Plan differentiated instruction around one topic

Introduction

The RAFT technique lets students express the same topic creatively through different combinations of role, audience, format and topic.

What is RAFT?

RAFT (Role, Audience, Format, Topic) is a differentiated instruction technique that develops students' critical thinking and creativity.

RAFT Tablosu

Task cards

1. Political Caricaturist in Regency London

Task description

Create a satirical political cartoon illustrating Napoleon's blockade of British trade (the Continental System) following the Battle of Trafalgar. Include visual symbolism, speech bubbles, and a written commentary explaining how your source's provenance reflects contemporary British anxieties rather than a single objective truth.

2. Revisionist Historian

Task description

Draft a three-part lecture transcript comparing the traditional Whig interpretation of the Glorious Revolution (focusing on the Bill of Rights and parliamentary liberty) against modern revisionist views. Highlight why historical interpretations change over time and analyse whether the settlement genuinely redistributed power.

3. Abolitionist Campaigner

Task description

Write a formal petition citing historical evidence such as the Zong massacre and Olaudah Equiano's testimony to demand the total abolition of slavery. Clarify the vital distinction that the 1807 Slave Trade Act abolished the trade rather than freeing all enslaved people across the British Empire.

4. Merchant in Nineteenth-Century Bengal

Task description

Compose a detailed letter outlining the consequences of the East India Company's increasing territorial control and escalating taxation across the early nineteenth century. Contrast the company's private commercial interests with the governance and living conditions of the local population.

5. Jamaican Labourer in 1866

Task description

Write an eye-witness testimony examining the systemic poverty and disenfranchisement that led to the 1865 Morant Bay uprising. Evaluate whether the subsequent direct Crown colony reforms enacted under Governor Grant meaningfully resolved deep-rooted economic hardship for Black Jamaicans.

Rehber

Role

The identity or perspective the student takes on

Examples: Journalist, writer, scientist, artist, historian, inventor, environmental activist

Audience

The audience the student addresses

Examples: Classmates, family, a jury, the government, future generations, aliens, cartoon heroes

Format (Format)

The form of expression or presentation the student uses

Examples: Article, speech, poster, video, song, diary, interview, play, leaflet

Topic

The main theme or content linked to the unit's learning outcome

Examples: Topics based on the lesson's learning outcomes and blended with students' interests

Implementation tips

Give students choices so they can use their own strengths

Offer a range of formats that suit different learning styles

Set the assessment criteria in advance and share them

Give students the chance to share their work with the class

To assess what students produce in this RAFT activity, you can build custom rubrics with the Rubric Generator, which prepares detailed assessment tools from the criteria you set.

Introduction

This lesson uses Bernice McCarthy's 4MAT model to guide learners through algebraic notation, rearranging formulae, and linking algebraic equations directly to linear graphs across 8 structured learning steps.

Learning objectives

• Substitute numerical values into formulae and expressions, and rearrange formulae to change the subject using inverse operations.

• Factorise single and quadratic expressions and simplify expressions by expanding brackets and collecting like terms.

• Plot and interpret linear graphs in the form y = mx + c, identifying the gradient and y-intercept algebraically and graphically.

4MAT learning styles (with metaphors)

Type 1: Creative Learner

- Seeks purpose and personal relevance

- Thrives in collaborative discussions and reflective thinking

- Asks 'Why do I need to know this?'

Type 2: Analytic Learner

- Focuses on formal structure, precise notation, and logical progression

- Enjoys teacher-led instruction and detailed conceptual analysis

- Asks 'What are the exact rules and definitions?'

Type 3: Common Sense Learner

- Prefers guided practice, manipulation of expressions, and algorithmic checks

- Needs to see how theoretical formulas operate in practical calculations

- Asks 'How does this procedure work in practice?'

Type 4: Dynamic Learner

- Enjoys open-ended tasks, finding alternative methods, and peer teaching

- Takes intellectual risks and challenges assumptions

- Asks 'What if we alter the parameters or constraints?'

4MAT 8-step lesson plan

1. Connect and Motivate

[Why] [Understand]

Learning style: Creative Learner

Ana Soru: Why do we use algebraic formulas and coordinate graphs to describe real-world rates and relationships?

Aim: Engage learners by connecting formula rearrangement and graphs to practical pricing and travel scenarios.

Activities

The Smartphone Tariff Dilemma

Students explore two mobile phone contracts represented as cost formulas and visual line graphs to evaluate which option is best depending on monthly data usage.

- Display two real-life tariff scenarios: Tariff A (£10 flat fee + £2 per GB) and Tariff B (£20 flat fee + £0.50 per GB).

- Ask students to quickly discuss in pairs which tariff is better for a light user versus a heavy user.

