To find the pattern rule in a table worksheet, you need to identify the relationship between the input and output numbers. Here's how:
Steps to Determine the Pattern Rule:
- Analyze Input/Output Pairs: Start by examining one input and its corresponding output value in the table.
- Identify the Operation: Determine the mathematical operation (addition, subtraction, multiplication, or division) that connects the input and the output.
- For example, if the input is 2 and the output is 6, it could be multiplication by 3 (2 x 3 = 6) or addition by 4 (2 + 4 = 6).
- Test the Pattern: After identifying a possible rule, check if it applies consistently to all other input-output pairs in the table. If it doesn't, return to step 2 and try a different operation.
- Confirm the Rule: Once you find a rule that works for all pairs, you've successfully identified the pattern rule for the table.
Examples:
- Addition:
- Input: 1, Output: 4
- Input: 2, Output: 5
- Input: 3, Output: 6
- Rule: Add 3 to the Input
- Multiplication:
- Input: 1, Output: 5
- Input: 2, Output: 10
- Input: 3, Output: 15
- Rule: Multiply the Input by 5
Here's a table illustrating various pattern rules:
| Input | Output | Pattern Rule |
|---|---|---|
| 1 | 5 | Input x 5 |
| 2 | 10 | Input x 5 |
| 3 | 15 | Input x 5 |
| 4 | 20 | Input x 5 |
| 1 | 6 | Input + 5 |
| 2 | 7 | Input + 5 |
| 3 | 8 | Input + 5 |
| 4 | 9 | Input + 5 |
| 6 | 3 | Input ÷ 2 |
| 8 | 4 | Input ÷ 2 |
| 10 | 5 | Input ÷ 2 |
| 12 | 6 | Input ÷ 2 |
| 7 | 2 | Input - 5 |
| 9 | 4 | Input - 5 |
| 10 | 5 | Input - 5 |
| 11 | 6 | Input - 5 |
As the reference stated, "to determine the rule for a table, simply look at one pair of input/output numbers and figure out what number has been added, subtracted, multiplied, or divided by it. Then, make sure that pattern matches the rest of the numbers." This method ensures that you've identified the accurate and consistent rule governing the table.
