Unit Plan 11 (Grade 6 Math): Coordinates in All Four Quadrants
6th graders plot rational-number points in all four quadrants, reflect them across axes, and find distances along grid lines. They interpret coordinates and reflections in maps and real-world contexts, emphasizing precision, units, and quadrant reasoning.
Focus: Place rational numbers on axes; reflect across axes; find distances on grid lines; solve real-world location problems.
Grade Level: 6
Subject Area: Mathematics (Number System • Coordinate Plane)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend integer and rational-number thinking to the coordinate plane. They locate and label points in all four quadrants, interpret the signs of coordinates, perform reflections across the x- and y-axes, and find distances along grid lines (shared x or shared y). Emphasis: precise graphing, units, and clear sentences that connect graphs to real-world locations (maps, game boards, navigation).
Essential Questions
- How do the signs of (x, y) tell me which quadrant a point lies in?
- What changes (and what stays the same) when a point is reflected across an axis?
- How can I find the distance between two points that share an x- or y-coordinate?
- How do coordinate graphs help solve location problems in context?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Plot and label rational-number coordinates (fractions/decimals) in all four quadrants with accurate scale.
- Explain how the signs of coordinates indicate quadrant and direction from the origin.
- Perform and describe reflections across the x-axis and y-axis and relate sign changes to the reflection.
- Compute horizontal/vertical distances between points that share a coordinate using absolute differences, and state units.
- Solve real-world location problems using graphs, reflections, and grid-line distances; write clear solution statements.
Standards Alignment — CCSS Grade 6
- 6.NS.6a–c: Understand a rational number as a point on the number line/coordinate plane; opposite signs indicate opposite directions; signs in ordered pairs indicate quadrants; reflections across axes relate to sign changes; find and position integers and other rational numbers on axes and in the coordinate plane.
- 6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants and finding the distance between points with the same first coordinate or the same second coordinate; interpret situations in context.
- Mathematical Practices emphasized: MP.1 (make sense), MP.2 (quantitative reasoning), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can plot rational-number points in the correct quadrant and label axes and units.
- I can describe a reflection across the x- or y-axis using sign changes.
- I can find a horizontal or vertical distance by subtracting coordinates and using absolute value/units.
- I can explain what a point or distance means in a real situation (map, grid, or game board).