Friday, October 3, 2008

Horray for the Open Array!

Today in class we worked on several student created multiplication and division story problems. One problem that we worked on was a multiplication story problem by Jacob. His story problem was: This year I recorded 12 hurricanes. Each hurricane dumped 8 inches of water. How many inches of water did the hurricanes dump in all? The students came up with many great strategies such a repeated addition, drawing pictures and using a ratio table.

During the closing meeting, I reminded the students that we can use arrays as models for solving small multiplication problems; but, we can also use them to solve larger multiplication problems. I drew a rectangluar array on the board with no columns or rows. I asked the students what numbers we could split the 12 into that are "easy to work with." Without hesitation, I got the answer "10 and 2." Perfect! Then I asked what we could split the 8 into that would be "easy to work with." Anna replied "4 and 4." Perfect again! I divided the rows into 4 and 4 (totaling 8) and I split the columns into 10 and 2 (totaling 12). We didn't draw all of the rows and columns because we decided that wouldn't be very efficient and we would probably get confused.

Now, we had four smaller arrays with dimensions that were very easy to solve. Once we were done finding the products of each small array we added them together and VIOLA! we had our answer!

I LOVE, LOVE, LOVE the Open Array strategy because it will create a better of understanding of the traditional multiplication algorithm when we are ready for that strategy. Today was the first day with this strategy. We will be using it a lot more in the future. Thanks for reading!

If you are interested in more information about this strategy please visit the math strategy videos, look under the Multiplication heading and click "Generic Rectangle." (Generic Rectangle and the Open Array are the same thing.)
-Miss Russell :)


Anonymous said...

Very nice. Extremely helpful! Thank you, Mary

Anonymous said...

From a parent in Maryland...

Searched for examples of open arrays for my third grader. Your blog was the only helpful page. And it was perfect!

Thank you!!