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6-N-3-2

Page history last edited by Brenda Butz 6 years, 2 months ago

6.N.3.2 Determine the unit rate for ratios.

In a Nutshell

A unit rate is a ratio in which the second number in the ratio is one. This means the denominator would be one for a unit rate written in fraction form. The unit rate for a ratio can be determined by dividing the numerator and the denominator by the number in the denominator. The work used to determine a unit rate can be organized by using equations involving equivalent fractions, tables, and graphs.

Student Actions	Teacher Actions
Develop models (words, ratio tables, tape diagrams, graphs, and equations) to discover patterns in the form of unit rates for a given situation. Develop mathematical reasoning for using division when comparing and determining the unit rate of a given ratio.	Implement tasks that promote reasoning by engaging students in solving and discussing unit rate problems. Use and connect representations by engaging students in making connections involving unit rate. (For example: “Riley earns $90 for mowing 3 yards. How much does Riley earn per yard?” A tape diagram could be used here to model finding unit rate. This will visually show that the $90 needs to be split among the three yards to find the amount Riley earns for mowing one yard.) Pose purposeful questions about unit rates that arise from students' real-world experiences (Ex: How can unit rates be used to compare ratios?)
Key Understandings	Misconceptions
That unit rates can be written as fractions in which the denominator is always one. That unit rates are formed by dividing the numerator and denominator by the number in the denominator. Through this process, it can be shown that ratios such as 8:4 and 2:1 are equivalent, and 2:1 is the unit rate associated with the ratio 8:4. That every rate situation can be written in two ways with two different unit rates, with either unit as 1. For example, the situation in which 6 pounds of bananas cost $3 can be written in terms of pounds per dollar or dollars per pound. The unit rates would be 2 pounds/$1 and $0.5/1 pound, respectively.	Believe a unit rate is a ratio in simplest form. Believe 1:3 and 3:1 are equivalent ratios and that both are unit rates. Not understand unit rates as fractions because they often see unit rates described with only one number visible (Ex: 25 mph.) Not recognize that 2:1 is the unit rate of 8:4. Believe only one unit rate exists for a given situation.