The Pumpkin Patch

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On a family trip to a farm from which we have bought a tremendous amount of produce this year, Griffin and I were heading to the pumpkin patch.

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We had already taken the wagon ride to the other pumpkin patch; where the pie pumpkins were grown. We had helped with the harvest and had chosen several to take home. Now we were on our way to the Jack-o-Lantern pumpkin patch.

Griffin [9 years old]: We have 5 pumpkins! Is that enough to make a pie?

Me: More than enough.

G: Enough to make 5 pies?

Me: Probably not.

G: How many pumpkins go into a pie, or how many pies do you get from a pumpkin?

Me: Hmmmm… I would say about 1\frac{1}{2} pumpkins make one pie.

NOTE: This was semi-truthful. I really have no idea how many typical pie pumpkins are needed to make a pumpkin pie. I was making what I felt to be a reasonable estimate. But at the same time, I was pretty pleased with the estimate and with the math that it might encourage Griffin to do.

G: Oh! So we could make … 3 … 3 plus 1\frac{1}{2}4\frac{1}{2} … three pies! And have half a pumpkin left over!

Me: Which is \frac{1}{3} of a pie.

G: Right.

NOTE: I do not trust that he got that \frac{1}{2} of a pumpkin makes \frac{1}{3} of a pie given my estimate. He may have gotten it, and he may not have. The pumpkin patch was approaching so I let it slide.

G: Will we make three pies?

Me: No. I don’t think I’ll have the patience for that. But we can make one pie for sure.

So What Do We Learn?

Griffin is thinking about division when he figures out how many pies we can make from five pumpkins. Other similar sorts of division problems include, How many feet tall are you if you are 49 inches tall? and How many groups of four can we make in our classroom of 30 students? The pumpkin pie problem is challenging because it involves fractions.

One of the hardest parts of the thinking Griffin does here is keeping track of the units. As he counts up to 4\frac{1}{2}, he is counting pumpkins. The first 3 he utters counts pumpkins. But at the same time, he is keeping track of a number of pies. That’s the final 3 he utters: 3 pies.

I play with that idea by referring to his \frac{1}{2} of a pumpkin as \frac{1}{3} of a pie. I understand that not every parent is ready to do this on the spot. Don’t worry about that. Griffin got enough thinking from the basic conversation; the rest is gravy (or maybe whipped cream?)

Starting the Conversation

This was a special opportunity. We had some pumpkins. Griffin wanted to make things with these pumpkins. I could involve fractions.

Other such opportunities could include bags of apples, cups of flour (a standard 5-pound bag of all-purpose flour has about 18 cups), et cetera. If your child doesn’t ask the how many pies (or batches, or cakes, or whatever) question, you can ask it. But don’t make it feel like a quiz. You can just say, I wonder how many pies we could make with what we have?

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