TES Maths Investigations Collection

Engaging investigation ideas to inspire creative thinking in your classroom

Since the abolition of maths coursework, there is no formal requirement to carry out investigations with your students. However, it is only through investigative work that students of all ages and abilities can start to appreciate the true beauty of the subject. They can hypothesise, be creative, challenge themselves, work with other students and potentially discover things that have never been discovered before.

At our school, we do an investigation with each year group every half term. They may last 20 minutes or five lessons. Here is a selection of the best investigations that the TES Maths community has to offer.

I really hope you and your students find them useful, enjoyable and stimulating.

Craig Barton, TES Maths adviser

  1. Creativity in maths
    This useful guide is worth reading before embarking upon any maths investigation. What does it mean to be creative and how can you provide opportunities for creativity in your classroom? It comes complete with five puzzles in a ready-to-print format.
  2. Maths investigations
    A collection of over 20 maths problems, puzzles, games and investigations that are designed for KS2, but which could easily be used to extend the learning and problem solving skills of younger KS3 students.
  3. More maths investigations
    This resource contains lots of ideas for real-life maths investigations, covering number, algebra, shape, space and measure. Again, while they are aimed at KS2 pupils, they could be adapted for use with KS3 students as well.
  4. Even more maths investigations!
    These starter sheets introduce a topic for investigation and come with levelled guidance to help students to self- and peer-assess as they progress through it. Although they are targeted at Year 7, these are suitable for year groups at both KS2 and KS3.
  5. Investigative lesson presentations
    A collection of classic maths investigations, including chessboards and tetrahedron towers, presented as PowerPoint presentations with learning objectives and level expectations.
  6. Challenging ideas for KS4 and Post-16
    This was one of my TES Maths Resources of 2014 and it’s easy to see why. These investigations are ideal for gifted and talented GCSE and sixth form students and include everything from code-breaking and Goldbach’s conjecture to the Riemann hypothesis and game theory.
  7. Diagonals of rectangles
    This may be one of my own resources, but it is one of my all-time favourites as it’s so versatile. It can be accessed by Year 6 students, while still challenging the most able Year 11s. The concept is so simple, but the potential depth is great.
  8. Investigating circle theorems
    Some of the best investigations are topic-specific and this activity is no exception. It uses the free dynamic geometry package, GeoGebra, to help students derive, identify and better understand all of the key circle theorems.
  9. Prison cells investigation
    The famous investigation about the numbers on prison cell doors is well-presented, has a really clear structure and some fantastic ideas for differentiation.
  10. Pentominoes
    Pentominoes are a superb, versatile teaching resource that can be used for investigating many aspects of shape. This resource takes you through lots of ideas for making the most of them.
  11. Mathemagic
    These maths magic tricks are engaging way of presenting a problem to your KS3 pupils, before challenging them to investigate how and why they work. Better still, can they go on to design their own?
  12. Noughts and crosses investigation
    Who would have thought you could get so much maths goodness from a game of noughts and crosses?  This game will appeal to secondary students of all ages.

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