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Strand: GEOMETRY (K.G) Standard K.G.2
Strand: COUNTING AND CARDINALITY (K.CC) Standard K.CC.5.
Strand: GEOMETRY (K.G) Standard K.G.3
Students will complete a variety of activities that will help them identify triangles and create their own triangles.
Geometry is the study of the property and relationships of points, lines, angles, surfaces and solids. Geometric shapes can be dated back 15,000 years. Geometric shapes were drawn on ancient artifacts and cave walls. Plane geometry is the study of two-dimensional objects in one plane. Two-dimensional objects have length, width, and area but no volume.
As teachers, we need to be careful about the terminology we use
when teaching children about geometric shapes. Correct vocabulary
should be used especially in kindergarten. Below is a list of important
words to use with kindergartners.
Circlea round figure where each point is the same distance from the center
Equilateral Trianglea type of triangle where all sides are the same length Isosceles Trianglea type of triangle where two sides are the same length
Plane shapea figure that lies flat on a flat surface; also known as two-dimensional objects
Quadrilateralplane shape with four sides and four points
Rectanglea special quadrilateral with four points, four right angels, and four sides where two sides are parallel with each other of the same length and the other two sides are parallel with each other of the same length
Scalene Trianglea type of triangle where all sides are a different length
Squarea special quadrilateral with four points and four sides where all four sides are the same length and form four right angles
Triangleplane shape with three sides and three points
Definitions adapted from: Cavanagh, M.C., (2000). Math To Know: A Mathematics Handbook. Great Source Education Group: Wilmington, MA.
Teachers need to use examples of all kinds of triangles (equilateral, scalene, and isosceles) and rectangles, in many different sizes and orientations. Students in kindergarten will be able to identify shapes of all different forms and sizes if we teach them about the many different ways they will see shapes all around them. The majority of teacher supplies available only offer equilateral triangles and vertical rectangles. As teachers, we may need to make additional examples of triangles and rectangles to use during teaching. This lesson is written for triangles. This same lesson could be adapted for rectangles, squares and circles also. This lesson is not the only lesson you would use to teach triangles but would be a part of several lessons on triangles. Below, there is a list of attributes (along with a few misconceptions of rectangles) for each of the four shapes kindergartners must be able to identify, name and draw (the list of attributes and misconceptions about triangles are included in the lesson on triangles).
A few examples of attributes for squares are as follows:
Some of the common misconceptions of rectangles are as follows:
1. Demonstrate a positive learning attitude.
2. Understand and use basic concepts and skills.
3. Communicate clearly in oral, artistic, written and nonverbal form.
Invitation to Learn
Read the book Triangles (or another book about Triangles). While reading, have the students identify triangles throughout the book and discuss their attributes.
Triangles have three sides
Triangles have three points, corners, or angles
All sides of a triangle are straight
All three sides of a triangle are connected
Triangles can be turned many different ways
Some of the common misconceptions of triangles are as follows:
Triangles have one point at the top and two points at the bottom
The bottom of a triangle is flat
Triangles have a point on top
Clements, D.H., & Sarama, J., (2000). Young childrens ideas about geometric shapes. Teaching Children Mathematics, 6(8), 482-488.
Clement and Sarama identified three levels of geometric shape understanding in young children. In the prerecognition level, children are unable to identify and distinguish among many shapes. When children are able to identify a shape by the way it looks, they are in the visual level. The final level, the descriptive level, students are able to identify and communicate the specific properties that make up individual shapes. Teachers need to provide examples of all types and kinds of squares, rectangles, triangles and circles when teaching shapes.
Clements, D.H., Wilson, D.C., & Sarama, J. (2004). Young childrens composition of geometric figures: a learning trajectory. Mathematical Thinking and Learning, 6(2), 163- 184.
Young children have been found to follow a developmental path in their thinking as they learn about two-dimensional geometric shapes through hands on experiences. This developmental sequence begins with children unable to create shapes. Next, children learn to combine shapes by trial and error first and then they begin to combine shapes to make pictures through an understanding of the shapes attributes. Finally, children are able to use a grouping of shapes to create a new shape.
Hannibal, M.A., (1999). Young childrens developing understanding of geometric shapes. Teaching Children Mathematics, 5(6), 353-357.
Students need to be able to identify and verbalize key attributes of basic shapes. Students need to be taught the difference between and a point and side. Teachers need to use correct terms and vocabulary when teaching geometric shapes to young children. A variety of sizes and types of triangles and rectangles need to be used when teaching shapes so students will be able to identify each shape in its various forms.