## How Do You Build Triangles?

• Lesson
3-5
1

Students investigate the basic properties of triangles. Students also investigate the relationships among other basic geometric shapes.

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

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

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?

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Questions for Students

1. 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.]

2. 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.]

3. 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.]

### Learning Objectives

Students will:

• Investigate basic properties of triangles
• Investigate the relationships among basic geometrical shapes

### NCTM Standards and Expectations

• Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
• Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids.
• Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes.
• Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.