This question got thrown out on Twitter the other day (full conversation here). It was something I had never thought about and struggled to think about where in our curriculum or standards it showed up. As always, I thought I would ask my students the following day what they thought happened when we divided by zero. Here are some responses:
It was interesting because most went to breaking into groups, but depending on how they reasoned about it,resulted in different answers. Sharing something between zero people or putting things into zero groups was either zero because there was nothing to put the number of things in OR it was that beginning number because they weren’t put anywhere and were leftover. Some also thought about inverse relationships which was nice and that is when our conversation got really confusing and people started questioning what in the world it was! One student punched it into his calculator and got Error, even more confusing while another asked Siri and got this, which they wrote in their journal…
Fawn tweeted a piece of student work that was really interesting in which the student had said 5 divided by zero was the same as 5/0, so (trying to quote this as accurately as I can) you cannot take five pieces of something with an area of zero. I am thinking that was like thinking something like 5/6 is 5 pieces when the unit is broken in to 6 pieces. In his case, it is five pieces with the unit cut into zero? Fawn, please correct me if I completely mess that one up!!
Very interesting and something I want to be sure I keep in the back of my mind. I love when a tweet can spark something I had never thought of before in elementary math work! Thanks Tina!