This article is part of a new series of subject-specific blog posts, written by our experienced Subject Leaders. Spanning a wide range of topics, each post aims to inform, inspire and embed IB approaches to teaching and learning in your classroom.

The subject guides suggest allocating 30 hours to the toolkit in both SL and HL, which is roughly the same number of hours as are assigned to Topic 2 of the SL course. These 30 hours comprise the exploration part of the internal assessment and the development of investigative, problem solving and modelling skills.

Syllabus outline screenTable 1: Syllabus outline, DP Mathematics AI Guide page 29

The IB Mathematics Diploma Guides recommend devoting 10-15 hours of teaching time to the exploration, which breaks down into:

  • time for the teacher to explain to students the requirements of the exploration
  • class time for students to work on the exploration and ask questions
  • time for consultation between the teacher and each student
  • time to review and monitor progress, and to check authenticity.

The question, then, is what to do with the remaining 15-20 hours allocated to the toolkit? The answer is to be found in the assessment objectives. Table 2 of the assessment objectives shows how Problem solving, Reasoning and Inquiry approaches, as well as technology (graphing display calculators for exams and math-specific software like GeoGebra, Desmos, etc for exploration), are all part of the assessment objectives.

Assessment Objectives screenTable 2: Assessment Objectives, IBDP Mathematics Guide page 28

Over the years, DP Mathematics courses have moved from content-based approaches to concept-based approaches. This change is also reflected in assessment practices and examinations. The time allocated for the toolkit is to give students opportunities to undertake inquiry-based approaches in class, focusing on conceptual understandings, teamwork and collaboration.

For example, think about the traditional way to introduce the sine rule. You would give students the formula or maybe show the proof as well, work through a few examples, and ask students to answer some exam-style questions. In an inquiry-based approach using technology, you would ask students to draw triangles and write the ratios of sides to sines of triangles, then ask them to generalize the sine rule.

Geogebra screenFigure 1: Using Geogebra to explore sine rule

Another use of “toolkit” time could be to focus on cognitive activators:

  • connecting to previous learning on the topic or different topics within the same concept
  • starting with an essential question that can be understood by the students but only successfully answered by the new learning material. This can be supported by, for example, a random group generator, no-hands-up activity, think pair share etc. to organise collaboration.
  • an activity that enables students to start their work on the topic
  • ideas for reflection and/or extension to further topics.
    (Teacher Support Material, IB, 2020)

A cognitive activator example activity I use to begin a statistics unit is explained below, entitled; “Why statistics can’t be trusted”.

Start the unit by showing cartoons from MathwithBadDrawings and I ask my students why we shouldn’t trust the statement in the cartoon. Many of them immediately relate to the second cartoon.

sample math tableFigure 2: A sample from Math with Bad Drawings statistics cartoons

Of course, modelling, team/collaborative work and other approaches to learning strands also need to be addressed. You can find some very good examples in the Mathematics: applications and interpretation teacher support material (TSM) section called “Toolkit” published by the IB to support teachers in implementing different aspects of the toolkit in their teaching.

If you want more ideas like this, or have other DP Maths questions, you can connect with me on MiniPD, and don’t forget to visit the ManageBac Subject Pages for more information.



Mathematics: applications and interpretation subject guide, IB, 2020
Mathematics: applications and interpretation teacher support material (TSM), IB, 2020.
Math with Bad Drawings,


About the author:

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Nuriye Singh
Mathematics Subject Leader
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Nuriye Singh is the Subject Leader for the ManageBac Mathematics Diploma Applications & Interpretations Subject Page.

The ManageBac Subject Pages are a collection of curated subject-specific resources to support teaching and learning in the IB Diploma. Access the Subject Pages via your ManageBac account.

Check that page regularly for resources, advice and teaching ideas.