Lesson 12

The purpose of this lesson is for students to partition rectangles into equal-size squares.

Students have arranged tiles to make arrays and rectangles, represented their rectangles by shading squares on a grid, and completed the partitioning of rectangles into equal-size squares. In this lesson, students partition rectangles into equal-size squares with and without guiding marks and represent the total number of squares within the rectangles with equations that show the sum of the number of squares in each row or the number of squares in each column. Monitor for the ways students use what they know about the structure of arrays to plan and partition their rectangles. It is not important that students partition the rectangles into exactly equal-size squares.

How did the work of arranging objects to make arrays support the understanding of partitioning rectangles into equal-size squares? What additional support is needed as students build this understanding?