6.4.D

Math6th Grade

The Standard

give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

Texas Essential Knowledge and Skills for Mathematics

Teacher's field guide

What Students Need to Do: Students compare two quantities with different attributes, such as distance and time or cost and number of items. They express the comparison as division and interpret the quotient with units.
What Mastery Looks Like: Students give examples such as miles per hour, dollars per pound, and words per minute. They write each rate as a division expression and explain what the quotient means with correct units.
Common Misconceptions: Students may call any ratio a rate, even when both quantities have the same attribute. They may reverse the division or leave units off the quotient.
How to Assess It: Exit ticket: A cyclist travels 24 miles in 2 hours. Write the rate as a quotient, calculate it, and label the units.

Lesson moves

Have students measure walking distance and time, then divide distance by time and label each rate in feet per second.
Ask students to explain why 12 dollars for 3 notebooks is a rate and what 12 divided by 3 means.
Use a card sort matching quantity pairs, division expressions, quotients, and labels such as miles per hour or dollars per pound.
Give students grocery ads and have them calculate and compare prices per item, pound, or ounce.

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