B58 — Connecting Multiplication to Division using the Array

The next few strings in this section generate the array to represent division. Tell the students that during this string, you will be thinking about an array of rows and columns. When representing division on the array, the divisor is the number of rows. The number of columns is the quotient. So, the first problem becomes represented as 10 ÷ 2 = ? Whereas, the last two problems in the string are missing divisor problems and can be written as 80 ÷ ? = 8. The nice thing about the array is that it can be rotated, and the columns then become rows. You might choose to begin these strings using a closed array (for example on 1" graph paper) so that students can count out the columns. But as they become more comfortable with the array, transition to an open array so that they focus more on the relationship between multiplication and division and do not count. Do one problem at a time. For example, with the first problem in the string below say, "I have an array that has a total of 10 squares in it, in just 2 rows. How many columns are in my array?" As you work with this string it is helpful after discussion of strategies on a problem to also ask, "So what equations can I write?" For the first problem you could write: 10 ÷ 2 = 5, but you could also write, 2x5 = 10, and 2 x ? = 10. Doing this after each problem will tighten the focus on the connection between multiplication and division.