1. Yes, the game is fair as both players have an equal chance of winning. Each player has the same probability of rolling any number between 1-6 on the number cube, and the ability to choose whether the integer is positive or negative allows both players to make strategic decisions.
2. The best strategies to win the game involve paying close attention to the current position on the number line and choosing the appropriate positive or negative integer. Players should aim to balance their moves between positive and negative integers to stay close to zero. Calculating the difference between the current position and zero before making a decision can help in making an informed choice.
3. To figure out who wins the game without using number lines, players can simply add or subtract the integers they choose based on their rolls. After five turns, they can compare their total scores, and the player with a total closest to zero would be the winner.
4. If the object of the game was to end farthest from zero, the winning strategies would change. Instead of trying to stay close to zero, players would aim to move as far away as possible in either direction. In this case, consistently choosing either positive or negative integers, depending on their starting position, would be a better strategy.
5. Two ways to change the game to make it more challenging and fun to play are:
a) Introducing a target number other than zero: Instead of aiming for zero, players could aim for a predetermined target number. This would require them to strategize their moves to reach the target precisely.
b) Using a different type of dice or multiple dice with more or fewer sides: This adds an element of variety and unpredictability, as players will have a wider or narrower range of numbers to choose from. This would also require players to adapt their strategies based on the possible outcomes.
Back and Forth Directions
• Each player starts at zero on an individual number line.
• Players should take turns rolling a standard number cube, labeled 1‒6.
• Each turn, the player must choose if the number rolled represents a positive
integer or a negative integer.
o If it is positive, the player moves that number of spaces to the right on
the number line.
o If it is negative, the player moves that number of spaces to the left.
• For each turn, the player should record the roll as a positive or negative
integer in the recording chart and then draw an arrow above or below the
number line to show that movement.
• Each player should roll and record five turns. The winner is the player who
ends closest to zero. If both players end at the same place, it's a tie.
Back and Forth Analysis Sheet
1. Is the game fair? Do both players have an equal chance of
winning? Explain.
2. What strategies work best to win the ga
3. How could you figure out who wins the game without using
number lines?
4. If the object of the game was to end farthest from zero, how would
that change the winning strategies?
5. What are two ways you would change the game to make it
more challenging and fun to play?
I
9 answers
Thanks
You're welcome! If you have any more questions, feel free to ask.
ok
Is there anything else you need help with?
nope
Alright then! Have a great day!
thank you you to
You're welcome, bye!