Rachel Fuhrman

“Don’t round up.” This was the advice my principal gave me after my first observation as a 6th grade math teacher. You might be wondering what he meant (I certainly was) and why it's something I needed to avoid. To put it simply, “rounding up” means filling in the gaps in your students' answers; rather than pushing students to give complete, precise answers, you accept a close enough answer, and add the missing pieces yourself.

Picture this; you’re in the midst of a challenging lesson and you really want students to get this content. You ask a question—maybe it’s “What is the area of this irregular figure?”—and, you're excited to see, hands go up! You call on a student and they say “14” which is almost correct. Obviously, we want to hear our students giving us complete answers with units, but this was a tough question and you just want to move on. So, you say, “Yes! The area is 14 square inches” and you keep moving.

This is rounding up. When you make your students’ answers just a little bit stronger, more precise by filling in some gaps. You can imagine how this would apply in many different mathematical situations beyond just units: When students solve a word problem and don’t give a complete sentence answer in context, when students solve an equation and don’t define their answer in terms of a variable, when students forget the negative sign in front of an answer, or when they use the incorrect mathematical vocabulary. Additionally, this could also look like a partial answer to a question where a student may have the correct numerical answer, but may not address, or may not fully address, the “how” or the “why” component of the question.

Let’s think through one more example and really focus in on the partial answer piece: This time, you show students an irregular figure and you ask “How could we find the area of this irregular figure?” You call on a student and they say, “just add it all up!” This is partially right, so maybe you just say, “Yes! We can decompose this figure into other shapes we know how to find the area of, and then add those areas up.” As the teacher in the situation, you’ve made a lot of assumptions about what your student meant, and how much they understand about this kind of problem. By rounding their answer up to be a more complete, accurate explanation of how you could find the area, you take the cognitive lift away from student and move on without really knowing if students understand.

It can feel really easy, and harmless, in the moment to just round your students’ answers up in order to keep the lesson moving. But, by doing so, you can stifle student learning and put more of the heavy cognitive lift on yourself, rather than your students.

When you round up your students’ answers, you not only give them an easy out, but you show students that they don’t need to be precise—you’ll do it for them. If you set the expectation that incomplete, or almost answers are acceptable in class, students will likely continue to give them.

Students will miss out on building the understanding of why precision matters.

Not only do we as math teachers recognize the importance of precision, but the Common Core State Standards for Mathematical Practice specifically require students to “Attend to Precision.” This Standard for Mathematical Practice outlines that proficient math students, “try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning.”

Thinking back to our example involving units, if students don’t understand why units, and specifically square units for area, are important, they aren’t going to remember to use them! Units help students make sense of answers and demonstrate a conceptual understanding of the procedure they are applying. So, if you are adding things like units for them everytime, how are they going to develop that understanding?

This same idea applies to mathematical vocabulary. If we don’t push students to use the appropriate mathematical vocabulary in class, they aren’t going to internalize the meaning of those words, and won’t feel confident using them in verbal or written contexts in the future.

Additionally, as much as we may not like to think about it, standardized exams are a reality for our students. And one thing we know for sure, is that there will be no rounding up on those standardized exams. To ensure you are preparing students to be their most successful, you need to hold them to the same expectation in the classroom, which means you can’t round up either.

When students give answers that are close, but not exact, it’s important to push them to consider what is missing and encourage them to refine their answers. This doesn’t mean you have to put them on the spot in a negative way! As math teachers, we know how difficult it can be for students to speak up in class and we therefore want to encourage them by making it a positive experience. But, we also can’t pretend their answers were perfect. Instead, we can prompt them to make the necessary adjustments, or call on other students to support them in finding the precise solution.

To avoid rounding up students’ answers in the moment, you can prioritize looking for precise answers during your intellectual prep process. Within your lesson plan, identify the key components of each solution you want students to identify, and consider how you will prompt them for any missing pieces. With Fishtank Math, this is easy to do as math lessons include the Sample Student Responses you should be looking for. Additionally, lessons include Guiding Questions you can use as a jumping off point to deepen student thinking if they are struggling to arrive at the precise answer you intended.

As mentioned before, rounding up students’ answers in class can stifle their learning, and doing so on their assessments can leave them less prepared for the high bar set on standardized exams. To help you better support students, Fishtank Math provides Post-Unit Assessment Analysis Documents for all units—available to Plus subscribers–that outline what a student must show to earn full credit for each problem on the Post-Unit Assessment. Additionally, the document includes a spectrum of possible student solutions to help you recognize and discuss with students the components of a complete answer.

Want more ideas to set your students up for success this school year? Dive into the Fishtank Blog to find strategies for engaging every student, guidance on using Fishtank resources, and the latest on what works in the classroom. Create your free Fishtank Learning account today to access thousands of free, standards-aligned, lesson plans in ELA and Math.

*Rachel Fuhrman is the Curriculum Marketing Manager at Fishtank Learning. Before joining Fishtank Learning, Rachel spent 5 years as a Middle School Special Education Teacher in New Orleans, LA and Harlem, NY. Outside of the classroom, she has been a frequent contributor to multiple education blogs and focuses primarily on student engagement and instructional practice topics. Rachel earned both her Bachelor of Arts in Economics and her Master of Science in Educational Studies from The Johns Hopkins University.*

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