Creating Functions

Year Levels

Targeted at Year 7 to 10 students working at levels from Year 2 to Year 7, specifically supportive for learners with autism, behaviour and mental health issues.

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Unit Context

Unit: Algebra in Everyday Life Lesson: 15 of 30 Title: Creating Functions from Context Duration: 45 minutes Class size: 20 students

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NSW Curriculum Alignment

Outcomes and Content Descriptions

Aligned mainly to the following NSW Mathematics Syllabus outcomes, particularly focusing on algebraic expressions and creating functions for Years 7-10:

• AC9M7Algebra04: Students create and interpret simple algebraic expressions and formulas from real-life contexts.
• AC9M8Algebra05: Students use tables, graphs, and algebraic notation to represent relationships between variables.
• AC9M9Algebra06: Students develop functions from real-world scenarios and describe those using algebraic expressions and graphs.
• AC9M10Algebra09: Students model and solve problems involving linear and non-linear functions in applied contexts.

Achievement standards emphasize students’ abilities to create tables of values related to algebraic formulas, represent relationships between variables, and interpret and solve real-world problems using algebraic thinking.

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Learning Objectives

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

1. Understand the term "function" as a relationship between variables in everyday contexts.
2. Identify independent and dependent variables from a simple, authentic situation.
3. Develop simple algebraic functions from a given real-world context.
4. Demonstrate understanding of creating tables of values to represent functions.
5. Use substitution to verify function outputs for given inputs.
6. Begin graphing these functions with teacher support or use digital tools where appropriate.

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Key Vocabulary

• Variable
• Function
• Independent variable
• Dependent variable
• Algebraic expression
• Input-output
• Table of values

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Materials Needed

• Whiteboard and markers
• Printed worksheets with real-world problems (differentiated versions)
• Graph paper or digital graphing tools (optional)
• Visual aids with diagrams to support dyslexic learners
• Manipulatives or counters for modelling functions (concrete examples)
• Calculators (if needed)

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Lesson Breakdown

1. Warm-up and Introduction (8 minutes)

• Activity: Use a simple real-world example, such as "calculating total cost when buying multiple ice-creams where each ice-cream costs $3".
• Discussion:
• Identify the quantities in the scenario (number of ice-creams as input, total cost as output).
• Introduce vocabulary: independent variable (number of ice-creams), dependent variable (total cost).
• Visual Support: Use picture cards or diagrams for clearer understanding.
• Differentiation: For students needing more support, use physical counters to represent quantities.

2. Guided Exploration – Creating Functions (12 minutes)

• Teacher-led discussion:
• Write the rule: total cost = 3 × number of ice-creams.
• Represent this as an algebraic expression: C = 3n.
• Activity:
• Together, create a table of values for n = 1 to 5, showing corresponding costs.
• Discuss the relationship and fill the table collaboratively.
• Scaffolding:
• Provide partially completed tables for lower-level students.
• For higher-level students, extend to other contexts, e.g., calculating distance travelled at a constant speed.

3. Independent or Paired Practice (15 minutes)

• Activity:
• Students work in pairs or individually on simple function creation task cards with contexts relevant to their interests (e.g., earning pocket money per hour worked, or recipe ingredient quantities).
• Tasks include:
• Identifying variables
• Writing algebraic expressions based on the context
• Completing tables of values
• Substituting input values to verify outputs
• Differentiation:
• Provide reading material with dyslexia-friendly font and layout.
• Offer sentence starters and formula scaffolds for students with limited algebra background.
• Advanced learners receive challenges such as creating functions with two variables or exploring simple nonlinear functions.

4. Group Sharing and Reflection (7 minutes)

• Invite pairs to share one function they created and explain the variables and relationship.
• Encourage the use of proper vocabulary.
• Teacher models feedback with specific praise and clarification.
• Clarify any misconceptions and reinforce learning points.

5. Wrap-up and Formative Assessment (3 minutes)

• Quick oral quiz or flashcards to assess understanding of key terms and concepts.
• Ask a simple input-output question to the class and have students write down or say the corresponding output.
• Provide praise and set a simple goal for next lesson.

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Differentiation Strategies

• For diverse learners including autism spectrum and mental health issues:
• Break tasks into clear, manageable steps.
• Use visual supports and hands-on materials.
• Repeat and paraphrase instructions.
• Allow frequent breaks or sensory tools if needed.
• For students with dyslexia:
• Provide dyslexia-friendly reading materials.
• Use clear fonts, lots of spacing, and avoid clutter.
• Use verbal instructions and visual cues.
• For advanced learners:
• Provide tasks involving multiple variables.
• Introduce piecewise or step functions.
• Allow digital exploration using simple graphing software or apps.
• English as an Additional Language (EAL/D):
• Use clear, simple language.
• Pair with peer mentors.
• Use multilingual glossaries if appropriate.

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Extension Activities

• Challenge students to find or imagine their own situations that can be modelled by an algebraic function (e.g., smartphone data plans, taxi fares).
• Introduce simple graphing on Cartesian planes for these functions.
• Explore how changing the formula (e.g., cost per ice-cream) affects the table and function.
• Use digital tools to experiment with function creation and graphing interactively.

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Cross-Curricular Connections

• Careers and Transition: Discuss how functions can model wages, budgets, or scoring systems for jobs students might pursue post-school.
• Social-Emotional Learning: Emphasise respectful collaboration and communication during paired/group work.
• Real-Life Skills: Connecting maths with everyday life encourages relevance and motivation.

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Assessment

Formative assessment through:

• Observation during activities and discussions.
• Checking completed tables and algebraic expressions.
• Quick oral or written checks for understanding.
• Feedback on ability to describe relationships in own words.

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This lesson plan fosters understanding of algebraic functions grounded in meaningful, supportive contexts tailored for diverse learners, aligned with NSW Curriculum requirements for Years 7 to 10, while acknowledging student needs and potential learning challenges. It blends concrete examples, visual aids, peer collaboration, and adaptable tasks to create an inclusive and engaging learning environment.