Budgeting with Percentages

Overview

In this second lesson of the four-part unit Everyday Number Decisions, students use equivalent fractions, decimals and percentages to solve realistic shopping-budget problems. They build on prior work converting between representations, then apply proportional reasoning to calculate discounts, final prices and spending choices.

Learning intentions

• WALT apply fraction, decimal and percentage conversions to make budgeting decisions.
• WALT calculate a percentage discount and final cost.
• WALT organise calculations in a table or digital spreadsheet.
• WALT justify a spending choice using accurate mathematical evidence.

Success criteria

• I can show an amount as an equivalent fraction, decimal and percentage.
• I can calculate a percentage discount and subtract it from the original price.
• I can stay within a given budget.
• I can explain why my choice is sensible using labelled calculations, a table or a spoken explanation.

Curriculum links

• Number and Algebra — use proportional reasoning and mathematics to solve authentic problems.
• Number — connect fractions, decimals and percentages and apply them to money.
• Mathematics and Statistics — represent, communicate and justify mathematical thinking.
• Key competencies — thinking, managing self, and participating and contributing through collaborative decision-making.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Open with the budgeting hook and retrieval question and display: “A $60 jacket is 25% off. Is the discount $15 or $45? How do you know?” Students think independently, explain their estimate to a partner, and recall that 25% is equivalent to 0.25 and one-quarter.

2. 5–13 min · Explicit modelling. Use the worked discount examples to model a consistent process: identify the original price, convert the percentage to a decimal or fraction, calculate the discount, then subtract it from the original price. For example, 20% of $50 is 0.20 × 50 = $10, so the sale price is $40. Students annotate the matching fraction, decimal and percentage forms and solve one similar example on mini-whiteboards.

3. 13–17 min · Check for understanding. Show three short problems from the hinge questions: find 10% of $70, find 25% of $40, and calculate the final price of a $90 item at 30% off. Students hold up answers or explain their method. Address common errors, especially confusing the discount amount with the final cost or subtracting the percentage number rather than the money amount.

4. 17–34 min · Budget investigation. Distribute the tiered budgeting investigation and, where suitable, provide the Budgeting and Trade-off Scenario Cards for groups to select or compare a scenario. In pairs, students choose items within a stated budget, calculate discounts and final costs, and record each item’s original price, discount percentage, discount amount and final price in a table. They must show at least one fraction–decimal–percentage conversion and justify their final choices. The teacher conferences with groups, prompting: “What does this percentage represent?” and “How do you know you are still within budget?”

5. 34–41 min · Compare and communicate. Use the comparison and discussion prompts to invite selected pairs to present one decision. Students compare methods, check another group’s calculations and discuss whether the cheapest choice is always the best choice. If using a digital spreadsheet, students enter the prices and formulas, then check the displayed totals against an estimate.

6. 41–45 min · Plenary and exit check. Display the plenary prompt: “A $120 bike helmet is 15% off. What is the discount, final price and equivalent decimal?” Students complete the final section of the worksheet or give a spoken response. Collect responses to identify who can calculate independently and who needs further modelling in the next lesson.

Resources

• the complete budgeting slide deck
• the tiered budgeting investigation
• the Budgeting and Trade-off Scenario Cards
• Mini-whiteboards, pens and erasers
• Calculators for students who need them
• Hundred grids and fraction–decimal–percentage reference charts
• Devices with a spreadsheet tool, if available
• Projector or interactive whiteboard

Assessment

• Listen to partner explanations and check mini-whiteboard responses during modelling and the hinge questions.
• During group work, assess whether students identify the correct whole, calculate the discount amount, subtract accurately and remain within budget.
• Use the exit response to check conversion, discount and final-price understanding; note whether the justification is supported by calculations.

Differentiation

• Provide tiered budgets and prices: begin with 10%, 25% and 50% discounts, then offer less familiar percentages such as 15%, 20% or 30%.
• Support learners with one problem per section, highlighted prices and percentages, icons beside key information, a step-by-step calculation template, hundred grids, fraction strips or a calculator.
• Explicitly model multi-step problems and offer sentence starters such as “I chose ___ because…” and “The discount is ___, so the final cost is ___.”
• For dyslexia-friendly access, use a clear sans-serif font, uncluttered spacing, short instructions and read instructions aloud. Provide audio or text-to-speech access, permit calculator use, and accept a spoken explanation or labelled table instead of extended writing.
• Extend advanced learners by comparing two discount strategies, including successive discounts such as 20% off followed by 10% off. Students calculate both final prices and recommend the better option with evidence, explaining why successive discounts are not simply added together.