- Prompt students to think about how to write each scenario as a formula and sketch it visually.

Real-life connection: Comparing consumer contracts, subscription services, and utility bills using linear pricing models.

Teacher role: Facilitator and motivator; poses open questions linking real life to algebra.

Student role: Active contributor; discusses real-world cost comparisons and shares intuition.

Materials: Whiteboard, Starter scenario slides

2. Analyse and Reflect

[Why] [Analyse]

Learning style: Creative Learner

Ana Soru: How do fixed values and varying rates change both an algebraic formula and its visual representation?

Aim: Analyse the structural components of linear relationships and distinguish between variables, coefficients, and constants.

Activities

Dissecting the Tariff Graph

Learners examine the plotted lines of the mobile tariffs on a coordinate grid and pinpoint where the lines start and how steep they climb.

- Show a graph with both tariff lines plotted across the positive quadrant.

- Ask pupils to identify what the y-intercept represents in terms of money.

- Ask pupils to explain why the line with the higher rate per GB is steeper.

Real-life connection: Interpreting graphs in financial contexts and understanding fixed costs vs variable costs.

Teacher role: Observer and discussion moderator; guides students to link steepness with rate and intercept with initial cost.

Student role: Reflective thinker; connects visual graph features (steepness, start point) to real-world quantities.

Materials: Coordinate grid display, Mini whiteboards

3. Conceptualise and Classify

[What] [Understand]

Learning style: Analytic Learner

Ana Soru: What is the precise mathematical vocabulary for algebraic terms, expressions, equations, and linear forms?

Aim: Define and classify terms, expressions, equations, identities, and the standard straight-line equation y = mx + c.

Activities

Algebraic Vocabulary and Graph Structure Matrix

Students systematically classify mathematical statements into expressions, equations, formulas, and identities, while linking y = mx + c to gradient m and y-intercept c.

- Introduce definitions of term, factor, expression, equation, formula, and identity.

- Present 4 mathematical statements (e.g., 2x + 3y, C = 2x + 10, 2(x + 3) = 2x + 6, 4x - 5 = 11) and have students classify each.

- Map y = mx + c directly to the components: m = gradient (rise/run), c = y-intercept (0, c).

Real-life connection: Standardised scientific and engineering notation where variables and constants define physical laws.

Teacher role: Instructor and definer; provides rigorous definitions and standard mathematical notation.

Student role: Note taker and conceptual analyser; organises definitions and identifies differences between equations and identities.

Materials: Vocabulary reference slide, Student notebooks

4. Direct Instruction and Manipulation Rules

[What] [Apply]

Learning style: Analytic Learner

Ana Soru: What systematic algebraic steps are required to rearrange formulae and factorise expressions accurately?

Aim: Demonstrate step-by-step rearrangement of formulae to change the subject and factorisation of single and quadratic expressions.

Activities

Mastering Rearrangement and Factorisation

Teacher models the formal steps to rearrange multi-step linear formulae (including where the subject appears once or in brackets) and factorise expressions.

- Model rearranging y = mx + c to make x the subject: y - c = mx, then x = (y - c)/m.

- Emphasise inverse operations in reverse order: subtract c first, then divide by m (highlighting why values do not simply 'swap').

- Demonstrate fully factorising 7y² - 14y into 7y(y - 2) by identifying the highest common factor.

- Show how to find the gradient from two points (x1, y1) and (x2, y2) using (y2 - y1) / (x2 - x1).

Real-life connection: Rearranging physics formulas (e.g., v = u + at rearranged for time t or acceleration a).

Teacher role: Expert demonstrator; models algebraic balance method and addresses common procedural misconceptions.

Student role: Attentive learner; follows structured worked examples and records key algorithmic rules.

Materials: Worked example sheets, Interactive board

5. Guided Practice and Problem Solving

[How] [Apply]

Learning style: Common Sense Learner

Ana Soru: How do we apply rearrangement and substitution techniques to solve algebraic and coordinate problems?

Aim: Execute accurate substitutions, formula rearrangements, and linear graph plotting through structured practice tasks.

Activities

Targeted Skills Practice Carousel

Pupils work through a set of scaffolded practice problems covering substitution, rearranging subjects, factorising, and identifying line equations.

- Distribute a three-tiered worksheet: Tier 1 (Substitution & Basic Factorising), Tier 2 (Rearranging Formulae), Tier 3 (Determining y = mx + c and plotting).

- Pupils complete questions independently: e.g., 'Make a the subject of (b + c)/3 = a + d', 'Fully factorise 9x² - 18x', 'Find the equation of the line passing through (0, 4) and (2, 10)'.

- Teacher circulates with green/red marking pens to provide immediate feedback on balance methods.

