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Number Detectives! The Suspects Keep Multiplying!

Hi All,

Kids like detective stories. Think Encyclopedia Brown and Jigsaw Jones. "Number Detectives" is based on using number concepts to provide clues to help players figure out a "secret number."

I first came across this idea in a series of books by Dale Seymour called, Getting Smarter Every Day (Dale Seymour Publications, an imprint of Pearson, 2000). He called his "Who Am I?"

This sounds simple, but can lead to some really good discussion and learning. Here's an example from Seymour's book for Grades 5-7, though I think younger students can handle these.

1.  If I were tripled, I would be seven greater than if I were doubled. Who am I?

At first read, many kids are thinking, "Huh? Wait. What?" (Same with me actually.) But tell the class, "Let's think about what we know here. Look for some key words or phrases and underline ones that might be good clues."

Maybe "tripled," "doubled," and "seven greater?" They are all words that talk about what is happening to something numerically. What do triple and double have in common? (Multiplying) Maybe we should think about a multiplication table. How about "seven more?" Where might that lead? (Seven times table.)

Well, what is 7 tripled? (21) What is 7 doubled? (14) Is 21 seven more than 14? (Yes). Then the answer is "7."

If you want to practice multiplication and get students to look carefully at a multiplication chart, problems like these are great. In fact, students can create their own, after doing a few together.

You can get at other math ideas with "Who Am I" as well. Mostly though, this is about approaching a problem logically and breaking it down by finding the important facts and, like a good detective, following where the clues lead.

Here's another one:

If you reverse my two digits, you get a number that is triple a number that is less than ten and more than five. I am odd. Who am I? 

In this one, and actually in all of them, you have to think about what the question is pretty carefully. Which number are we looking for? A number that is tripled? Well, on the way yes, but the number we really want to know about it the one at the beginning of the problem whose digits are reversed. Three numbers are actually mentioned in the problem.

What do we know? Well, we know the suspect number has two digits and we know it is odd. We also know if those digits are reversed we get a second suspect number. The second suspect number is triple a third number that is either 6, 7, 8, or 9. Well then

3 x 6 = 18     Reverse 18 and get 81

3 x 7 = 21    Reverse 21 and get 12

3 x 8 = 24    Reverse 24 and get 42

3 x 9 = 27    Reverse 27 and get 72

Really the hard part is thinking clearly and breaking the problem up. The math is, as that great detective Sherlock Holmes would say, "Elementary."

Best,

Bob 

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