Christmas Tree Angles

A Geometry Measurement Lesson Plan for Grades 4, 5, 6 or 7

Skills:

Materials required:

paper, pencil, graph paper, green construction paper, scissors, protractor

Compose and scale a tree of triangles:

  1. Sketch some Christmas trees using ONLY TRIANGLES. Try different shapes and sizes of triangles to make a tree shape.
  2. Pick a sketch with different sizes and shapes of triangles. Avoid designs with many small triangles to make it easier to measure later.
  3. Cut small rectangles that measure 8 squares x 11 squares from the graph paper, one for each triangle in your design.
  4. Beginning with the largest triangle from your design, draw each triangle on a small graph paper rectangle and arrange them to form your tree. You can adjust your design to fit the 8 x 11 rectangles better or make a better tree.
  5. To scale your design: for EACH triangle, on a sheet of green construction paper draw an 8 x 11 grid of 1" squares.
  6. To create a larger scale version of your tree: using the gridlines as guides, draw each small graph paper triangle on a sheet of full-size green paper.
  7. Cut out the green triangles and arrange them to form your tree.

Measure and analyze the angles:

  1. For each triangle, use a protractor to measure each corner angle. Write the number of degrees in each vertex.
  2. Add all three angles and write the total in the center of the triangle.
  3. What can you say about the total number of degrees in each triangle? Is there a difference? If so, compare the differences to the degrees that are marked on the protractor.
  4. Display your tree and compare your angle results with what others found.
  5. Later, after you take down the tree display, take a triangle and tear off each of the three vertices with its written angle measurement. Fit the three torn pieces together so that the vertices meet. How does this show what you discovered about the angles of a triangle?