## Four Poker Chips in a Square Array

Much of the information we use each day is presented to us in a structure of rows and columns – calendars, names and addresses, and all kinds of tabular information. We sit in rows and columns in school classrooms and in auditoriums. We line up that way to check out at the supermarket. We work with rows and columns on our phones and computers. Children are continuously learning many new names for things they experience. Why not teach children early about “rows” and “columns”? I believe young children could become engaged in “Excel for prekindergarten.” Start here.

## A Dozen Poker Chips in a Rectangular Array

- Lay out 2 rows with 2 poker chips in each row. What are some everyday ways we might see or think of this 2 by 2 array?
- Now, let’s add another row of two chips at the bottom. We now have 3 rows with 2 in each row (2 columns) or 6 chips all together 3 × 2 = 6. Note that the basic shape of our array has changed from square to rectangular.
- Now, let’s add a new column of 3 chips to the right of our array, which squares things up again.
- Finally, create an array of 12 by either adding a column to the right (or row underneath).

Thinking of objects in rectangular array structures of rows and columns is a key visual quantitative skill for understanding multiplication and later for memorizing the multiplication tables. For the 3 by 4 array, The ideas of repeated addition (3 + 3 + 3 + 3) and counting by 3s (3, 6, 9, 12) can both be illustrated and talked about with an array growing from 2 rows and 3 columns to 4 rows and three columns

Repeated addition: 2 + 2 = 4 3 + 3 = 6 3 + 3 + 3 = 9 3+ 3 + 3 + 3 = 12

Multiplication: 2 × 2 = 4 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12

Again, don’t begin with symbolic language like I’ve shown you here in explaining the ideas of multiplication to young children. Talk about how many rows or columns; how many in each; and how many that makes all together.