Growing Quantities

Overview

In this 45-minute lesson, students investigate percentage increases in familiar contexts, including prices and populations. They build on prior learning about fractions, decimals and percentages, comparing an original amount with a new amount and explaining the size of the change.

Learning intentions

• WALT find the amount of a percentage increase.
• WALT calculate a new value after a percentage increase.
• WALT compare original and new values using mathematical language.
• WALT explain whether an answer is reasonable in an everyday context.

Success criteria

• I can identify the original value and the percentage increase.
• I can find the increase and add it to the original value.
• I can check that my answer is greater than the original value.
• I can explain the change using numbers, words or a diagram.

Curriculum links

• Mathematics and Statistics — proportional reasoning involving fractions, decimals and percentages.
• Mathematics and Statistics — solving and communicating solutions in everyday contexts.
• Mathematics and Statistics — using representations, estimation and reasoning to check whether answers are sensible.
• Mathsteasers — higher-order thinking questions that challenge learners to deepen understanding and communicate mathematical reasoning.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Display a supermarket price changing from $40 to $50 using the price-change opening slide. Ask, “Has the price increased by 10%, 20% or 25%?” Students estimate independently, then justify their choice to a partner; accept different methods without confirming the answer immediately.

2. 5–13 min · Explicit teaching. Use the percentage-increase teaching slides to model a consistent process: identify the original amount, calculate the percentage increase, then add the increase to the original. For example, a $40 item increasing by 25% has an increase of $10 because 25% of $40 is $10; the new price is $50. Connect 25% to one quarter and 10% to one tenth. Students annotate the steps on the percentage-increase practice sheet and explain why the new amount must be greater.

3. 13–18 min · Guided examples. Reveal two examples on the guided-practice slides: a $60 jacket increasing by 10%, and a town population of 2,000 increasing by 5%. Solve the first together using a percentage bar or known fraction, then have students solve the second on mini-whiteboards. Check answers and ask, “What was the increase? What is the new value? How do you know it is reasonable?”

4. 18–32 min · Pair problem solving. Distribute the percentage-increase practice sheet to pairs. Students solve everyday problems involving prices, populations and quantities, recording the original value, increase, new value and an explanation. Encourage more than one method where possible, such as finding 10% then adjusting, using a fraction, or converting to a decimal. Circulate and ask, “What does the percentage refer to?” and “Have you added the increase to the correct amount?”

5. 32–40 min · Reasoning and discussion. Show the comparison prompts on the reasoning-and-discussion slides. Pairs compare statements such as “A $20 item increasing by 50% costs $30” and “An increase from 80 to 100 is a 20% increase.” Students decide whether each statement is correct, incorrect or needs more information, then explain their reasoning. Invite selected pairs to share different representations and address the common error of calculating the percentage of the new value instead of the original value.

6. 40–45 min · Exit check and reflection. Students complete the final question on the percentage-increase practice sheet: “A school roll of 400 students increases by 15%. What is the increase and the new roll? Explain your method.” Use the plenary slide for a final sentence stem: “The original value matters because…”. Collect responses as students leave.

Resources

• the percentage-increase slide deck
• the percentage-increase practice sheet
• Mini-whiteboards and pens
• Calculators for checking, if appropriate
• Projector or interactive display
• Pencils, rulers and highlighters
• Fraction or percentage bars drawn on the board

Assessment

• Listen to partner explanations during the hook and guided examples, noting whether students identify the original value correctly.
• Check mini-whiteboard responses and question pairs about their choice of method, calculation and reasonableness check.
• Use the exit question to identify students who can calculate both the increase and the new value, and those who need further support with percentage relationships.

Differentiation

• Support students with a percentage bar, a worked example, a step-by-step checklist and sentence starters such as “The original amount is…” and “The increase is…”.
• Allow students to find 10% first and build other percentages from it; pair students strategically and provide a calculator only for checking, not replacing reasoning.
• Use accessible contexts, read questions aloud and clarify terms such as original, increase, population and new value for English language learners and students needing language support.
• Challenge confident students to compare two different percentage increases, explain why the same percentage change produces different numerical increases, or create a problem with a particular new value.