Financial Mathematics A: Earning, Saving and Spending Money Stage 5 · Year 10 · Unit of Work

Rationale

At a glance

  • What: the three parts of Financial mathematics A, which are earning money, simple interest and spending money.
  • Why: students are already starting to earn and spend, and these decisions need percentages and rates.
  • How: the main teaching choices in each part of the unit, each explained below.
Earning money (Lessons 1–3)

One driving questionRecurring charactersReal documentsWorked examples firstAssessment feeds forwardKey words taught explicitlyWorking Mathematically

Simple interest (Lessons 4–6)

Percentages to interestFamiliar contextWorked examples firstPaced graph workLinked representationsKey words with diagramsWorking MathematicallyErrors guide teaching

Spending money (Lessons 7–9)

Real financial decisionsGradual complexityWorked examplesContrasting offersAssessment informs teachingLiteracy supportTechnologyInclusion and closing case

What the unit covers

The unit teaches the three parts of the Stage 5 Financial mathematics A content, which are earning money, simple interest and spending money (NSW Education Standards Authority [NESA], 2022a).

Students solve problems with wages, penalty rates, commission, pay periods, leave loading, Pay-As-You-Go (PAYG) tax, simple interest, buying on terms, buy now pay later, and short-term loans.

Why it is important

Students are already earning. Financial mathematics is percentage and rate work in a setting students are about to meet. The Programme for International Student Assessment (PISA) 2022 financial literacy framework notes that "many 15-year-old students are also already engaged in some form of paid work outside school hours" (Organisation for Economic Co-operation and Development [OECD], 2023, Chapter 3, Education and work section). It lists "understanding payslips" as a typical task in this context (OECD, 2023, Chapter 3, Education and work section).

The content matches what the OECD expects. The same framework names the kinds of income taught in Lessons 1–3, including "salary, commission" (OECD, 2023, Chapter 3, Planning and managing finances section). It also expects students to "understand different ways of discussing income (such as hourly wage and gross or net annual income)" (OECD, 2023, Chapter 3, Planning and managing finances section).

It needs mathematics. The framework notes that "some financial decisions may require people to perform some basic calculation, such as percentages" (OECD, 2023, Chapter 3, The interaction of financial literacy with knowledge and skills in other domains section). This is why the content belongs in mathematics.

It leads to later study. Taxable income is "revisited and explored further in the taxation section of the Stage 6 Mathematics Standard syllabus" (NESA, 2022a, Financial mathematics A, Teaching advice section). NESA also links the content to using spreadsheets for wages, overtime, PAYG tax and net earnings.

Pedagogical approach

Earning money (Lessons 1–3)

One question runs through all three lessons

In the lessons. Lesson 1 asks "Which job pays the most?" and shows that it cannot be answered yet. Lesson 3 answers it with gross and net weekly pay. This gives students a reason to learn pay periods and tax, not just a list of skills.

Why. "Pays the most" is not yet clear. NESA's language guidance points out that in a comparison "the term 'better' can be interpreted in multiple ways" (NESA, 2022b, Hypothetical comparisons section). Students have to decide whether they mean per hour, per week or after tax before they can answer.

The same people come back

In the lessons. Ella the barista, Jess the phone salesperson and the office assistant from Lesson 1 reappear in Lessons 2 and 3, so each lesson starts from numbers students already know.

Why. This follows NESA's advice of "providing students with a problem they are familiar with before introducing more complex problems" (NESA, 2022b, Unpack and scaffold the use of language section).

Students check their work against real documents

In the lessons. In Lesson 2 students check $26.44 × 1.5 against the overtime rate printed in a Fair Work Ombudsman pay guide. In Lesson 3 they read the Australian Taxation Office (ATO) weekly tax table that employers use from 1 July 2026.

Why. The syllabus asks students to "investigate sources of published tables" (NESA, 2022a).

Each new idea is shown once in a fully worked example before students try it

In the lessons. Every step is written on the board as the class watches, and key questions ask why each step is done. Guided practice ("We do") then comes before independent practice ("You do").

