This project addresses the confusion students have distinguishing between unit rates & ratios.

This project is not meant to give any sure fire ways of addressing the difference between unit rates and ratios, it is meant to provide opportunity for reflection, and some possible lesson ideas. Feel free to make use some, none, or all. Please make it your own. If you have any suggestions feel free to email them to pfossat@alpine.k12.ut.us.

The Problem
:

When students are taught about ratios and unit rates together, they often mix up using a unit rate, and a simplified ratio. For example, when asked to write a simplified ratio for "5 boys for every 10 girls", a student who recently learned about unit rates may use a calculator to write 0.5 boys/1 girl. This is not an incorrect statement, but does not reflect understanding of the difference between a unit rate and a reduced ratio (1 boy / 2 girls). How can a teacher address this misunderstanding?

Things To Understand:

According to Math.Com "A rate is a ratio that compares two different kinds of numbers, such as miles per
hour or dollars per pound. A unit rate compares a quantity to its unit of
measure."
The key to this is that a unit rate compares to the "unit of measure". For example, a person does not usually say "I am traveling 100 miles / 2 hours."The reason we don't is that we don't measure the unit of 2 hours. The unit of measure is 1 hour, so we say, "I am traveling 50 miles / (1) hour." It becomes apparent that the denominator, will always be one. The reason we do this is to have a uniform measurement by which we can compare things.

Possible Student Challenges or Misunderstandings:
• The student does not see the unit rate as a standardized measurement.
• \$150 for 9 hours of work = \$16.67 per hour.
• The student does not understand the reason, or value of a unit rate.
• \$150 for 9 hours of work = \$16.67 per hour. = Better Rate
• \$65 for 5 hours of work = \$13 per hour. = Lower Rate
• One colleague suggested that students would better understand slope as a
measure of steepness if we had
students express it as a unit rate.
• The student does not understand the reason or value of a ratio.
• Unit rates compare different types of data-not same.
• Ratios for part to whole relationships.
• 3 out of 5 boys makes more sense than 0.6 boys per 1 boy.
• 45 out of 50 points-not .9 points for every point.