Unit Plan 7 (Grade 6 Math): Measurement Conversions & Dimensional Analysis
6th graders use ratio reasoning to convert measurements within and across systems. They apply tables, double number lines, and unit-canceling to decide when to multiply or divide, estimate reasonableness, and extend understanding to area and volume conversions.
Focus: Use ratio reasoning to convert within and across measurement systems; track and transform units.
Grade Level: 6
Subject Area: Mathematics (Ratios & Proportional Reasoning • Measurement)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students apply ratio reasoning to convert measurements within metric and within customary systems, then bridge across systems using given reference conversions. They organize thinking with ratio tables, double number lines, and beginner dimensional analysis (unit-canceling). Emphasis: write the units every step, decide multiply vs divide from the unit language, and estimate first for reasonableness.
Essential Questions
- How do I decide whether to multiply or divide when converting units?
- How do ratio tables and double number lines make conversions transparent?
- What special care is needed for area and volume conversions?
- How can I use a reference conversion (for example, 1 inch = 2.54 cm) to move between systems?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Convert within a system (metric and customary) using ratio tables and double number lines.
- Use a reference conversion to convert across systems (approximate results and rounding when appropriate).
- Track and cancel units in simple dimensional analysis chains (one or two steps).
- Explain and apply square/cubic conversion factors conceptually for area/volume (intro level).
- Estimate before computing and write clear unit statements that answer the question.
Standards Alignment — CCSS Grade 6
- 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
- Mathematical Practices emphasized: MP.1 (make sense), MP.4 (model), MP.5 (use tools), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can set up a conversion ratio and decide to multiply or divide.
- I can show my work with a ratio table or double number line and keep units on every step.
- I can convert between systems with a given reference (for example, inches ↔ centimeters) and tell if my answer is reasonable.
- I can explain that area conversions use squared units and volume conversions use cubed units.
- I can write a final sentence with units that answers the problem.