Real-life connection: Calculating fuel consumption rates and converting units between metric and imperial using conversion formulas.

Teacher role: Facilitator and coach; checks individual working, corrects notation errors, and scaffolds struggling pupils.

Student role: Problem solver; applies standard algorithms carefully, showing all intermediate working steps.

Materials: Tiered practice worksheets, Calculators, Grid paper

6. Interactive Diagnostic and Common Errors Check

[How] [Evaluate]

Learning style: Common Sense Learner

Ana Soru: How can we diagnose and correct common algebraic and graphical misconceptions?

Aim: Critique non-examples and identify subtle errors in formula rearrangement and coordinate substitutions.

Activities

Spot the Flaw: Maths Crime Scene

Students inspect four worked solutions that contain deliberate classic misconceptions, identify the exact error, and write the corrected version.

- Display 3 flawed student workings: 1) 'Rearrange 2x + 8y = 34 for y: y = (34 - 2x) -> forgotten division by 8'; 2) 'Line through (0, 3) with gradient 4 written as y = 3x + 4'; 3) 'Factorise 6x² - 12x = 6(x² - 2x)'.

- Pupils use mini whiteboards to hold up the error number and write the single step that fixes the solution.

- Conduct a rapid whole-class check and review.

Real-life connection: Quality assurance and auditing calculations in construction and finance to prevent costly mistakes.

Teacher role: Challenger and diagnostic evaluator; prompts pupils to justify why a step is mathematically invalid.

Student role: Analytical evaluator; spots algebraic errors and provides mathematically sound corrections.

Materials: Mini whiteboards and dry-wipe markers, Misconception challenge cards

7. Create and Formulate

[What If] [Create]

Learning style: Dynamic Learner

Ana Soru: What if you design your own multi-step algebraic rule and translate it into a graphical puzzle for a peer?

Aim: Synthesise algebra and graphing by constructing an original linear problem with hidden parameters.

Activities

Linear Function and Formula Creator

In pairs, students design a contextual formula (e.g., taxi fare, heating cost, or gym membership), express it algebraically, rearrange it for a secondary variable, and plot the corresponding line graph.

- Students invent a real-world scenario with a fixed cost c and a rate per unit m.

- Write the formula: Total Cost = mx + c.

- Rearrange the formula to make x (the quantity/units) the subject.

- Plot the line on a small coordinate grid and formulate two challenge questions (e.g., 'If the total cost is £28, how many units were used?').

Real-life connection: Designing business models and pricing structures for start-up ventures.

Teacher role: Advisor and consultant; encourages creative real-world scenarios and checks algebraic consistency.

Student role: Creator and mathematical author; synthesises formula rearrangement and graphical representation into an original challenge.

Materials: Task template cards with mini coordinate grids, Rulers and coloured pens

8. Share and Peer Teach

[What If] [Evaluate]

Learning style: Dynamic Learner

Ana Soru: How effectively can you explain your mathematical reasoning and verify someone else's algebraic graph solution?

Aim: Communicate mathematical reasoning clearly and peer-assess algebraic solutions using structured mark scheme criteria.

Activities

Peer Challenge and Solution Exchange

Pairs swap their created puzzle with another pair, solve each other's problems using inverse operations and graph reading, and then evaluate the accuracy.

- Swap challenge cards with an adjacent pair.

- Solve the received puzzle by rearranging the formula and reading values off the plotted graph.

- Return the card to the authors; authors mark the working using a 2-mark criterion (1 mark for correct algebraic manipulation, 1 mark for correct graph interpretation).

- Conclude with 1 minute of whole-class reflection on key lesson takeaways.

Real-life connection: Peer review and cross-verification used by engineers and analysts to ensure reliability in technical reporting.

Teacher role: Evaluator and synthesiser; highlights standout peer explanations and delivers final summary comments.

Student role: Peer teacher and evaluator; explains reasoning, checks peer work, and reflects on personal learning.

Materials: Peer evaluation rubric slips, Completed challenge cards

Notes

Assessment tips

• Use mini whiteboards frequently during steps 3 to 6 to quickly gauge individual confidence with inverse operations before moving on.

• Ensure students show complete balance steps when rearranging formulas rather than skipping straight to the final line, which leads to sign errors.

• Provide clear mark scheme criteria (e.g. method mark for correct inverse operation, accuracy mark for final expression) to guide peer assessment in step 8.

Implementation notes

• Maintain strict pacing across the 8 steps so that the lesson moves smoothly from motivation to practical creation within 40 minutes.

• For students needing additional scaffolding, provide pre-drawn axes with clear scales for the plotting segments in steps 5 and 7.

• For high-attaining pupils, extend step 7 to include factorising quadratic expressions into double brackets or finding perpendicular gradients using -1/m.