Topic A Conceptual Understanding of Multiplication

Topic A lessons provide students with time and space to build conceptual understanding of multiplication, through concrete and pictorial exploration, with equal groups and arrays. Students expand their foundational understandings of multiplication from grade 2. The relationship among the number of groups, the number in each group, and the total is established, and students repeatedly practice identifying the number of groups and the number in each group. Building conceptual understanding in this topic helps establish tools and strategies that students can use to make sense of multiplication facts and to recognize situations where they can multiply to solve problems.

The topic opens with students counting a collection of objects. This serves as an informal formative assessment of the foundational understanding of multiplication from grade 2 and provides teachers with insight as to how students organize, count, and represent the collections. In addition to its mathematical content goals, the lesson’s format sets the stage for students to work with and learn from each other throughout the year.

Unit form and skip-counting provide bridges from repeated addition to multiplicative thinking. Equal-groups representations progress from concrete objects to drawings, to arrays, and finally to tape diagrams. Regardless of representation, the number of groups and number in each group are consistently related to unit form and multiplication expressions and equations. Precise use of language and symbols are emphasized throughout the topic to maintain consistency between similar and interchangeable terminology (e.g., the convention of multiplication as the number of groups times the number in each group and the use of terms such as factor, product, multiply, multiplication, and times).

In topic B, students build conceptual understanding of division by using what they know about multiplication and the relationship of the number of groups, the size of the groups, and the total.