My current group of third graders range significantly in their understanding of place value. (I teach on a military post so my students will range in their understanding as any group of students will with the additional factor of having had quite different experiences in school previously.) A strong foundation in place value is critical so that students can continue on with computation and more complex math skills.
I’ve been mulling over an open middle problem to support this and I, finally, last week slowed down enough to think it through. This was the result:
I was concerned that some kids would be able to answer these two open middle problems quickly while others would take a while. It took all of my students a bit to explain their thinking even if they knew the answer quickly. But some definitely got to the answer more quickly than others. I had challenges ready for them.
Nearly half of my class got to the point of this challenge. For some this was super easy. For others it was a reasonable challenge.
A few students moved on to the final challenge.
In the time we had, no one solved this one accurately. They got close, but not quite.
It was, by far, the most engaged my students have been during a math workshop so far this year.