In the third grade lessons, students focus on shared attributes of shapes and further refine their understanding of the relationships among shape categories. They enlarge their understanding of the quadrilateral category with an introduction to rhombuses, kites, and deltoids. They classify squares, rectangles, trapezoids, parallelograms, kites, deltoids, rhombuses, and other four-sided closed shapes as quadrilaterals. They partition shapes into parts with equal areas and express the area of each part as a fraction of the whole.
Students review circles, half circles, and quarter circles as well as the defining attributes of triangles, quadrilaterals, pentagons, and hexagons. They also review the concepts of right angles and parallel sides using manipulatives and sort shapes based on these attributes.
Students review the defining attributes of the special quadrilaterals studied at previous grade levels (trapezoids, parallelograms, rectangles, and squares). They also explore other important mathematical properties of each shape.
Students are introduced to rhombuses. They engage in sorting activities that focus attention on the defining attributes of rhombuses and then explore other important properties of rhombuses.
Students are introduced to the defining attributes of kites. They engage in sorting activities that focus attention on important attributes of quadrilaterals and the differences among them.
Students explore shared attributes of sets of quadrilaterals that place them in the same larger category and identify larger categories into which the quadrilaterals can be placed. They draw examples of quadrilaterals do not belong to a given set of categories.
Students are introduced to partitioning rectangles into equal-area parts. Over the course of this two-day lesson, they partition rectangles presented on square grids into two, three, four, six, and eight equal-area parts using a variety of methods. They describe each part as a unit fraction of the whole.
Students partition a variety of shapes into equal-area parts without the benefit of a square grid. They reason about equal area using both an intuitive understanding of congruence and the recognition that equal-area parts of the same whole can vary in shape. They continue to describe each part as a unit fraction of the whole.
The Grade 3 lessons address the fourth critical area of focus in the geometry domain of the Common Core State Standards (CCSS):
Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole (CCSS, 2010, p. 21).