The third graders are taught to look at the number of vertical lines, the number of horizontal lines and the intersections that happen when the lines meet. The vertical lines represent one factor, the horizontal lines represent the second factor and the intersections represent the product.
For example, if you take 3 vertical lines and line them up with 2 horizontal lines, you will make 6 intersections.
3 x 2 = 6 - factor x factor = product
Ask your mathematician how many intersections there would be if you had 5 vertical lines and 4 horizontal lines!
Multiplication can also be represented using arrays. An array is a rectangle arranged into equal rows and equal columns. For example, if I have 3 rows with 5 squares in each row, I have a multiplication problem. I can find out how many squares in all by multiplying 3 x 5. (You probably learned this as finding the area. We will make that connection in a couple of months.)
Today we discussed that the dimensions of the rectangle are also the factors. Thinking about the previous example, 3 x 5 are the dimensions of the rectangle, and also factors of fifteen.
Ask your third grader what multiplication sentence they can use to represent this array: