Mia Buljan asks Erika Isomura how — given some students’ strategies for working on the card sort — she might use the students’ thinking to plan subsequent instruction.

Mia highlights the pedagogical enormity of one student decomposing a fraction; Erika says they have worked with students’ ideas a lot, for example, the idea of making wholes, quantities being “____ away from a whole” or “____ away from the unit of 1.”

Erika describes wanting to return to students’ thinking, inviting them to write on their posters “things to clarify for other people,” then to do a gallery walk to share their thinking with each other.

After students do group sharing, Erika plans to engage them in “investigations” of the points that proved puzzling. Mia connects this work to Standard for Mathematical Practice 8 (“Look for and express regularity in repeated reasoning“), challenging students to generalize their thinking and to identify when strategies are valid.

Erika responds that she often asks her students “Is this is a trick, or is this true math?” She also makes posters with her students about the rules they discover about, for example, working with decimals. Erika notes that while there are some students working on rules, their thinking is not yet “firmed up enough” to make patterns with decimal places a rule.

5th Grade Math – Decimal Place Value*Erika Isomura, Glassbrook Elementary School, Hayward Unified School District, Hayward, California*

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