To Infinity: Game Rules

Objective: To be the first player to get your pawn to the zero space.

Number of Players: 2-4

Equipment: Tokens, One or two dice, Main Deck (see next page for examples), Help Deck (see next page for examples), Game board (see p. 3 for a photo)

Basic Play:

• To start, every player rolls two dice (or rolls one dice twice).  The product of the two outcomes is the starting position of the player.
• Shuffle the two card decks and place them facedown on the game board.
• Pick a player to go first and then proceed clockwise.
• On all turns, take the top card from the main deck and move accordingly (i.e. if the card says "+1", move 1 space in the positive direction; if the card says "-1", move 1 space in the negative direction).  Then, place card on the opposite side of the board, face up.
• If a player is stuck at positive or negative infinity for more than one turn the player may choose a get out of infinity free card from the help deck.  Someone else reads the card to them. If the player answers correctly, the player moves as directed by the card.

Notes:

• When a player pulls an infinity card they must move their pawn to the respective infinity space (either positive or negative infinity); they'll remain there until they pull a positive card (if on negative infinity) or a negative card (if on the positive infinity), until then the player forfeits their turn.
• Bump another player to infinity. One card allows you to go to the position of an opponent and send them to infinity.
• 2, 3, 8 and 11 cards allow the player to choose to move forward or backward.
  • The 11 card also allows the player to switch places with any of the other players.
  • The 2 card also allows you the player to draw again.

Advanced Play

All regular rules apply except:

• At the beginning of the game every player is given three cards from the main deck.
• On all turns, the player must choose their next move from their hand.  They then place that card in the out pile while picking up a new card from the original pile.
• If a player plays an infinity card, then they don't move but the next player must move to infinity and forfeits their next turn.

Examples of movement cards (main deck)

Examples of get out of infinity free cards (help deck)

To Infinity game board

This could possibly be imitated with several other game boards with slight modifications to the boards or the rules of this game.

Teacher Lesson Plan

Subject:  Middle School math                                                                      Topic:  Number Sense

Standards: Find and position integers (including negative integers) on the number line. (Based on Massachusetts 2000 Math Framework)

Do Now:  Solve (17 + 16), (12+7), (20-12), (15-20)

Initial Instruction (Mini Lesson):  Have the students demonstrate their strategies for solving the problems.  Some will use objects (e.g. M&Ms) to solve the problems, while others may have used a number line.  Anticipate varying answers to the final problem, assuming that the children have no prior experience with negative numbers.   You could choose not to give the correct answer to the final problem until the end of the class during the debriefing segment.

Processing/Small Group Work:  Divide the class into groups (2-4 students).  Introduce the class to the math game, To Infinity, while briefly going over the rules of the game.  First, have the groups of students play the basic version of the game, while recording the math facts that they accumulate during the game.  Once the students get through the basic play, time permitting, encourage them to try the advanced version of the game.

Sharing/Debriefing:   Fifteen minutes before the end of class, ask the students to return to their desks with their student activity sheets.  Discuss the student activity sheets.  Go over the proper way to use the number line and solve the final problem from the Do Now as a class.

Homework:  Complete a worksheet about adding and subtracting positive and negative integers.

To Infinity:

Student Activity Sheet

Basic Game

~Find a group of friends (2-4 players) and play To Infinity, following the game rules on the sheet attached.

~Write down the math facts that describe your moves before you move.  For example, if you're at the +24 spot and then you draw -5 write down:

(+24) + (-5) = .  Solve for the answer by using the board to count the appropriate number of spaces.  Note your answers (so you should have written down: (+24) + (-5) = (+19).

Make a list of all of your moves:

~Do this for every move, until someone wins.

Questions:

Was it easier to do the math facts before or after writing the facts down?

How would you explain to your friends the answer to (-22) + (-12) ?

Advanced Game

~Follow the same steps as in the Basic game, but after writing down your math facts, make a list of the cards that you need to win the game.

~Do this for every move, until someone wins

Questions:

Was it always a good idea to play the card that got you the closest to zero?

Is it easier to win while on the positive side of the board (spaces +1 to +infinity) or on the negative side of the board?

Notice that everyone starts on the positive side of the board.  Does that help?

Did you come up with a winning strategy?

To Infinity:

Student Activity Sheet (with Solutions)

Basic Game

~Find a group of friends (2-4 players) and play To Infinity, following the game rules on the sheet attached.

~Write down the math facts that describe your moves before you move.  For example, if you're at the +24 spot and then you draw -5 write down:

(+24) + (-5) = .  Solve for the answer by using the board to count the appropriate number of spaces.  Note your answers (so you should have written down: (+24) + (-5) = (+19).

Make a list of all of your moves:

~Do this for every move, until someone wins.

Questions: *

Was it easier to do the math facts before or after writing the facts down?

How would you explain to your friends the answer to (-22) + (-12) ?

Advanced Game

~Follow the same steps as in the Basic game, but after writing down your math facts, make a list of the cards that you need to win the game.

~Do this for every move, until someone wins

Questions: *

Was it always a good idea to play the card that got you the closest to zero?

Is it easier to win while on the positive side of the board (spaces +1 to +infinity) or on the negative side of the board?

There is no actual difference in difficulty although students may perceive one depending on the cards they are dealt.

Notice that everyone starts on the positive side of the board.  Does that help?

Did you come up with a winning strategy?

*Answers will vary unless otherwise stated

This lessons is written by students at Massachusetts Institute of Technology (M.I.T.), as part of their coursework for 11.124, Introduction to Teaching and Learning Science and Math.