So by now, you understand the reasons that these crazy, open-ended math tasks are so beneficial (even if you were a bit reluctant at first, like me!). You know why you’re using them and you’ve got your routines in place (If not, check out part 1 & part 2 here). And honestly, that is definitely enough to get started, but experience quickly showed me there are some hacks you can use to make things run even more smoothly. Knowing how to group your students, how to create your own math tasks, and how to grade students’ work are things you will definitely need to consider. The exact methods will vary from teacher to teacher, but I have some tried-and-true suggestions to help you as you begin!
Through some trial and error, I have discovered I like to have students work on open ended math tasks in groups of 2 or 3. Any larger than that, and there tends to be at least one student sitting quietly, and any smaller and you lose the discussion and collaboration piece. As with everything. feel free to experiment until you find the size that best meets your students’ needs.
I always have my groups pre-planned to eliminate any arguing or hurt feelings in the classroom. There are lots of approaches to grouping your students, and each has its positives and negatives. Your groups will likely change frequently, and should be created with your desired outcome in mind.
Ability-grouping can be used very effectively with open-ended math tasks, although maybe not in the traditional method. You can start by considering each student’s test scores, anecdotal evidence, and other data you have about their math capabilities to sort them into high, medium, or low groups. (Obviously, it goes without saying that these groups are kept confidential.) From here, you can select different ways to form your open-ended math task groups. Sometimes you might want to provide some built-in scaffolding by grouping a high, medium, and low student together. Other times, you might want to allow for students to challenge each other, and group two higher students together. I have even randomly grouped students at times. I look at the specific task and consider what my goals are when deciding the best approach. I also reflect on how previous groups have worked together, and use that to inform my future decisions.
Since I had my groups pre-determined, it did not take much time at all to set them up in class. I just called the students’ names for each group and they would come forward with a pencil. I’d hand them one paper for the group, and they would go find a comfy spot to work. This routine was not hard to learn, and took minutes once they had it down pat. Having a routine is critical because you do not want to waste valuable time arranging groups when they could be working!
Creating Open-Ended Math Tasks:
When I first started using open-ended math tasks, I was able to find some through sites like TeachersPayTeachers. These were great resources, but sometimes I would get frustrated that I couldn’t find tasks that directly related with the topic we were working on. I quickly realized, though, that I could make some small changes to the traditional word problems in the math book to make them work!
Keeping the key components of open-ended math tasks in mind, I realized there were a few things I could do with traditional word problems to make them more open-ended. After all, these problems generally had many “knowns” (or numbers that we are given) and one “unknown” (number we are trying to find out). It couldn’t take too much work to change them around to fit my needs.
- Turn the question around to make it open-ended. Instead of asking for a specific unknown, you can ask how you would figure it out. This is simple, but may require some guidance to show students that you expect them to walk you through the steps in their answer.
- Ask for explanations. This might be the easiest approach, as you can simply ask students to “Solve this problem in two ways”, or present another student’s work and have them decide if they agree with the answer and the approach. I like this type of problem, but keep in mind it works best when you have a less-intensive task since you are requiring them to solve it more than once.
- Remove the known. Quite honestly, this is my preferred method and the first one I felt comfortable using. By eliminating one or more of the given numbers, you can instantly make the problem open-ended and provide multiple points of entry.
- Swap the “known” with the “unknown”. Many of the word problems in our math program followed a rather prescribed format. By simply turning the “known” into an “unknown” (and sometimes providing a value for the “unknown”), I could change the problems to be more open-ended and still give some numbers to my class (which the often found comforting).
- Change the unknown. Sometimes, you just need to change the unknown, or even provide a follow-up question that asks them to solve for a second unknown.
Having these different strategies for converting traditional problems into open-ended math tasks really allowed me to have a much larger pool to pull from than I had before. I was also able to always find a task that aligned precisely with the topic we were working on. Almost any word problem can be changed into a math task using one (or two) of these methods.
Grading and Tracking
With all of the changing groups and the fact that there is no “right” answer to this type of work, I had no clue how I was going to grade (or even keep track of) these problems at first. I also wasn’t comfortable not giving a grade since this was fairly labor intensive for my students. So, eventually I came up with this grading scheme. It is a great place to start, and then you can obviously make any necessary tweaks to make it work for you and your class!
Participation Grades: After realizing that not every group was able to complete the entire task every week (even when they had been diligently working on it), I decided that a participation grade was the way to go. After all, my goal was to build confidence in solving problems using new strategies. If students were getting bad grades because these they had to switch gears or revise some work halfway through and were unable to finish, my grading would be counter to my intent!
Tracking: Once I decided to assign participation grades, I felt like a weight had been lifted. But then I realized I still needed a way to keep track of these grades…and I was stressed again! This is where these grading pages became a life-saver.
They are simple to use, and kept my data nice and organized in one place. That was great for calculating grades, and also because I could see which students might need more support at a glance.
The basics of this sheet are fairly standard. I put the dates across the top, and the names alphabetically down the side. (I loved this particular chart because I could fit 3 months’ worth of weekly task grades on one sheet of paper!) The bottom row gave me a spot to record the standard (or topic) that we worked on each week.
From there, you can decide how you want to use it! You can get as detailed as you like, or keep it fairly open. At the most basic level, you can mark a check for students who are working. I like to combine that system with a “C” for students who complete the task, and “NC” for students who weren’t able to finish. I don’t use the “C” or “NC” in grading, but it helps me see if there are some students who may need some guidance managing their time, or help me arrange the next week’s’ groups. You could create your own system to show different levels of participation as well. I have seen teachers use “check-plus”, “check”, and “check-minus to rate participation. You can fine-tune this scale to meet your needs, obviously. However, this is a simple and effective way to keep data about what is happening in your class during this time!
Open-ended math tasks hold such potential to get our students thinking at that higher level. They do take a bit of work to get going in your classroom, but they pay dividends if you can do it! I have seen growth in independence and confidence in all of my students, and especially in some of the ones who had traditionally struggled with math! So, despite my initial reservations, open-ended math tasks will always have a place in my math program.
If you are ready to begin, you might want to check out the Create-abilities Open-Ended Math Tasks Webinar that has a wealth of information and an eBook full of resources.
Do you have any good tricks for pairing or grouping students in your classroom?