Making Algorithms Meaningful

Grid Model
Text Box: The grid model is another way to represent the partial products algorithm. It helps students organize their thinking. Question 1: What does it look like? See Figure 3. Question 2: How is it useful? It serves as a graphic organizer for scaffolding students’ thinking about the partial products algorithm Mental computational strategies can be used to add the “friendly” partial products (there are a lot of numbers that end in zero, so they are easier to add). The ties to place value can be illuminated (based on the zero observation). This differs from the students who simply try to remember “which ones do we carry”? Students can be asked to explain the origins of the partial products. For example, a teacher might ask, “Tell me about the 100, where did it come from.” It can be used to highlight the point that the algorithm works no matter how many digits are in the factors. For example, consider the grid representation for 114 x 12 shown in Figure 4.

Figure 3.  Grid array for 14 x 12.