Using Algebra in Finance

Lesson Overview

This lesson will engage Year 7-10 students in exploring how algebra models financial situations, focusing on budgeting. It is lesson 12 of 30 in the unit "Algebra in Everyday Life." Students will solve simple algebraic equations related to income and expenses and create real-world budgeting models. This lesson aligns strongly with the NSW Mathematics Curriculum, supporting learners with varying readiness and needs, including students in a support unit.

NSW Curriculum Links

Mathematics Content Descriptions (Year 7-8 focus with support for lower levels)

ACMNA170 (Year 7): Use algebraic expressions to represent situations, describe relationships between variables from authentic data, and substitute values into formulas to find unknown values.
ACMNA188 (Year 8): Use mathematical modelling to solve practical problems involving ratios, percentages and financial contexts.
Represent and solve linear equations related to finances (budgeting) and interpret results.
Develop understanding of variables and how changes affect outcomes in a financial context, justifying choices of representation.

Relevant Achievement Standards

Students use algebraic expressions to represent financial scenarios (Year 7).
Solve problems involving rational numbers and percentages in applied contexts (Years 7-8).
Model and solve linear equations connected to budgeting (Years 7-8).

Learning Objectives

By the end of the 45-minute lesson, students will be able to:

Understand how algebraic expressions can model financial situations, such as income, expenses, and budgeting.
Create and solve simple linear algebraic equations linked to personal or household budgeting problems.
Interpret the solutions to algebraic expressions and equations in a financial context to make informed decisions.
Develop confidence using algebraic language and symbols when discussing money management.
Recognise the importance of budgeting and planning finances.

Materials Needed

Whiteboard and markers
Student worksheet with budgeting algebra problems (with scaffolded prompts)
Manipulatives or cards showing income/expense items (optional for tactile learners)
Calculator and graph paper (optional)
Computers/tablets with spreadsheet software (extension activity)
Dyslexia-friendly font handouts and colour-coded formula sheets

Lesson Structure (45 minutes)

1. Introduction & Engagement (5 minutes)

Begin with a short, relatable discussion: "What is a budget? Why do people need to manage money?"
Show a simple example with a monthly income and a list of expenses.
Introduce the idea that algebra is a "tool" to help us plan and understand these finances better by using symbols to represent unknowns (e.g., saving money).

Teacher Tip: Use simple, concrete terms and visuals. Avoid rushing. Reinforce vocabulary like "income," "expense," "variable," and "equation."

2. Concept Exploration & Modelling (10 minutes)

Present a real-world scenario:

"Anna earns $500 a week. She spends $x on food, $100 on transport, and saves $50. How much does she spend on food if she balances her budget?"

Write the algebraic expression: 500 = x + 100 + 50
Guide students to isolate x: x = 500 - 100 - 50
Calculate x and interpret the solution meaning.
Use a step-by-step approach: break down how to rearrange the equation and substitute known values.
Allow students to suggest other budgeting scenarios to create algebraic expressions.

Differentiation:

For students requiring more support, use number lines or blocks to represent positive and negative amounts.
For more advanced learners, introduce multi-step expressions or variables for unknown income or multiple expenses.

3. Guided Practice (15 minutes)

Distribute worksheets with problems like:
Calculate savings if given income and expenses, where one expense is unknown.
Model a scenario with weekly allowance, spending, and saving.
Create algebraic expressions from word problems related to budgeting.
Teacher circulates to provide one-on-one support, clarifying steps, and rephrasing problems in accessible language.

Dyslexia-Friendly Strategies:

Provide worksheets in dyslexia-friendly font with clear spacing.
Colour-code terms and numerical values (e.g., blue for income, red for expenses).
Use bullet points and simple headings.

4. Independent or Pair Activity (10 minutes)

Students create their own budget problem involving an algebraic expression (e.g., "I want to save $100, I earn $y per week, and spend $60 on transport, $30 on food. How much can I spend on entertainment?").
Pairs share and solve each other's problems.

Extension for Advanced Learners:

Use spreadsheet software or graphing tools to input variables and model the budget dynamically, adjusting values and seeing effects on savings.

5. Reflection and Assessment (5 minutes)

Class discussion: "How did algebra help us understand budgeting?"
Quick verbal quiz: Ask volunteers to explain how they solved for the unknown variable in one scenario.
Collect worksheets to assess individual understanding.

Differentiation Strategies

For students with autism, behaviour, and mental health needs:
Use clear structure and predictable routine in the lesson.
Provide visual supports and concrete examples.
Allow movement breaks or sensory tools as needed.
Use explicit, step-by-step instructions with repetition.
For diverse learning levels:
Scaffold tasks with partially completed examples.
Offer manipulatives or visual aids for conceptual understanding.
Adjust difficulty by varying complexity of expressions.
For dyslexic learners:
Use dyslexia-friendly fonts (e.g., OpenDyslexic) and ample spacing on printouts.
Incorporate colour coding and icons.
Read instructions aloud or use audio support.
For advanced learners:
Challenge with multi-step problems or introduce budgeting involving percentages or rate of change.
Encourage exploration of digital financial tools or simple formula modelling in spreadsheets.

Assessment

Observe students’ ability to form and solve basic algebra equations related to budgeting.
Review student worksheets for correct solutions and reasoning.
Monitor participation and explanation during peer sharing.
Use verbal questioning to confirm conceptual understanding.

Teacher Reflection Notes

Note any students struggling with the abstract nature of algebra and plan additional revisiting with concrete manipulatives.
Adjust pacing depending on how well the class engages with financial contexts.
Incorporate more authentic, student-interest based budgeting scenarios in following lessons.
Connect this lesson with the school's Careers and Transition services by discussing budgeting for life post-school, linking maths with real-world job readiness and independence skills.

This lesson plan integrates practical life skills using algebra, designed for a diverse Year 7-10 classroom, promoting both mathematical understanding and essential financial literacy, in line with NSW curriculum standards for mathematics and economic awareness.

Teaching Instructions