In upper elementary, there are a grand total of ten common core math standards that refer to place value by name. That’s already a sizeable amount, and that’s not even considering how many other standards build upon the foundation of place value concepts! It’s for good reason, too: understanding place value is essential to build effective number sense.
We already know how important number sense is in your classroom. However, before your students can develop a firm grasp on number sense and master higher-level math concepts, they need to develop an in-depth understanding of place value.
Place value is the basis for so many math concepts, from basic operations to decimals and even fractions. That’s why it’s crucial that students are able to not only recognize place value errors in their work, but fix those mistakes as well. When they can identify and resolve issues reliably, students are able to explore more advanced concepts as well as make connections and solve more challenging problems on their own.
That being said, how can we help students identify place value errors in order to achieve excellent number sense and that long-awaited independence? Never fear: I have several strategies, but first, let’s examine the importance of place value in mathematics.
Place Value’s Importance in Mathematics
Place value is the foundational math concept that shows the value of the number is equal to its place in the number. Now, I’m sure we all understand place value, but that definition may sound a bit complicated for the kiddos! Another way to phrase it is by saying that place value is the value of each digit based on its place—so it’s each place’s value!
For example, in any given number, a digit can be in the ones spot, tens spot, hundreds spot, and so on. When students understand place value of a number to the point where they can determine it at a glance, then we’re at the point where kiddos can perform mathematical operations and truly understand why they work—in short, they develop number sense!
That being said, there are several common mistakes that educators often encounter when exploring place value in their classrooms. Recognizing when these place value errors occur is the first step in place value comprehension! By being aware of these issues, you can help students fix mistakes before they find themselves drowning in more complicated problems.
Let’s take a look at some of the more common place value errors!
Identifying Common Place Value Errors in Student Work
It’s common for upper elementary students to make mistakes in writing numbers; I mean, I’ve been working with numbers for nearly four decades, and I still slip up from time to time! Some of the more prevailing mistakes include incorrectly placing digits or flipping them, such as writing “315” instead of “351.”
In addition, students may also make simple errors in addition, subtraction, multiplication, and division, which leads to place value mistakes! Being able to quickly spot these place value errors will help your students fix their work quickly and make fewer mistakes as they go. That being said, let’s check out some techniques to help course-correct those common place value errors and set students on the right path!
1. Visualization Techniques
Like many other concepts in math, place value sometimes feels a bit too abstract for students to fully comprehend. However, using visualization techniques through manipulatives can bring those abstract ideas to a more tangible level, no matter what grade level you’re teaching—manipulatives aren’t just for lower elementary!
Using number lines, grids, and other tools help students see the place value errors in their work. I especially love using manipulatives such as base-ten blocks to help kiddos physically see how place value works! When they are able to use blocks to represent a number, they can quickly identify their mistakes.
Place value sliders are also incredible tools to help students visualize place value and determine where they may be running into errors.
2. Technology Tools
When it comes to teaching concepts, we’re quick to think of technology to help kiddos learn in a modern, engaging way that also helps build those digital skills. However, technology can be used for much more, like correcting place value errors!
There are plenty of software and apps on the expansive world of the Internet that can assist students in recognizing place value errors. These educational software and programs are designed to reinforce place value concepts through engaging activities and provide students with immediate feedback! One excellent example is the Math Learning Center’s tool “Number Pieces,” which “helps students develop a deeper understanding of place value while building their computation skills with multi-digit numbers.”
Wherever you choose to hunt for technology tools to use in your math classroom, it’s worth checking for place value materials, too. Incorporating digital tools into your math block is a sure way to keep students engaged and provide them with real-time feedback to help mend place value errors.
3. Guided Practice
In guided math workshop, the “I do, we do, you do” model is crucial for an effective learning experience, and for good reason! Providing step-by-step guidance and working through problems together helps your students recognize where mistakes may occur. In addition, talking through problem solving reinforces how place value works and encourages kiddos to identify place value errors.
Sometimes, when working through the “we do” phase, I make mistakes on purpose for students to identify. By having students spot and correct the place value errors, it lets them know that I am human and we all make mistakes! I can also demonstrate for them how to recover from a mistake without getting discouraged.
Of course, if your students don’t catch on to the mistake right away, it’s okay to point it out yourself! I like to make a dramatic “Oops!” to catch everyone’s attention, then work through correcting the mistake like I would if a student had pointed it out.
If you’re looking for more information about using guided math workshop with place value, check out my blog post here! I also have several exciting examples (and a freebie!) of using “I do, we do, you do” in the classroom here. Otherwise, let’s check out a couple more strategies to help kiddos fix their place value errors!
4. Peer Review
Peer review is such a handy tool! It allows you to meet with specific students while the rest of the class is busy, or even gives you a breather while your classroom is occupied. Think-pair-share is probably the most common example of peer review, but there are plenty more options for cooperative learning strategies, such as those outlined in this blog post!
Ultimately, peer review boils down to encouraging students to work in pairs or small groups and review one another’s work. Peer review fosters collaboration and allows your learners to catch place value errors they might overlook on their own. And besides, what student doesn’t love the opportunity to chat with their partner?
5. Scaffolded Instruction
Scaffolding is an integral part of any good instruction in the classroom. For many of your students, if not all of them, it’s important to break down entire concepts into bite-sized pieces and gradually increase the challenge level. This allows for the all-important differentiation and for students to build their understanding incrementally. In turn, this helps students identify place value errors at the base level before moving into more complex problems.
Of course, with scaffolding, it’s important to remember to let your students do the heavy lifting! Check out this blog post to establish the difference between scaffolding and rescuing your kiddos. Once you feel you’re comfortable with scaffolding, you can head over to this post for a variety of scaffolding strategies to implement in your classroom!
Ultimately, there are so many ways to help your students recognize and identify place value errors. From visualization techniques to innovative technology tools, these strategies help students recognize and fix place value errors in their work. When combined with engaging ways to teach place value, you’re sure to make a lasting difference on students’ mathematical careers.
Place value is a foundational math skill with plenty of resources to help students make real-world connections and foster higher level math skills. What strategies will you use to help your students identify place value errors?