Volume and Missing Blocks

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On Monday my fourth grade crew worked on tasks related to perimeter and area.  Today they discussed volume. The volume discussion began when I brought out a large container filled with water.  I asked the students what they thought volume was.  Was it the amount of substance contained in an object or the space inside of the object?  It was interesting to hear their perspective.  I wrote down their thinking on the whiteboard. Some students were positive that volume measured how many cm cubes that could fit into the cylinder.  Another student stated that there wasn’t anymore volume left because the water took up the space.  I then took the same cylinder and dumped the water out.  Another student mentioned that you didn’t need to use cubes to fill up the cylinder.  You could’ve used sand instead to measure the volume.  Throughout this class conversation I thought students were testing their understanding of volume and not just regulating it to filling up objects with cubes. The class then made a math journal entry and created a t-chart of examples and non-examples of volume.

Afterwards, students went back to their table groups to discuss volume and I used Steve’s image from the tweet below.

I asked students to think about the shape and how many cubes might need to be added to create another layer.  Students were confused at first, but then gradually came around to thinking about how to add another layer.

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Some students wanted to add a layer on top, but then realized that making that top layer would mess up the stair sequence.  Eventually, after some major perseverance, I asked students to create a model.

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That model proved helpful as students could see and start thinking about how many blocks could be added to the bottom.  I noticed that students started to think of arrays and how helpful they were in creating another layer.

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At that point class ended.  We’ll be discussing this problem again tomorrow.  I’m looking forward to seeing what the students discover, their solutions, and what strategy they end up using.

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