numeric Patterns & Function Machine Worksheets

These numeric patterns and function machine worksheets help students master mathematical relationships through hands-on practice. Students work with addition, subtraction, multiplication, and division to identify rules, create equations, and analyze functions using tables, graphs, and input-output machines.

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Function Machines

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About these worksheets

Function machine worksheets develop input-output reasoning skills. Students figure out the rule a function machine uses — whether addition, subtraction, multiplication, division, or a two-step operation — by analyzing input-output pairs, then apply the rule to find missing values. Resources span third through sixth grade.

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• Figure out the missing input or output number when a machine adds, subtracts, multiplies, or divides by a rule.
• Use the given input-output pairs to identify the operation and number being used in the rule.
• Work backward through an operation to find an unknown value (like undoing +, −, ×, or ÷).
• Check that a rule works for more than one pair in the table before filling in the blank.