## 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.

Instructions

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

Part 1: https://teacher.desmos.com/activitybuilder/custom/61cd0d782f7ddbd7a8698c08

Part 2: https://teacher.desmos.com/activitybuilder/custom/61cde7805c82cb0a114e355b

Part 3: https://teacher.desmos.com/activitybuilder/custom/61d10450c4f5850a3d8056c1

### Questions

- 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?
- Determine all the possible routes between each of the 7 towns. How many are there?
- Where will your shortest-route path end and begin?
- Will a continuous or non-continuous road be shorter?
- What is the shortest loop-route that connects all 7 towns?

Original graph: https://www.desmos.com/calculator/lvnokthxjd

Exit Ticket

CCSS Math Practice

- I can reason abstractly and quantitatively.

NGSS Crosscutting Concepts

- Patterns