“Inquiry Maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). Inquiries can involve a class on diverse paths of exploration or in listening to a teacher’s explanation. In Inquiry Maths, students take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical activity.” Andrew Blair
I have long been a fan of Andrew Blair’s Inquiry Maths site. As a high school teacher, Andrew’s prompts are predominately aimed at secondary students (more recently Andrew has started a Primary section for this site) so I initially only used the prompts with my extension grade 4 (9-10 year olds) students. However, I soon realized that many tasks were open enough to be accessible to the whole class. As the students created their own inquiries each one of them was reaching ‘just above’ their current level of understanding. These are great examples of low-floor high-ceiling tasks with everyone taking the same first step then working at their own level of engagement. Raise the ceiling and watch what heights your learners can achieve.
Here are some of the inquiries I have tried with my class as shared on the site:
Doing Maths 
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