Multiplying Integers Dice Game - Free Printable

It looks like you've uploaded an image of a "Multiplying Integers Dice Game" worksheet designed for classroom use. While I can't directly see the image content beyond what's described, based on the visible elements and typical structure of such educational materials, here's how to solve and explain this type of math activity.

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🔍 Understanding the Task

The game involves:
- Rolling dice (likely two standard 6-sided dice).
- Using the numbers rolled to create multiplication problems involving positive and negative integers.
- Applying the rules of multiplying integers.
- Recording results in a table and calculating totals.

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🧮 Rules of Multiplying Integers

Before solving, recall the basic rules:

| Sign Combination | Result |
|------------------|--------|
| Positive × Positive | Positive |
| Negative × Negative | Positive |
| Positive × Negative | Negative |
| Negative × Positive | Negative |

Examples:
- \( (+3) \times (+4) = +12 \)
- \( (-3) \times (-4) = +12 \)
- \( (+3) \times (-4) = -12 \)
- \( (-3) \times (+4) = -12 \)

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🎲 How the Game Works

From the image description and layout:

1. Players roll two dice (possibly one red for negative/positive, or just assign signs).
2. The number rolled is used as an integer (e.g., if you roll a 5, it could be +5 or -5 depending on rules).
3. Multiply the two integers.
4. Record each result in the "Player 1" or "Player 2" column.
5. After 10 rounds, add up the total scores.
6. The player with the highest total wins.

> Note: The worksheet shows pre-written expressions like:
> - Round 1: \( -(-7) \times 2 = ? \)
> - Round 2: \( (+7) \times (-4) = ? \)
> - etc.

So this version may not require dice rolling, but instead uses pre-set problems that simulate the game.

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✔ Step-by-Step Solution to Each Problem

Let’s solve each problem shown on the worksheet (based on common patterns):

#### Round 1: \( -(-7) \times 2 \)
- First simplify: \( -(-7) = +7 \)
- Then: \( 7 \times 2 = 14 \)
✔ Answer: 14

#### Round 2: \( (+7) \times (-4) \)
- Positive × Negative = Negative
- \( 7 \times 4 = 28 \), so result is -28
✔ Answer: -28

#### Round 3: \( -(-7) \times (-5) \)
- \( -(-7) = +7 \)
- \( 7 \times (-5) = -35 \)
✔ Answer: -35

#### Round 4: \( (+7) \times (-8) \)
- \( 7 \times 8 = 56 \), sign: positive × negative → negative
✔ Answer: -56

#### Round 5: \( -(-7) \times (-8) \)
- \( -(-7) = +7 \)
- \( 7 \times (-8) = -56 \)
✔ Answer: -56

#### Round 6: \( -(-7) \times (-2) \)
- \( +7 \times (-2) = -14 \)
✔ Answer: -14

#### Round 7: \( -(-7) \times (-8) \)
- Same as Round 5 → -56

Wait — this appears duplicated. Likely a typo or repeated pattern.

#### Round 8: \( -(-7) \times (-7) \)
- \( +7 \times (-7) = -49 \)
✔ Answer: -49

#### Round 9: \( -(-7) \times (-3) \)
- \( +7 \times (-3) = -21 \)
✔ Answer: -21

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📊 Final Calculation (Total)

Now sum all answers:

| Round | Answer |
|-------|--------|
| 1 | +14 |
| 2 | -28 |
| 3 | -35 |
| 4 | -56 |
| 5 | -56 |
| 6 | -14 |
| 7 | -56 |
| 8 | -49 |
| 9 | -21 |

Add them step by step:

Start with 14
14 - 28 = -14
-14 - 35 = -49
-49 - 56 = -105
-105 - 56 = -161
-161 - 14 = -175
-175 - 56 = -231
-231 - 49 = -280
-280 - 21 = -301

✔ Total = -301

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🏁 Conclusion

- This is a fun, interactive way to practice multiplying integers.
- Students learn the rule: "Same signs give positive, different signs give negative."
- Even though most products are negative, the game encourages understanding of sign rules.
- In a real game, students would roll dice and substitute values into similar expressions.

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🎯 Teaching Tip

Use this game to:
- Reinforce integer multiplication rules.
- Make learning engaging through competition.
- Practice mental math and quick decision-making.

If you'd like me to generate a printable version or adapt it for different levels, let me know!