Introduction This unit bundles student expectations that address distinguishing attributes that define two-dimensional geometric figures and using attributes to identify, classify, sort, compose, and create two-dimensional figures. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, 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 Kindergarten, students identified, classified, sorted, and created circles, triangles, rectangles, and squares and identified attributes of these two-dimensional shapes using both informal and formal geometric language.
During this Unit Students use formal and informal geometric language to describe the attributes that identify and define circles, triangles, rectangles, squares, rhombuses, pentagons, hexagons, and octagons. Students distinguish between attributes that define a two-dimensional figure (sides, vertices) and attributes that do not define a two-dimensional figure (size, color, orientation, texture, etc.) as they sort and classify a collection of two-dimensional shapes. While exploring attributes that define two-dimensional figures, students not only determine the number of vertices and sides, but also examine if the sides appear to be equal in length and if the corners appear to be square. It is important for students to be exposed to both regular figures where sides are the same length and irregular figures where sides are not the same length. Although students at this grade level are expected to use both formal and informal geometric language, the term “right angle” when referring to corners is not an expectation until Grade 4. However, teachers may begin to associate the words “square” and “right” when describing corners of two-dimensional figures. Students develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they create circles, triangles, rectangles, squares, rhombuses, pentagons, hexagons, and octagons using drawings and a variety of materials. Spatial visualization is also reinforced as students compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible.
After this Unit In Unit 13, students will continue to develop the concept of geometry as they extend their knowledge to include three-dimensional figures. Students will distinguish between attributes that do and do not define three-dimensional figures in order to identify and describe three-dimensional figures.
Additional Notes In Grade 1, distinguishing attributes that define geometric figures and using attributes to identify, classify, sort, compose, and create two-dimensional figures are foundational building blocks to the conceptual understanding of the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Analyzing attributes of two-dimensional shapes and three-dimensional solids. 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; 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.
Research According to the article “Young Children’s Concepts of Shape,” teachers should capitalize on geometry skills since “some children’s competence with geometric and spatial concepts exceeds their number skills” (Clements et al. 1999). The National Association for the Education of Young Children believes that “children’s mathematical thinking in geometry allows them to make a connection to number” (2002). Many researchers make connections between geometric concepts and other mathematical concepts. Students with well-developed understandings in geometry are more likely to be successful with the concepts of number, measurement, and fractions due to the development of spatial reasoning and deductive reasoning.
Clements, D. H., Swaminathan, S, Hannibal, M, & Sarama, J. (1999). Young Children’s Concepts of Shape. Journal for Research in Mathematics Education, 30, 192-212. National Association for the Education of Young Children (NAEYC). (2002). Early Childhood Mathematics: Promoting Good Beginnings. A joint position statement of the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM). Retrieved from www.naeyc.org/about/positions/psmath.asp. 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 |