Fractions for Cooks (with Special Bonus Recipe)

For a little weekend fun, here’s another real life math problem you or your kids may enjoy. This one is about fractions. I like it because it’s very concrete, covers a lot of ground, and might have something to interest you regardless of how old you are. Here goes:

1. I have a recipe that uses 3 eggs and half a cup of flour. (True story; for actual recipe, see below.) I want to use 4 eggs instead of 3, and I need to measure out the right amount of flour for the recipe. My Pyrex measuring cups with fractional increments on the side are in the dishwasher and I don’t feel like cleaning them (I told you, true story). But I do have these:
That is, four large measuring spoons, with sizes 1/4 cup, 1/3 cup, 1/2 cup, 1 cup. How can I measure out the flour I need?
2. How can I measure out the flour I need if I’m going to use just one egg?
3. What’s the smallest unit of flour I can measure out accurately with these measuring spoons?
4. If I have measuring spoons of sizes 1/n1, 1/n2,…, 1/nk (OK, this is getting kind of fictional), what’s the smallest unit of flour I can measure out accurately?

We talked about the first two of these at the math workshop for 3rd-6th graders that I ran in Montclair this fall (see here). The first is about addition or multiplication of fractions (1/3 + 1/3 = 2/3 or 2 × 1/3 = 2/3). It’s easy enough as long as you take the time to figure out how much flour you actually need (which wasn’t easy for my kids at first). The second one is about subtraction, and I like it because it lets you explain the fractional equation at the heart of the problem (1/2 – 1/3 = 1/6) with something very concrete: 3 eggs – 2 eggs = 1 egg. When we did it at the workshop, that made as much sense to the kids (maybe even more) as cutting up a pie into 6 slices.

The third and fourth problems are about common denominators and least common multiples. You actually need what’s usually thought of as higher math (Euclidean algorithm) to solve the last one fully, but both of them are meant to encourage experimenting. No matter how old you are, you can get started and see how far you get. You might even discover the Euclidean algorithm on your own!

Here’s the recipe, by the way. It’s for our current favorite weekend breakfast item, Russian cheese pancakes, known as syrniki (“syr” is Russian for cheese):

Ingredients
1½ lbs of farmer cheese (e.g., 3 half-pound packs)
3 eggs
½ cup of flour

Mix ingredients together in a large bowl.

Cover a cutting board with flour. Take out a handful of cheese mixture and roll it in the flour on the cutting board to make a ball-shaped dumpling. Repeat until all the mixture is used up (usually makes 20 or so dumplings). If your cutting board is well-covered with flour, the dumplings shouldn’t stick to it.

Heat a skillet over medium to high heat and cover the bottom with a layer of oil. Flatten each dumpling so it’s about half an inch thick, and place in the skillet (depending on the size of the skillet, you’ll likely be able to fit between 6 and 10 dumplings at once). Cook on each side until light brown (2-4 minutes a side). Serve covered with sour cream and/or sugar. Yum!