Exploring Functions

Unit: Algebra in Everyday Life

Lesson 8 of 30

Duration: 45 minutes

Class size: 20 students

Year level: 7-10 (students working between Year 2 and Year 7 levels)

Lesson Overview

Students will develop an understanding of functions and their representations through interactive, concrete, and real-life examples. This lesson breaks down the concept of functions into accessible parts with repetition and authentic connections designed for students with autism spectrum disorder, behavioural and mental health challenges. Visual supports, clear step-by-step instructions, and dyslexia-friendly materials will support comprehension. Advanced learners will have opportunities to extend thinking by identifying real-life functional relationships.

Learning Objectives (NSW Curriculum Aligned)

Understand the concept of a function as a rule that assigns each input exactly one output (AC9M7SP02 - Algebra Year 7 Level, adapted for lower levels)
Create simple tables of values and represent these as mappings or graphs showing the relationship between variables - Recognise everyday situations that can be modelled using functions - Develop initial skills to test and justify conjectures about relationships using digital tools or graphic organisers

Curriculum Link

NSW Mathematics Syllabus: Stage 4 (Years 7-8), focusing on the strand "Algebra" and topic "Functions and Graphs"
Achievement Standard focus: Students use algebraic expressions to represent situations and describe relationships between variables. They create tables of values and describe the effect of variation
This lesson is foundational, targeted to bridge gaps for students with learning difficulties while preparing for more complex symbolic work in higher years

Resources

Whiteboard and markers
Printed function mapping worksheets with visuals (dyslexia-friendly fonts such as OpenDyslexic or Comic Sans, high contrast colours)
Counters or physical objects (e.g. fruit shapes, toy cars) for hands-on activity
Graph paper with large grids
Tablets or computers with simple graphing/digital drawing tool (optional for digital representation)
Real-life examples pictures/cards (e.g., vending machine, time vs. distance tracking)

Lesson Breakdown

1. Introduction to Functions (10 minutes)

Begin with a simple verbal explanation: "A function is like a machine — when you put a number in, the machine is designed to give you one answer out."
Use physical objects to demonstrate this: present number cards as inputs, show corresponding output cards (e.g., input "2" produces "4" when doubled).
Emphasise the idea that for each input, there is only one output (Introduce 'rule' concept: doubling, adding 1, etc.).
Show a function as a 'mapping diagram' with arrows connecting inputs to outputs on the board, reinforcing the 'one input-one output' rule through visualisation.

2. Guided Activity: Create Your Own Function Table (15 minutes)

Provide students with a simple function rule such as "add 3" or "double the number."
Demonstrate filling out a table of inputs and outputs (e.g., input: 1, 2, 3; output: 4, 5, 6 or 2, 4, 6).
Students work in pairs with counters or objects to physically model the function: pick an input counter number and physically add or double it, placing the result as the output.
Worksheet prompt: "Draw arrows to show the function mapping," reinforce sequencing and organisation.
Circulate and assist, scaffold with sentence starters: "The input is __. The output is __ because we __."

3. Real-world Connection & Discussion (8 minutes)

Show pictures of real-life scenarios that use functional relationships:
Vending machine (you press one button, you get one snack)
Bus timetable (each time, the bus arrives at a particular stop)
Simple pay rate example (hours worked → money earned)
Invite students to describe in their own words how these are like functions.
Reinforce language: input, output, rule, one-to-one match.
Encourage linking their own experiences to these ideas (e.g., "When I put money in the vending machine...").

4. Dyslexia-Friendly Reading and Visual Supports (5 minutes)

Distribute simple function summary handout with:
Clear bold titles
Large, well-spaced text in dyslexia-friendly font
Visual diagrams of function mappings
Colour-coded steps for recognising functions
Read through key points aloud together as a class using choral reading for reinforcement.

5. Extension for Advanced Learners (5 minutes)

Challenge: Choose one real-life scenario and describe the function rule in words or symbols of their choice (e.g., "If input is x, output is x + 5").
Encourage making up their own function and testing it with classmates or digital tools.
Optional: Using graph paper, plot points from a function table to see if the line formed matches the pattern, introducing concept of graphing.

6. Assessment and Review (2 minutes)

Quick oral quiz: teacher calls out input, students reply with output according to the function rule learnt.
Check student worksheets for completion and ability to identify function mappings.
Praise effort and understanding, note students needing more reinforcement in future lessons.

Differentiation Strategies

Learner Type	Strategy
Students with Autism, Behavioural Challenges	Use clear, consistent routines; visual schedules for lesson flow; calm, predictable environment; provide movement breaks as needed. Use tangible objects to cement abstract ideas.
Students with Dyslexia	Use dyslexia-friendly fonts and colours; minimise text; incorporate oral explanations and repetition; allow answers in multiple formats (diagrams, oral responses).
Lower Ability Learners	Frequent use of manipulatives; one-on-one or small group support; repeat key concepts using multiple sensory modalities (visual, tactile, oral).
Advanced Learners	Provide extension questions; encourage exploration of function rules in symbolic notation; introduce simple graphing and algebraic description of functions.

Teacher Reflection Notes

Did students grasp the 'one input-one output' concept?
Were real-life connections effective in making abstract concepts relatable?
How well did students engage with physical modelling?
Modify pacing/repetition for next lessons based on observed comprehension.

This detailed lesson plan blends tangible, visual, and contextual learning tailored for students with diverse learning needs who require foundational reinforcement in algebraic thinking. The stepwise breakdown with classroom routines will foster success and confidence in exploring functions.

Teaching Instructions