In prior lessons, students have learned to use a Place Value Table to represent two-digit numbers as a number of tens and ones. In this lesson, the concept of multiplication is illustrated as an array. Multiplication statements are shown in an array, then they are translated into the Place Value Table.
When multiplication is represented as an array, students see visually that multiplication involves a constant relationship between one factor and the product. This is another way to represent repeated addition. At the same time, the use of the Place Value Table to derive the final result of the multiplication reinforces place value concepts in generating a two-digit number with multiplication.
In the lesson before, students learned to use an array to think of the relationships inherent in multiplication. In this lesson the array is used to represent the commutative property of multiplication. When an array is rotated, the numbers represented in the array are commuted. The fact that when rotated, the array remains but the numbers are commuted, communicates clearly the basis for the commutative property.
In the problems in this lesson, students are given an array, and write two multiplication statements from the array using the commutative property.
In the first two lessons in this series, arrays were used to represent multiplication and the commutative property. In this lesson, they are used to illustrate the distributive property of multiplication.
The distributive property is illustrated by separating an array that represents multiplication into two arrays. With this representation, students can see visually why the distributive property holds.
Students are given multiplication problems represented in an array with two groups differentiated. They describe the array by writing the sum of the two products in the array.