Input Output Math Tables worksheet for practicing number patterns and calculations.

Problem Analysis:

The task involves analyzing input-output math tables to determine the pattern governing the relationship between the "IN" and "OUT" values. Once the pattern is identified, we need to calculate the missing numbers in each table.

Step-by-Step Solution:

#### Table 1:
| IN | OUT |
|----|-----|
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
| 5 | 6 |
| 6 | 7 |

- Pattern: The "OUT" value is always one more than the "IN" value.
- Formula: \( \text{OUT} = \text{IN} + 1 \)

#### Table 2:
| IN | OUT |
|----|-----|
| 10 | 8 |
| 12 | 10 |
| 15 | 13 |
| 17 | 15 |
| 20 | 18 |
| 21 | 19 |

- Pattern: The "OUT" value is obtained by subtracting 2 from the "IN" value.
- Formula: \( \text{OUT} = \text{IN} - 2 \)

#### Table 3:
| IN | OUT |
|----|-----|
| 2 | 6 |
| 3 | 9 |
| 5 | 15 |
| 6 | 18 |
| 8 | 24 |
| 10 | 30 |

- Pattern: The "OUT" value is three times the "IN" value.
- Formula: \( \text{OUT} = 3 \times \text{IN} \)

#### Table 4:
| IN | OUT |
|----|-----|
| 4 | 5 |
| 5 | 6 |
| 9 | 10 |
| 11 | 12 |
| 14 | 15 |
| 15 | 16 |

- Pattern: The "OUT" value is one more than the "IN" value.
- Formula: \( \text{OUT} = \text{IN} + 1 \)

#### Table 5:
| IN | OUT |
|----|-----|
| 3 | 4 |
| 2 | 5 |
| 5 | 8 |
| 7 | 13 |
| 9 | 17 |
| 8 | 11 |
| 10 | 27 |

- Pattern: This table does not follow a simple arithmetic pattern. Instead, it appears to involve a combination of operations or a non-linear relationship. However, based on the provided data, no consistent formula can be derived without additional context. For now, we will assume this table requires further clarification or a different approach.

#### Table 6:
| IN | OUT |
|----|-----|
| 2 | 4 |
| 3 | 6 |
| 7 | 14 |
| 9 | 18 |
| 12 | 24 |
| 15 | 27 |

- Pattern: The "OUT" value is twice the "IN" value.
- Formula: \( \text{OUT} = 2 \times \text{IN} \)

#### Table 7:
| IN | OUT |
|----|-----|
| 5 | 2 |
| 6 | 3 |
| 9 | 6 |
| 12 | 8 |
| 15 | 12 |
| 18 | 15 |

- Pattern: The "OUT" value is obtained by dividing the "IN" value by 3 and then rounding down to the nearest integer.
- Formula: \( \text{OUT} = \lfloor \frac{\text{IN}}{3} \rfloor \)

#### Table 8:
| IN | OUT |
|----|-----|
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
| 10 | 30 |

- Pattern: The "OUT" value is three times the "IN" value.
- Formula: \( \text{OUT} = 3 \times \text{IN} \)

#### Table 9:
| IN | OUT |
|----|-----|
| 0 | 0 |
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
| 10 | 30 |

- Pattern: The "OUT" value is three times the "IN" value.
- Formula: \( \text{OUT} = 3 \times \text{IN} \)

Final Answer:

Each table's pattern has been identified, and the formulas are as follows:

1. \( \text{OUT} = \text{IN} + 1 \)
2. \( \text{OUT} = \text{IN} - 2 \)
3. \( \text{OUT} = 3 \times \text{IN} \)
4. \( \text{OUT} = \text{IN} + 1 \)
5. No clear pattern (requires further clarification)
6. \( \text{OUT} = 2 \times \text{IN} \)
7. \( \text{OUT} = \lfloor \frac{\text{IN}}{3} \rfloor \)
8. \( \text{OUT} = 3 \times \text{IN} \)
9. \( \text{OUT} = 3 \times \text{IN} \)

\boxed{\text{Patterns Identified}}