Problem-solving Investigation Tools

Hamilton’s Problem-solving Investigation Tools provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

Mathematical problem solving and investigation are fundamental to the maths curriculum for England and for developing sophisticated and modern mathematicians everywhere.  However, the skills required to solve mathematical investigations do not fall naturally out of the teaching of the maths curriculum itself. They require dedicated time, content and pedagogy. Most challengingly, they require teachers to present children with graded activities and problems that are relevant to the curriculum while at the same time developing skills in mathematical reasoning and logical thinking, and giving children sufficient practice to feel confident in these.

Hamilton's Problem-solving Investigation Tools provide materials and advice for teaching these skills well, in a variety of ways and contexts, and with confidence.

Problem solving and reasoning investigations are now implemented within our New Flexible Maths Blocks. Follow these links to each maths year group page to see how the investigations are displayed within the individual units.

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6

Guidance and sample materials for investigations

  • Guidance from Ruth

    Professor Ruth Merttens explains how to get the most from Hamilton's investigations for Years 1 to 6.
  • Guidance from Nick

    Nick Barwick discusses how to use open-ended tasks to develop problem-solving skills in Early Years.
  • Children's Worksheets

    Child sheets come with child-friendly explanations and suggestions for how to get started.
  • EYFS Investigative Tasks

    Open-ended investigative tasks introduce EYFS children to mathematical language and concepts.
  • Investigation Examples

    Look at some examples of worked investigations, with explanatory notes about the process.
  • Maths in Topics

    Find mathematical problems and investigations in cross-curricular topics in all Key Stages.
  • Video: Investigations Impact

    In this video, Nick Barwick describes the impact of an investigative approach on a Year 5 class.
  • Video: Mrs Multiple's Cakes

    In this video, Nick Barwick discusses using the investigation "Mrs Multiple's Cakes" with a Year 2 class.

Additional Maths Challenges

For further maths problems and puzzles for your class, try these National Numeracy publications from 2000.  They come with answers too!