Go Deeper with Hamilton's Problem-solving Investigations

The skills of mathematical problem solving and investigation are fundamental to the maths curriculum for England and for developing sophisticated and modern mathematicians everywhere. However, these skills 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 develop skills in mathematical reasoning and logical thinking, and give children sufficient practice to feel confident in these.

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

Individually, investigations are incorporated into every unit in our maths blocks.
Y1 | Y1/2 | Y2 | Y3 | Y3/4 | Y4 | Y5 | Y5/6 | Y6

Or, you can find all of our investigations for a specific year group on our resources page.
Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6

These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside.
Reception Maths: Open-ended Investigations

See examples of worked investigations, with explanatory notes about the process.

• Dotty Triangle Corners - A Year 1 Investigation
• Puzzling Squares - A Year 3 Investigation
• No Zero - A Year 4 Investigation

Topics present abundant opportunities for contextual maths. Have fun with meaningful maths and explore a cross-curricular topic at the same time. Find hidden maths treasures.

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

• Download Maths Challenges