Unit Plan 20 (Grade 6 Math): Polygons on the Coordinate Plane

Focus: Draw polygons from coordinates; compute side lengths on horizontal/vertical segments; apply to maps/designs.

Grade Level: 6

Subject Area: Mathematics (Geometry — Coordinate Plane & Polygons)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students use the coordinate plane to plot points, draw polygons, and determine side lengths when edges are horizontal or vertical. They work in all four quadrants, attend to signs and units, and apply these skills to map-style and design tasks (planning routes, outlining spaces). Emphasis: precise plotting, clear vertex order, correct length calculations via coordinate differences, and well-labeled diagrams.

Essential Questions

• How do I move from a list of coordinates to an accurate polygon?
• How can I use x- and y- coordinate differences to find horizontal/vertical side lengths?
• Why do units and careful labels matter on a coordinate diagram?
• How can coordinate geometry help me model and solve map or design problems?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Plot points in all four quadrants and connect vertices in order to draw polygons.
2. For sides parallel to axes, find lengths using coordinate differences:
   • Horizontal side from (x₁, y) to (x₂, y): length = |x₂ − x₁|
   • Vertical side from (x, y₁) to (x, y₂): length = |y₂ − y₁|
3. Label vertices, axes, and units; compute perimeter of polygons with axis-parallel sides.
4. Interpret and solve map/design problems using coordinates (e.g., plan a path, outline a fenced area, compare layouts).
5. Check reasonableness by counting grid squares and verifying coordinate differences.

Standards Alignment — CCSS Grade 6

• 6.G.3: Draw polygons in the coordinate plane given coordinates of the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y-coordinate; apply to real-world and mathematical problems.
• 6.NS.8 (spiral): Solve real-world and mathematical problems by graphing points in all four quadrants; find distances between points with the same first coordinate or same second coordinate.

Success Criteria — Student Language

• I can plot each vertex where its x and y go and connect them in order to close the polygon.
• I can find a horizontal or vertical side length by taking the difference of coordinates and using absolute value.
• I can compute the perimeter and write a clear unit sentence.
• I can use coordinates to explain a design or route on a map-style grid.