Connect the Dots

How it works

Connect the Dots is a 2-player game. Here's how to play:

  • You start with a set of dots. (You can play with different numbers of dots and different arrangements of dots.)
  • The 2 players take turns drawing lines between dots.
  • You can only draw straight lines.
  • You can't draw a line that crosses another line.
  • Whoever draws the last line wins.

Can you beat an expert at this game if you're allowed to choose where to draw the dots and whether to go 1st or 2nd? What if the expert is allowed to draw the dots (but you still get to choose whether to go 1st or 2nd)?

In this activity, students start by playing this 2-player game with specific arrangements of dots. Then they play a version where one of the players gets to choose where to draw the dots. They also explore a solitaire / cooperative version of the game where the goal is to draw as many lines as possible for a given arrangement of dots, and they connect this exploration back to the original 2-player game.

Data recording handout

Why we like this activity

  • It’s fun! Students enjoy playing the game and figuring out how to draw the maximum number of lines.
  • It helps students develop numerical reasoning.
  • It helps students develop spatial reasoning.

  • It requires students to engage in mathematical habits of mind:

    • Using logic, finding and using strategies, and understanding and explaining when trying to figure out how to beat an expert at the 2-player game

    • Finding patterns, making and testing predictions, and understanding and explaining when exploring the maximum possible number of lines for different arrangements of dots

  • It has a low floor and a high ceiling: Students can start playing the game by trial and error, but figuring out how to beat an expert is more challenging, especially as the number of dots increases. And there are many interesting patterns to find (and to try to understand) when exploring the maximum possible number of lines for different arrangements of dots.