Trees

Goals

• • Explore trees and identify when two trees are the same or different

What To Do

It is very important for this task to use manipulatives for this task as the it is important to be able to transform trees that may look different to see if they are really the same. I constructed the manipulatives from craft sticks and connectors. I drilled holes in either end of the craft sticks so they could be linked with the connectors

• 1. Possibly introduce the topic using the Good Will Hunting problem video (Draw all homeomorphically irreducible trees of size 10)

  2. First we need to understand what a tree is:

     1. Give each student 3 sticks and ask them to connect them together.

     2. Draw the results on the board and ask if there are any other possible shapes

     3. Note that by manipulating the shapes ther are 3 shapes that can be made

     4. Explain that only 2 of these are trees because no 'loops' are allowed.

  3. Four stick trees

• • 1. Give every one an extra stick and challenge them to find all the possible trees.

    2. Ask them to check carefully with their neighbours whether the shapes are actually the same. This can be done by moving the stick to different angles and comparing,

• 4. Continue with more sticks as far as the group can manage

Additional Work

• 1. For more advanced students:

     1. Explain what "homeomorphically irreducible" means for trees. i.e. that you can not have any joins with only 2 sticks. All joins must have 3 joins or be an end point.

     2. Start with 5 or 6 sticks for this version as there will be less possible solutions. See if you can get all the way to 10.

Background Information

• The Problem in Good Will Hunting