Problem Description:
The image shows a game board with a grid of numbers ranging from \(-12\) to \(12\). There are two dice: one with faces labeled \(-5\) and \(5\), and the other with faces labeled \(-2\) and \(2\). The task is to determine the possible outcomes when rolling these dice and how they affect the position of a counter on the board.
Solution Explanation:
#### Step 1: Understand the Dice
-
First Die: Faces are \(-5\) and \(5\).
-
Second Die: Faces are \(-2\) and \(2\).
When rolling both dice, the total outcome is the sum of the values shown on the two dice. Let's calculate all possible outcomes:
1. If the first die shows \(-5\) and the second die shows \(-2\):
\[
-5 + (-2) = -7
\]
2. If the first die shows \(-5\) and the second die shows \(2\):
\[
-5 + 2 = -3
\]
3. If the first die shows \(5\) and the second die shows \(-2\):
\[
5 + (-2) = 3
\]
4. If the first die shows \(5\) and the second die shows \(2\):
\[
5 + 2 = 7
\]
Thus, the possible outcomes when rolling the dice are:
\[
-7, -3, 3, 7
\]
#### Step 2: Interpret the Game Board
The game board is a grid with numbers from \(-12\) to \(12\). The objective is to move a counter based on the outcome of the dice roll. For example:
- If the counter is currently at position \(0\) and the dice roll results in \(-7\), the counter moves to position \(-7\).
- If the counter is at position \(4\) and the dice roll results in \(3\), the counter moves to position \(7\).
#### Step 3: Strategy for Moving the Counter
The player can choose to "Pass" or "Place a counter." If the player chooses to place a counter, they must decide where to place it based on the possible outcomes of the dice roll. The goal is typically to strategically position the counter to either block the opponent or reach a favorable position on the board.
#### Final Answer:
The possible outcomes when rolling the dice are:
\[
\boxed{-7, -3, 3, 7}
\]
These outcomes will determine how the counter moves on the board. The player should use these outcomes to plan their strategy accordingly.
Parent Tip: Review the logic above to help your child master the concept of printable integer games.
