How might we slow down and think – contemplate before we calculate – look before we leap? How might we teach others to do the same?

Have you tried any of Robert Kaplinski’s Open Middle Tasks? Prior to offering them to your students, have you and your team anticipated how students might tackle the task, what solutions they might find, and what pitfalls they might encounter?

Let’s look at Owen Kaplinski’s 4th Grade Equivalent Fractions Open Middle Task. Please stop reading now and try it yourself before reading below the graphic.

Now, the questions begin to flow.

Did you find a solution? More than one? All of them? How do you know?

• For students who might be stuck or frozen, did we offer them number tiles or Post-It notes to free up thinking?
• Is/was there an opportunity to use a non-permanent, vertical writing surface to think and reason, to draft and redraft?
• Have we taught students how to look for and make use of structure? What might that mean in the context of this task?

What if we teach our students to slow down and think, to contemplate before calculating, and to look before leaping? In the task above, we are looking for equivalent fractions. What if we generate possibilities before guessing to get started? What if we made possible equivalent fractions visible? Would we be better off than guessing and checking?

In our learning progression “for look for and make use of structure,” Jennifer and I highlight composing and decomposing to make sense, rewriting expressions into equivalent forms to make visible what isn’t readily seen.

Here’s my first equivalent fraction list:

What do you think? If our learners took the time to see all the fractions equivalent to 1/2, would they make strategic choices instead of guessing?

Here’s my work on this task using structure so that I know I’ve found the equivalent fractions that solve this Open Middle task.

I’d love to know what you think.