Number Talk, Talk, Talk

An activity we did this week in the Lab Class was representative of the shift that we're making in our classroom.  We did a number talk where students were asked to come up with all of the different ways that they could represent 3 within a given time period.  They first worked individually and then in groups.  In their groups they were to share what they came up with, and then decide on one that they thought no other group would have come up with.  They all came up with unique answers, but for the most part used fairly traditional equations.  We challenged them to try to come up with some more creative answers as a part of their homework.

They all came in with their new, more creative answers.  They were encouraged not to just use traditional whole numbers.  They shared them with their groups and came up with another answer that they thought no other group would have.  A couple of the groups shared their answers.  One answer used the whole number 81 inside parenthesis.  The class didn't want there to be any whole numbers.  One student threw out the suggestion of turning 81 into a fraction.  He had a great idea but then kind of got lost in his idea.  So we turned to the rest of the class to find how we can make 81 into a fraction.  This turned into a 20 minute conversation.

Almost immediately a student suggested 81 over 1.  We then looked for another way to get 81 with a fraction.    Shortly later a student came up with 162 over 2 and explained his reasoning.  This became known as the "Luke method".  Other students came up with other equivalent fractions using the "Luke method".  We then had students share their learning about equivalent fractions and their relationship to division.

All-in-all our number talk (designed to take about 15 minutes) took over an hour spanning over two days.  We got a lot of rich discussion about various parts of number sense and many students developed a deeper understanding of division and fractions (among other things).  This is what math looks like in the Lab Class.

Students reflecting on their learning.