Partitioning Rectangles into Even Rows and Columns

Learning how to partition a rectangle into smaller, same-sized pieces is a second grame, Common Core math skill: 2.G.2. Below we show a video that demonstrates this standard. Then, we provide a breakdown of the specific steps in the video to help you teach your class.

Prior Learnings

Your students should be familiar with working with shapes, drawings, “manipulatives” and real-world objects.. In the first grade, students will have described and classified shapes based on their geometric attributes (1.G.1). Additionally, your students will have learned to distinguish between defining and non-defining attributes. 

Future Learnings

Eventually, your students will apply these second grade concepts to further their understanding in future classes. Students will be able to connect the concept of equal groups to multiplication (3.OA.1). Students will be able to connect different shape categories and form relationships between categories and subcategories (3.G.1). Additionally, your students will understand how to use written fraction notations (3.NF.1, 3.G.2). 

Common Core Standard: 2.G.2 - Partition a rectangle into rows and columns of same-size squares

Students who understand this principle can:

1. Explain how rectangles can be divided into rows and columns.
2. Understand how to explore geometric relationships.
3. Understand how shapes are used to explain parts of a whole or totals.
4. Divide a rectangle into equal rows and columns, creating an array. 
5. Determine the number of shapes in an array.

A Video to Help You Teach Common Core Standard: 2.G.2

Below we provide and breakdown two videos to help you teach your students this standard. 

Video 1: Cutting Brownies into Even Shapes

The video starts by explaining that students will learn to break a “large rectangle into many smaller, same-sized squares.”

The speaker says that she and her mom decided to make brownies for her birthday. They made them in a 3” x 4” pan. The speaker wants to cut the brownies into smaller, same shape pieces. The video then shows 2 cutting options, asking students whether the cuts are even.

1. Shapes are not the same size nor are they squares.
2. Reminds students that all 4 sides must be the same length to make a square.
3. Reminds students that the pan is 3” x 4”.
4. Suggests using rows and columns to create equal sized pieces.

Before cutting the brownies, the speaker explains what a row and column are:

1. A row is part of a shape that goes across.
   a. Shows what 3 rows across look like on the brownies.
   b. This can get confusing since there’s only 2 lines.
   c. But now there are 3 long parts.

1. A column is part of a shape that goes up and down.
   a. The speaker put columns on top of the rows, ending with 4 columns.
   b. There are only 3 cuts, but there are 4 columns.

After cutting the brownies into rows and columns, the speaker asks the students if they successfully cut the brownies into equal square shapes.

Yes! The pieces all look like squares and are the exact same size! Hurray! 

Lastly, the speaker counts the number of brownies and finds that there are 12 equal-sized, square pieces.

The speaker summarizes what the students accomplished in the video, and relates the process to other shapes.

Want more practice?

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*Information on standards is gathered from The New Mexico Public Education Department's New Mexico Instructional Scope for Mathematics and the Common Core website.