Pumpkin Measuring: Planning for Mistakes

Last year, I was a part of a leadership math team that received professional development from a measurement guru, Rich Lehrer.  This linear measurement unit is from his research and writing team.

One of the many things I love about Rich’s measurement units is the intentional planning for mistakes.  In many ways, his units set kids up to make mistakes…which is sometimes opposite of what we think we should do as teachers.  But, I’ve learned that kids have to make mistakes in measurement to learn why their mistake is a problem.  And those mistakes make for some very lively and deep math conversations about what is actually important when we measure!

No mistakes means kids are just copying our “how to measure steps” and that makes it hard to transfer that measuring skill to a new object or with a different unit.

Pumpkin Attributes

Our math practice goal for this unit was “#6: I can attend to precision.”  We referred back to this word and why it’s important that we are precise when measuring throughout the whole unit.

We looked at one of our pumpkins and answered the question: “How can I describe this pumpkin?”  As we got responses, we charted them.  If my first grader said, “It’s bumpy,” then I answered with, “Yes, bumpy describes its feel.  One attribute of objects I can describe is feel.”  I wanted to chart the attributes, not the adjectives.

After we charted, we discussed which attributes are measurable.  For example, I cannot accurately measure color, but I can measure weight.  I then told students we would be measuring height and circumference of our pumpkins.  I added the pumpkin stickers to those words to help us remember since we would be working on this project for a few days.

Measuring Pumpkin Circumference

I had 4 pumpkins as the unit recommended, and put kids in groups of 6.  Each person in the group had a job: pumpkin holder, streamer holder (2), cutter, labeler, taper.  {Side note: 4 pumpkins was not enough in my opinion….the groups were too big and caused some management issues….I would recommend 6 pumpkins so the groups are only 3-4 kids.}

Some groups measured the circumference just fine…

Other groups measured the circumference around the bottom.

{And other groups, not pictured, measured a vertical circumference instead of a horizontal circumference.}  All of these mistakes were fine by me because it gave us some things to discuss during our share time.

Planning for Mistake #1: Measuring the circumference of a pumpkin is difficult because the roundness of the pumpkin varies from top to bottom.  Using a sphere shape for this activity was important because it meant kids would make this mistake…and then we would be able to talk about where circumference is measured (at the point where the object is the biggest around)….that wouldn’t have meant anything to kids if we didn’t have this problem to start with!

Once the streamer was cut to measure the circumference, the labeler wrote the pumpkin number on the streamer.

The groups had about 2 minutes at each pumpkin station.  Then, the groups were to use the streamers from each pumpkin station and large construction paper to order the circumference lengths in a display.  The taper taped the streamers on with tape so they would be easier to come on and off during share time.

During share time, we looked at all of the circumference streamer from pumpkin number 1 and discussed these questions:

Did each group measure the same circumference?  Are they all the same length?

Why aren’t they the same length?  What mistakes did we make that may have caused our measurements to not be precise?

What is important when we measure so that we don’t make these mistakes?

Measuring Pumpkin Height

The next day, we repeated the same steps as Day 2, but with height instead of circumference…

Planning for Mistake #2: Measuring the height of a round object is difficult to do….do you follow the curve of the pumpkin or measure a straight line up for the height?  I had groups that did each of these…which made for a very important conversation about why length and height must be measured in a straight line.

Measurement Anchor Chart

During share time, we discussed the same questions and continued to chart them…

We referred to this chart all year long during our measurement math talks.  Not everything on this chart was added the first day, or even by the end of this unit.  In fact, last year’s group didn’t add “no gaps” to this list until our second measurement unit…because using streamers solves the problem of gaps.  It wasn’t until we started measuring with paperclips that we had issues with gaps! {Planning for mistake #3}  And even though they had added “no overlaps” they continued to make mistakes and overlap when measuring with new materials….so this was an ongoing discussion.  And we reread through our “measurement rules” before each measurement activity during the year.

While I would change a few things like I mentioned earlier, this unit is a fantastic way to get kids excited about measurement and it’s perfect for making kids make mistakes when they measure so that we have something to discuss and learn from!

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