Here is a solution from eighthgraders at Central Middle School, in Dover, Delaware...
(January 2007)

Snowflake (+2)
We know that snowflake equals 2 because in all
of the equations, when you add the numbers up and you
get 2 less than the real answer. So then you add 2 and
get the final answer so snowflake is +2.
Donald Johnson, Cynthia George, Rochelle Bazil, Alycia Casey

What do you think of their explanation? Is it correct? Is it clear?
Can you tell how they got their solution?
Here is another solution from Central Middle School, in Dover...
(January 2007)

The thing we did to get the answer is add 2 to everything.
Our first problem was 8*8=18.
First we added 8+8 which gave us 16+2 =18.
Then our second problem was 3*3*4=14 so 3+3 =6+4=10+2+2=14.
The third problem was 1*6=9 so 6+1=7+2=9.
The fourth answer was 2*3=7 so 3+2=5+2=7.
Timothy Gray , Shaquoia Jones, Colin Larimore

Compare that to this solution from New
Jersey.
This group has come up with a different
solution  but it's a little difficult to understand!

Dear Tim,
We are in eighth grade at Salem Middle School in Salem,
New Jersey. We belive that we have another solution to Mystery Op 1.
We added two squared minus two and added were the mystery operation
symbol indicated. We hope you like our solution.
Your New Friends in New Jersey,
Amanda, Caressa, Hector, Najamah, Denise, Dahlia, Miss Kalitan
(Math Teacher), and Mr. Parsley (BSI)

And from Los Angeles the older (and more
orthodox) solution...

Solution:
We are two fifth graders from Los Angeles, California. We
have solved the problem called Mystery Op 1. We think the answer is
+2+. One clue says 2*3=7. We saw that 2x2=4 and 4+3=7. But that
doesn't work on the other problems. Then we noticed that 2x2 is the
same as 2+2. So 2+2=4 and 4+3 equals 7. That worked on the other
problems. The answer is +2+.
From, Maggie Hoyt and Robert Baskin.

Maggie and Robert did an interesting thing
 they described a solution they tried but didn't work out. These
"blind alleys" are an important part of problem solving.
Also, note that these are fifthgraders. If
you know algebra, you know other ways of describing the solution.
Even so, their way  " +2+ " is pretty clear.
Maggie and Robert also attempted
Mystery
Op 2. See what you think!
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