Mathematics · Year 10

Active learning ideas

Introduction to Functions and Mappings

Functions and mappings can feel abstract to students, so active learning helps them see inputs and outputs in concrete ways. Working with visuals and hands-on tasks makes the one-output-per-input rule clearer than abstract definitions alone.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Algebra

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Card Sort: Functions vs Relations

Prepare cards with input-output pairs: some functions, some not. In pairs, students sort into two piles and justify choices using mapping rules. Follow with class share-out to discuss edge cases like empty sets.

Differentiate between a function and a general relation using examples.

Facilitation Tip

During the Card Sort, circulate and listen for students to justify their groupings with clear language about inputs and outputs.

What to look for

Provide students with three sets of ordered pairs. Ask them to circle the sets that represent functions and underline the sets that represent relations. Then, ask them to identify the domain and range for one of the function sets.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 35 min · Small Groups

Mapping Diagram Construction

Provide sets of domain and range values on cards. Small groups draw arrows to create valid functions, then swap to critique others' mappings for one-to-one properties. Extend by inventing their own sets.

Explain the significance of domain and range in defining a function.

Facilitation Tip

When students construct mapping diagrams, ask them to pause after each arrow and state, 'This input maps to exactly one output.'

What to look for

Give students the function rule f(x) = 3x - 2 and the domain {1, 2, 3}. Ask them to: 1. Construct a mapping diagram for this function. 2. List the range of the function.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 30 min · Whole Class

Function Machine Relay

Set up a 'machine' with hidden operations. Whole class relays inputs through, predicting outputs aloud. Reveal the rule at end and graph results to identify domain restrictions.

Construct a mapping diagram for a given function and identify its properties.

Facilitation Tip

In the Function Machine Relay, time each student’s turn to keep energy high and ensure all students contribute at least once.

What to look for

Present a scenario: 'A student council election where each student (input) can vote for only one candidate (output).' Ask students: 'Is this a function? Why or why not? What would make it NOT a function?'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 20 min · Individual

Domain-Range Hunt

List everyday scenarios like temperatures to Celsius. Individuals identify domains and ranges, then pairs verify with mapping sketches. Class votes on trickiest examples.

Differentiate between a function and a general relation using examples.

Facilitation Tip

For the Domain-Range Hunt, provide calculators and colored pencils to help students visualize restrictions and avoid rushing through the scenarios.

What to look for

Provide students with three sets of ordered pairs. Ask them to circle the sets that represent functions and underline the sets that represent relations. Then, ask them to identify the domain and range for one of the function sets.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Experienced teachers start with the visual and tactile—mapping diagrams and card sorts—before moving to abstract notation. They avoid defining functions too early and instead let students discover the uniqueness rule through examples. Research shows that letting students debate borderline cases (like piecewise or step functions) deepens understanding of the domain-range relationship.

Students will confidently identify functions and relations, explain why mapping diagrams show valid functions, and distinguish domain and range using both visual and numerical examples. They will use precise function notation in their reasoning and discussion.

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Watch Out for These Misconceptions

• During Card Sort: Functions vs Relations, watch for students who group all relations with multiple outputs into the function pile without checking the one-output rule.

  During the Card Sort, give each pair red pens to mark any mappings that fail the one-output-per-input test. Require them to revisit those pairs and re-sort them into the relation pile, explaining their reasoning aloud to a partner.

• During Domain-Range Hunt, watch for students who assume all real numbers are allowed in the domain without checking for restrictions like division by zero or square roots of negatives.

  During the Domain-Range Hunt, have students highlight any numbers or operations in the scenario that might limit inputs. Ask them to write a sentence explaining why each restriction matters before finalizing their domain lists.

• During Mapping Diagram Construction, watch for students who list every possible output in the range even when some values aren’t actually achieved by the function.

  During Mapping Diagram Construction, ask students to trace each arrow and only list the outputs that appear in their diagram. Encourage them to cross out any predicted outputs that don’t actually occur in their mappings.

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Methods used in this brief

• Stations Rotation