13 x 7 = 28

Teacher's page 
Student page
Watch Abbott and Costello do some
mathematical hocuspocus with multiplying 13 x 7.
Explain how Costello "cheated" to get the answer
he wanted.

Resources: No software needed here. Just the video of Lou Costello  the math genius  at work.  Youtube version (QT version) The video: The clip is from Best of Abbott and Costello – Live! http://www.amazon.com/BestAbbottCostelloLive/dp/6301106385 
Setting the Stage • Tell students they are about to watch a math genius at work. Doing the Activity • Watch the video – 47 secs. • Hand out the student page and ask the students to explain mathematically how Lou Costello cheated to get the answer he wanted. Debrief A common response that students make is that Costello was not putting the numbers in the "right" places. But why do you put numbers in these places? This is an opportunity for students to see and understand why the 7 goes under the 2 and not the 1. After a student says the 7 should go under the 2 instead of the the 1, ask him why there? Why not some other place? How about on top of the 1? Many students (and adults) would respond "That’s how I was taught to do it." Of course, the reason you place the 7 under the 2 is because 13 x 7 is really a problem that involves the distributive property. What that means is that you will do the multiplication in 2 parts. First multiply 3x7 to get 21. Then you multiply 10 x7 to get 70 and add them together. 21 + 70 = 91! Now can you see why the standard algorithm works? It's not because you have to put the 7 under the 2, but rather you have to add 7 to the tens column because 7 represents 7 tens!!! Extensions See the entire video (3:39) where Costello demonstrates that 13 x 7 = 28 in three different ways. This is a great way to have your students think about what they do when they carry out the four computation algorithms. 

Student's page 