PrimeTime Directions

Object:

To end the game with the most points, which are acquired by landing on prime number spaces and collecting coins.

Set-Up:

The game board consists of a path of hexagonal spaces. Each prime number space is worth that many points (e.g., the 17 hexagon is worth 17 points), and other spaces may contain coins, reverse or roll again options, or a passport.

Play:

On each turn a player is able to choose which random number generator they will use. There are several options:

Dice – One or two dice can be rolled. If two are used, the results can be added or subtracted.

Spinner – The player can select a spinner with just four numbers, and the player controls which numbers appear on the spinner; or, the player can select a spinner with unequal regions and determine which numbers occupy the largest regions.

Coins – Players can choose to flip some of the coins in their bank, and move based on the result of the flip. When a coin is flipped, it is then removed from the player’s bank.

Players then move around the game board. Points are earned each time a player lands on a prime number space.

Bonus points are earned for the following:

  • A bonus of 2n is awarded for landing on 2, where n is the roll of one die.
  • A 50 point bonus is awarded for landing on both numbers in a prime number pair.
  • A 50 point bonus is awarded for landing on two numbers in a prime number triplet; an additional 100 point bonus is awarded for landing on the third number.
  • A 50 , 150 , and 300 point bonus is awarded for landing on two, three, or four of the “lonely prime” numbers (23, 37, 47, 53), respectively.

There are also several special spaces on the board:

Roll Again – Allows the user to take another turn.

Reverse – Allows the user to take another turn, but the player’s token moves back toward the start instead of forward.

Passport – Allows the user to move to any space on the board.

The game ends when one player reaches the end of the game board.

Winning the Game:

At the end of the game, the player who reached the end receives a 250 point bonus; the other player receives all of the points in the Remaining Primes area. In addition, both players receive 25 points for each coin in their bank.

The player with the most points wins.

Math Concepts: Probability, Prime Numbers

What You Can Do: Probability exists all around us. Many games involve probability concepts since children often have to roll dice or spin a spinner to determine how far they get to move or how many points they acquire. But probability also plays a role in everyday occurrences, such as weather, car accidents, illness, or the likelihood of running into a friend at the supermarket.

Throughout the day, encourage your child to think about probability. Ask questions such as, “The weatherperson said there’s a 40% chance of rain today. Should we take an umbrella?” Or, “How likely is it that you’ll see someone you know when you go to the supermarket?”

In many cases, just discussing the odds generally can be sufficient for building understanding, such as describing an event as “very likely” or “impossible.” But in other circumstances, actually calculating the probability can be fun and educational. Lotteries provide a good example. Consider a lottery in which a player is allowed to choose a three digit number, and the player wins if his number matches a randomly selected three-digit number. Compare that to a lottery in which the player chooses a six digit number. The probability of winning either lottery could be described as “unlikely, ” but comparing the theoretical probabilities — 1/1,000 versus 1/1,000,000 — can be enlightening.

Math in the Game: Students will need to think about which random number generator will give them the greatest chance of landing on a space that earns points. For instance, a player on 16 could earn 17 points by moving 1 space or could earn 19 points by moving 3 spaces. Therefore, a spinner with the numbers 1 4 would have a 50% chance of landing on one of those two spaces, but rolling a six-sided die would only have a 33% chance of landing on one of them.

Students earn points for landing on the prime number spaces on the game board. In addition, bonuses are earned for twin prime pairs and other numbers with special relationships, so students are implicitly exposed to several number theory topics.

Related Resources:

Sticks ‘n Stones

In this Native American game, player moves are determined by throwing three sticks. The number of spaces that a player moves is determined by the outcome of the throw.

SKUNK

Students play the game of SKUNK to practice decision-making skills, leading to a better understanding of choice versus chance and building the foundation of mathematical probability.