Illuminations: Building with Triangles

Building with Triangles


What's So Special About Triangles, Anyway?

Students explore ways of building different basic shapes from triangles. They also investigate the basic properties of triangles, as well as relationships among other basic geometric shapes.

Learning Objectives

 
Students will:
  • explore ways of building different basic shapes from triangles
  • investigate basic properties of triangles
  • investigate the relationships among basic geometrical shapes

Materials

 
Just Two Triangles Activity Sheet
Scissors, Glue, Masking Tape
Duplicated examples of a square, a triangle, and a parallelogram
How Do You Build Triangles? Activity Sheet
Triangular shapes of various sizes
Pattern blocks
Patch Tool

Instructional Plan

Note to Teachers:This lesson includes two activities. Depending upon the ability level of your students, you may accomplish the tasks in one class session. Or, you may wish to separate into two lessons.

What Can You Build With Triangles?

Begin the class by reviewing triangles. You may ask questions such as:

  • What is a triangle?
  • How can we classify triangles based on their sides?
  • How can we classify triangles based on their angles?
  • Using different quadrilaterals, how can you cut or fold paper to create triangles?

 

Distribute the Just Two Triangles activity sheet to each student.

Just Two Triangles Activity Sheet Just Two Triangles Activity Sheet

Have students cut out two triangles from the activity sheet.

Use the models of the square, triangle, and parallelogram to encourage students to make various shapes. Ask them to try to make these shapes with two triangles. Have the students glue the "new" shapes onto the activity sheet.

In a whole-class discussion, encourage students to share at least one important thing that they noticed about one of the new shapes: likenesses and differences; where it could be seen in the classroom, playground, school, or at home; and so on.

Some possible drawings for the activity sheet include:

 

 

How Do You Build Triangles?

Next, display various triangular shapes and ask, "How do you know that these shapes are triangular?" The following properties of triangles should emerge from this discussion: three sides, three corners and angles, straight rather than curved sides.

Distribute pattern blocks to each group of two to four students. Have students explore ways to make triangles with the patterning blocks.

Alternatively, you can use the Patch Tool for pattern blocks. This is an applet version of physical pattern blocks.

Patch Tool Patch Tool

Have students share solutions with each other. As a class share any common findings and anything unique that students may have discovered.

Distribute and follow directions in the How Do You Build Triangles? Activity Sheet.

How Do You Build Triangles? Activity Sheet How Do You Build Triangles? Activity Sheet

Have students work in pairs to give or write directions for building one of the triangles, then see if another pair of students can build it by following the directions.

Some possible solutions for the activity sheet include:

 

 

Have students compare their drawings with those of several classmates. What do they notice?

Questions for Students

 

What shapes were you able to build with your triangles?

[Students may reply by saying they were able to build squares, parallelograms, and other triangles.]

What three-dimensional shapes were you able to build with your triangles?

[Students may reply by saying they were able to build triangular pyramids and triangular prisms.]

How many different triangles can be built with two, three, and then four shapes?

What happens if all twelve shapes are used to build one "huge" triangle?

[Note: One more small triangle is needed because the pattern for the triangular area is one, four, nine, sixteen, and twenty-five small triangles.]

What is the largest triangle that can be built with twelve shapes?

[You may wish to challenge students' responses to this question by asking them how they know they have discovered the largest triangle.]

How many different symmetrical designs can be created for the largest triangle?

[It may be helpful to record the various symmetrical designs on chart paper as students discover them.]

Extensions

 
  1. In the second half of the lesson, challenge students to make as many different triangles as they can. As they are doing so, ask them to describe the characteristics which make triangles "different."
  2. Pose questions such as the following, to correspond to the second half of the lesson:
    • Can you make a triangle using only one shape? [4 triangles can make a bigger triangle.]
    • Can you make a triangle that uses each of the four shapes? What's the fewest number of pieces you need to make it?

NCTM Standards and Expectations

 
Geometry 3-5
  1. Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes.
  2. Build and draw geometric objects.
  3. Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids
  4. Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
  
1 period   

NCTM Resources

Navigating through Geometry in Grades 3‑5

 Activities


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