Unit Plan 17 (Grade 7 Math): Angle Relationships—Build and Solve
7th graders use complementary, supplementary, vertical, and adjacent angle relationships to write and solve equations. They justify each algebraic step, check solutions for reasonableness, and express precise angle measures with correct degree units.
Focus: Use complementary, supplementary, vertical, and adjacent angles to write and solve equations in geometric contexts.
Grade Level: 7
Subject Area: Mathematics (Geometry • Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students use angle relationships to create and solve one-variable equations. They identify complementary (90°), supplementary (180°), vertical (congruent), and adjacent/linear pair relationships in diagrams, then build equations (for example, x + (2x + 15) = 180) to determine unknown angle measures. Emphasis: translating words/diagrams → equations, justifying steps, and writing clear conclusion statements with units (degrees).
Essential Questions
- Which angle relationships help me set up an equation from a diagram?
- How do I justify each algebraic step and check whether my solution is reasonable?
- How do complementary, supplementary, vertical, and adjacent relationships connect in multi-angle figures?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Identify complementary, supplementary, vertical, and adjacent/linear-pair relationships in a figure.
- Translate a geometric relationship into an equation (for example, “these two angles are supplementary” → sum is 180).
- Solve multistep linear equations with rational numbers to find unknown angle measures and justify steps.
- Check solutions by substitution and by reasonableness (does the diagram and context make sense?).
- Communicate a unit-based conclusion (degrees) and explain which relationship(s) they used.
Standards Alignment — CCSS Grade 7
- 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.EE.4a (connection): Use variables to represent quantities; solve word problems leading to equations of the form px + q = r and p(x + q) = r; assess reasonableness.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can spot which angles are complementary, supplementary, vertical, or adjacent.
- I can write an equation from the diagram and solve it step by step.
- I can name the property or relationship that justifies each step.
- I can check my answer (substitute and look for reasonableness on the diagram).
- I can state the angle measure with degrees and explain why it’s correct.