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Describe pattern rules using words

A verbal pattern rule explains how terms in a sequence or outputs in an input–output relationship are generated, using precise language about operations, quantities, and their order. At this level, rules may describe constant additive or multiplicative changes and relationships involving whole numbers, integers, fractions, or decimals; the rule must distinguish the term’s position or input from its value, preparing for algebraic expressions and equations.

Detailed Explanation: Describe pattern rules using words

A pattern rule in words tells exactly how to get a value from its input or position. Be clear about:

  • what you start with,
  • which operation you do,
  • the order of the operations,
  • and the result you get.

Example

InputOutput
1111
2244
3377
441010

Step 1: Compare the outputs.

The outputs increase by 33 each time:

1, 4, 7, 101,\ 4,\ 7,\ 10

This suggests that the input is being multiplied by 33, because the output changes by groups of 33.

Step 2: Test multiplying the input by 33.

  • 1×3=31 \times 3=3
  • 2×3=62 \times 3=6
  • 3×3=93 \times 3=9
  • 4×3=124 \times 3=12

These results are all 22 more than the actual outputs. So subtract 22.

Step 3: State the rule in the correct order.

The rule is:

Multiply the input by 33, then subtract 22 to get the output.

Step 4: Check the rule.

For an input of 33:

3×32=92=73 \times 3-2=9-2=7

The output is 77, which matches the table.

The input is the number you start with, and the output is the value you get. The rule can also be written symbolically as

output=3(input)2,\text{output}=3(\text{input})-2,

but the verbal rule explains the operations in words.

Learn by doing: Describe pattern rules using words

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Input/Output Tables (Multiply then Add/Subtract) - Full Table to Rule


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