1.G.A.1

Reason with shapes and their attributes

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

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Summary:

Early introductions to geometry include a basic understanding and ability to name shapes including triangles, squares, circles, and rectangles. In first grade, students need a more sophisticated vocabulary and understanding of the attributes of shapes. They should encounter a variety of shapes, which means that there should also be a variety of orientations, using different colors and sizes. Attention should be given to unfamiliar variants of shapes (i.e., obtuse triangles, rotated squares, etc.).

Understanding the Standard:

    • Students will have ample opportunity to explore a variety of shapes and begin classifying them according to specified attributes (e.g., sides, closed, vertices, edges, and faces). Variety also includes orientation of shapes, such as color, size, and direction. 
    • Students will evaluate objects they encounter in their everyday world and determine the basic geometric shapes that compose them.
    • Exploration of three-dimensional objects may include items that are found in the home, outside, and in the classroom. Description of those objects should include appropriate geometric language, as well as discussion about what attributes let us know whether a shape is a triangle, cylinder, or square.
    • Students are provided with a variety of manipulatives (objects that can help students understand abstract concepts in mathematics - may be actual blocks, coins, rods, or computer-based items) and technologies to encourage and support their exploration and conclusions.
    • Students will be asked to draw or build shapes with specified attributes. For example, "Draw a shape with exactly three straight sides", or "Build a cube whose faces are all squares".
    • Students will determine the defining attributes of shapes. For example, what differentiates a cylinder from a cone?

      Specific Questions to Focus Instruction:

        • Can my students identify two-dimensional shapes and describe them according to specific attributes (e.g., number of sides, closed, number or vertices)?
        • Can my students distinguish between an open (gap in outline) and closed shape (no gap in outline)?
        • Can my students name three-dimensional shapes and identify the number of faces, edges and vertices?
        • Can my students identify 2-dimensional shapes as faces of 3-dimensional figures?
        • Can my students draw or build a shape with specified attributes?
        • Can students communicate the specific attributes that constitute a shape? (Example: regardless of size, all triangles have 3 sides).
        • Can my students draw or build a shape with specific attributes? In other words, can they make the shape "to order"?
        • Can my students make a sphere (or any other 3 dimensional shape) out of clay or playdough?

          Skills

          Prior to: Students can sort shapes according to non-defining attributes such as color, orientation, and size. See K.G.B.4.

          At Grade Level: Using appropriate geometric vocabulary, students are able to distinguish, draw, and build two and three-dimensional shapes according to specific attributes. At this level, the shapes students build out of clay or that they draw may be lumpy or inexact, but sufficiently close to the shape. Students can compare and contrast shapes with attention given to their defining attributes, using vocabulary and reasoning to support their answers.

          Moving Beyond:
          Students can take a shape that they have created or drawn and figure out how to make it more exact. Students may be able to combine two-dimensional shapes in order to create a new shape, and break shapes apart into many equal parts that make smaller shapes. Students can describe their physical world in reference to the geometric configurations that surround them.  Go to 2.G.A.1. to see the progression of related skills.