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Thursday, July 23, 2009

A Lesson Plan Using a Virtual Manipulative

This post at dy/dan got me thinking about this thing from Utah State's Library of Virtual Manipulatives.

Pretty cool, right? A way to play with volume that avoids water fights. Love it. I used this in a remedial geometry class several years ago. It was fun for the kids for about five minutes. We merely used it to poke at the edges of our intuition. I didn't really know how to exploit it.

It raises a compelling question for teachers: there are some really good digital resources out there, but how do you best use them in a classroom to enhance learning? I'd like to use it this year when I teach Geometry, but I need to write an effective lesson around it.

The barest outline of a plan:

1. Playtime. Let kids slide the height thing and push the buttons, or be teacherbot and do what they instruct me to do. Solicit guesses for heights. Have kids verbalize why they think their guess is correct. Test to see how close they are.

2. Start talking about how you would calculate the new height. Go back to universal problem solving techniques that you should be hitting over and over again. What is the given information? What do you want to find? What stays the same? Encourage/coach them to do this with the rectangular prisms. They should be able to find numerical solutions easily. Develop and write on the board an equation involving equal volumes with an unknown height and solve it. Test to see if it works in the virtual manipulative. Have them calculate a few more.

3. Go through the same procedure with cylinders, then cones. It's going to look different depending on if they already know formulas, what age the kids are, what level, etc.

It wants for structure. I could develop a worksheet and break out the laptops. I'm not a huge fan of many worksheets, because I think they shift the focus from the problem-at-hand to "guess what to write in the blank." (I'm also not a fan of the laptops.) I could try to keep it as a large group discussion, but that could easily turn into me talking to 2-3 kids while everyone else zones out.

What would you do with this?


  1. Your last couple of statements make me curious... Can you explain some specifics about why you dislike using laptops?

    I love the NLVM site and use it frequently throughout the year.

  2. Sure RichTCS. I do use the laptops when they are the best solution. But if I can think of a way to achieve the same results, I avoid them.

    I only have 43 minutes for a class period. Our laptops come in a big cart. I have to slice 5 minutes off the front and back of my class because checkout/in requires supervision. Then we have to wait for startup/login. Then at least 2, often more, laptops won't turn on or login, and those kids have to start the process over or share for the class period. It's all a big headache.

    Besides all that, once the kids login successfully, my little lesson about comparing volumes has to compete with the whole Internet. Most kids are fairly cooperative when they have a well-defined task, but the temptation for them to check their email or their fantasy football for whatever is great. I do have software that can take control of or freeze their machines, but I have received no training on it, and it's complicated to figure out on the fly.

  3. How exactly do you "use" the NLVM site? How do you organize a lesson?

  4. As a particular case of number 2, direct and joint variation leaps out here, and in other volume problems. Specifically, the volume of the cylindrical column of water varies jointly as the height of the column and the square of the radius. To a decent first approximation, many real-world models are similar joint (and sometimes inverse) variations.

  5. With this particular app I'd probably throw it on the projector and have the students make their predictions as a whole class; while there is value in having them try it individually I don't think this one beats the wasted-time vs. learning-accomplished ratio.

  6. I use manipulatives like this one mainly to draw students into whatever lesson I've planned. There doesn't seem to be enough depth in this particular activity to justify laptop time. Whole group structure might work better here. To prevent the zoning out issue, I would try to have a lot of why and what if questions ready. Call on everyone. I like the idea of using the manipulative to check assumptions after crunching the numbers. I think you have just the right amount of structure in this lesson. Too much planning always backfires on me.

    This is a great topic for discussion. Are digital manipulatives ever used outside of school? Some manipulatives, like this one, simulate real world objects. Others encourage exploration of parameters. Are there examples of manipulatives that permit creativity? I suppose pattern blocks and, to some extent, geoboards might work. Any others?

  7. Your spirograph of course. Unless you don't call it a manipulative.

  8. I might use this to intro what I call the r:r-squared:r-cubed theorem. That is, the relationship between the perimeters, areas and volumes of similar figures. I see what you mean about the time ... and the zoning. I would probably put this up on my smartboard and let student volunteers play around with it. Then after we learn the material, we could go back to it to see if the students could figure things out faster.

  9. Thanks everyone who shared your perspective. It helps to have my instincts validated. I recommend checking out the other offerings from LVM. There's some nice stuff in there.


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