Function Machines: Input-Output Rules

About This Resource

A free Grade 4 math worksheet on input-output rules and function machines: a number goes in, a rule changes it, and a new number comes out. Students find the output, work backwards to find the input using the inverse operation, discover the rule from pairs of numbers, complete input-output tables and try two-step rules (multiply, then add or subtract). Includes a timed lesson plan, a six-activity worksheet, an editable Word version and answer key.

Overview

Students meet the function machine: a number goes in (the input), the machine follows a rule such as × 4 or + 15, and a new number comes out (the output). They practice finding outputs, then work backwards with the inverse operation to find a missing input. Next they look at pairs of numbers and work out the rule, and they complete input-output tables. Finally they try two-step machines that multiply and then add or subtract. These skills build a strong base for patterns and early algebra.

Resource Details

Subject: Math
Topic: Input-Output Rules
Category: Number Sense
File Type: PDF
File Size: 248.4 KB
Published: 08 Nov 2026
Downloads: 0

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Grade 4 math (ages 9–10) 45 minutes Patterns mental calculation inverse operations early algebra reasoning

Student Task

Draw a big function machine on the board with the rule × 3. Students call out inputs and you say the outputs, then swap roles.
Do activities 1 and 2 together, saying the rule aloud each time.
Students complete activities 3 to 6 on their own or in pairs. Answers are in the answer key.

Classroom Use

Guess my rule: a student secretly picks a rule. Classmates give inputs and try to guess the rule from the outputs.
Human machine: one student is the machine and holds a rule card; others pass in number cards and receive the answers.
Machine chains: join two machines (× 2, then + 5) and ask the class to predict the output before checking.

Differentiation

Support: use only + and − rules with numbers up to 20, and let students use a number line. Challenge: students write their own two-step rule, make a table for it, and swap with a partner to find the rule.

Answer Key & Assessment

Activities 1 to 5 check finding outputs, inputs and rules (answer key included). Activity 6 shows whether students can explain how they found a missing input.

Learning Objectives

Apply a rule to an input to find the output.
Use the inverse operation to find a missing input.
Find the rule from pairs of input and output numbers.

Teacher Tips

When finding the rule, ask students to test their idea on every pair, not just the first one. For example, 2 → 6 could be + 4 or × 3, but 5 → 15 shows that only × 3 works for both.

What's Included

6-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (6 words with meanings and examples)
Student worksheet (6 activities)
Editable Word version of the worksheet
Complete answer key (also as a separate PDF)