IA modelling practice

Weekly IA modelling challenge

One real dataset and one modelling question, new every Monday. About 30 minutes: fit, compare, reflect. Good practice before your own IA.

This week

Choose any challenge below — they rotate each Monday.

How to do a challenge

  1. Open the data in the grapher (or download the CSV).
  2. Say which models make sense before you fit them, and why.
  3. Fit two or three and compare them with residuals and the sum of squared residuals.
  4. Write two sentences of reflection: what the model shows, and where it would break.
  5. Log your attempt in your IA process journal if you want your teacher to see it.

All challenges

  1. 1. Stopping distances

    Fit a quadratic to total stopping distance against speed. Then fit thinking and braking distance separately. Does adding your two models give the same curve?

    A strong answer shows:

    • A reason, from physics, for each model type before fitting
    • Parameters with units
    • A residual check at 70 mph

    Data: UK typical stopping distances (The Highway Code). Methods: quadratic, straight line, power.

    Open the data in the grapher

  2. 2. CO₂ at Mauna Loa (monthly)

    Fit y = a sin(b(x − c)) + mx + k to the 24 months. What does b tell you, and does it match one year?

    A strong answer shows:

    • The period worked out from b
    • The trend (m) in ppm per year
    • Which month the model says is highest, checked against the data

    Data: Atmospheric CO₂ at Mauna Loa, monthly mean (2023–2024). Methods: sinusoidal, straight line.

    Open the data in the grapher

  3. 3. World population

    Fit an exponential and a logistic model to world population. Which predicts 2025 better if you only use data up to 2000?

    A strong answer shows:

    • Fitting on 1960–2000 and testing on 2001–2025
    • The carrying capacity of the logistic model, interpreted
    • A sentence on why the better fit might not be the better forecast

    Data: World population (1960–2025). Methods: straight line, exponential, logistic.

    Open the data in the grapher

  4. 4. Global temperature (GISTEMP)

    Choose a year where you think warming changed pace. Fit a two-piece linear model with that break and compare it with one straight line.

    A strong answer shows:

    • A reason for the break year
    • Slopes in °C per decade
    • SSR for both models, and whether the extra piece is worth it

    Data: Global surface temperature anomaly, NASA GISTEMP (1880–2025). Methods: straight line, piecewise, cubic and polynomials.

    Open the data in the grapher

  5. 5. India CO₂ emissions

    Linearise the data with a natural log. What is the doubling time of India's emissions, and has it changed?

    A strong answer shows:

    • ln(y) against x with a fitted line
    • Doubling time = ln 2 ÷ gradient
    • Doubling times for two different periods compared

    Data: India carbon dioxide emissions (1950–2024). Methods: exponential, logarithmic, logistic.

    Open the data in the grapher

  6. 6. Sea level rise

    Fit linear and quadratic models and use each to predict the rise by 2100. How far apart are the predictions?

    A strong answer shows:

    • Both models with R² and residual plots
    • Extrapolation stated as a risk, not a fact
    • A comparison with a published projection (cited)

    Data: Global mean sea level change (1880–2013). Methods: straight line, quadratic, piecewise.

    Open the data in the grapher

  7. 7. UK CO₂ emissions

    Split the series into rise, plateau and fall. Fit a model to each piece and say what happened at each break.

    A strong answer shows:

    • Breaks justified by evidence, not just the graph
    • Rates of change with units
    • A check that the pieces join sensibly

    Data: UK carbon dioxide emissions (1900–2024). Methods: piecewise, cubic and polynomials, straight line.

    Open the data in the grapher

  8. 8. Shrinking glaciers

    Find the average rate of ice loss in the 1960s and in the 2010s. Does a quadratic model capture the change?

    A strong answer shows:

    • Rates read from the model, not just the table
    • The derivative of the quadratic interpreted
    • A limitation of averaging many glaciers

    Data: Glacier mass balance, world reference glaciers (1956–2023). Methods: straight line, quadratic, piecewise.

    Open the data in the grapher

  9. 9. CO₂ at Mauna Loa (yearly)

    Fit linear, quadratic and exponential models to 1959–2000. Which one predicts 2025 best?

    A strong answer shows:

    • Training and test data kept apart
    • Prediction errors for 2025 compared
    • A reflection on why the winner wins

    Data: Atmospheric CO₂ at Mauna Loa, yearly mean (1959–2025). Methods: straight line, quadratic, exponential.

    Open the data in the grapher

Frequently asked questions

What is the weekly modelling challenge?

A short modelling task on a real dataset from the IA data bank, changing every Monday. It is practice for the modelling part of the IB Maths IA: choosing, fitting, comparing and reflecting on models.

Can I use a challenge in my IA?

Use it to practise. An IA needs your own question and your own decisions; if a challenge sparks an idea, take it further with a question of your own and tell your teacher where it started.

Is there an answer to check against?

No answer is published: there is more than one good answer. Each challenge lists what a strong answer shows, and Model my data checks your fit step by step.

Free: the IA checklist an examiner uses

Every check for Criteria A–E in a 4-page PDF, the mistakes that cost the most marks and a self-assessment grid. We'll email it with a short IA tip every few days, timed to your deadline if you give it. Free — no account, no payment.

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