Why. The Centre for Education Statistics and Evaluation (CESE) recommends that teachers "complete worked examples in 'real time', rather than showing students pre-prepared solutions or responses" (CESE, 2020, p. 11). It also places guided practice before independent practice.

Assessment information moves forward

In the lessons. The Lesson 1 diagnostic quiz is mapped to the skills Lessons 2 and 3 need. Each exit ticket is sorted by type of error, and the largest group decides the next starter.

Why. CESE advises teachers at the start of a unit to "use formative assessment to assess previously covered skills, concepts or content knowledge, so that lessons can be adjusted or paced to students' skills and knowledge" (CESE, 2020, p. 11). Wiliam (2011) argues that "for assessment to support learning, it must provide guidance about the next steps in instruction" (p. 13). The sorted exit tickets are how these lessons do that.

Key words are taught explicitly, with pictures

In the lessons. Terms such as commission, penalty rate, gross, net and tax-free threshold are new to most students. Each lesson's vocabulary list pairs the key terms with a photo or a diagram, and Lesson 3 builds a "pay words" list on the board as each term appears.

Why. NESA advises that "pre-teaching vocabulary reduces the cognitive load of reading a task" (NESA, 2022b, Explicitly teaching terminology section). It also advises that "as each word or phrase is introduced", teachers "show an image … and explain what it means in context" (NESA, 2022b, Explicitly teaching terminology section).

Working Mathematically is built into the content, not added on

In the lessons. Each Working Mathematically indicator is attached to a named activity. For example, in Lesson 2 students explain in a "because" sentence why Jayden's working is wrong. He added his 6 Saturday hours to his hourly pay instead of multiplying by them.

Why. NESA states that "the Working mathematically processes should be embedded within the concepts being taught" (NESA, 2023, Overarching Working mathematically outcome section).

Simple interest (Lessons 4–6)

Saving builds on percentage work

In the lessons. Lesson 4 opens with Ella's $1000 savings in a fictional account paying 5% p.a. Before any formula appears, students write 5% as a decimal and find 5% of $1000.

Why. The OECD framework quoted above connects percentages with financial literacy (OECD, 2023, Chapter 3, The interaction of financial literacy with knowledge and skills in other domains section). Students now interpret these calculations in a saving context.

Ella and the same rule come back

In the lessons. Ella, the barista from Lessons 1–3, is the saver in Lesson 4. The rule A = 2000 + 120n is graphed in Lesson 5 and interpreted again in Lesson 6.

Why. NESA recommends familiar problems before more complex ones (NESA, 2022b, Unpack and scaffold the use of language section), the advice quoted for Lessons 1–3. Reusing Ella and the same investment values lets students focus on the changing mathematical task.

Worked examples come before independent work

In the lessons. In Lesson 4 the teacher models M1 and M2 on the board, the class works W1–W4 together, and students then answer Y1–Y4 on their own.

Why. Rosenshine's (2012) Principles 4 and 5 support models and guided practice (pp. 15–16), including "modeling, guiding practice, and supervising independent practice" (p. 15). Teacher think-alouds and shared questions prepare students for the independent calculations.

Graphs are drawn in one lesson and interpreted in the next

In the lessons. Lesson 5 builds the first amount graph by hand, from formula to table to points. Lesson 6 starts from that same graph to explain the initial value and the gradient.

Why. CESE (2018) describes the part-whole approach in Strategy 1, which breaks a complex task into sub-tasks before combining them (p. 5). Here, Lesson 5 builds the graph with basic interpretation and Lesson 6 adds deeper interpretation.

Rule, table and graph are linked

In the lessons. In Lesson 6 pairs predict how changing the rate to 4%, 6% or 8% changes the table and graph, check in the spreadsheet, and verify one row by hand. They then match rules, tables and graphs.

Why. Ainsworth (2006, p. 189) identifies relational understanding, in which learners connect representations, within the constructing functions of the DeFT framework. Lessons 5 and 6 link A = P + Prn, a values table and a graph, showing P as the initial amount and Pr as the increase per year.

Key words are taught with diagrams

In the lessons. Principal, interest and total amount are shown on a labelled money bar in Lesson 4, and gradient on an annotated graph in Lesson 6.

