Unit Plan 32 (Grade 6 Math): Percent & Ratio Mastery—Decisions with Data

Focus: Blend percent problems (tax, discounts, tips), constant speed/unit pricing, and measurement conversions to make real-world recommendations.

Grade Level: 6

Subject Area: Mathematics (Ratios and Proportional Relationships — Percents, Rates, Conversions)

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

I. Introduction

This capstone ratio unit pulls together percent reasoning, unit rates, and conversions so students can make and defend everyday decisions: Which deal is better? What final price should we expect with tax and tip? Which route is faster at a constant speed? Students practice modeling with double number lines, tape diagrams, and ratio tables, and communicate recommendations clearly with units and reasoning.

Essential Questions

• How do I use unit rate and percent to compare options and make a decision?
• When is a ratio table or double number line more helpful than a one-step calculation?
• How do conversions (time, distance, capacity, weight) affect which choice is best?
• How do I explain my recommendation with clear units and assumptions?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Interpret and compute unit rates from ratios and use them to compare prices and speeds.
2. Solve percent problems including tax, discount, and tip using multiple representations (ratio table, double number line, tape diagram).
3. Use equivalent ratios to convert measurement units within and across systems (customary and metric).
4. Integrate percent, unit rate, and conversions to make a recommendation and support it with math evidence.
5. Communicate solutions with precise units, state assumptions, and check reasonableness.

Standards Alignment — CCSS Grade 6

• 6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b; use rate language in the context of a ratio relationship.
• 6.RP.3a: Make tables of equivalent ratios relating quantities; find missing values; plot pairs on the coordinate plane; use the tables to compare ratios.
• 6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed.
• 6.RP.3c: Find a percent of a quantity as a rate per 100; solve problems involving percent (including discounts, markups/tips, tax).
• 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately.
• Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision), MP.7 (structure).

Success Criteria — Student Language

• I can find and use a unit rate to compare options.
• I can solve percent problems for tax, discount, and tip with a diagram or table.
• I can convert units and keep track of labels.
• I can make a recommendation and justify it with numbers, units, and assumptions.
• I can check if my answer is reasonable for the situation.