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 questioning, conjecturing, generalising and proving and, when required, listening to or giving an explanation. In Inquiry Maths, students learn to take responsibility for directing the inquiry while the teacher acts 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.

New on the site

Sanchita Dalal, a teacher in Gurugram, contacted the website to request inquiry prompts suitable for grades 1 to 3.

July 2024

Andrew Blair used the new volume of revolution prompt to encourage his year 12 Further Maths A-level class to explore.

June 2024

Amelia O'Brien, a year 5 teacher in Melbourne, generated excitement and interest through the place value inquiry.

May 2024

Most viewed inquiries in June

The Mathematics Hub funded by the Australian Government Department of Education, Skills and Employment recommends 50 inquiries from this site.

What students say about Inquiry Maths

Year 11 students evaluate an Inquiry Maths lesson on mini-whiteboards.

After supporting in a year 7 inquiry lesson on the combined transformations prompt, Husine, a year 12 Further Maths A-level student, said:

"When we were in year 7 we just learnt how to do things, like reflections, without thinking about it. In the inquiry you dig into why things are the way they are. 

"I was really surprised by the connections between the transformations. The inquiry was much better because the year 7s were really interested."

"My maths this week using a prompt has improved significantly because I have noticed and seen things I didn't even know was possible." Year 6

“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

"It was a new technique, a maths prompt. For some reason questions just flew out of me." Year 6

"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

"The inquiry was so interesting that it was the first time I talked about my maths lessons at home." Year 7

A year 7 student gives written feedback.

What teachers say about Inquiry Maths

"The whole class came together to collaborate on the inquiry. The energy in the room contributed to a brilliant sense of community." Zack Miodownik

"I love the focus in Inquiry Maths on developing mathematical behaviours in students whilst keeping the integrity of the subject." Claire Lee

"I was blown away by the by the depth of student responses." Devon Burger

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

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

"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

"Some brilliant work from the students. One of those lessons that makes you love being a teacher." Chris McGrane

"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

More comments from teachers

Habits of Mind poster

Hamdi Ahmed, a teacher in north London (UK), designed this poster for her classroom. The inner ring displays specifically mathematical habits of mind, while the outer ring shows more general habits of mind that are developed through inquiry. 

Hamdi focuses on one of the habits in each of her Inquiry Maths lessons. She says that perhaps the most important is the management of impulsivity. When students notice something in a prompt, they often want to dive in and explore without first thinking of the best way to inquire. The regulatory cards help students learn how to direct their inquiries.

Inquiry Maths habits of mind poster.pdf 

Dr Andrew Blair, a secondary school teacher in London (UK), created the website in 2012 to promote inquiry learning in mathematics classrooms.  

Independent of all companies and organisations, the site is being developed in collaboration with teachers from around the world. Their experiences and reflections enrich its pages. 



We welcome feedback from teachers who use Inquiry Maths prompts in the classroom. Contact Inquiry Maths


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