This unit bundles student expectations that address identifying basic elements of geometry, lines of symmetry, and the classification of two-dimensional figures based on properties and attributes. According to the Texas Education Agency, mathematical process standards including application, tools, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.
Prior to this Unit
In Grade 3, students used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories. Students also classified and sorted two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language. In Grade 4 Unit 08, students identified parallel and perpendicular lines and used these attributes to develop the formulas for perimeter and area of rectangles and squares.
During this Unit
Students examine the foundations of geometry by identifying points, lines, line segments, rays, angles, and perpendicular and parallel lines. These concepts are essential for the ability to classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Although students have recognized examples of quadrilaterals in previous grade levels, students are expected to use formal geometric language such as parallel, perpendicular, acute, obtuse, and right angle to classify two-dimensional figures. Additionally, students apply knowledge of right angles to identify acute, right, and obtuse triangles. Symmetry is explored within two-dimensional figures as students identify and draw one or more lines of symmetry, if they exist, for two-dimensional figures.
After this Unit
In Unit 10, students will closely examine angles as they measure angles in degrees using a protractor and draw angles of a given measure. They will also determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures. In Grade 5, students will classify two-dimensional figures based on their attributes and properties in a hierarchy of sets and subsets using graphic organizers.
In Grade 4, identifying points, lines, line segments, rays, angles, and perpendicular and parallel lines as well as identifying and drawing one or more lines of symmetry, if they exist, for a two-dimensional figure are STAAR Supporting Standards 4.6A and 4.6B. These standards are part of the Grade 4 Texas Response to Curriculum Focal Points (TxRCFP): Grade Level Connections. Applying knowledge of right angles to identify acute, right, and obtuse triangles is STAAR Supporting Standard 4.6C, while classifying two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size is STAAR Readiness Standard 4.6D. Both of these standards, along with STAAR Supporting Standard 4.6A are part of the Grade 4 Focal Point: Measuring Angles (TxRCFP). All of the standards in this unit are included in Grade 4 STAAR Reporting Category 3: Geometry and Measurement. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning D1, D2; III. Geometric and Spatial Reasoning A1, B1; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.
According to Van de Walle and Lovin (2006), “Children need experiences with a rich variety of both two- and three-dimensional shapes. It is useful for students to be able to identify common shapes, notice likenesses and differences among shapes, become aware of the properties that different shapes have, and eventually use these properties to further define and understand their geometric world. As students find out more about shapes over time, they can begin to appreciate how definitions of special shapes come to be” (p. 212). The National Council of Teachers of Mathematics (2000) concludes that the development of geometric concepts should take “a broader view of the power of geometry by calling on students to analyze characteristics of geometric shapes and make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry is a natural area of mathematics for the development of students’ reasoning and justification skills” (p. 3).
National Council of Teachers of Mathematics. (2000). Executive summary: Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades 3 – 5. Boston, MA: Pearson Education, Inc.