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Making Triangles

Carol Midgett
Location: unknown

In this activity, students use 45- and 90-degree angles to create triangles, and develop an understanding of the relationship between angles and the shape of triangle. Students use their knowledge of number, measurement and geometry to design a "virtual path" using two different angles to help a ladybug reach its hiding place under a leaf.

Initiating the Excursion

To introduce this excursion, distribute two coffee stirs and one twisty tie to each student. Demonstrate how to attach the stirs together with the twisty ties to create a movable angle manipulative. Students should use these twist ties to produce angles and measures of 45 and 90-degrees. This will help them understand the relationship of the angle to the shape of the triangle.

pdficon My Triangles Activity Sheet 

Distribute a copy of the My Triangles Activity Sheet

Once the angles have been illustrated on the activity sheet, discuss the properties of the different triangles, and ask students to share their triangles with the class.

Developing the Excursion

Place students into teams of two and distribute a Make My Path Activity Sheet to each group.

pdficon Make My Path Activity Sheet 

If this is the first time your students have used the Hiding Ladybug Applet, you should provide a brief overview of the four directional buttons used to navigate the ladybug at the interactive applet. It is important for students to understand how clicking each of the buttons affects the direction of the ladybug. Remember to include movements for left, right, forward and backward. (See directional figures below). Students should also review strategies that can be used to help the ladybug turn corners.

4013 backwards
move backward 

4013 forwards
move forward 

4013 45 degrees
45 degree 

4013 90 degrees
90 degree 

After students understand how to manipulate the directional buttons, they should visit the Hiding Ladybug Applet.

appicon Hiding Ladybug Applet 

Working together, partners share the responsibilities of "Mouse Driver" and "Reader/Recorder." The "Reader/Recorder" will read the directions from the activity sheet and record observations while guiding the activity. The "Mouse Driver" controls the action of the mouse and movement on the computer screen. Partners should switch roles until all have moved the ladybug.
Demonstrate that two "small turns" (45-degrees) are required to equal a "big turn". Ask students to predict how many corner-turns are required to equal a "big turn" (90-degrees).
Students should experiment with specific strategies to plan the route for the ladybug to reach the leaf, based on an understanding of the 45 and 90-degree options that are available on the applet. As the students are developing solutions for the ladybug to hide under the leaf, the following guided questions will encourage reflection.


Now that the students have experimented with the ladybug applet, distribute the Make My Path Activity Sheet to each member of the class. The mission is to help the ladybug navigate a path to the leaf using a different route from the one they created on the applet. Ask students to compare their first route with the second describing the similarities and differences with particular emphasis on the 45 or 90-degree angles.
For example you could have students consider questions similar to the Questions for Students.


  1. An extension to this activity would be for one student to create a ladybug path and then orally describe it to a partner. The partner would then try to duplicate the path, and record his efforts on paper.
  2. Move on to the next lesson, Making Rectangles.

Questions for Students 

  1. Describe the path you created for the ladybug to reach the leaf.  
  2. How many different directions did you travel?  
  3. Did you find the shortest route to get the ladybug to the leaf? How do you know?  
  4. Can you find another way?  
  5. What is the fewest number of turns you might use?  
  6. What is the most number of turns you might use? 

Designing a Virtual Path

In this activity, students use their knowledge of number, measurement and geometry to design a "virtual path" which enables a ladybug to hide under a leaf. They also develop navigational skills by testing to see if their path is accurate and revising their solutions.
MakingRectangles ICON

Making Rectangles

In this activity, students use their knowledge of number, measurement and geometry to plan the steps necessary for a ladybug to draw rectangles of different sizes. As they experiment, students begin to understand the relationship between the shape of a rectangle and the lengths of its sides. They also develop a sense of the amount of turn in a right angle.

Ladybug Mazes

In this activity, students plan a series of moves that will navigate a ladybug through a maze. Their plans turn the ladybug at the appropriate corners and keep it on a path without crossing the walls. This activity helps students gain experience in estimating length and angle measures.

Learning Objectives

Students will:

  • Use 45- and 90-degree angles to create triangles.
  • Develop an understanding of the relationship between angles and the shape of a triangle.
  • Name, describe and use orientation, direction and measurement concepts in planning paths.

NCTM Standards and Expectations

  • Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.
  • Describe, name, and interpret relative positions in space and apply ideas about relative position.

Common Core State Standards – Mathematics

-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.

Grade 6, The Number System

  • CCSS.Math.Content.6.NS.C.8
    Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Grade 7, Geometry

  • CCSS.Math.Content.7.G.A.2
    Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Common Core State Standards – Practice

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