When learning multiplication, students are encouraged to use arrays to organize their objects. If you learned math by memorization and without visual models you might be asking, "What is an array in math?" An array is an arrangement of pictures or objects into columns and rows.  They need to be arranged into a square or a rectangle with no holes in the middle to be an array. 

This is a 3 x 4 array…

This is not a 3 x 4 array…

An array supports students in thinking about the meaning of multiplication.  It also supports them in thinking about multiplication as repeated addition as well as its connection to division.  Finally, it gives students a way to build an understanding of partial products and later, the standard algorithm for multiplication.

Developing Multiplicative Thinking

Around third grade students move from additive thinking to multiplicative thinking. Students start by thinking about arrays as "groups of." Here we are using the same 3x4 array to think of "3 groups of 4" and then "4 groups of 3."

Eventually students realize it is much more efficient to see this array as a 3x4 array and multiply to find out how many objects there are in total.

By using arrays and area models students can start to make sense of the commutative and distributive properties.  Students also start to think about one number as being “3 times bigger” or “one tenth the size” of the other. The development of  multiplicative thinking students enables students to be successful with fractions, ratios, decimals, and percents.  Arrays support all of this work to come and that is why it is important to help students learn to use arrays.  

Math Arrays in Our World

Once you start thinking about arrays you will see them everywhere!  Look at garage doors, muffin tins, cubbies at school, etc.   You can have fun looking at this website which has lots of images of arrays.  Click on the “arrays” button and enjoy all the photo