# Ambitious mathematics: Ratios, decimals, fractions and time for Ta’ovala:Sharing back: Teacher observation matters

## Introduction/Whakataki

In this lesson, Problem (b), the aspirational second mathematical task, has challenged all of these Year 8 learners. The ‘Sharing back’ part of a DMIC lesson brings all of the groups back into a whole class context to report on their progress in solving the problems.

At the outset David Ahlquist reviews Problem (a) with the students and they explain the strategy they used to solve this straightforward ratio problem. He reflects their thinking back to them and highlights the correct mathematical terms and thinking behind the strategies they used – for example: common factors.

David models the interpersonal respect that is foundational to the DMIC pedagogy. His approach is deeply respectful of the children as he takes time to value each step of their progress. Individual students also have the opportunity to question those reporting back to better understand their problem solving approach.

Problem (b) proved more problematic for the groups and David has identified the importance of the strategy one group uses to break the time into hours and minutes. He leaves this group to report back last and his sequencing strategy works. This group’s thinking becomes a resource for the whole class.

The sharing back takes the whole class on a journey through the problem solving involving the use of ratios, decimals, division, and the translation of fractions into time.

The teacher explains how the students have progressed through to a ‘lightbulb moment’. He reflects that this particular ratio problem and strategy used to solve it will need to be built on. It will be important for the students to encounter different ratio problems in further contexts.

Both consolidation and further stretch of learning are built into the DMIC model. These students know that at the next lesson they will be working more independently on similar ratio problems. At the next lesson the other half of the class will work collaboratively in groups with the teacher, solving their next challenging problem related to a big mathematical idea.