In Common Core, many standards refer to using visual models such as arrays or area models. For example, students in Grade 4 are expected to use place value, arrays, or area models to multiply 2-digit by 2-digit numbers. In Grade 4, students are
not required to know the standard multiplication algorithm. This algorithm is delayed until Grade 5. Here is a visual model for multiplying 17 by 14. Notice how the area grid has four parts. By finding the area of each part and then adding, students can find the product without learning a new algorithm.
I feel that requiring students to understand visual models
before using algorithms is extremely important for three reasons.
- Many students don't slow down to think about problems. Once they know a shortcut, they just try to get answers quickly. Visual models help students learn that answers need to make sense!
- The visual model is a bridge to understanding the algorithm. With 2-digit by 2-digit multiplication, the model helps students see that both tens and ones need to be multiplied and then added.
- Students often have difficulty with word problems. Drawing visual models for problems helps students make the connection from the word problem to the related operation.
Although drawing and using models requires time and effort, the result is that students will develop a deeper understanding of important concepts.
