Partition Shapes Using Arrays in Common Core Math

By Christopher Danielson

In Common Core math, second grade students learn how to draw shapes based on their properties. They also use arrays to partition, or cut, these shapes.

Students learn to imagine shapes that have particular sets of properties. For example, they may be asked to “draw a six‐sided figure with sides that are different lengths.” This task is more challenging than to “draw a hexagon.”

In math class, an array is a series of things arranged in rows and columns. Students use arrays to cut rectangles up using lines (the word partition describes this process of cutting with lines) into rows and columns of squares.

The resulting figure looks like an array of squares. This is an important thing to practice leading to the study of area in third grade.

In second grade, students partition circles and rectangles for another reason — to study basic fractions. Second grade introduces halves, thirds, and fourths as words and as parts of circles and rectangles. (The figure shows some examples.)

Partitioning circles and rectangles to show halves, thirds, and fourths.

Partitioning circles and rectangles to show halves, thirds, and fourths.

The important idea in second grade is that the parts need to be equal‐sized in order to be called thirds (or halves, or fourths). The parts do not need to be the same shape, though, and second graders can have a lot of fun cutting rectangles into equal‐sized, but not same‐shaped pieces. The symbols for fractions, such as


may not be introduced in second grade; they’re a third grade standard in the Common Core.