IB Maths AI SL 2.6 - Developing Models Notes

This IB Maths AI SL 2.6 resource introduces developing mathematical models from data and real-world contexts, and is fully aligned with the IB Applications and Interpretation SL syllabus.

Students learn how to create, fit, and use models from previous function types. The notes introduce the modelling cycle, including posing a question, developing a model, testing the model using data, and deciding whether the model should be applied, refined, or extended.

The resource develops students’ understanding of independent and dependent variables, interpolation, and extrapolation. Students learn why interpolation is usually more reliable because it stays within the observed data range, while extrapolation is less reliable because the trend may change beyond the data.

Structured examples guide students through using regression and contextual modelling. A heating-liquid example introduces linear regression from a data set, including choosing an appropriate model, identifying a useful domain and observed range, and making predictions at different input values.

The notes then develop quadratic modelling through a Sydney Harbour Bridge arch example. Students use key points from the context, including endpoints and the summit, to form and solve a quadratic model that represents the shape of the bridge.

The resource finishes with cubic regression in a bike-track mound context. Students use technology to determine coefficients, write a cubic model, predict a height at a given point, and check whether the result makes sense in the real-world situation.

Ideal for IB Maths AI SL teachers teaching regression, mathematical modelling, interpolation, extrapolation, linear models, quadratic models, cubic models, predictions, and reasonableness checks.

This pairs great with ourslidedeck!