worth the time to do this

Math teachers I know in middle school bemoan the ability of students to visualize ratios. This activity, when all the steps are followed through, provides students an opportunity to visualiz... See More

Math teachers I know in middle school bemoan the ability of students to visualize ratios. This activity, when all the steps are followed through, provides students an opportunity to visualize both density and how lines on a graph represent ratios (and equivalent fractions). While I think leading the classroom discussions must be done with care (which is probably why the authors provide so much detail here) to be sure to not introduce misconceptions (like how the sinkers end up on the top of the graph rather than the bottom) I believe students will have a much better grasp of both topics. I have done parts of this lesson in my class, but I have not spent the time to explain the meaning of the graphs, and that is something I should spend more time addressing in the future, instead of rushing through this and later having to reteach graphing. This lesson would be good for intermediate, middle, and as a review wouldn't hurt physical science students in high school, either.

Understanding Density Graphically

This article provides a series of activities to help students better understand the difficult concept of density. Two simple activities are used to have students explore the nature of sinki... See More

This article provides a series of activities to help students better understand the difficult concept of density. Two simple activities are used to have students explore the nature of sinking and floating and how changes in volume can affect sinking and floating. In the explain part of the activity students graph their data and try to explain what they did. This series of activities and data analysis will lead to deeper understanding of the relationship between mass and volume when determining density. The extension to the activity involves changing the medium in which objects float. If students can understand relationships that are represented in graphs then this will be a successful in understanding density.