Unit Plan 26 (Grade 6 Math): Proportional Modeling—Recipes & Conversions

Focus: Test proportionality with tables/graphs; compute unit rate; convert measurement units within proportional models.

Grade Level: 6

Subject Area: Mathematics (Ratios & Proportional Relationships — Modeling, Unit Rate, Conversions)

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

I. Introduction

Students model real situations (especially recipes and measurement conversions) using ratios, tables, and graphs. They test proportionality, identify the unit rate (constant of proportionality), and represent pairs on the coordinate plane (through the origin). Learners convert within/between measurement systems using conversion factors, and communicate results with clear units and reasonableness checks.

Essential Questions

• How do I know when two quantities are in a proportional relationship?
• How do tables, graphs, and unit rates help me model and solve recipe and conversion problems?
• Why does a proportional graph go through the origin, and what does its steepness mean?
• How do conversion factors function as ratios to change units without changing amounts?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Build and analyze ratio tables; use them to test proportionality and find missing values.
2. Represent relationships on the coordinate plane and explain why proportional graphs pass through the origin.
3. Compute and interpret unit rate (constant of proportionality) in recipe and speed/cost contexts.
4. Use conversion factors (e.g., 12 in/1 ft, 1 L/1000 mL) to convert units and solve problems with precise units.
5. Apply percent as a rate per 100 for quick recipe adjustments or ingredient comparisons (light integration).
6. Justify answers with models, units, and reasonableness (estimation and bounds).

Standards Alignment — CCSS Grade 6

• 6.RP.2: Understand the concept of a unit rate associated with a ratio; use rate language in context.
• 6.RP.3a: Make tables of equivalent ratios, find missing values, and plot the pairs on the coordinate plane; use tables to compare ratios.
• 6.RP.3b: Solve unit rate problems (e.g., constant speed, price per unit).
• 6.RP.3c (light integration): Find a percent of a quantity as a rate per 100; solve word problems involving percent.
• 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately.
• Mathematical Practices emphasized: MP.1 (make sense), MP.2 (quantitative reasoning), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure).

Success Criteria — Student Language

• I can test if two quantities are proportional with a table or graph that goes through the origin.
• I can find and explain the unit rate and use it to solve and check problems.
• I can plot ratio pairs and read what a point means (including the origin).
• I can use a conversion factor to change units and write a clear unit sentence.
• I can use percent as per 100 to make a small adjustment and justify my answer.