A Math Teacher's Bag of Tricks

When you're a math teacher, you need a bag of tricks that you can reach into for those moments when some part of the lesson went faster than you imagined - or maybe there was an assembly scheduled that was suddenly cancelled and you are left with your class for 90 minutes (instead of the usual 45 you are used to)...that happened to me last week!

Sometimes you might just be able to continue with the lesson on the fly depending on where you are, but sometimes you just have to reach into you math teacher bag of tricks.

Here is one of my favorites that usually takes freshmen or sophomores at least 20 minutes before they want to give up or someone finally gets it.  (Junior high students can mathematically do this problem too).

One day I went to visit my friend George who is a mathematician. 
I went inside and had a nice visit.  
I saw a picture of his three children hanging on the wall.  
I asked him, "How old are your children?"  
He said, "The product of their ages is equal 72."
I said, "That doesn't give me enough information to tell how old they are."
He said, "The sum of their ages is equal to my house number."
I went outside to look at the house number.  
I scratched my head and went back inside - I said to George, "That still isn't enough information."  
He said, "You're right, I should also tell you that the oldest one likes ice cream sundaes."  
I said, "Oh, now I know, their ages are..."

There are several variations of this problem, but the idea is that the students have to list the possible ages of the children that could yield a product of 72.  Then, they must realize that if you list all the possible sums of those products, there are two that yield the same sum.  The piece of information about the ice cream sundaes is only there to help the students know which possible set of products and sums they need to use.  (The two possible products that have the same sum are 3, 3, and 8 and 6, 6, and 2.  Students must choose the one that only has one oldest child).

Final answer is  3, 3, and 8.

Have a great weekend!