Overview

Unit: Algebra Adventures Unlocked (Lesson 5 of 10)
Duration: 45 minutes
Class Size: 30 students
Age: Year 6 (ages 10-11)
Subject: Maths
National Curriculum Reference:

Year 6 Programme of Study - Mathematics – Number and Algebra
- Use simple formulae: solve problems involving formulae expressed in words
- Express missing number problems algebraically
- Substitute values into formulae
- Generate and describe linear number sequences

Learning Objectives

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

Understand what a formula is and where it is used.
Recognise and interpret simple formulae expressed in words and symbols.
Substitute numbers into formulae to calculate an answer.
Rearrange simple formulae (one-step) to find a missing value.

Curriculum Links

This lesson supports these statutory requirements from the National Curriculum for Year 6:

Solve problems involving the calculation of unknown quantities (algebraic expressions)
Use simple formulae expressed in words or symbols
Substitute numerical values into formulae
Understand the use of letters to represent variables in mathematical contexts

Resources

Whiteboard and pens
Individual mini-whiteboards and pens for students
Printed formula cards with worded and symbolic formulae (e.g. Perimeter: P = 2l + 2w)
Worksheets with substitution and simple rearrangement problems
Real-life objects (e.g. rectangular trays, boxes, for perimeter/area discussions)
“Mystery formula” envelopes (for starter activity)
Stopwatch or timer

Lesson Structure

1. Engage & Starter Activity (7 mins)

Begin by showing 3 “Mystery formula” envelopes (each with a card inside describing a simple formula, e.g. formula for perimeter, area of rectangle, calculating average speed).
In pairs, pupils predict what the envelope’s formula might be used for.
Share predictions with the class and reveal the content inside envelopes.
Explain that today they will "unlock" how to use formulae for various problems.

Purpose: Capture interest and connect formulae to familiar, real-life contexts (linking to reasoning and fluency).

2. Introduction to Formulae (10 mins)

Define: What is a formula? Use simple language: a way to write rules or steps for calculation using letters to stand for numbers.
Show formulae expressed in words and then in symbols (e.g. “Perimeter of a rectangle = 2 times length plus 2 times width” → P = 2l + 2w) displayed clearly on the board.
Demonstrate substitution with a simple example: If l = 3, w = 4, what is P?
Model working step-by-step on whiteboard, emphasising substitution and following order of operations.

Teacher Tip: Use consistent font colours or highlighting for variables and numbers to visually scaffold understanding of substitution.

3. Guided Practice in Pairs (10 mins)

Pupils work in pairs with formula cards and mini-whiteboards.
Given different values, they substitute and calculate answers for:
- Perimeter of rectangle (P = 2l + 2w)
- Area of triangle (A = ½ bh)
- Calculating total cost (C = p × q, where p = price per item, q = quantity)
Teacher circulates, asking probing questions to encourage reasoning about which value goes where.
Challenge: Give one missing value and one known total — can they use feedback to guess the missing number? (Introduce very simple rearrangement subtly.)

4. Paired Challenge: Simple Rearrangement (12 mins)

Introduce idea of rearranging formulae: What if we know P and w but don’t know l? How can we find it?
Scaffold with: P = 2l + 2w → 2l = P − 2w → l = (P − 2w)/2
Provide 2 or 3 examples for pupils to solve by rearranging one-step.
Encourage use of mini-whiteboards for trial and error and to build confidence.
Extension challenge: Show a word problem requiring this rearrangement (e.g. “A rectangle has perimeter 20cm and width 3cm. Find the length.”)

5. Group Reflect & Consolidate (5 mins)

Gather whole class.
Invite pairs to share how they worked out missing values using substitution and rearrangement.
Draw attention to the importance of formulae in everyday life and how algebra helps solve problems.
Emphasise the link to future maths topics like solving equations and formulae manipulation.

6. Plenary: Quick Quiz & Self-Assessment (1 min)

Use a slide or flashcards with quick “true or false” and “fill in the blank” questions related to the lesson’s learning objectives (e.g. “A formula can only use numbers - True or False?”, “To find the perimeter, we add...?")
Ask pupils to hold up thumbs up/down based on confidence with today’s material.
Collect anonymous colour-coded exit tickets (green/yellow/red) about how well they understood formulae.

Assessment & Differentiation

Formative assessment: Observations during pairing tasks, questioning during group work, mini-whiteboard responses.
Scaffolded support: Provide formula cards with examples and hints for pupils needing extra help.
Challenge: Extension problems involving two-step rearrangements or unfamiliar contexts (e.g. converting temperatures, simple speed-distance-time problems).
Encourage peer support and reasoning aloud for deeper understanding.

Cross-Curricular Links & Enrichment

Science link: Using formulae to calculate speed or density can be previewed.
Design & Technology: Formulae apply to measurements in building projects or materials.
English link: Clear use of language to describe formulae in words encourages precision in communication.

Teacher Reflection Prompts

Did pupils grasp the concept that formulae represent general rules, not just maths tricks?
Were pupils able to confidently substitute values into formulae?
How well did students engage with rearranging formulae to find missing values?
What adjustments can be made for lessons 6-10 in the unit based on today’s outcomes?

Notes to Teacher

Use positive reinforcement to build students' confidence with algebraic thinking. Consider using simple real objects alongside formulae to help visualise formula components and enhance conceptual understanding. An interactive approach keeps algebra fun and accessible at this early stage.

Formulae Foundations

Teaching Instructions