Mathematics · Junior Infants

Active learning ideas

Patterns and Functions: Input-Output Tables

Active learning helps young students see the connection between concrete actions and abstract rules in input-output tables. When they physically manipulate objects or move through sequences, the rule becomes visible and memorable. This hands-on approach builds confidence and clarity before moving to symbolic representation.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.9

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

Activity 01

• Outdoor Investigation Session
• 25 min · Pairs

Manipulative Tables: Counter Patterns

Provide trays with counters and simple input-output cards (e.g., input 2, output 4: double). Pairs build their table by placing inputs, applying the rule, and recording outputs on a large chart. They swap rules and predict the next three entries. End with sharing one prediction.

Analyze how to identify the rule that connects input and output values.

Facilitation Tip

During Manipulative Tables, have students record each step in a notebook so they can see the progression of inputs and outputs side by side.

What to look for

Present students with a simple input-output table, such as: Input (apples) | Output (juice boxes) 1 | 2, 2 | 3, 3 | 4. Ask: 'What is the rule? How many juice boxes will you get if you bring 5 apples?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Outdoor Investigation Session
• 30 min · Small Groups

Function Machine Game: Small Group Relay

Create a 'machine' from a cardboard box with a rule inside (e.g., add 1). One student inputs a number verbally or with fingers, the next processes it secretly, and a third checks the output. Groups rotate roles and adjust rules midway. Record results on a class table.

Predict the output for a given input based on an identified pattern.

Facilitation Tip

For the Function Machine Game, place the relay stations far enough apart to encourage physical movement but close enough for peer discussion.

What to look for

Give each student a card with a table showing 2-3 pairs of inputs and outputs (e.g., Input (blocks) | Output (towers) 2 | 4, 3 | 6). Ask them to write the rule and draw the output for an input of 4 blocks.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 20 min · Whole Class

Whole Class Chain: Human Patterns

Students line up as a chain. Teacher gives first input (clap 1), next adds rule (clap 2 more), passing output down. Predict what the last student claps. Repeat with new rules like 'double', drawing the table on the board as a class.

Construct an algebraic rule to represent a linear pattern from a table.

Facilitation Tip

In Whole Class Chain, pause after each child’s turn to ask the class to predict the next output before moving on.

What to look for

Show a table with a missing value. For example: Input | Output 1 | 3, 2 | 4, 3 | ?. Ask students to explain how they figured out the missing output and what the rule is. Encourage them to use the terms 'input', 'output', and 'rule'.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 15 min · Individual

Individual Drawing Boards: Picture Tables

Give laminated sheets with input pictures (e.g., 1 car). Students draw outputs using crayons (e.g., 3 cars: add 2). Circle the rule from options. Share drawings in a gallery walk.

Analyze how to identify the rule that connects input and output values.

Facilitation Tip

With Individual Drawing Boards, provide colored pencils so students can visually separate inputs, operations, and outputs.

What to look for

Present students with a simple input-output table, such as: Input (apples) | Output (juice boxes) 1 | 2, 2 | 3, 3 | 4. Ask: 'What is the rule? How many juice boxes will you get if you bring 5 apples?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teach this topic by letting students experience the rule first and name it second. Avoid giving rules upfront; instead, ask them to describe what they did with the counters or blocks. Research shows that when children discover patterns themselves, they retain the concept longer. Limit whole-group explanations until after exploration, so misconceptions surface naturally during activities.

Successful learning looks like students articulating the rule aloud, predicting outputs accurately, and explaining their reasoning with examples. They should use terms like 'input', 'output', and 'rule' with confidence. Tables should be completed consistently, showing they trust the pattern rather than guessing.

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Watch Out for These Misconceptions

• During Manipulative Tables, watch for students who guess outputs without touching the counters or writing a rule.

  Prompt them to show you how they arrived at the output using the counters. Ask, 'What did you do to the 3 blocks to get 6?' and have them demonstrate the action.

• During Function Machine Game, notice when students change the rule midway through the relay, especially after a pause.

  Call a brief huddle after two rotations to ask, 'Was the machine the same for every turn? How do you know?' Have them check previous entries to confirm consistency.

• During Whole Class Chain, observe students reversing the direction of the rule, saying 'You put in 3 and get 6, so 6 must go to 3.'

  Point to the arrow on the board and say, 'The arrow shows the direction. What did we do to 3 to get 6?' Use gestures to reinforce the one-way flow.

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Methods used in this brief

• Outdoor Investigation Session