Functions with Tables

Overview

This lesson introduces second-year students (ages 7–8) to representing functions using input-output tables, building on their prior knowledge of mapping diagrams and ordered pairs. They will also be introduced to the key vocabulary of domain, range, and codomain in the context of functions.

This lesson aligns with the Primary Curriculum Mathematics Strand Unit: Patterns and Relationships (Strand Unit 4, Year 2) as outlined by the Irish Primary Curriculum, supporting students in understanding and representing relationships using multiple methods.

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Learning Objectives

By the end of the lesson, students will be able to:

• Understand and complete input-output tables representing simple functions.
• Explain the meaning of domain, range, and codomain in the context of functions.
• Recognise that each input relates to exactly one output.
• Use mathematical language accurately when discussing functions.

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Resources

• Whiteboard and markers
• Printed input-output table templates (one per student)
• Cards with numbers for inputs and outputs
• Visual aids showing previous lesson’s mapping diagram and ordered pairs
• Interactive function machine model (box or table with input and output slots)
• Mini-whiteboards and markers for all students

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Curriculum Links

• Primary Curriculum Mathematics, Ireland (1999 Revision, updated 2019)
  • Strand Unit 4: Patterns and Relationships
  • Learning Outcome: Recognise and represent functions and relationships using tables and diagrams.
• Mathematical Methods & Reasoning
  • Encourage reasoning about relationships between numbers.
  • Encourage vocabulary development and precise mathematical explanations.
• Supports the NCCA's focus on interconnected learning, language development, and visual representation.

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Timing and Structure (40 minutes)

Time	Activity	Description
0-5 min	Starter: Recall previous lesson	Quick review of mapping diagrams and ordered pairs using whole-class questioning. Use visual aids.
5-15 min	Introducing Input-Output Tables	Model a simple input-output table on the whiteboard with a function machine demonstration. Discuss inputs/outputs.
15-25 min	Vocabulary Introduction: Domain, Range, Codomain	Define each term using visuals and link to the table. Use age-appropriate explanations and examples.
25-35 min	Guided Practice in Pairs	Students complete an input-output table worksheet, identifying domain and range, supported by teacher.
35-40 min	Plenary and Reflection	Whole class shares answers; teacher consolidates vocabulary and concept understanding. Quick formative assessment with mini-whiteboards.

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Detailed Lesson Breakdown

Starter (0-5 minutes)

• Begin with a warm-up question: "Who can remind us what we learned about functions last time?"
• Show a simple mapping diagram on the board, relate it to ordered pairs.
• Ask students to share examples and explain that today they will look at how to show functions using a table.
• Reinforce that a function links each input (number or item) to one output.

Introduction of Input-Output Tables (5-15 minutes)

• Draw an input-output table with two columns: one labelled Input and the other Output.
• Use a function machine: e.g., "Double the number" or "Add 3".
• Model how to fill the outputs given inputs.
• Demonstrate how each input has exactly one output.
• Engage students by asking what output they expect for a given input.

Introducing Vocabulary (15-25 minutes)

• Display the table alongside the function machine.
• Introduce Domain: "The set of all the inputs" — point to input column.
• Introduce Range: "All the outputs the machine can give" — point to output column.
• Introduce Codomain: Explain that it is a list of all possible outputs that could happen if we had all numbers to put in — more theoretical but keep simple.
• Use examples and ask students to repeat back definitions in their own words.
• Use flashcards next to input-output to reinforce vocabulary visually.

Guided Practice (25-35 minutes)

• Distribute input-output table worksheets with simple functions (e.g., "Multiply by 2", "Add 4").
• Students work in pairs to complete the tables and identify domain and range.
• Teacher circulates to support and ask probing questions (e.g., "What is the domain here?", "Why can’t an input have two outputs?").
• Encourage use of mathematical terms.

Plenary and Reflection (35-40 minutes)

• Gather the class and invite pairs to show their answers.
• Use mini-whiteboards to ask quick questions: "What is the range for this function?" or "Is this a function if one input has two outputs?"
• Provide positive feedback and clarify misconceptions.
• End with a quick summary of how input-output tables help us understand functions and the importance of domain, range, and codomain.

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Assessment and Differentiation

• Formative Assessment: Observation during pair work, questioning during plenary, mini-whiteboard responses.
• Adapt task difficulty by varying functions’ complexity in worksheets.
• Use additional visual supports for learners needing assistance.
• Challenge advanced students by asking them to create their own input-output tables or explain codomain further.

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Extension Ideas and Cross-Curricular Links

• Create a class function machine corner where students can input numbers and find outputs physically using cubes or counters.
• Link to literacy by asking students to write simple sentences describing a function.
• Use story problems involving functions in real-life contexts, supporting numeracy across subjects.

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This lesson plan balances concrete experiences with abstract vocabulary, fostering a deep understanding of functions appropriate for second-year learners within the Irish curriculum framework. It engages learners with multi-modal activities and ensures they acquire essential mathematical language and concepts for future foundation in functions.