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function machines Worksheets

This section features 7 function machine worksheets designed for grades 3-6 that help students develop algebraic thinking skills. Students analyze input-output relationships to determine mathematical rules involving addition, subtraction, multiplication, and division, including multi-step operations with variables.

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3rd Grade 6th Grade

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Function Machines

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.

function machines Worksheets - Determining Function Machine Rule (+ or -) (MC) worksheet

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Determining Function Machine Rule (+ or -) (MC)

3oa9

Figure out what number is being added or subtracted to turn each input into the output.
Use a few input-output examples to spot a consistent pattern and name the rule.
Check that the same rule works for every pair in the table before choosing an answer.
Tell the difference between an “add” rule and a “subtract” rule by comparing inputs and outputs.

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function machines Worksheets - Determining Function Machine Rule (+ or -) worksheet

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Determining Function Machine Rule (+ or -)

3oa9

Use a few input-output examples to spot a consistent pattern and write the rule.
Check that the rule works by testing it on another input-output pair.

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function machines Worksheets - Add/Sub/Mult/Div worksheet

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Add/Sub/Mult/Div

6rp3a

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.

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function machines Worksheets - Adding & Subtracting below 50 (Multiple Choice) worksheet

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Adding & Subtracting below 50 (Multiple Choice)

Figure out what number is being added or subtracted by looking at an input and its output.
Use addition and subtraction facts within 50 to check which rule makes the outputs match.
Choose the correct rule from a few options by testing it on the numbers shown.

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function machines Worksheets - Adding & Subtracting below 50 worksheet

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Adding & Subtracting below 50

Figure out what a function machine is doing by looking at the input and output numbers.
Use addition and subtraction to find the rule that changes one number into another.

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function machines Worksheets - +,-,×,÷ With Variables (2 Steps) worksheet

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+,-,×,÷ With Variables (2 Steps)

Figure out the rule that changes an input number into an output number using a letter like x or n.
Use two-step rules that mix operations like add/subtract and multiply/divide.
Check that a rule works by plugging in different inputs and seeing if you get the matching outputs.

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function machines Worksheets - +,-,×,÷ With Variables worksheet

Load up one problem at a time! Ideal for projectors, tablets and computers.

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+,-,×,÷ With Variables

Figure out the rule that changes an input number into an output number.
Choose which operation and number make the rule work for all the examples in a table.

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