the line segment from A to B.
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.
Keep all previous problems and work displayed throughout the talk.
Supports accessibility for: Memory, Organization
Student Task
Here are some line segments.
Decide mentally whether each statement is true.
- CD+BC=BD
- AB+BD=CD+AD
- AC−AB=AB
- BD−CD=AC−AB
Sample Response
- True. Sample reasoning: CD and BC are next to each other and share the endpoint C, so when they are added together they make BD.
- False. Sample reasoning: AB+BD makes the full segment AD, but CD+AD adds to the full segment AD, so they are not equal.
- False. Sample reasoning: AC is made of segments AB and BC, so when AB is removed BC remains, not AB.
- True. Sample reasoning: BD−CD leaves BC, and AC−AB leaves BC, so they are equal.
Activity Synthesis (Teacher Notes)
To involve more students in the conversation, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone use the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to ’s strategy?”
- “Do you agree or disagree? Why?”
- “What connections to previous problems do you see?”
After each true equation, ask students if they could rely on the same reasoning to determine if other similar problems are equivalent. After each false equation, ask students how the problem could be changed to make the equation true.
Advances: Speaking, Representing
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
- 7.G.B.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Solving for Unknown Angles
5 min
Teacher Prep
Setup
Narrative
This Math Talk focuses on line segment measure relationships represented as equations. It encourages students to think about combinations of line segments. As students mentally solve problems, they rely on what they know about how segment lengths relate to each other. The strategies elicited here will be helpful later in the lesson when students explore the relationship of angle measures.
To compare line segment measure relationships, students need to look for and make use of structure (MP7).
In describing their strategies, students need to be precise in their word choice and use of language (MP6).
Launch
Remind students that we refer to a length of a segment by naming its endpoints. For example, AB means the length of the line segment from A to B.
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.
Keep all previous problems and work displayed throughout the talk.
Supports accessibility for: Memory, Organization
Student Task
Here are some line segments.
Decide mentally whether each statement is true.
- CD+BC=BD
- AB+BD=CD+AD
- AC−AB=AB
- BD−CD=AC−AB
Sample Response
- True. Sample reasoning: CD and BC are next to each other and share the endpoint C, so when they are added together they make BD.
- False. Sample reasoning: AB+BD makes the full segment AD, but CD+AD adds to the full segment AD, so they are not equal.
- False. Sample reasoning: AC is made of segments AB and BC, so when AB is removed BC remains, not AB.
- True. Sample reasoning: BD−CD leaves BC, and AC−AB leaves BC, so they are equal.
Activity Synthesis (Teacher Notes)
To involve more students in the conversation, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone use the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to ’s strategy?”
- “Do you agree or disagree? Why?”
- “What connections to previous problems do you see?”
After each true equation, ask students if they could rely on the same reasoning to determine if other similar problems are equivalent. After each false equation, ask students how the problem could be changed to make the equation true.
Advances: Speaking, Representing
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
- 7.G.B.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.