Unit Plan 35 (Grade 6 Math): Number System Power-Up—Rationals & Coordinates

Focus: Polish fluency with fraction/decimal operations, ordering/absolute value, and coordinate-grid distances (horizontal/vertical).

Grade Level: 6

Subject Area: Mathematics (The Number System — Rational Operations & Coordinate Reasoning)

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

I. Introduction

This power-up consolidates the Grade 6 Number System. Students model and compute fraction ÷ fraction in context, refine decimal operations with estimation and error checks, compare and order rational numbers using absolute value to reason about magnitude, and apply coordinate-plane skills to plot points, reflect across axes, and find distances along grid lines. Emphasis is on units, representations, and clear unit sentences.

Essential Questions

• How do I model and solve fraction division problems so my answer makes sense in the context?
• How does estimation help me check decimal operations for reasonableness?
• What is the difference between order (which is greater) and magnitude (how far from 0 via absolute value) for rational numbers?
• How do coordinates and the grid help me describe location and distance (horizontal/vertical) precisely?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Model and compute fraction–fraction division and write unit sentences that match the story.
2. Perform decimal operations (add/subtract/multiply/divide) with place-value reasoning, estimate, and check results.
3. Compare and order rational numbers; use absolute value to describe distance from 0 and interpret in context.
4. Plot points in all four quadrants, reflect across axes, and find distances along horizontal/vertical lines and simple grid paths.
5. Communicate solutions with units, identify assumptions, and justify reasonableness.

Standards Alignment — CCSS Grade 6

• 6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
• 6.NS.2: Fluently divide multi-digit numbers using the standard algorithm.
• 6.NS.3: Fluently add, subtract, multiply, and divide decimals using the standard algorithm.
• 6.NS.5: Understand positive and negative numbers to describe quantities having opposite directions/values; use absolute value to describe magnitude.
• 6.NS.6a–c: Understand rational number locations on the number line and coordinate plane; plot in all four quadrants.
• 6.NS.7a–d: Compare and order rational numbers; interpret absolute value as magnitude and apply in context.
• 6.NS.8: Solve real-world problems by graphing points in all four quadrants and finding distances between points with the same x- or y-coordinate; describe grid paths.
• Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision), MP.7 (structure), MP.8 (regularity).

Success Criteria — Student Language

• I can model and solve a fraction ÷ fraction problem and explain what the answer means with units.
• I can do decimal operations and use estimation to check if the answer is reasonable.
• I can order rational numbers and use absolute value to talk about distance from 0.
• I can plot points, reflect across axes, and find horizontal/vertical distances on a grid.
• I can write a clear unit sentence and explain why my method works.