We are working in a unit on rates and ratios, and I wanted students to be able to understand different applications of rates, such as area. In one workshop, I introduced some warmup questions and then a mini-lesson on unit rates, followed by some work time on some more complicated area questions. These are just old CSAP/TCAP released items, but they’re great problems that can be solved a number of different ways. The kids worked hard and came up with some clever solutions. Some pitfalls came up – some obvious, others not so. I’ll put a link to the whole activity below. It was exported from the SMART board software.
Area and Unit Rates
Misconceptions & pitfalls:
Moving right into calculating the time to plow the field, without calculating the “square feet per minute” rate first.
Calculating “feet per minute”, or the length of the field that can be plowed in one minute, instead of area.
Dropping zeroes when multiplying, making the field an order of magnitude smaller.
Not converting minutes to hours, or converting incorrectly (for example, 240 minutes equals 2 hours, 40 minutes)
I really encouraged students to think about the reasonableness of their answers, knowing any of the above mistakes would give them answers that should raise flags. All in all, it was a good activity and I was pleased with how well the students worked together and struggled with the problems. Some groups moved on to the food court problem, but many groups did not get there yet, and we haven’t summarized that part.
We have 3 teachers on the seventh-grade team at our school, so we often have flexible grouping days. We use these days to split the kids into “support”, “target”, and “enrichment” groups. We work with the kids on remediation of some concepts they are not secure with, or extension and depth if they’re ready. Since the topic of study this week was unit rates, we gave the kids a pre-assessment and then grouped them into three groups.
Support: These kids struggled with the idea of a unit rate, and correctly labeling which unit rate they calculated (such as misunderstanding ounces per dollar, versus dollars per ounce). We gave them this activity. unit_rate_flex_group
Target: These kids seemed to understand some concepts of unit rates, but struggled some with how to find the correct unit rate to make a valid comparison. We wanted them to work with ideas around comparing and scaling rates, using this activity. Making Comparisons of Two or More Rates
Enrichment: These students understood the how and why of calculating and comparing rates. With these kids, we dug deeper and used technology so they could understand table/graph/equation relationships. Comparing Water Usage Investigation
My team felt this was a pretty successful day of flexible grouping, where all groups of kids made some growth toward their targets. Another big success was that we went paperless! With class sets of netbooks in every classroom, we posted our activities on our websites and had students access them online, edit, save, and submit. We hope to do this more and more!