Road Building on Mathlantis

Type: Mini-lesson

Theme: Combinations and Permutations

Grades: 6, 7, 8, 9, 10, 11, 12

Learning Target: Students will develop a sense of discrete mathematics and combinations.


This activity is an introduction to permutations, combinations and discreet mathematics.

Part 1:

Part 2:

Part 3:


  1. You've been given enough materials to pave 52 miles of trails between the seven towns of Mathlantis. Will you have enough materials to connect each town?
  2. Determine all the possible routes between each of the 7 towns. How many are there?
  3. Where will your shortest-route path end and begin?
  4. Will a continuous or non-continuous road be shorter?
  5. What is the shortest loop-route that connects all 7 towns?

Original graph:

Exit Ticket
CCSS Math Practice
  • I can reason abstractly and quantitatively.
NGSS Crosscutting Concepts
  • Patterns