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Objective: Students will be able to use the array method to represent and compute one-digit by two-digit and two-digit by two-digit multiplication problems.

During the math lesson, I took a group of five students to the library. Once we were settled, I began the lesson by discussing ways in which we can learn as a group and respect each other. We then jumped into the lesson, beginning with a discussion about situations that require multiplication and then moving on to how to set up and use the array method with one-digit by two-digit multiplication problems. With each step of the array method, I first modeled what I expected and then worked on the problem with the students through guided instruction. After we completed the step together, I asked them to turn to a separate problem to complete that step independently.

The pedagogical goal of the lesson was to select and use representations to make mathematics meaningful and draw connections between mathematical concepts. In using the array method, I hoped to “help students connect procedures, properties of operations, and understandings of place value” (Russell, 2000, p. 156). Specifically, I wanted students to see how arrays and place value are linked to multiplication and hoped that drawing an array would make multiplication more transparent. In other words, because I noticed many students had only a “instrumental understanding” of multiplication—or that they used “rules without reasons”—I wanted to increase students “relational understanding” in that they “[knew] both what to do any why” (Skemp, 1976, p. 2). I had also hoped to connect the array method to the traditional method and the lattice method, but we did not have time to discuss this during the lesson. Unfortunately, because time was an issue and because this was only one lesson, I do not think students fully understood the array method and thus did not make many meaningful connections between concepts.

Furthermore, although the initial mathematical goal of my lesson was for students to be able to use the array method to represent and compute both one-digit by two-digit and two-digit by two-digit multiplication problems, we only got through solving one-digit by two-digit multiplication. However, by the end of the lesson it seemed most students were on the verge of understanding how to use this method and with a follow up lesson would be able to apply the array method to more complex multiplication problems.

On the following pages, the lesson is further analyzed by tasks, tools, discourse, normative practices, and evidence of student.


Class notes.
Russell, S. J. (2000). Developing Computational Fluency with Number. Teaching Children Mathematics, November.
Skemp, R.R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20–26.