# 1.11 - Geometric Shapes

The student will

a)  Identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles; and

b)  identify and describe representations of circles, squares, rectangles, and triangles in different environments, regardless of orientation, and explain reasoning.

### BIG IDEAS

• So I can continue to describe shapes, and objects commonly seen in our lives.
• So that I can see and identify geometric figures  that are seen in my class and home, and community (doorknobs, clocks, windows, tables, desks, etc.)

### UNDERSTANDING THE STANDARD

 Early experiences with comparing, sorting, and subdividing figures assist students in analyzing the characteristics of plane figures.A plane figure is any closed, two-dimensional shape.A vertex is the point at which two or more lines, line segments, or rays meet to form an angle.  The term vertices is the plural form of vertex.An angle is formed by two rays that share a common endpoint called the vertex. Angles are found wherever lines or line segments intersect.A polygon is a closed plane figure composed of at least three line segments that do not cross.A triangle is a polygon with three sides.A quadrilateral is a polygon with four sides.A rectangle is a quadrilateral with four right angles.A square is a quadrilateral with four congruent (equal length) sides and four right angles.  At this level, students might describe a square as a special rectangle with four sides of equal length.Students at this level do not need to use the terms polygon, quadrilateral, or congruent.A right angle measures exactly 90 degrees.A circle is the set of points in a plane that are the same distance from a point called the center.  A circle is not a polygon, because it does not have straight sides.Presentation of triangles, rectangles, and squares should be made in a variety of spatial orientations so that students do not develop the common misconception that triangles, rectangles, and squares must have one side parallel to the bottom of the page on which they are printed.Representations of circles, squares, rectangles, and triangles can be found in the students’ environment at school and at home. Students should have opportunities to identify/classify things in the environment by the type of figure those things represent.A common misconception students have when a figure such as a square is rotated is that they will frequently refer to the rotated square as a diamond.  Clarification needs to be ongoing (e.g., a square is a square regardless of its location in space; there is no plane figure called a diamond).Building geometric and spatial capabilities fosters enthusiasm for mathematics while providing a context to develop spatial sense.Polygons can be constructed using other polygons (e.g., six equilateral triangles can be used to construct a hexagon; a triangle can be added to a rectangle to create a pentagon, etc.).Early experiences with comparing, sorting, and subdividing figures or manipulatives (e.g., pattern blocks) assist students in analyzing the characteristics of plane geometric figures.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Identify the name of the plane figure when given information about the number of sides, vertices, and angles. (a)
• Trace triangles, squares, rectangles, and circles. (a)
• Describe a circle using terms such as round and curved. (a)
• Describe triangles, squares, and rectangles by the number of sides, vertices, and angles. (a)
• Recognize that rectangles and squares have special types of angles called right angles. (a)
• Sort plane figures based on their characteristics (number of sides, vertices, angles, curved, etc.). (a)
• Identify and describe representations of circles, squares, rectangles, and triangles, regardless of orientation, in different environments and explain reasoning. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018