Friday, May 9, 2014

Test Prep I Can Believe In

As we wrapped up a unit on volume, and with the state standardized test looming on the near horizon, Rich and I decided to try out a project involving cereal boxes.

The kids brought these in from home.

First, they needed to find the volume of their box.  Since we figured they could use some practice multiplying mixed numbers, we decided to alter the requirement: instead of measuring to the nearest centimeter, the kids would need to measure the length and width of the base of their box to the nearest 1/8 inch.

We decided that they should use the rulers they were going to have to use on the state test.  The 7-inch rulers were not up to the task of measuring the heights and the widths of the boxes, but Rich and I decided that was OK...

...they would figure it out.

     I was most excited to use the opportunity to revisit an area model for multiplying fractions and mixed numbers, so we had the kids outline the area of the bases on square inch grid paper.

7 1/2 by 2.  We had originally thought they would do it on blank paper.  But we decided the grid paper was better because it more effectively expressed the idea that the fractions were pieces of actual squares.

At some point I had the idea that the model might be made more powerful if it was color coded by each partial product.  I felt it lent a visual aspect that was missing in the original design.  Then they had to multiply the area of the base by the height of the box to come up with the volume.

Rich's student teacher, Shannon, made a chart to to help the kids keep track of the data. (Note to self: next year have the kids create the chart themselves).  This would be used to compare findings, and also to provide them with referents for the dimensions of a standard sized cereal box.

This continued for several days.  They got a lot of practice working with fractions, multiplying, dividing, and measuring, and the fun was just beginning... because now they would have the chance to create their own cereal, and design the box.

Drawing a three dimensional shape on paper presented some challenges.  This student's ingenious use of two rulers gave Rich and I the idea that protractors could be used to make the representations even more accurate.  Duly noted for next year.

Nike is into everything these days.

Love the mascot!

For the One Direction fan in all of us.

Check out the expiration date.

This is a "mini-box".  Each group had to come up with one that was half the length, width, and height of their standard sized box.

We also had them come up with the dimensions of a jumbo box by tripling the length, width, and height of their standard sized box.  There was quite a bit of calculation involved here, but we felt it was good practice, and it was embedded in the project.  Multi-digit multiplication and addition, multiplying and dividing fractions and mixed numbers, adding fractions, converting improper fractions into mixed numbers...lots of opportunity for review, formative assessment, and on-the-spot reteaching.  Turns out that there were quite a few kids who forgot how to do many of these operations.  Go figure.
     The kids loved it.  There was a high level of engagement, great collaboration and problem solving, and a nice blend of computation, measurement, and geometry.  As we put the projects away (we're not done with them yet!), and headed into the week of the NJASK, my one thought was: That's the kind of test prep I can believe in.


  1. I can't wait to do this with my 5th graders. Please excuse me if this is obvious (I can only blame all the Christmas eating of junk food for my hazy mind), how did your model work, when most cereal boxes are larger than a sheet of paper? What am I missing?

    1. I'm glad you liked this project! When we had the kids design their own, we gave them big white poster paper. If you don't have that, the kids could tape sheets of 8 1/2 by 11 together. Hope this helps. Let me know if you need any more help or have any more questions, and let me know how it goes!

  2. Good Morning Mr. Schwartz,

    I found saw your project online and I would like to try that with my fifth graders. However, I haven't been able to find the grid paper that you used. Can you email it to me or send me the link?

    1. You can find 1 inch grid paper here:
      Good luck with the project and let me know how it goes!