One thing I appreciate about the beginning of the school year is the chance to start teaching with a fresh mind again. Last year, I started working with mathematical openers as a way to start class. Dan Finkel, a fellow math educator, thinks of mathematical openers as “genuine warm-ups”; I took one of his online workshops where I learned about resources for mathematical openers, and how to implement them in the classroom.

Mathematical openers are a specific kind of warm-up with a low floor and high ceiling; they engage all learners and can set the tone for the entire class. Instead of the teacher talking for the first few minutes of class, students jump right into a problem that is “appropriately sized”, as Finkel says. These problems not only give students something to do at the start of class, but they get students ready for later deeper mathematical thinking in class. They also get students talking to each other about math right away. Finally, they boost students’ numerical fluency on a daily basis.

In the photos below, one can see a number of students working on a mathematical opener. Some students are working on “the number problem”, where students need to use the digits 1, 3, 4, and 6 to create the numbers 1-24, using the order of operations. Other students are working on a “plus times” puzzle where students must use given numbers along with one addition and one multiplication to make a true statement. Both of these problems serve to “level up” straight-forward order of operations practice. They allow for self-differentiation in that students can work up to the level they’re currently at.

I am looking forward to continuing to work on mathematical openers with your students!

Here is a closer look at some work: