Decomposing a Factor: What is it?

Decomposing a factor is a multiplication strategy used by many students when multiplying single digit numbers. 

Overview

Decomposing a factor is a multiplication strategy that focuses on working with portions of a factor, rather than the whole factor. Students tend to rely on their known facts, or numbers that are easy to skip count by, in order to find a portion of a multiplication question to begin with, followed by working out the product of remainder. Students then add both portions together to arrive at the correct answer. Decomposing a factor is used for single digit by single digit multiplication questions. Either factor can be decomposed however the student chooses.

For example, when thinking about 4x7, students may decompose the 7 into a 5 and 2. They may then be able to automatically recall or skip count to quickly figure out 4x5 followed by 4x2 and add the products together to arrive at 28. Again depending on the stage of development, opportunity for concrete, visual and abstract representation are essential to building confidence.

Supporting Students Using Decomposing a Factor

Building fluency with some known facts (x2, x5, x10) supports the use of decomposing a factor. If students are able to work with decomposition of one factor, rather than as a whole, thinking will more likely shift from additive to multiplicative. It is important for students to see how decomposing a factor can support their thinking, first through concrete representations such as building arrays with square tiles and physically portioning the array into sections. Representing each portion using mathematical equations will also help to support the shift from visual to abstract thinking. Once students have built confidence representing thinking using concrete materials, educators can model the use of open arrays to shift to visual models.

      Concrete (building with tiles)                                            Visual (open array model)                                    Abstract (equations)

Where to Next?

Once students are efficient with decomposing a factor, they may be encouraged to begin to work with larger numbers using 'Partial Products'

Looking to learn more? Check out the recorded session!