Unit Plan 2 (Grade 7 Math): Ratios to Unit Rates
7th graders master ratio reasoning by converting real-world comparisons into precise unit rates, including complex fractions and mixed units. They connect tables, double number lines, and y = kx equations to understand proportional relationships with accuracy and clarity.
Focus: Move from ratio language to unit rate, including complex fractions and rational quantities in measurement contexts.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Relationships)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week transitions students from informal ratio talk (“3 packs for 5 dollars”) to precise unit-rate reasoning (“$1.67 per pack”). Students convert among ratio forms, compute unit rates from fractions of fractions (complex fractions), and communicate with correct units in measurement contexts (speed, density, price, recipe). Multiple representations—tables, double number lines, and equations of the form y = kx—support sense-making.
Essential Questions
- How does a unit rate help us compare situations fairly?
- How do we compute unit rates when quantities are fractions or mixed units?
- How do tables, double number lines, and y = kx show the same proportional relationship?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Translate ratio language (A to B, A:B, A/B) into a unit rate with correct units (per 1).
- Compute unit rates when quantities are rational numbers, including complex fractions (for example, 3/4 mile in 1/3 hour).
- Interpret the constant of proportionality (k) from tables and contexts and explain its meaning as a unit rate.
- Choose and use representations (table, double number line, equation y = kx) to solve and explain proportional problems.
- Check reasonableness of results with estimation, benchmark rates, and unit analysis.
Standards Alignment — CCSS Grade 7
- 7.RP.1: Compute unit rates associated with ratios of fractions, including quantities measured in like or different units.
- 7.RP.2a: Recognize and represent proportional relationships between quantities; decide whether two quantities are in a proportional relationship (table of equivalents, graph through origin, or equation of the form y = kx).
- Mathematical Practices MP.1–MP.6 emphasized (make sense, reason, model, tools, precision).
Success Criteria — Student Language
- I can write a unit rate with correct units (per 1).
- I can find unit rates when the numbers are fractions (complex fractions).
- I can tell if a situation is proportional and explain why (table, graph through origin, or y = kx).
- I can say what k means in my problem (for example, dollars per pack, miles per hour).
- I can estimate and check whether my answer makes sense.