Engaging, hands-on learning

Mathematical investigations that inspire – and work!

Mathematics is more than tests and worksheets. Instructive’s rich mathematical investigations invite students to explore real problems, reason deeply, and communicate their ideas with confidence. These hands-on experiences build curiosity and rigour at the same time – and they’re designed for real classrooms, not ideal ones.

“The (mathematical investigations) provided are excellent and easy to follow. They engage the students and keep them motivated to continue learning and achieving.”
Leah Farwell, Primary Teacher

What are mathematical investigations?

Instructive includes a library of rich mathematical investigations: structured, curriculum-aligned tasks that help students apply and extend their learning. Typically:

1–2 investigations per semester, each running over two to three lessons.
Suitable for Years 5 to 10, aligned with every curriculum Strand.
Students can work in groups, pairs or individually.
Can be used as project-style assessments, complete with clear student handouts and marking guides

Whatever the format, every task develops reasoning, communication, and genuine mathematical thinking — all within a structure that fits comfortably into a normal school term.

“Every student gets to explore the beauty and power of maths through rich investigative lessons, not just the advanced class.”
Lachlan Champion, Director of Mathematics

Designed by teachers, ready to run

Each investigation is written by teachers who understand what makes a task meaningful, manageable, and ready for the classroom.

Everything you need, in one pack

Clear teacher and student instructions, printable student handouts, and model solutions are all included. No extra prep required.

Scaffolded from start to finish

Tasks guide students through each stage of reasoning and reflection, so learning feels challenging but achievable for everyone.

Practical to assess

Each investigation comes with marking guides / rubrics. Students produce a structured write-up which they submit for marking.

Flexible for real classrooms

Can be run either as learning activities or assessment tasks. Using the handout, students can easily complete and submit later.

Try one in your next lesson – the sample activities here are free to download and use.

Download Sample Investigations x6 (ZIP)

“The projects are really well set out, as they have step-by-step instructions for the first section. I do like that, and having the answers is a bonus. If someone else is taking your class, and they’re not mathematically minded, they’ve got the answers there that they can check on.”
Sharon Antonello, Secondary Mathematics Teacher

Other ways to bringmaths to life

Alongside full investigations, Instructive also includes shorter, ready-to-use activities that add variety and energy to your lessons. They’re optional, but many schools find them a great way to keep classes active and curious.

Energisers

Quick, 10-minute activities often used at the beginning of a lesson — getting every student thinking from the moment the bell rings.

Teacher-led, fast-paced and interactive
Run from a PowerPoint file with built-in timers
A fun, interactive way to revise concepts or spark discussion

Download sample Energisers (ZIP)

Rich Tasks

Open-ended with a low floor and high ceiling — accessible for all students, yet rich enough to challenge advanced learners.

Typically running over a single lesson
Usually not assessed directly
Drawn from a broad library of tasks, including some created in collaboration with ATSIMA (Aboriginal and Torres Strait Islander Mathematical Alliance)

Download sample Rich Task (ZIP)

Mini-Lessons

Targeted, small-group lessons that run for 20–30 minutes. Perfect for building deep understanding through discussion and collaboration.

Run with a small group of around 3–8 students, while others continue their individual work.
Include a detailed lesson plan with everything needed to teach it effectively.
Hands-on and interactive, led by the teacher at a table with the group
The Mini-Lesson Planning tool groups students who are ready to learn the same thing, making data-driven planning a breeze (for details, see more on Data).

Download sample Mini-Lesson (PDF)

The difference you see straight away

These investigations:

Showcase students’ communication, collaboration and creativity
Offer variety across strands — geometry, probability, algebra, data, etc.
Build confidence through real-world, problem-solving contexts
Deliver a rigorous yet enjoyable way to capture authentic mathematical thinking

They fit naturally into a school term, create genuine engagement, and produce clear evidence of learning, without adding to teachers’ workload. Rigorous, practical, and easy to manage, Instructive’s rich learning tasks and hands-on investigations bring maths to life for every student.

“When I come into class the students wait for me to direct them as to the nature of the class. On some occasions when I have paused for dramatic effect, the students have started a chant: “Rich Learning Task, Rich Learning Task” hoping that we will be doing one in the class. I have been thrilled at the change in their attitude; from many students groaning and asking if they could just do their module work and not waste time, to the students chanting and being engaged where I have to wrestle with their enthusiasm!”
Paul Matthews, Secondary Mathematics Teacher