Wednesday, September 12, 2012

Distributive Duo Quilt (Part 2 of 2)

After I had such a good time making the first distributive property quilt, I just knew that my work was not complete! I had to make another quilt to show a different way to look at the same problem-29 x 39. So basically, here is a new quilt illustrating a new strategy using the same problem!
This strategy is basically single number partitioning by a decade number. For example, I did not partition or break up the factor 29. The only factor partitioned was the 39 using the decade number 10, so I ended up with 10 + 10 + 10 + 9 = 39.
This strategy is easier for me to do mentally because I only have to keep track of the partitioning of one factor in my mind.  Also, when students think of this problem in context of a real-life situation, many times they will use this strategy because it doesn't always make sense to break up the amount in the group. Let's look at an example: Bettina has 39 photo albums. There are 29 pictures in each album. How many total pictures does she have? Based on the context of the problem, a child would likely partition the photo albums (groups) and keep the number in each group together.

The quilt also helps visualize how you could use compensation to solve the problem.  For example, since 29 is so close to 30, I can actually solve the problem by using (30 x 10) + (30 x 10) + (30 x 10) + (30 x 9). The tricky part in finding the exact answer comes from making sure to deal with the extra at the end because I added a row of 39 by rounding to 30. So, now I have to subtract a row of 39. Can you follow my thinking?

Back to the pictures...
The Distributive Duo! 29 x 39 = 1,131 (in square inches)
Two different quilt backs. The left one has beautiful elephants and the right one has feathers!

Thanks for reading about my quilts and the mathematics involved! Can you think of another way to look at this same problem? My friend Diana did! I think I might have to make a 3rd quilt. 
Could this be the beginning of the distributive trio?

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