National Math Storytelling Day!

Did you know that today, September 25 is Math Storytelling Day!  Yahoo recommends celebrating this quirky holiday with the following Abbot and Costello video clip:

In the clip, the donut baker (Costello) is convinced that 7 goes in to 28, 13 times.  In fact, in trying to convince Abbott he’s correct, he’s able to show this three different ways!

In each explanation, Costello misuses the idea of place-value to convince Abbott that 28 divided by 7 is 13.  But guess what?  From the mathematics he does, what he’s really showing Abbott is that 28 divided by 7 equals 1 + 3, which is exactly what we expect (and know) 28 divided by 7 equals!

Let me show you:

Costello’s first attempt at 7 into 28 is this, 2 can’t be divided by 7 (he says).  But, remember the 2 doesn’t represent 2 ones; it actually represents 2 tens (more commonly known as 20) so if he wanted to he actually could divide part of 20 .  .  . but we’ll get to that later.  Right now, its just important that you remember that the 2 actually represents 20.

Then, he divides 7 into 8, which is 1 with a remainder of 1 (he does this correctly).  So, he asks his sous chef to give him back the 2 (which is really 20) and writes “21.”  Now he proceeds to take 21 divided by 7, which is 3 and tells Abbott that 7 into 28 is 13, BUT 1 and 3 are both in the “ones” place meaning that 7 into 28 actually equals 1 + 3, or 4.

Costello really does this: Now, I have three questions for you:

1. Can you give similar explanations for the other two methods shown in the video?

2. If you were Abbott, how would you have convinced Costello he was incorrect?

3. Remember if 28 divided by 7 did equal 13, that means that we could take 28 things and divide them into 7 groups each containing 13 (in this case) donuts.  Suppose Costello really did take his 28 donuts and make 7 groups, each with 13 equal-sized donut pieces.  What fraction of a donut would each person get?