INSIDE THE CLASSROOM: MATH

Joe Walston, Second-Grade teacher, Brooklyn Ascend Lower School, Brooklyn

In second grade, students begin to develop the foundations of multiplication and division. That may seem early to many parents; in the past, multiplication was introduced as a procedural skill in the third or fourth grade.

But we at Ascend believe t hat procedural f l uency evolves f rom conceptual understanding, which unfolds over several years. In line with the Common Core, we give second graders many opportunities to practice and understand the concepts and strategies related to multiplication.

Students explore the concept of “equal groups” over a series of lessons in the 2nd-grade math curriculum.

The big idea here is that they can use repeated addition to figure out the total number of items if all groups have the same number of items in them. They practice making arrays — a display of objects arranged in equal rows and columns — and they write “repeated addition” equations to match. They discover that this concept applies to any arrangement with equal groups. For example, when second-graders see three groups of five apples, they know that 5+ 5+ 5= 15, so there are 15 apples all together. In effect, students are using multiplication before they ever label it as such.

Building on that, we use math routines — short, structured activities that develop students’ eff iciency with counting or calculating.

For instance, in a unit on equal groups, students participate in a routine known as “Counting Around the Room.” I select a number, and students take turns with repeated additions ( skipcounting) by that number. Challenges like these lay the groundwork for their eventual memorization of multiplication facts.

All of our math units incorporate rich problem-solving tasks that students may approach in a variety of ways. I encourage students to use strategies they feel are the most efficient for solving a given problem, leaning on the skills they learned from pre- vious lessons and routines.

In one lesson, I askeded students to f ind thehe Mr. total Green amount spentof money one five shirts if each shirtrt cost $7. Some studentsts drew models of equalal groups, while otherss skip-counted, and stillll others solved the problem with an equation.n. Students discussed and compared strategies with one another, making connectionss between the concretee representations and t he more abstract equations.

In each strategy, students used skip-counting (as in the example shown right) to f igure out the total number of i tems, demonstrati ng a conceptual understanding of equal groups t hat builds the foundat i on f or t ackling multiplication.