Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Differential equations & dynamics

How fast does news spread through a year group?

AI SLAI HLAA SLAA HL Solid Also in: Statistics, Networks & graphs

Research question

Does the number of students who have heard a (harmless, invented) piece of news over a day follow a logistic model, and does a model with “stiflers” who stop spreading fit better?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

Why it makes a good exploration

Rumours spread like diseases but people stop repeating stale news. An ethical, harmless experiment in your year group gives unusual primary data for a modelling question.

The mathematics you'll need

Logistic growth and fitting
A simple rumour model (Daley–Kendall style) with Euler's method (HL)
Comparing models with residuals
Survey design and sampling

Modelling the data, step by step

This idea usually needs a logistic model. See it worked step by step, with a criterion tip at every step: Logistic y = L/(1 + C e^(−kx)) · Choosing and comparing models.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

Where the data comes from

With teacher approval, seed harmless news (e.g., a fun fact) with a few students and survey who has heard it at set times.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

A possible outline

Design the experiment ethically with your teacher.
Collect timed survey data.
Fit a logistic model.
Build a rumour model with spreaders and stiflers.
Compare and reflect on social groups and online spreading.

Pitfalls that cost marks

Anything that could embarrass or mislead people — keep it harmless and approved.
Self-reported timing errors.
Too few time points.

Showing personal engagement

Run the experiment yourself and describe surprises.
Compare spreading within friendship groups and across them.
Relate to misinformation online.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Logistic growth and fitting; Comparing models with residuals
AA HL	Good fit	Logistic growth and fitting; A simple rumour model (Daley–Kendall style) with Euler's method
AI SL	Good fit	Logistic growth and fitting; Comparing models with residuals
AI HL	Good fit	Logistic growth and fitting; A simple rumour model (Daley–Kendall style) with Euler's method

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: anything that could embarrass or mislead people — keep it harmless and approved; and self-reported timing errors. Say how each one affects your answer.

Use of mathematics (E)

SL: logistic growth and fitting; comparing models with residuals; survey design and sampling, each explained in your own words and carried out correctly.

HL adds: a simple rumour model (Daley–Kendall style) with Euler's method, each explained in your own words and carried out correctly.

How differential equations explorations reach the top bands in general: Differential equations & dynamics IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

HL: explain why the classic rumour model predicts that about 20% of people never hear the rumour, and test that against your data.

Extending it for HL

This idea already has HL mathematics in it: A simple rumour model (Daley–Kendall style) with Euler's method. Make that the centre of the exploration and use it with full rigour.

See a complete IA, marked

Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroom (AI HL) is a complete differential equations exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Logistic growth and fitting, a simple rumour model (Daley–Kendall style) with Euler's method (HL), comparing models with residuals and survey design and sampling.

Where can I get data for this IA?

With teacher approval, seed harmless news (e.g., a fun fact) with a few students and survey who has heard it at set times. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “How fast does news spread through a year group?” filled in: the question, the maths and the data sources.

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