National Curriculum Reference

Mathematics Programme of Study: Year 8 (Ages 12-13), Number - Ratio and Proportion

Use ratio notation, including reduction to simplest form
Divide a given quantity into two parts in a given part:part or part:whole ratio
Understand and use proportion as equality of ratios
Solve problems involving direct proportion using algebraic and graphical representations

Lesson Overview

Duration: 45 minutes
Class size: 30 students
Topic: Applying ratio and proportion to real-world contexts, including problem-solving with financial data

This lesson builds on Year 7 understanding of ratios and proportion, pushing into multi-step problems and connecting with real-world applications, notably banking and financial data. The idea is to simultaneously develop mathematical fluency, problem-solving, and critical thinking skills within authentic contexts.

Learning Objectives

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

Understand and use ratio notation in real-life contexts, reducing ratios to their simplest form (NC Maths Yr8)
Interpret and solve problems involving part:part and part:whole ratios
Apply direct proportion reasoning to solve financial problems involving banking data
Translate bank-related scenario data into ratio problems, promoting numeracy literacy
Develop confidence in explaining ratio/proportion solutions clearly and precisely

Success Criteria

Correctly express scenarios using ratio notation and simplify them
Accurately divide quantities according to given ratios
Solve direct proportion problems involving multi-step calculations
Contextualise solutions in a financial/banking scenario similar to the Mercury account example
Participate actively in discussions and group work demonstrating reasoning

Resources

Whiteboard and markers
Student exercise books
Printed copies of simplified banking data excerpt (adapted from mercury-bank-letter-8402.pdf), e.g., account opening dates, bank routing numbers as example numerals for ratio problems
Ratio problem worksheets specifically designed with banking-themed contexts
Calculators (optional)
Timer or stopwatch

Lesson Structure

1. Starter (5 minutes) — Ratio Warm-up

Pose a quick fire question: “If the bank has 12 female customers and 18 male customers, what is the ratio of female to male customers? Simplify it.”
Write student answers on the board using ratio notation e.g., 12:18 = 2:3
Discuss difference between part:part and part:whole ratios briefly

2. Introduction (10 minutes) — Understanding Ratios in Banking Data

Present an adapted version of banking data from the Mercury letter (e.g., dates, numbers in the account details) as a real-world source of numbers.
Ask: “How can we use these numbers in ratio or proportion problems?”
Show example: Account opened on October 6 (6/10), Mercury Bank details include 091311229 (9:13:11:22:9?), discuss simplifying and interpreting.
Emphasise importance of ratio notation in describing relationships between such numbers (e.g., routing numbers, days to opening date, etc.)

3. Main Activity (20 minutes) — Exploring Ratio and Proportion Problems

Part 1: Group Work (10 minutes)

Divide class into groups of 5 (6 groups total).
Each group receives a banking scenario worksheet with three ratio and proportion problems based on:
- Dividing a sum of money (e.g., £30,000) in a given part:part ratio from two accounts as described.
- Calculating what proportion of the bank customers opened accounts in October compared to the full year, expressing in simplest form.
- Determining direct proportion of transaction fees to amounts transferred, e.g., if fee is £2 per £100 transferred, how much fee for £4575 transferred?

Groups discuss and solve each problem collectively, recording answers and explanation steps.

Part 2: Class Discussion & Modelling (10 minutes)

Select 2-3 groups to share their solutions on board.
Model how to simplify ratios and solve proportion problems clearly, including use of algebraic methods for direct proportion (e.g., y = kx).
Clarify misconceptions, reinforce correct notation and simplification.

4. Plenary (7 minutes) — Reflect and Apply

Quick quiz: Pose 2 rapid questions verbally, e.g.:
- “If the bank's routing number digits 09 form one part and 13 another, what is their ratio reduced?”
- “If £10,000 was split in a 4:1 ratio between two company's accounts, how much money does each get?”
Students write answers on mini whiteboards or in books.
Discuss answers briefly.
Recap objectives and ask students to rate their confidence on ratio and proportion from 1–5.

Assessment and Feedback

Informal assessment through group discussions and sharing answers.
Observe student participation and reasoning in groups for understanding.
Plenary quick quiz checks retention and application skills.
Provide verbal and written feedback highlighting clarity of ratio notation and solving methods.

Differentiation

Provide simpler ratios or worked examples for lower-ability groups.
Challenge higher-ability groups with multi-step, algebraic ratio problems or inverse proportion problems.
Use scaffolding questions and prompts for those needing more support.

Cross-Curricular Links and Stretch

Financial Literacy: understanding basics of banking and interpreting official-looking documents like the Mercury bank letter enhances real-world numeracy skills.
Literacy: students practise precise mathematical language and clear explanation of problem-solving steps.
Critical Thinking: evaluating how abstract numbers relate to real-world situations.

Reflection for Teachers

This lesson uses authentic financial data to contextualise ratio and proportion, making maths relevant and engaging. Use the Mercury bank letter’s numeric details creatively—not to overwhelm but to spark curiosity about how maths is found everywhere, including banking! Encouraging student discussion and group problem-solving improves confidence with key numeric reasoning skills.

Ratio and Proportion

Teaching Instructions