Calculating Percentages

Overview

This 45-minute lesson is designed for a Year 7 student to build confidence and fluency in calculating percentages of whole numbers, aligned with the National Curriculum for England mathematics standards. Students will engage with concrete examples, visual models, and word problems to connect percentages with fractions and decimals before applying their skills to real-life contexts.

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National Curriculum Links

Number – Fractions (KS3 to build on Y7 expectations):

• Solve problems involving the calculation of percentages [National Curriculum, Mathematics Programmes of Study, Year 7]
• Use knowledge of percentages to solve problems, including those involving percentage increase and decrease, and to interpret fractions and decimals as percentages

Key Stage 3 Programmes of Study - Maths (Years 7–9):

• Calculate exactly a simple fraction of a quantity and find a quantity given a simple fraction
• Use the language of ‘percentage’ and interpret percentages as a fraction or a decimal, and convert between these representations

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Learning Objectives

By the end of the lesson, the student will be able to:

• Calculate a given percentage of a whole number using a variety of strategies
• Solve practical word problems involving percentages
• Understand the relationships between fractions, decimals, and percentages in the context of whole numbers

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Equipment and Resources

• Whiteboard and markers
• Student workbook and pen
• Percentage calculation visual aids (e.g., 100 square grids)
• Calculator (optional, to check work)
• Word problem worksheet tailored to real-life contexts (provided)
• Timer or clock

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Lesson Structure

Starter (5 minutes)

• Activity: Mental recall of equivalent fractions, decimals, and percentages (e.g., 1/4 = 25%, 0.5 = 50%)
• Purpose: Reinforce prior understanding of fractions and percentages, activating prior knowledge.

Introduction (10 minutes)

• Teacher Explanation: Demonstrate calculation of percentages of whole numbers using three methods:
  • Using fractions (e.g., 25% = 1/4, find 1/4 of 80)
  • Converting percentages to decimals and multiplying (e.g., 25% = 0.25, 0.25 × 80)
  • Using unitary method by finding 1% first (e.g., 1% of 80 then multiply by 25)
• Visuals: Show how to use a 100-square grid to visually represent percentages of whole numbers.

Main Activity (20 minutes)

• Task 1: Calculation practice with step-by-step guided questions:

  1. Find 20% of 150
  2. What is 15% of 200?
  3. Calculate 5% of 360

• Task 2: Word problems involving real-world contexts to enhance application skills:

  • Example: A jacket costs £80 and is on sale for 25% off. How much discount will you get?
  • Another: A school has 120 students. If 30% are girls, how many girls are there?

• Encourage the student to explain their reasoning aloud to deepen understanding.

• Provide hints through questioning rather than answers to foster independent thinking.

Plenary (5 minutes)

• Recap key points - ask the student to verbalise the process developed to find percentages of whole numbers.
• Quick quiz: Write two percentage problems on the spot to check understanding.
• Discuss any errors or misconceptions calmly and provide strategies for improvement.

Extension/Challenge (optional for fast finishers)

• Introduce reverse percentages (e.g., “If 25% of a number is 40, what is the whole number?”) to encourage deeper thinking and preparation for next lessons in the unit.

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Assessment

• Formative: Observation during main activity, student explanations, and calculation accuracy.
• Summative: Completion and correctness of word problem worksheet submitted post-lesson or reviewed at home.

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Differentiation

• Support: Use more visuals, concrete materials (e.g., counters for percentages), and guided questions.
• Challenge: Increase complexity of word problems; introduce decimal percentages or combined percentage change problems.

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Reflection Points for Teacher

• Was the student able to move flexibly between fractions, decimals, and percentages?
• Did the word problems help bridge maths skills with real-life contexts?
• How well did the student apply mental calculation strategies vs. calculator use?
• How might this lesson inform personalised intervention for stronger foundational skills or enrichment?

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Notes for Next Lessons

Build on this lesson by exploring percentage increase and decrease in Lesson 5, incorporating real-world scenarios such as price rises, discounts, and data interpretation to deepen problem-solving skills.

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Thank you for your great work supporting this student to master percentages!