Math in Our World: Gaming Map

Do you like creating your own towns? If you do, you’ll love this game! On this map, you’ll build a town around the mountains and the canyon in the center. You can draw forests, villages, farms, or water.

Every section has to be a rectangle with at least four grid squares inside. Monsters will live in any spaces left over.

Your score is the sum of the areas of the sections you draw. You lose 1 point for each monster village. You earn bonus points for larger sections.

Area of Section
(in square units)
Bonus Points
Greater than 9 but less than 16 square units2
16 or more square units3

Images from Cartographers by Thunderworks Games

  1. What do you notice? What do you wonder?
  2. Use pictures, models, or numbers to show what is happening.
Use this 11 by 11 grid to show what's happening. Mountains: row 2, column 9. Row 3, column 4. Row 8, column 6. Row 9, column 10. And row 11, column 3. Canyon covers rows 5 and 6 in column 5, rows 4–7 in column 6, and row 6 in column 7.
  1. What mathematical questions can you ask about this situation? Answer all the questions you can!
  • What is the largest rectangle you could draw? Will that cause a spot that could be taken over by monsters?
  • What sections of the map might be the hardest to cover? You could start there to avoid leaving spaces for monsters.
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer!

Make your own rules for this game. For example, maybe the map can include L-shaped or T-shaped sections.

Five squares form a capital L shape.
Five squares form a capital T shape.