13 x 7 = 28
|Setting the Stage
• Tell students they are about to watch a math genius at work.
Doing the Activity
• Watch the video – 46 secs.
• Hand out the student page and ask the students to explain mathematically how Lou Costello cheated to get the answer he wanted.
Ask the students for their reactions to this clip. 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!!!
Have the students watch 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.
There are other misconceptions in math that students can share with their classmates using a Costello Method. Another example involves reducing fractions. For example to reduce 16/64 to lowest terms all you have to do is cancel the 2 sixes and you get 1/4. It works because 16/64 DOES equal 1/4. The students can do research and find other examples to share. Having students share misconceptions sounds contrary to what they should, but once they are familiar with the idea of a Costello method, I'm sure they would never fall victim to a misconception again.
No software needed here. Just the video of Lou Costello - the math genius - at work. - Youtube version (46 seconds)
Entire video (3:39) where Costello demonstrates the result of 13 x 7 = 28 in three different ways.