Unit Plan 3 (Grade 6 Math): Equivalent Ratios—Tables, Graphs, and Patterns
6th graders extend ratio reasoning by creating and scaling ratio tables, finding missing values, and graphing equivalent pairs through the origin. They connect unit rates to straight-line graphs, compare proportional relationships, and justify conclusions using precise tables, graphs, and units.
Focus: Make ratio tables, find missing values, and plot pairs on the coordinate plane to see constant ratios.
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 deepens ratio understanding by building equivalent ratio tables, using scale factors to find missing values, and graphing ratio pairs to visualize the constant relationship as a straight line through the origin. Students connect “for every” language to patterns in tables and structure on a coordinate plane, and they use unit rate (from last unit) to check work.
Essential Questions
- How do ratio tables show equivalent relationships and help find missing values?
- Why do points from a proportional situation lie on a straight line through (0,0)?
- How do scale factors and unit rate connect tables and graphs?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Build ratio tables and use multiplicative scaling to generate equivalent ratios and fill missing entries.
- Explain and apply scale factors (multiply or divide both terms by the same number) to move within a table.
- Plot ratio pairs on the coordinate plane with labeled axes and interpret points in context.
- Recognize the straight-line-through-the-origin pattern for proportional relationships and use unit rate to check.
- Compare two situations using tables and graphs to decide if they represent the same ratio.
Standards Alignment — CCSS Grade 6
- 6.RP.3a: Make tables of equivalent ratios relating quantities with whole-number measurements; find missing values; plot the pairs on the coordinate plane; use tables to compare ratios.
- 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 context.
- Mathematical Practices emphasized: 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 complete a ratio table using scale factors.
- I can plot ratio pairs and label axes with units.
- I can explain why proportional graphs make a straight line through (0,0).
- I can use unit rate to check a table or predict a new pair.
- I can compare two tables/graphs and decide if they show the same relationship.