How to Play Racetrack Game with a Paper and Pencil

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Have you ever heard of the Racetrack game? This racing game is a fun and educational pencil and paper game played by 1-4 players. It would be a great activity for kids to keep busy this summer! Take it on a road trip or play while waiting for appointments.

This Racetrack game, also called a vector race, can help teach concepts related to vector addition, graphing, inertia, acceleration, and strategic planning. But it’s not as complicated as that sounds. It’s quite fun! Read on for a step-by-step guide on how to play the graph paper race game.

Supplies Needed for the Racetrack Game:

As I mentioned it is a game you can play with just paper and a pencil. However, you do need graph paper for this game.

You can play this game just with a pen or pencil, but it is better with different colored pencils or pens for each player. If you want, you can also use a ruler to connect your dots, but that’s totally optional. Freehand drawing is just fine, too.

How to Play the Racetrack Game:

The goal of this car racing game is to be the first player to move your “race car” from the starting line to the finish line without crashing. You crash by moving your car across the sides of the track.

This game can be played alone or with multiple players. If playing alone, you compete against yourself and see if you can reduce the number of turns it takes you to complete the circuit of the track. If playing with multiple players, you are racing each other.

This picture shows a single player game.

Setting Up the Racetrack Game

Begin by drawing the racetrack. Use a piece of graph paper to draw a race track. Fill most of the paper with an oval-type shape. Make wavy lines and shape it as desired. Next, draw a smaller inner oval shape. The track should be wide enough to allow you to move through it, but narrow enough to be somewhat challenging.

A wider track is easier and better for first-timers. Draw a line to show the starting and finishing point on the track. Try different shape variations for more of a challenge.

Draw a line to indicate the start and finish of the race. Each player then needs to choose their starting position along the starting line. You can start from any grid point on that line. Mark your starting points with dots. It’s best if each player uses a different color pen to be able to tell the difference more easily.

Decide who will be the first car to go. You can choose to have the youngest go first, or roll a dice to choose. Then, take turns going clockwise or counterclockwise around the circle.

Rules to Play the Game:

Moving Your Car
Your car is represented by the dots you draw. The cars all begin stationary. Each turn you can move your car in the same direction and distance as the previous turn. Or you can accelerate or slow down by one square in each direction. For example: if the car moved 2 squares forward and one square up, they would need to move the same amount on the next turn, or to any of the 8 squares surrounding that point. Mark each point that you move to with another dot. Then connect the dots with a pencil line.

In mathematical terms, you can move your car by changing the velocity vector each turn. Velocity vector is represented by the number of squares moved horizontally and vertically. Each turn, a player can change their velocity by one square in any direction (up, down, left, right, or diagonal).

Increasing that length is the same as acceleration for a race car. You do not want to accelerate too much or you will crash into the walls of the track, or into another car.
Velocity and Position
Begin motion with a velocity of (0,0) on the first move. This means your starting point is the same as 0 on the x axis and 0 on the y axis on a graph. For each turn, players add the current velocity vector to their position to determine the new position. Each turn, a player can adjust their velocity by ±1 in either direction (horizontal or vertical) from their previous move. For example, if a player’s current velocity is (1, 2), they can change it to (2, 2), (0, 2), (1, 3), (1, 1), etc.

Example of a Turn: Let’s say a player is at position (3, 4) with a velocity of (1, 2). The player decides to change the velocity to (1, 3) (moving upward by 1). The new position will be (3 + 1, 4 + 3) = (4, 7). If the new position is outside of the track boundaries, the player crashes. If not, the game continues with the next player.
Crashing
This game takes some planning and strategy to stay within the lines of the racetrack. If you accelerate too quickly, you will cross over the lines of the track. This is considered a crash.

If the player crashes into a wall, you can decide to either have them skip a turn, send them back to their previous location, or allow them to start at zero and move on from that point for their next move. If they are starting from zero and continuing on, they will start at that exact point and move forward beginning with just a single square like when the game began.

You can cross over the lines of other players, but you cannot land on the same point they are currently on.
Winning the Game

The first player to reach and cross the finish line is the winner of the game.

Variations of the Racetrack Game:

Do Multiple Laps: Make the game longer by doing multiple laps around the track.

Add Obstacles on the track that players must avoid such as an oil slick or a hill. You can mark a hill by indicating the required direction with arrows. Mark an oil slick by shading in small parts of the track. You cannot increase your speed on an oil slick.

Power-ups: Include power-ups that players can collect for a speed boost or extra moves.

See More Fun Paper & Pencil Games for Kids

Dots and Boxes Game: How to Play
Fun Math Game: The Great Graphing Race
Free Printable Blank Sudoku Grids
Fun Printable Mad Libs for Kids
Printable Road Trip Scavenger Hunt for Kids

How to Play Racetrack Game with a Paper and Pencil

Supplies Needed for the Racetrack Game: