When teaching volumes of solids to 8th graders, I prefer to allow them to make sense of volume as being the space inside something rather than simply a formula we plug numbers into. For that reason, I incorporate an inquiry-based lesson when teaching the volume unit. After students have been acquainted with volume formulas for typical solids, I fill a cylinder with marbles and give them the open-ended question, “How many marbles are in this jar, and how can you accurately calculate it?” Students work in groups to answer the question, and we go back and forth between group discussions and class discussions until we converge on the following idea. There are pockets of air, or empty space, in the jar between all the marbles. If we fill the jar with water, we cover the air pockets. We can measure the volume the water takes up by pouring it into a separate jar, calculate the volume of the cylinder by measuring its height and radius, and calculate the volume of a single marble by measuring its radius and using the sphere’s volume equation. When we figure out how much of the volume is just marbles, we can divide that by the volume of a single marble and get an accurate estimate for the number of marbles in the jar.
How does this address the standard?
Element D: I demonstrate a knowledge of the content, central concepts, and specialized character of the disciplines being taught in this lesson by having students dig deeper into the meaning and application of volume in a real-life context, having them construct an estimate and understanding beyond just the formulas. Inquiry is an evidence-based practice, and I utilize tools of inquiry by posing an open-ended question, having students collaborate on an answer, and utilizing whole group discussions about progress and ideas towards a solution. While algebra skills are embedded into using the volume equations, and those are important skills for 8th graders, the Common Core StateStandards require an application of that knowledge to real-life contexts (CCSS.MATH.CONTENT.8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.)
here are student presentations/summaries of the lesson
Unfortunately, I no longer have the original versions of the students' work, so these are scanned pictures of the projects (with names blacked out for privacy).