Understanding Rates

My sixth graders have been hard at work finishing up our work on proportional reasoning.  We just spent the last few weeks on measurement conversion and have covered most of the Common Core Standards for Ratios and Proportions in grade 6.  This week we were finishing up measurement conversion and working on some basic distance, rate and time formulas.

Last summer, I read several proportional reasoning books and in one of them (can't remember which at this time!) they talked a great deal about research around how kids do not understand rates such as miles per hour.  They often think of it as one word and do not understand it is a rate between two quantities.

As we were solving distance, rate and time problems my students seemed to be doing a good job with problems in the context of miles and hours and miles per hour but were having a harder time with other contexts.  They also quite often were getting the correct numerical answer but did not know the meaning of the quantity they came up with.  Was it miles or hours?


I decided to address these issues by starting off class by meeting the kids at the door with a pile of markers and having them go to the board and write a quantity under one of the labels, time, distance or rate.  I was predicting that there would be many more examples under time and distance than there would be under rate.  My formative assessment showed me that students really didn't understand rates.

Here is what I got for responses.  As you can see students had many more examples of time and distance than they did about rate.  

We opened class by discussing these ideas starting with time and moving to the right.  As we discussed them, kids thought of other ideas and we added to the list.

Here are our additions to the list.  As we started getting into more rates, the students really got the idea that there was a distance and a time included in each rate.   

After finishing this discussion, we went back to the distance, rate and time formulas and connected them to what we already know about multiplication and division.

This helped clear up more thinking!  Also kids were able to make the connection between a rate being a combination of distance and time by taking another look at these formulas.

The Common Core standards have certainly increased the amount of proportional thinking required of sixth grade students!  How are your students handling the change?