How do I make extra math exercises for students without working evenings?

A math teacher runs into the need for extra exercises every week. Some students finish the lesson’s tasks in half an hour, while others need three more rounds of practice on the same core idea. Before a test you need review exercises, and a student who was absent should get a package of their own.

Ready-made task banks help surprisingly little here. In Finland, free materials lean towards primary school, and a teacher in upper secondary or vocational education ends up writing extra exercises themselves. This is exactly the work worth doing in a new way, because by nature it’s about varying what already exists, not inventing from scratch.

A good extra exercise isn’t “more of the same”

For a student who calculates quickly, ten more identical tasks are mostly a way to pass the time. The guidance on extending fast learners in Dimensio, the magazine of the Finnish association of mathematics and science teachers MAOL, points the other way: add challenge through depth and application, not through quantity.

In practice, extra exercises fall into three types. A variation practises the same skill with new numbers in a new situation. An extension version asks the student to justify and apply. A supported version breaks the same task into steps. All three come from the same base task, and that’s exactly why AI suits this work.

Way 1: variations of a task that works

Take a task that has already worked with your group and ask the AI for variations of it: the same solution steps, different starting values and a different context. An application of the derivative can move from the volume of a cone to the concentration of a drug, while the core stays the same. A review package for a test comes together in a quarter of an hour this way, and every task practises exactly the skill you chose yourself.

Way 2: an extension version for fast students

Ask for a version of the same task that requires the student to justify a claim, explore special cases or apply the result to a new situation. The multi-part problems of the Finnish matriculation examination are a good yardstick: give the AI an instruction such as “add a part c in which the result must be justified in general”. The fast student then gets a genuinely more demanding task, not just a longer list of tasks.

Way 3: a supported version with steps

From the same base task you also get a version for a student who needs support: the intermediate steps made visible, a worked example alongside and guiding questions to lead the way. The core of the task and its level of difficulty stay the same, but the path to the solution is signposted. The guide on differentiation with AI covers this way of working in more depth.

Check the solutions before you share

In math, the AI’s suggestions always have to be worked through. Language models make calculation errors, and a variation’s starting values can produce a messy intermediate result or an impossible situation. The national AI recommendations of the Finnish National Agency for Education state that staff assess outputs before use. In math this means something concrete: solve or check the tasks yourself before you share them with students. Checking is still a job of a different size from inventing ten tasks from scratch.

How Bruukki helps

Bruukki is built for this way of working. You bring your own task package or test as the starting point and ask for variations, extension versions or a supported version with steps. If you teach in Finland, Bruukki takes the objectives of the Finnish national core curriculum into account when you choose the subject and level, so the tasks stay tied to the core content of the course. The AI suggests, you decide which package goes to whom.

Where to start

Pick one topic you need extra exercises for this week anyway, and take one of your own tasks that works as the base. First ask for three variations of it, then for one extension version, and compare the results with your own group. Once the way of working is familiar, the same preparation session will cover the whole range, from the fastest student to the one who needs support.

If you want to try how your own task package turns into new extra exercises, try Bruukki for free. We’re glad to receive teachers’ feedback, so do tell us if something doesn’t work.

Sources

• Savolainen, I. (2024). Ylöspäin eriyttäminen: Miten teen sen? Dimensio, MAOL ry (in Finnish).
• Finnish National Agency for Education (2025). National AI recommendations for early childhood education, teaching and training published. (in Finnish)

Read also: differentiation with AI and how to make AI tasks that fit your own class.