## Learning the Language of Math with “What Number Am I?” riddles

One of Daegan’s favourite sort of question for our ‘Problem of the Day’ is what I call a “What Number Am I?’” riddle. Here’s some that we’ve done in the past few weeks:

All three of my digits are the same. The sum of my digits is 6.

I am a 2-digit even number. I am less than 30. The product of my digits is 12.

I have 3 different digits, all of them odd. Digits are in order from least to greatest. I am evenly divisible by 5.

Daegan also did some hundred board “What Number Am I?” logic problems, in which he needed to eliminate possibilities from the board until he was left with the only (and correct) answer. Here’s two of them, that we got off this site:

So why do both Daegan and I enjoy these sorts of questions? Aside from the obvious (we LOVE riddles and logic here), I think it is because these riddles are a fun way to learn and practice “the language of math.” In order to solve the above riddles, one needs a solid understanding of ‘math language words’ like ** sum**,

**,**

*digit***,**

*even***,**

*less than***, etc. as well as familiarity with math concepts that form part of our ‘common knowledge’ in our culture: How many pennies in a dollar? Days in a month? etc.**

*product*There is an element of creativity to this as well when Daegan creates a problem for me to solve. I begin by having him write a number on a small piece of paper on the table where I cannot see it (so he can refer to it easily), and to think of some ‘clues’ about that number. For example, he wrote this riddle on the board for me after solving the second riddle (“I am a 2-digit even number…”) above:

I am a 2-digit even number. I am less than 100. My digits add to 12.

“How interesting!” I replied. “There’s actually several answers. 48, 66, and 84. You’ll have to make another clue for me so I can solve this riddle.” Daegan was a bit stumped at first, as in the model question 3 clue statements were sufficient information to solve the riddle. So we started talking about other math concepts and terms: greater than and less than, fractions and ratios, prime numbers, etc. He then created this additional clue for me:

My units digit [i.e., ones digit] is half my tens digit.

And I was now able to give him his answer: 84. I offered a few other possible clues he could have used: my digits are not identical; my tens digit is larger than (or double) my units digit; if you add my units digit to itself, you get my tens digit, etc. Daegan thought is was interesting how many ways you could give information in math—even identical information. (e.g., A is half of B means the same as B is double A, or B+B = A).

Have fun with “What Number Am I?” problems, and if you or your kids create some fun ones, please share! I should add that these were also among my class favourites when I taught grade 5/6, especially creating their own riddle for a classmate to solve. We made them in little lift-the-flap books (think typical birthday card shape turned sideways), with the clues on the front, and the solution and the working out of the clues on the inside (lift the flap to see the answer). Some kids got very into decorating them with math symbols, shapes, terminology to boot! We put them up on the bulletin board (wall) for parent-teacher conference night, and it was quite fun watching “math anxiety’” stricken parents learn that their child created this riddle, AND could teach them (the parent) how to solve it!

May 20th, 2010 at 6:27 pm

Sounds great Risa!! ;D I’ll have to give some to Jessie! ;D

May 20th, 2010 at 9:44 pm

Cool activity. Great way to introduce a variety of math language concepts in an interesting way.

May 21st, 2010 at 7:02 am

KarateKid and I thought these were very fun – we did the three from the file you linked to this morning and he’s grabbed right on to the amusing challenge of making these up for me to solve. He wanted to share his first problem with you!

GoGoGirl loved to play with dolls. Her mother, on the other hand, really wanted to go to this neat museum. But GoGoGirl always got bored with museums. Finally, she struck up a deal. The deal was that they would stay home and let GoGoGirl play for one half hour. GoGoGirl agreed. We weren’t keeping track. After KarateKid, her brother, felt it was close to a half hour, he went in and asked her how long it had been (she had covered up the clock). Here are her clues.

1. I have been playing for more minutes than there are pennies in a dime.

2. I have been playing for less minutes than there are pennies in five dimes.

3. I have been playing for more minutes than there are pennies in one quarter.

4. The two digits add up to one less than ten.

5. The units digit is one more than the tens digit.

May 22nd, 2010 at 12:56 am

Oooh another link – thanks! Have just printed one out to see if Billy enjoys them..

May 26th, 2010 at 4:08 pm

[...] week I wrote about the “What Number Am I?” problems Daegan has been enjoying, and asked you to send along any questions you or your kids made up. [...]