Why. NESA recommends teaching vocabulary with visual support (NESA, 2022b, Explicitly teaching terminology section), the advice quoted for Lessons 1–3.

Working Mathematically is part of each task

In the lessons. Students generalise Ella's table to I = Prn (Lesson 4), check a missing rate by substitution (Lessons 5 and 6), and explain why simple-interest growth is linear (Lesson 6).

Why. Sentence frames, explanations and checks connect the Working mathematically processes, which NESA describes as embedded within the outcomes and content (NESA, 2023, Embedding the processes section).

Errors decide the next step

In the lessons. Exit tickets and independent work are sorted by type of error: rate, time, amount or interest, and base. The result chooses the opening retrieval for the next lesson. Lesson 6 ends with an independent 8-mark checkpoint: rule (1), table and graph (2), interpretation (2), missing rate and check (2), and linearity (1).

Why. Black and Wiliam (1998, pp. 7–8) define formative assessment through information used to modify teaching and learning. Mini-whiteboards and exit tickets guide the next step; for example, an answer of 5% = 0.5 prompts revisiting 5/100 = 0.05 before substitution.

Spending money (Lessons 7–9)

Curriculum and real financial reasoning

In Financial mathematics A, NESA (2022a) explicitly includes purchase terms, BNPL costs and short-term borrowing. OECD (2023, Chapter 3) defines financial literacy through using financial knowledge in decisions and separates identifying information, analysis and evaluation. Therefore students calculate complete costs and critique the information available for a decision, rather than treating the lesson as arithmetic alone.

Gradual introduction of complexity

Sweller et al. (2019, Introduction and Split-Attention Effect sections) explain that limited working memory can be burdened by unnecessary processing and separating information that must be integrated. We place offer terms beside labelled calculation rows and begin with fee-free plans before adding fee conditions. The progression is our application of the theory, not a sequence prescribed by the authors.

Worked examples and transfer

Renkl (2014, Section 4.1) explains that studying solutions is more productive when learners explain steps and compare examples. We ask why a deposit is counted once and how duration changes totals. The $900 worked model differs from the $1,200 independent comparison so students apply a structure rather than reproduce the model’s answer.

Comparisons that expose misunderstandings

Renkl (2014, Section 4.1) describes comparison as a route to understanding underlying principles. Students compare a lower monthly payment over a longer period with a higher payment over a shorter period, then justify the full-cost result. Brief, focused questions prevent the explanation demand from overwhelming the initial calculations, consistent with the qualification in that section.

Assessment that changes the next action

Black and Wiliam (2009, Section 2) explain formative assessment in terms of eliciting and interpreting evidence that informs subsequent instruction. Our simultaneous hinge response identifies whether to proceed or remodel a particular error, followed by a fresh check. AoL exit criteria in Lessons 7 and 8 separately record attained outcomes; that recorded evidence also informs next-lesson AfL feedback. An 80% pacing threshold is our planning choice, not a recommendation or validated mastery cutoff from the paper.

Language support and financial interpretation

OECD (2023, Chapter 3, Processes section) includes identifying relevant financial information and analysing and evaluating it. Students annotate “including today”, “per month” and “original amount borrowed” before calculating. Vocabulary and sentence frames support the interpretation and explanation required by those processes; the framework itself does not prescribe these classroom scaffolds.

Technology used to investigate a model

NESA's (2022a) outcome MAO-WM-01 includes connecting concepts, choosing techniques and communicating reasoning. We apply this to student-built spreadsheets: students check formulas against hand calculations, vary a fee or duration and explain a change. Completed teacher workbooks and visible formula snapshots make the activity and expected outcomes inspectable, while paper tables retain the reasoning demand.

Inclusion and the integrated close

Sweller et al. (2019, Worked Example Effect and Expertise Reversal Effect sections) discuss why support should vary with expertise. Labelled rows assist students who need structure; equal-cost and crossover problems extend those already fluent. OECD (2023, Chapter 3) connects financial knowledge with decisions in context. Our final case therefore joins weekly income, matured simple-interest savings and a purchase choice, using fictional circumstances so personal financial disclosure is unnecessary.

References