Inquiry Maths

Inquiry Maths is a model of learning that encourages students to regulate their own activity while exploring a prompt (an equation, statement or diagram). Inquiries involve the class in questioning, conjecturing, generalising and proving and, when required, in listening to an explanation. In Inquiry Maths, students learn to take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical knowledge and activity.

Inquiry Maths establishes a culture of curiosity, collaboration and openness in the classroom. Students meet new concepts and procedures when they are necessary, meaningful and connected – necessary to make progress on a line of inquiry, meaningful in the context of the inquiry and connected to other concepts and procedures in the field of inquiry.

Inquiry Maths introduction.ppt

Most viewed inquiries in January 2021

Place value

Mathematical inquiry processes: Make connections; generate examples and problems. Conceptual field of inquiry: Place value in the decimal number system.


Mathematical inquiry processes: Identify properties; generate examples and counter-examples. Conceptual field of inquiry: Multiplication of numbers with two and more digits; algebraic expressions.

Sum and product

Mathematical inquiry processes: Search for examples that satisfy the condition; conjecture, generalise and prove. Conceptual field of inquiry: Four operations with fractions.

New on the site for February 2021

Inquiry prompt

The factors and prime factors prompt gives students the opportunity to explore connections, test particular cases, explain why the statement is always true and extend it to other cases with more than two distinct prime factors.

Online inquiry

Online inquiry is a new section on the number line page. Andrew Blair describes an inquiry with his year 7 class during school closures. From a deprived area, many of the students were disadvantaged by the digital divide.

New extension

Extending the inquiry describes a new line of inquiry for the substitution prompt. Originating in a student's question, it involves reasoning about values that satisfy inequalities and comes with slides designed for online learning.

What students say about Inquiry Maths

Illustrations: Year 11 students evaluate an Inquiry Maths lesson on mini-whiteboards and a year 7 student gives written feedback.

“Doing Inquiry Maths was the best maths lesson I ever had because it taught me how to think." year 7

"My independent learning ability has improved. It made me think outside the box!" year 11

"Having a say in what we do makes me work harder." year 10

"I ask lots more questions in maths after doing inquiry lessons. Last week I made up my own inquiry on enlargements." year 8

"I used to just explore a problem, but now I have to stop and decide what to do." Year 10

What teachers say about Inquiry Maths

"The Inquiry Maths process gave the students the experience of being real mathematicians, something which is far too rarely the case in schools. They loved it and I felt that I learned much more about their strengths than I had in the preceding lessons." Luke Pearce

"The students’ responses were inspiring, amazing, and truly beyond any of my expectations." Michelle Cole

"Inquiry Maths has proved successful in increasing personalisation, differentiation and students' independence." Amanda Kirby

"Inquiry Maths empowers students by giving them a voice. It celebrates the value of an individual's ideas, whilst linking those ideas to a wider web of mathematical thinking." Jhahida Miah

"Using Inquiry Maths has made my year 7 students into active learners who are fearless and methodical when attacking a problem." Emma Morgan

"An inquiry approach is ideal for a mixed attainment class because it supports and challenges all students and allows them to direct their own learning." Helen Hindle

"Inquiry Maths is a new way of teaching which is actually working and more useful than a whole exercise on a topic." Pal Rayit

"The prompts encourage students to stretch just beyond their current knowledge." Caitriona Martin

"Every time I teach in this way I am always surprised at what my students can do." Nichola Sowinska

"I didn’t expect the level of commitment and mathematical language from the class. It was one of the best lessons I have had with them!" Shawki Dayekh

"Inquiry Maths creates an excellent learning environment. The classroom becomes a safe space in which students can investigate, look for connections and know that it is OK for earlier assumptions and thoughts to be wrong." Rachel Mahoney

"The prompts are inspirational lesson ideas. Each seemingly simple prompt is designed to intrigue students, leading to a rich mathematical task that can be explored in a variety of ways." Steve Lyon

"It was an absolute joy to teach in this way." Emmy Bennett

Habits of Mind poster

Inquiry Maths habits of mind poster.pdf

Hamdi Ahmed, a mathematics teacher in north London (UK), designed this poster for her classroom. Hamdi focuses on one of the habits in each of her Inquiry Maths lessons.

The website is independent of all companies and organisations. It was created by Andrew Blair, a secondary school teacher in London (UK), to promote inquiry learning in mathematics classrooms and is being developed in collaboration with teachers from around the world. Their experiences and reflections enrich its pages.


We welcome feedback about the Inquiry Maths model and using the prompts in classroom practice. Contact Inquiry Maths


The first five prompts on the Inquiry Maths website were developed with the assistance of a Teacher Fellowship in 2004-05 from the Gatsby Charitable Foundation.