Running an inquiry The story of a mixed attainment year

7 class inquiring into the steps prompt.

Inquiry Maths

Questions and observations about the prompt

This was the students’ first inquiry. The teacher gave each pair five minutes to write down a question or observation using the stems. One student then read out the pair’s ‘best’ question or observation to the class, while the teacher recorded them on the board. The teacher typed them up (above) to consider at the start of the second lesson.

Questions and observations about the prompt

Some students wrote about their observations in full sentences.

Regulating the inquiry

Each pair of students were then given the set of six regulatory cards to make a choice about how the inquiry should proceed. The majority wanted to find more examples by changing the starting number. Two pairs were already thinking about how to change the prompt to develop new inquiry pathways.

Finding more examplesStudents found more examples using the two operations in the prompt (multiply by 2 and add 3) before going on to change the operations and starting numbers. Each time, they noticed the difference was the same for each pair of operations.

Conjectures

At the end of the first lesson, students suggested the conjectures above and the teacher recorded them on the board.

Generalisation and proof

At the start of the second lesson, the teacher demonstrated how students could prove their conjectures. Students adapted the model for their own inquiry pathways.

Generalisation and proof

Students are making the transition from numerical thinking to algebraic reasoning. Computational errors are evident, as are unconventional notation in the use of ‘N5’.

Students enjoyed proving the difference between the outputs is always the same and were excited to use algebra.

Generalisation and proof

The use of algebra became more conventional as the inquiry developed.

Proof

The inquiry ends with Janatul writing her proof on the board and explains her reasoning.

Proof