Using Open Questions to Differentiate Your Whole Group Math Instruction
This post is part of a blog series about differentiating whole group instruction. You can read about WHY whole group instruction should be part of our math classrooms by reading Four Ways to Differentiate Whole Group Instruction.
One way to differentiate your whole group math instruction is to use open questions. Open questions are tasks that are open to multiple approaches and multiple solutions. With these types of questions, students are able to solve the problem at a level that is appropriate to them based on their own understanding of the concept. Students end up attacking the problem differently or entering the problem at varying levels because all students go into the problem with their unique understanding of the math concept at hand.
I view open questions a bit differently than inquiry-based tasks. In my classroom the goal of these tasks isn’t necessarily that students discover a profound new math concept. Instead, I implement these tasks with the intention of extending students understanding of a previously learned concept by applying it in a new way. When students experience applying what they already know to a new situation that demands a different type of thinking or a higher level of challenge, their understanding of the math inevitably grows. In the process of completing these tasks, students may recognize new patterns or make new generalizations.
The best way for me to show you what an open question looks like is to give you an example of one I have used with my students.
You are given a card with a four-digit whole number written on it. When the number is rounded to the nearest thousand, it rounds up. When the number is rounded to the nearest hundred, it rounds down. When the number is rounded to the nearest ten, it rounds up. What could the number written on the card be?
What a student knows about a concept influences how they approach a task. This problem is open to a variety of approaches. At the lowest level of thinking, students will create a four digit number and test it out to see if it fits the requirements. If it doesn’t, they may scrap that number and try a new number until they find success. They may begin tweaking individual numbers to fit the requirements. Students with a higher level of understanding of this concept may approach this problem with a very clear plan. They may think through what each digit would need to be (less than 5 or equal to or greater than 5) to fit the requirements of the problem.
The reason these problems are so beneficial in a whole group setting is because when you bring everyone together to discuss their different approaches to the problem and their solutions, students will have the opportunity to compare their strategies with the strategies of others and determine how they could have approached the problem differently. If they happened to be rounding incorrectly, they will realize that by listening to others discuss how they got to their number. There is a lot of learning that comes from talking about this task together as a whole group.
The book Good Questions by Marian Small is a fantastic resource for these types of questions. This isn’t a book that you would sit down and read cover to cover. It is resource with tons and tons of problems for K-8th grade classrooms and it is divided up by grade band, math strand, and it is STANDARDS-BASED! Seriously this is a book that should be sitting on your desk every day for you to quickly pull a problem from to easily differentiate your whole group instruction. She even provides some sample questions for you to ask after specific problems/tasks. I could not have been more excited when I found this resource!
Even more valuable than the tasks she provides is the chapter that teaches you how to tweak questions that you already have and turn them into open questions. A lot of times we are inundated with curriculum resources and programs, so there is a lot of power in knowing how to use the resources we already have (or are required to use) in a more effective way.
If you are looking for more strategies to differentiate whole group instruction, head back to the first post in this series to be linked to the three other strategies we’ve discussed!