How many books are on each shelf?

2/26/2010

Today I had 8 kids from the second grades at my advanced math lesson.

Here is the problem that I gave to them.
There are 42 book on two shelves. First shelf has 12 books more than the second one. How many books are on each shelf?

I asked kids to give me an answer writing it on their small whiteboards they brought to the class. Surprisingly they all gave me the right answer within several minutes. They just tried several numbers combinations and found the correct one.

Then I showed on the blackboard we have in the classroom how I would solve the same problem using simple equation. At each step I asked them questions to make it more interactive and ensure that they are engaged.

Second shelf has ? books.
How many books are on the first shelf?: ? + 12.
How many books all together? 42. Or you need to add number of books on the first shelf, ?, and number of books on the second shelf, ? + 12.
So we have, ? + (? + 12) = 42 =>
? + ? + 12 = 42 =>
(? + ?) = 42 - 12 =>
? + ? = 30 =>
2 x ? = 30 =>
What number you need to multiply by 2 to get 30? They answered 15.
So now we know that the second shelf has 15 books.
How many books are on the first shelf? 15 + 12 = 27 books.
Let's check the answer. 15 (number of books on the second shelf) + 27 (number of books on the second shelf) = 42 - Correct!

Next I gave them different variations of the same problem, asking one of them to come to the blackboard and solve the problem while others would do the same on their whiteboards. I asked them not to try different combinations but rather use equations we just learned.
30 books, first shelf has 4 more books than the second, 18 books with the first shelf having 2 more books, etc.