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

When might the Arctic be nearly ice-free in September?

AA SLAA HLAI SLAI HL Solid Also in: Modelling, Statistics

Research question

Which models (linear, quadratic, exponential) best fit the September Arctic sea-ice extent since 1979, and how widely do their predictions of when extent falls below 1 million km² disagree?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

“Ice-free Arctic” predictions make headlines, often without uncertainty. Showing how much the answer depends on the model — with NSIDC's official data — is an IA about the limits of extrapolation.

The mathematics you'll need

Linear, quadratic and exponential models
Residual analysis and R²
Solving model equations for a threshold
Discussing uncertainty in extrapolation

Modelling the data, step by step

This idea usually needs quadratic or exponential models. See it worked step by step, with a criterion tip at every step: Quadratic: three points, completing the square, regression · Exponential y = a e^(kx) + c and y = a·bˣ · 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

Download monthly extent (September values) from the NSIDC Sea Ice Index.

NSIDC Sea Ice Index — Daily and monthly Arctic and Antarctic sea-ice extent since 1978, CSV.

Real data for this idea

Primary source: NSIDC Sea Ice Index: Sea Ice Index, version 3. Use the monthly Arctic extent for September: one value per year from 1979. Licence: Free to use; NSIDC asks you to cite the dataset.
Readable chart: Our World in Data: Arctic sea ice extent. Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Arctic sea ice extent’, CC BY 4.0. Original source: National Snow and Ice Data Center, Sea Ice Index (2026).

Links checked October 2026; we link to the data and never copy it. More free data sets.

Ready to use: Sea level rise in the IA data bank — cited, licensed for reuse, and one click to open in the grapher.

A possible outline

Explain what extent measures and the 1 million km² threshold.
Fit several models.
Solve each for the threshold year.
Test models on the most recent years.
Reflect on why the models disagree so much.

Pitfalls that cost marks

Presenting one model's year as a prediction.
Using daily data without averaging.
Ignoring year-to-year variability.

Showing personal engagement

Compare your range with published scientific estimates (cite them).
Look at March maxima as well.
Discuss what the answer means for people living in the Arctic.

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	Linear, quadratic and exponential models; Residual analysis and R²
AA HL	Good fit	Linear, quadratic and exponential models; Residual analysis and R²
AI SL	Good fit	Linear, quadratic and exponential models; Residual analysis and R²
AI HL	Good fit	Linear, quadratic and exponential models; Residual analysis and R²

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: presenting one model's year as a prediction; and using daily data without averaging. Say how each one affects your answer.

Use of mathematics (E)

SL: linear, quadratic and exponential models; residual analysis and R²; solving model equations for a threshold; discussing uncertainty in extrapolation, each explained in your own words and carried out correctly.

How environment explorations reach the top bands in general: Environment & climate IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Fit models on data up to 2012 (a record low) and see how badly they predicted later years.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL environment exploration adds.

See a complete IA, marked

When can we launch? Modelling the tide at our sailing club's slipway (AA SL) is a complete environment exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

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

What mathematics does this IA use?

Linear, quadratic and exponential models, residual analysis and R², solving model equations for a threshold and discussing uncertainty in extrapolation.

Where can I get data for this IA?

Download monthly extent (September values) from the NSIDC Sea Ice Index. Checked sources and tools: NSIDC Sea Ice Index and Our World in Data.

Turn this idea into your IA

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