Understanding Arrays

Over the past few weeks, we have been studying factors, multiples, and arrays. Friends have learned that
factor x factor = multiple (product). The first couple of times we explored with arrays, we had the dimensions facing up (like in the picture below). Given those factors, friends had to figure out the product. They used different strategies in order to help them solve the problem. We noticed many things. One thing in particular was that square numbers can easily be defined as a number that has a square array. In order to have a square array, the dimenions (factors) have to be the same number. The 6 x 6 and 7 x 7 arrays show the square numbers 36 and 49. We explored with array cards again last week, except this time we had the product facing up and had to figure out the dimensions. Not only did we have to know the factors for that product, but we had to eliminate ones that would not make sense based on the shape of the array. For example, for 42, we know that 42 definitely has the factors of 1 and itself. However, we know that 1 x 42 or 42 x 1 array would not make sense at all when looking at the rectangle in the picture below. As friends were working, I noticed a few groups who came across 49 and 42. This was definitely something to talk about in closing meeting. They said from practicing their multiplication combinations and seeing that 49 is a perfect square, they know the dimensions must be 7 x 7. When trying to figure out the dimensions for 42, They put 42 on top of and then next to 49. They realized that 42 and 49 have the same number of columns but a different number of rows. Some explanations from the kids were:

42 has one less row than 49.

49 has one more row than 42.

42 has one less group of 7 than 49.

49 has one more group of 7 than 42.

Because of what they knew about 49, friends were able to conclude that 42 was missing 1 x 7 (read as 1 'group of ' 7) and that the dimensions are 7 columns x 6 rows. Awesome job!

*Practicing your multiplication facts at home is so important. Using what you know can really help you solve problems that you are still working on ;)