Mathematics · Year 3

Active learning ideas

Input-Output Machines (Function Machines)

Active learning builds Year 3 students’ concrete understanding of input-output machines by letting them physically move, test, and verbalize the rules. Using whole-body movement, manipulatives, and peer discussion transforms abstract operations into visible patterns they can explain and defend.

• ACARA Content Descriptions
• AC9M3A01

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 30 min · Whole Class

Whole Class: Human Function Machine

Select one student as the machine with a secret rule (add or subtract a number). Class members provide inputs verbally; the machine announces outputs. After 5-6 examples, the class discusses and guesses the rule. Rotate the machine role twice.

Explain the rule of an input-output machine given several examples.

Facilitation Tip

During Human Function Machine, have the rule poster held high so every observer sees the operation and the changing inputs and outputs at once.

What to look for

Present students with a machine diagram showing input numbers and corresponding output numbers. Ask them to write down the rule and then calculate the output for two new input numbers.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 25 min · Small Groups

Small Groups: Rule Detective Challenge

Provide cards with 4-5 input-output pairs per group. Groups identify the rule, write it down, and predict two new outputs. Test predictions by applying the rule. Groups then swap cards to verify each other's rules.

Design an input-output machine that transforms numbers using a specific rule.

Facilitation Tip

When running Rule Detective Challenge, circulate with a checklist of the four operations and mark which ones students test before settling on an addition or subtraction rule.

What to look for

Give each student a card with a number and a simple rule, for example, 'Input: 15, Rule: Subtract 7'. Ask them to write the output number on the back of the card and then create one new input-output pair for a machine with the rule 'Add 4'.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 20 min · Pairs

Pairs: Design Your Own Machine

Pairs choose a rule (add or subtract 3-10) and create 6 example pairs without revealing it. Exchange with another pair to solve. Discuss matches and mismatches, refining explanations.

Predict the output of a function machine given a new input and its rule.

Facilitation Tip

While students Design Your Own Machine, supply blank templates with a clear input column and output column to keep their designs focused on one operation.

What to look for

Pose the question: 'If a function machine's rule is 'add 3', and the output is 10, what was the input?' Discuss strategies for working backward to find the input.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Prediction Relay

Students receive a machine black box with examples and predict outputs for 3 new inputs on a worksheet. Share predictions in a quick class huddle, then check with the rule.

Explain the rule of an input-output machine given several examples.

Facilitation Tip

In Prediction Relay, pause between rounds to ask students to whisper their prediction to a partner before revealing the output, building confidence.

What to look for

Present students with a machine diagram showing input numbers and corresponding output numbers. Ask them to write down the rule and then calculate the output for two new input numbers.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Teach function machines by starting with physical movement so students feel the shift from input to output. Use a simple two-column table on the board to record each tested input-output pair, reinforcing that one rule must fit all examples. Avoid rushing to the answer; instead, let students debate why a rule that works for three pairs fails on the fourth, deepening their pattern recognition.

Watch for students who can verbalize a consistent rule, justify it with multiple examples, and apply it to new numbers. They should also recognize addition and subtraction as inverse operations when working backward through the same rule.

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Watch Out for These Misconceptions

• During Rule Detective Challenge, watch for students who assume the rule must be multiplication or doubling after seeing one pair like input 3 yields output 9.

  Have them test a new input such as 4; if the output were 8, the rule ‘double’ would fail, pushing them to reconsider addition or subtraction.

• During Rule Detective Challenge, watch for students who think the rule changes between examples because outputs vary.

  Ask them to sort all pairs by output size and look for a consistent difference, using the card layout to spot the single rule.

• During Human Function Machine, watch for students who believe a subtraction rule means subtracting the input from itself, producing zero or negative results.

  Have the student inside the machine subtract a fixed number like 5 from each input and verbally report the output so peers hear a clear pattern.

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Methods used in this brief

• Plan-Do-Review