Percentages in Context

Overview

In this 45-minute maths lesson, students connect percentages to real-life money examples (for example, 20% of $120) and learn to represent and compare percentage amounts as parts of a whole. The lesson also uses a science story about gravity, tides, and launching payloads to create meaningful percentage calculations for Year 5.

Learning intentions

• WALT use 100% to mean the complete whole when working with percentages.
• WALT represent percentage amounts by partitioning wholes into equal parts.
• WALT calculate and explain percentage amounts such as 20% of $120 using reasoning, not just procedures.
• WALT link percentages to their decimal and fraction equivalents for common percentages.

Success criteria

• I can explain why 100% represents the whole amount.
• I can show a percentage amount using a model (for example, a grid or bar) and match it to the correct value.
• I can calculate “p% of a quantity” (for example, 20% of $120) and explain my method clearly.
• I can check if my answer makes sense using estimation.

Curriculum links

• Number — VC2M5N04: students recognise 100% as the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to decimal and fraction equivalents.
• Number — using representations to support understanding of relative size (grids/arrays/bar models).
• Explaining reasoning and reasonableness of solutions (using estimation to check).

Lesson structure (45 minutes)

1. 0–5 min · Hook (science story + prompt). Teacher reads a short scenario: “A space agency budgets for fuel. A bonus cost is 20% of the base launch cost of $120.” Students think-pair-share: “What does 20% mean in this situation?”

2. 5–15 min · Direct teach (100% whole + modelling). Teacher models with a 10×10 grid (or 100-square). “100% is the whole. 20% means 20 squares out of 100.” Teacher guides students to:

• shade 20 squares to show 20% of 120,
• connect 20% to “20 out of 100” and to the decimal 0.2 and fraction 1/5 (as appropriate for this common percentage),
• show a quick calculation path: 0.2 × 120 = 24. Students practise on mini-grids with another example shown by teacher (for example, 50% of $120) while teacher circulates for correct modelling.

3. 15–25 min · Worked example (money context: 20% of $120). Teacher writes and explains step-by-step reasoning on the board:

• “20% means 0.2 (20 out of 100).”
• “0.2 of 120 is 24.”
• “So 20% of $120 is $24. Explain: I took 1/5 of $120 because 20% = 1/5.” Teacher links context: “Gravity keeps planets and moons in orbit; similarly, launch planning uses careful percentages. If fuel cost rises by 20%, how does that affect the total budget?” Students complete a “model then calculate” task for one new number pair (teacher provides: 20% of $180). They must use a grid/bar or fraction reasoning and then write a short explanation sentence.

4. 25–35 min · Guided practice (compare relative size). Teacher displays three percentage statements about a “payload leaving Earth” budget:

• A: 10% discount
• B: 20% extra cost
• C: 50% of the base cost Students work in pairs to decide which is greatest, and to calculate the missing value for one of the statements. They must justify using models or equivalences (for example, 50% = 1/2). Teacher checks that students understand relative size, not just the numbers.

5. 35–42 min · Independent check (reasonableness + written explanation). Students answer a short problem sheet item:

• “Find 20% of $120 and estimate using rounding to check your answer.” Teacher prompts estimation: “20% is close to 1/5, and 1/5 of $120 is about $24—does it match exactly?” Students write one sentence explaining why their estimate agrees.

6. 42–45 min · Exit ticket (quick formative assessment). Each student completes:

• “What does 100% represent?”
• “Calculate 20% of $60.” Teacher collects and scans for misconceptions (for example, treating 20% as 20 dollars rather than 20 out of 100).

Resources

• 10×10 grid / 100-square templates (paper or digital)
• Coloured pencils or markers
• Slide/board prompts with money contexts (include “$” amounts)
• Mini whiteboards and pens
• Simple fraction cards for common equivalents (for example, 1/2, 1/5)
• Estimation scratch paper
• Problem sheet with one worked-style question and one independent question

Assessment

• Teacher observation during grid shading: correct partitioning into hundredths and correct equivalence (20% = 0.2 = 1/5).
• Guided practice discussion: students justify which percentage is larger using relative size and models.
• Exit ticket: definition of 100% and calculation of 20% of $60.

Differentiation

• Support for students needing extra scaffolding:
• Provide partially completed 100-square grids with labels “100%” and “20%”.
• Sentence starters: “I know 20% means 20 out of 100, so …” and “My answer makes sense because …”.
• Use step-by-step choice cards: “Multiply by 0.2” or “Take 1/5”.
• Support for EAL learners:
• Keep language consistent: “whole”, “part”, “percent means out of 100”.
• Use visual models more than written explanation at first; then add short oral explanations.
• Extension for advanced learners:
• Ask for two different methods and a comparison: “Calculate 20% of $180 using a grid and using fractions; explain why both match.”
• Challenge: “Fuel cost increases by 20%, then you get a 10% discount on the new total. What is the final change compared to the original $120?”
• Dyslexia-friendly reading options:
• Provide the problem statements in a larger font and on one step per line.
• Offer an audio version of the scenario (teacher reads problems aloud; students follow on the page).
• Provide a simplified text version with key words highlighted (whole, percent, part, total, estimate).