Multiplication is approached from 8 different perspectives and representations, and both the translations and the transformations from and to other representations creates the opportunity for students to develop conceptual understanding.
In this first section, you will see how students might approach multiplying a one digit number by one, two or more digit numbers using both a grouping strategy and the idea of decomposing numbers. Let me clarify.
In multiplication such as 4 x 26, the first number (4) is always the number of groups, whereas the second number (26) is the quantity inside each group. Students are led to represent 4 x 26, first as four groups with 26 in each group. However, counting by 26 is not easy, therefore, the quantities inside the group (the number being repeated) is decomposed or broken down into what I call the easy counting numbers, 1, 2, 5, 10. As the numbers we multiply get larger, the easy counting numbers grow to include 20, 50, 100, 200 etc.
Depending on the response and feedback I get from those of you who download , examine and use this section, I will be posting the entire 9 part series on multiplication that focus on representing and modeling multiplication for the purpose of developing conceptual understanding.