As students explore, they learn to wonder about the mathematics of a situation. They identify and pose questions related to quantities, patterns, spatial relationships, and probabilities. They gather initial data. They observe. They estimate, using known referents and benchmarks and by building onto insights from past experiences. This exploration leads to an understanding of the need for a solution and allows for the creation of solution criteria.
Questions and comments from students help to identify their unique starting point; what knowledge and skills they have and which need to be developed.
A model, made from 1 liter pop bottles filled with different amounts of water, encouraged students to wonder about fractions. We wondered:
Why do the different water levels make different sounds?
Is there a pattern?
What musical notes can we play?
Through this exploration, students’ prior knowledge of fractions was evaluated and next steps for learning could be developed.