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Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits
Prerequisite: able to identify fractions as part of a whole

This is how I tell the story:

• We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. An 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.

• How big is your piece compared to the whole, original cake?

• But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your new piece? Color it in.

• How much of the whole, original cake do you have now? How can you tell?

• I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?

• Now how much of the whole, original cake do you have? How could we figure it out?
  [Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below‌—‌identify how much of the cake is left out.]

• Even for being on a diet, I still don’t feel very hungry…

Continue reading Infinite Cake: Don Cohen’s Infinite Series for Kids