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Making Virtual Triangles

Carol Midgett
Location: unknown

In this lesson, students use virtual manipulatives to explore triangles. They create virtual representations of triangles on an electronic geoboard. They also identify shapes within shapes using tangrams. This activity is appropriate for a computer lab, so all students have access to the virtual manipulatives.

Review properties of triangles by having students share the recordings they made in the previous session.

Invite students to the computer area and demonstrate how to create triangles using the Making Triangles Applet.

appicon Making Triangles 

Guide students through the steps of clicking and dragging geobands to the geoboards to create triangles with three corners (angles). Remind students how to create a triangle on a real geoboard and that the number of sides of a triangle does not change.  Instruct students to create at least five different triangles and to copy these triangles on their Geoboards Activity Sheet.

pdficon Geoboards Activity Sheet 

 4015 triange on geoboard 

Specifically, you may ask students to create triangles with particular traits. Depending upon students' experiences with triangles, they could create triangles with:

  • all 3 sides different lengths.
  • 2 sides the same length.
  • one right angle.
  • etc.

Then students can record their examples on the Geoboards Activity Sheet.

Assessment Options 

  1. Record your observations of students’ work and comments on the teacher resource sheet Class Notes.
    pdficon Class Notes 
  2. Collect students' Geoboard Activity Sheets to assess students' pictorial representations of triangles.

Questions for Students 

1. Can you tell me how many sides each triangle has? 

[A triangle has 3 sides.]

2. Describe the different kinds of triangles you made. How are they alike? How are they different?

[They are alike because they all have different sides. They are different because they are different sizes. ]

Teacher Reflection

  • Which strategies worked well with the students? Which strategies did not work well?
  • Which ideas did the students give you that will influence how you teach this lesson next time or reinforce the objectives of this lesson later in the school term as a review?
  • What key vocabulary words did I use in the triangle lessons? Do students understand what these vocabulary words mean?"

Three Sides

In this lesson, students compare and contrast shapes using attribute blocks. Because the equilateral triangle (a triangle with congruent sides and congruent angles) is the most common example used in textbooks and other reference materials, this is an important opportunity for you to help students realize that other triangles exist and that triangles can have angles of different measures. The lesson is designed to accommodate multiple learning styles and intelligences.

Tracing and Drawing

In this lesson, students continue to discuss attributes of triangles. They  trace and draw triangles individually. Students recognize objects in their environment that are shaped like triangles and explain to the class how they recognized the shape.


Students use appropriate vocabulary to describe shapes to their classmates. Students focus on the properties of shapes to develop mental images of objects from descriptors. They create multiple representations of triangles using geoboards, string, and crayons and paper.

Learning Objectives

Students will:

  • Identify and recognize triangles using multiple representations.
  • Construct triangles.

NCTM Standards and Expectations

  • Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.
  • Recognize and represent shapes from different perspectives.

Common Core State Standards – Mathematics

-Kindergarten, Geometry

  • CCSS.Math.Content.K.G.A.2
    Correctly name shapes regardless of their orientations or overall size.

-Kindergarten, Geometry

  • CCSS.Math.Content.K.G.B.4
    Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).

-Kindergarten, Geometry

  • CCSS.Math.Content.K.G.B.5
    Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Grade 1, Geometry

  • CCSS.Math.Content.1.G.A.1
    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.

Grade 2, Geometry

  • CCSS.Math.Content.2.G.A.1
    Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP4
    Model with mathematics.