Tes Maths: Top investigation ideas

Craig Barton
31st January 2016
Maths investigations,tes maths,maths,secondary maths,ks3,ks4,ks5,year 7,year 8,year 9,year 10,year 11,year 12,year 13

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

  • 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.
  • 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.
  • 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.
  • Investigative lesson presentations
    A collection of classic maths investigations, including chessboards and tetrahedron towers, presented as PowerPoint presentations with learning objectives and level expectations.


Creativity in Maths

For all teachers of maths, this is a guide in booklet form about how you can view Creativity in Maths. What does it mean to be creative and how can you provide opportunities for creativity? There are five puzzles/tasks included in a ready to print format.
By DaveGale

Maths Investigations

A list of over 20 Maths problems, puzzles, games and investigations that I collated during my MaST (Maths Specialist Teacher) course last year. Whilst easy to use as they are in KS2, most could easily be adapted for KS1 too. Please use them as a starting point to extend and develop where you, or your class, want to take them: 'What would happen if ...'
By andrewchadwick

Maths Investigations

Based on the Science tasks produced in East Sussex, these investigation starter sheets give an introduction to a topic for investigation, with levelled guidance for progressing the investigation and to allow self- and peer-assessment. Targetted at Y7, these may be suitable for several year groups in KS2/3 Please note that the levelling guide is a first draft and may change. There are currently six investigations: one based on positive & negative numbers, one on sequences, one on area/perimeter, one on polyominoes, one on handling data, and the sixth on probability. Any suggestions warmly welcomed at tafkam.tes@googlemail.com

By tafkam

Maths Investigations : Chess Board, Happy Numbers

A range of mathematical investigathions for KS3 (11-14) Year olds including How many Squares on a Chess board, Happy Numbers, Largest and Smallest Answers, Deciimal Multiplications, Mystic Rose, Vedic Square, Bacteria, Staircases, Types of Number and Tetrahedron Tower

By davecavill
  • 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.
  • 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.
  • 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.
  • 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.


100 Maths Investigations Ideas - 90 page pdf!

Maths investigations for gifted and talented GCSE and sixth form students. Everything from code breaking to Goldbach's Conjecture, the Riemann Hypothesis, Faster than light time travel, Modelling diseases, Predator-prey models, Game theory, visualising the 4th dimension, war maths, Benford&'s law to catch fraudsters and much much more!
By andrewchambers

Rich Maths Task 20 - Diagonals of Rectangles

Have a play around with this task, and please share any questions, extensions, simplifications, modifications, or lines of inquiry in the comment box below. The idea is to collect loads of suggestions that can then be used for effective differentiation. The full set of these tasks, along with additional notes, can be found here: http://www.mrbartonmaths.com/richtasks.htm
By MrBartonMaths

Investigating Circle Theorems with Geogebra

KS4 Maths activity, using ICT A set of dynamic web-pages and accompanying workbook to guide pupils through the various circle theorems. They can see and manipulate the visualisations and use them to deduce the theorems for themselves. They can then test their understanding on some of the problems. I have found this really successful in teaching for understanding and have found pupils remember the theorems far better having seen them in action. Outstanding computer lesson!
By Laura Rees-Hughes

Prison Cells: Number and logic maths investigation

Group activity. Maths investigation. Pupils work in 4s to get the most points. They can 'buy' a laptop (10 points) to use the interactivity (http://bit.ly/qYd7Ih), a calculator for 5, ask a question for 2 points or have an emergency envelope (with a clue/question) for 1 point.
By daniquinn
  • 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.
  • 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?
  • 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.


Pentominoes. Lesson plan, investigation.

This unit is made up of a number of mini activities. After finding the 12 pentominoes pupils use the shapes in the following activities: Find the symmetry and rotational symmetry of the shapes Investigate which pentominoes will tessellate without being rotated, then which will tessellate when rotated Fit the shapes into varying sizes of rectangles The unit contains pentomino shapes to download and print out.

By Hwb Digital Learning for Wales

Mathemagic. Games. Investigation. KS3 Ages 11-14

NEW!! Excel Spreadsheets for the effect Total Disbelief.

A collection of mathematical magic tricks for teachers. Particularly suitable for KS3 but also popular with older children. Each trick gives an anecdotal account of the effect being used in the classroom, followed by the explanation and teaching points if used for further work. Appendix includes details of simple sleights such as coin vanishes etc.

By maths126

Noughts and Crosses Investigation. Lesson plan.

As it says on the tin sadly due to size restrictions couldnt post video which go with lesson but youtube links provided.

By GoldMaths

Contact us

Visit our forums

Latest education news

New to TES Resources ? Find out more about becoming an author on TES, or dive straight in and start downloading.