Unit Plan 2 (Grade 6 Math): Ratios to Unit Rates
6th graders explore ratios and unit rates through real-world contexts like pricing, recipes, and speed. They build tape and double-number-line models, compute “per 1” comparisons, justify best-buy decisions, and communicate reasoning with precise units and representations.
Focus: Develop ratio language, build tape/double-number-line models, and move to unit rate in context.
Grade Level: 6
Subject Area: Mathematics (Ratios & Proportional Reasoning)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week moves from ratio meaning to unit rate. Students describe ratios with clear unit language, model with tape diagrams, double number lines, and ratio tables, then compute and interpret unit rates (for example, price per item, miles per hour). Emphasis: units, multiplicative thinking, and reasonableness.
Essential Questions
- What does a ratio mean and how do I represent it clearly with units?
- How does a unit rate help me compare different situations (best buy, speed, density)?
- How do double number lines and tables show equivalent ratios and support finding “per 1”?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Use ratio language (“for every,” “to,” “per”) with units and order (A:B vs B:A).
- Represent ratios using tape diagrams, double number lines, and ratio tables; generate equivalent ratios by scaling.
- Compute and interpret unit rates from ratios (a:b with b ≠ 0) in real contexts (pricing, speed, recipes, density).
- Choose and justify best-buy or fastest/slowest decisions using unit rates and reasonableness checks.
- Communicate solutions with labeled representations, complete sentences, and clear unit statements.
Standards Alignment — CCSS Grade 6
- 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
- 6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b (b ≠ 0), and use rate language in the context of a ratio relationship.
- Mathematical Practices (threaded all week): MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can describe a ratio with units and keep the order consistent.
- I can show a ratio on a tape diagram or double number line and make equivalent ratios.
- I can find and explain a unit rate (“per 1”) and say what it means in the situation.
- I can use unit rate to decide which option is better and explain why.
- I can check if my answer makes sense using estimation and units.