Volume and Fixable Mistakes

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My fourth grade students have been exploring volume and area for the past few weeks. Lately, they’ve investigated different methods to find the volume of prisms, pyramids, cones, and cylinders. Through this process, they created their cities of volume and have been studying this topic extensively.  This fourth grade crew has made a lot of progress in finding the volume of objects when given the dimensions.  This particular unit of study is more focused on making spatial connections and using formulas to find volume.  Although the kids have been showing a better understanding, I’m observing very similar errors when I give checkpoints.

  • Using inappropriate units (squared vs. cubed)

Students need constant reminders to show appropriate units.  When I whiteout the unit line it’s interesting which students automatically write down the correct units and those that leave it blank.  Lately I’ve been bringing out the base-ten blocks to show the difference between linear measurements, area, and volume.  Students tend to not have any issues with telling the difference at that time, but when concentrating on formulas, the units are sometimes omitted.  I’m currently looking at different ways for students to show their understanding of the differences between square and cubic units.  I don’t want to heavily focus on this, but I’m noticing it as more of a student afterthought than something that they think of while answer a question.

  • Find the lengths of a side or the circumference with volume is given

Students seem to be efficient when trying to find the volume of prisms and cylinders.  When given the measurements of each side, students tend to perform the calculations correctly.  It’s a bit of a different story when students are given the volume and are asked to find other dimensions.  Some students rock this and do well, others not so much.  The class reviewed these types of problems by using a variable for the missing side or circumference.  We then created a few different steps that can be taken when tackling these types of problems.  I’d say the majority of issues with this specific problem came when students were given the volume of a cylinder or cone and needed to find the volume.  This is something that the class is still reviewing.

  • Remember that in r^2 actually means r * r and not r * 2

I’m going to chalk this up to not having enough practice with exponents.  At this level, students have used exponents, but more so to show Scientific notation.  When students hear “to the second power”, some hear that the word second and just multiply the radius by two.  Some students also problematically use the diameter and call it the radius.  Digging deeper into this issue has also revealed that some students aren’t using the Order of Operations to solve for volume.  Next week I’m planning on co-creating an anchor chart to address this.  Also, Pi Day (3/14/18)  is coming up soon and the class will definitely address the vocabulary and formulas associated with that soon.

These three issues have come up fairly consistently during the past week.  I’m looking forward to addressing them next week, but also having the students become more aware of what fixable mistakes exist so we can be more proactive. I’m also looking into having students create a culminating volume activity.  Putting that together is in my plans for tomorrow.



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