Learn on PengienVision, Mathematics, Grade 6Chapter 5: Understand and Use Ratio and Rate

Lesson 6: Compare Unit Rates

In this Grade 6 lesson from enVision Mathematics, students learn how to calculate and compare unit rates to solve real-world problems, including finding unit prices to determine better value. Using Common Core standards 6.RP.A.3a and 6.RP.A.3b, students practice dividing rates to find a single-unit quantity, then compare the resulting decimal values to draw conclusions. The lesson covers contexts such as speed, laps per minute, and cost per item, building fluency with ratio and rate reasoning in Chapter 5.

Section 1

Application: Interpret Comparisons in Context

Property

The interpretation of a "better" rate depends on the context:

  • Performance (e.g., speed, output): A larger unit rate is greater or faster.
  • Cost (e.g., unit price): A smaller unit rate is cheaper or a better value.

Examples

Section 2

Using Unit Rates to Compare Ratios

Property

When two rates are given, it can be difficult to determine which rate is higher or lower because they have different values.
It is not until both rates are converted to the same unit (a unit of one) that the comparison becomes easy.
This is useful for finding the better deal or determining which object is moving faster.

Examples

  • Store A sells 10 pens for 2 dollars. Store B sells 12 pens for 3 dollars. Store A's rate is 210=0.20\frac{2}{10} = 0.20 dollars per pen. Store B's is 312=0.25\frac{3}{12} = 0.25 dollars per pen. Store A is cheaper.
  • A train travels 210 miles in 3 hours. A bus travels 130 miles in 2 hours. The train's speed is 2103=70\frac{210}{3} = 70 mph. The bus's speed is 1302=65\frac{130}{2} = 65 mph. The train is faster.
  • One faucet fills a 10-gallon tub in 4 minutes. Another fills a 12-gallon tub in 5 minutes. The first faucet's rate is 104=2.5\frac{10}{4} = 2.5 gal/min. The second is 125=2.4\frac{12}{5} = 2.4 gal/min. The first faucet is faster.

Explanation

To compare different deals or speeds, convert them to a common language: the unit rate. By finding the 'cost per one' or 'distance per one,' you can easily see which option is cheaper, faster, or better.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Application: Interpret Comparisons in Context

Property

The interpretation of a "better" rate depends on the context:

  • Performance (e.g., speed, output): A larger unit rate is greater or faster.
  • Cost (e.g., unit price): A smaller unit rate is cheaper or a better value.

Examples

Section 2

Using Unit Rates to Compare Ratios

Property

When two rates are given, it can be difficult to determine which rate is higher or lower because they have different values.
It is not until both rates are converted to the same unit (a unit of one) that the comparison becomes easy.
This is useful for finding the better deal or determining which object is moving faster.

Examples

  • Store A sells 10 pens for 2 dollars. Store B sells 12 pens for 3 dollars. Store A's rate is 210=0.20\frac{2}{10} = 0.20 dollars per pen. Store B's is 312=0.25\frac{3}{12} = 0.25 dollars per pen. Store A is cheaper.
  • A train travels 210 miles in 3 hours. A bus travels 130 miles in 2 hours. The train's speed is 2103=70\frac{210}{3} = 70 mph. The bus's speed is 1302=65\frac{130}{2} = 65 mph. The train is faster.
  • One faucet fills a 10-gallon tub in 4 minutes. Another fills a 12-gallon tub in 5 minutes. The first faucet's rate is 104=2.5\frac{10}{4} = 2.5 gal/min. The second is 125=2.4\frac{12}{5} = 2.4 gal/min. The first faucet is faster.

Explanation

To compare different deals or speeds, convert them to a common language: the unit rate. By finding the 'cost per one' or 'distance per one,' you can easily see which option is cheaper, faster, or better.