Learn on PengiBig Ideas Math, Course 1Chapter 5: Ratios and Rates

Lesson 3: Rates

In this Grade 6 lesson from Big Ideas Math Course 1, Chapter 5, students learn to define and apply rates, unit rates, and equivalent rates using ratio tables and double number lines. They practice writing rates from real-world situations, finding unit rates by dividing, and scaling equivalent rates to solve problems involving distance, earnings, and cost. The lesson builds foundational ratio reasoning skills essential for proportional thinking in middle school math.

Section 1

Understanding Rates and Unit Rates

Property

A ratio compares two quantities, often of the same kind.

A rate is a special type of ratio that compares quantities with different units (like miles and gallons, or dollars and hours).

Section 2

Calculating Unit Rates

Property

A unit rate is a rate with a denominator of 1 unit.
To convert a rate to a unit rate, we divide the numerator by the denominator.
This gives us a denominator of 1.

Examples

  • If Anita was paid 384 dollars for 32 hours, her hourly (unit) pay rate is 384 dollars32 hours=384÷32=12\frac{384 \text{ dollars}}{32 \text{ hours}} = 384 \div 32 = 12 dollars per hour.
  • If a car travels 455 miles using 14 gallons of gasoline, its unit rate is 455 miles14 gallons=455÷14=32.5\frac{455 \text{ miles}}{14 \text{ gallons}} = 455 \div 14 = 32.5 miles per gallon (mpg).

Book overview

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Chapter 5: Ratios and Rates

  1. Lesson 1

    Lesson 1: Ratios

  2. Lesson 2

    Lesson 2: Ratio Tables

  3. Lesson 3Current

    Lesson 3: Rates

  4. Lesson 4

    Lesson 4: Comparing and Graphing Ratios

  5. Lesson 5

    Lesson 5: Percents

  6. Lesson 6

    Lesson 6: Solving Percent Problems

  7. Lesson 7

    Lesson 7: Converting Measures

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Understanding Rates and Unit Rates

Property

A ratio compares two quantities, often of the same kind.

A rate is a special type of ratio that compares quantities with different units (like miles and gallons, or dollars and hours).

Section 2

Calculating Unit Rates

Property

A unit rate is a rate with a denominator of 1 unit.
To convert a rate to a unit rate, we divide the numerator by the denominator.
This gives us a denominator of 1.

Examples

  • If Anita was paid 384 dollars for 32 hours, her hourly (unit) pay rate is 384 dollars32 hours=384÷32=12\frac{384 \text{ dollars}}{32 \text{ hours}} = 384 \div 32 = 12 dollars per hour.
  • If a car travels 455 miles using 14 gallons of gasoline, its unit rate is 455 miles14 gallons=455÷14=32.5\frac{455 \text{ miles}}{14 \text{ gallons}} = 455 \div 14 = 32.5 miles per gallon (mpg).

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Ratios and Rates

  1. Lesson 1

    Lesson 1: Ratios

  2. Lesson 2

    Lesson 2: Ratio Tables

  3. Lesson 3Current

    Lesson 3: Rates

  4. Lesson 4

    Lesson 4: Comparing and Graphing Ratios

  5. Lesson 5

    Lesson 5: Percents

  6. Lesson 6

    Lesson 6: Solving Percent Problems

  7. Lesson 7

    Lesson 7: Converting Measures