Comparing Arrays

Last week in Math Workshop, our young mathematicians spent time arranging different amounts of chairs into rows and columns (arrays). We looked first at ways to arrange 12 chairs. Then, during Work Session students paired up to explore with two other arrangements. Exploring with the numbers 9, 15-21, 23-25, 27, and 30 helped us to see how differently numbers can be arranged, and gave us the opportunity to discuss the similarities and differences among the varying arrays.  

For example, look at the arrangement of 16 and 17 chairs below:

What do you notice about these arrays? Do any of the arrays have a special or unique shape? What do you notice about the number of arrays that can be made with 16 chairs compared to 17 chairs?

Hopefully, you notice that 16 chairs can be arranged in several different arrays. That is because it has many factors: 1, 2, 4, 8, 16. A number that has more than two factors is called a composite number. You probably noticed that 17 only has two arrays. This is because 17 is a prime number. Any number that has only two factors, one and itself, is a prime number. The factors of 17 are 17 and 1.Also, you may have noticed that 16 can be arranged into a perfect square with 4 rows and 4 columns. Any number that has an array that is a square is a square number.  Our young mathematicians talked about square numbers when we analyzed the arrays for 9 (3x3) and 25 (5x5).

Students also realized that you could skip count by either the column or the row to get the product. Sixteen, for example, has an array that is a 2x8. You can count by 2's eight times... 2, 4, 6, 8, 10, 12, 14, 16 or you can count by 8's two times... 8, 16.

Stay tuned this week as our young mathematicians learn how to decompose an array to make a more difficult multiplication equation simpler.