Teaching place value is always a challenge when it comes to my third graders. They come in with very different levels of understanding, and I find that I need to spend a lot of time differentiating to meet their needs and get everyone on the same place.
It can be a struggle to figure out how to teach place value for those students who are struggling with the abstract thinking required to visualize really big (or really small) numbers. While most students can break down a three-digit number without math manipulatives, once the numbers get larger, things get dicey.
While some students are ready for independent practice with only a short mini-lesson, others need lots of repeated exposure. These easy ways to teach place value have been a huge help for those students who might be struggling with the abstract nature of place value.
While these tips cannot replace conceptual understanding, they help students who might otherwise flounder build strategies and experience success until they internalize these math concepts and their understanding catches up with their procedural abilities.
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The easiest ways to build a solid understanding of place value & converting numbers between forms for upper elementary students
As we dig into the strategies, please remember that most aren't focused on conceptual understanding. Instead, they are designed to help students who are ready for the more abstract concepts.
Not all issues are deeply rooted when it comes to place value. Many of my 3rd grade students struggled because they just tried to rush through the process of didn't check their work. I found giving a step-by-step checklist like the one below was a great way to put a check system in place to avoid these issues.
These strategies will help them build fluency with their ability to convert between number forms and compare and order numbers. They aren't a replacement for work with concrete manipulatives, like number disks or tiles, when you're teaching place value. However, they can be a great tool for working with struggling learners who just need a strategy to help them organize their thought processes.
These tips focus on step-by-step methods and using math tools and resources to make it easy to see the process.
Like I mentioned, they are not designed to replace the lessons you teach on the conceptual level. However, they will help students build procedural fluency while they continue to work through the abstract nature of learning place value. They can also be a big help when you're working to plan place value interventions for struggling learners.
1) Teaching students to convert place value between standard and expanded form
The conversion to expanded form can really challenge students. As part of the Common Core Math Standards, students in grades 3-5 are beginning to work with much larger numbers, which only exacerbates the issue.
Converting from standard to expanded form requires learners to break down numbers and keep track of the value of each digit while they write a series of very large numbers. For students who struggle with motor planning or dysgraphia, the process of getting all those zeros on paper can be overwhelming. However, there are a number of simple ways to help them.
The first only requires a simple piece of paper! Graph paper is so helpful when converting from expanded to standard form because it allows your students to line up the zeros accurately. This free graph paper can be quickly and easily printed for use when working on expanded form problems.
Alternatively, you can grab an inexpensive multisensory writing pad to help students better align their numbers, too. This version offers both boxes, like graph paper, and some color-coding to help keep students' work neat and aligned correctly.
Since so many students seem to really struggle going back and forth between standard and expanded form that I prepare in advance by having this special paper ready when I teach this lesson.
Teaching Tips for Converting Standard to Expanded Form
When it comes to teaching my struggling students to convert from standard to expanded form, I like to teach them to use visual cues to ensure they've correctly written all the pieces of a multi-digit number.
First, I have them underline each digit in the number. Then they record the first digit (largest place value) and count the number of underlines behind it. That helps them know how many zeros to put after that digit.
I like to have students practice these steps multiple times during guided practice exercises before I have them work through them independently. I'll also consider using an error analysis model during math talks to help keep the conversation going and build in opportunities to discuss more of the underlying foundational concept of place value.
2) Simplify converting place value between standard and word form.
Converting between word form and standard form is another common challenge I see with place value. When students continue to struggle despite having a number of re-teach lessons, I like to give them a visual strategy as part of my Tier 1 classroom intervention efforts.
In this case, the strategy centers around the comma.
I teach my students that when they see a comma in word form, there must be a comma in the same spot in the number.
I keep erasable highlighters at my small group station, and we use a highlighter to make sure the commas stand out and help students really pay attention to them.
More support to help students master the transition between word form and standard form
If a student still struggles after we begin to use the highlighters, I add in an additional visual by teaching them to box the word “thousand”.
We underline and read the number before the box. Then we put a comma in place of “thousand”, and they write the number after the box. Finally, they cross off the first digit and repeat the same process with all the rest.
Making the process visual has been a really great approach for students, and I consistently see it used during our math practice.
3) Converting numbers with zeros: a common challenge when teaching place value
Other learners find the process of converting numbers to be easy but still really struggle when zeros are involved. Here are two tricks I've taught my students for checking their work:
Expanded form to standard form: Check your work by counting how many digits are in the first number of the expanded form version. This is the number of digits that must be in their answer.
Standard form to expanded form: Check your work by counting how many non-zero digits are in the number. This is how many addends you should have in your expanded form version.
Simplify Supporting Learners with this Place Value Cheat Sheet
In our classroom, we keep math journals to help organize our learning. In addition to differentiating the assignments and math centers I use for those who are struggling to master place value concepts, I also created a cheat sheet.
The goal of this printable is to help my students remember the steps to converting numbers between different forms. I'd love to share it with you for free!
Assessing place value mastery – the most important piece of the puzzle
One of the most important things I do with my struggling students is using formative assessments or quick checks. If you're unfamiliar with formative assessment, they aim to give you more information on the next steps for teaching and aren't designed to be included in the grading process.
Since place value tends to be one of the most challenging things I teach all year, I start right away assessing all students that receive a re-teach lesson. This helps me keep track of who is mastering specific skills during my guided math groups. It also helps me make sure I am filling the gaps that occur across the unit.
For some kids, this process continues as a Tier 1 intervention through guided math groups and mini-lessons spread across the next few units because they aren't quite developmentally ready to leap to the abstract nature of place value and large numbers.
Here's an example of one of the formative assessments I use in my class:
As you may notice, I always try to include one question that requires students to explain their thinking. This helps me see who has mastered the procedure and who truly understands the concept.
Recently, I also created a digital version of these to support formative assessment during virtual learning. These are in Google Forms which makes it easy because they are self-correcting!
Using the formative assessment data to differentiate while teaching place value
I have a set of 12 of formative assessments – two per skill – for my place value and money unit. This lets me recheck students who still need additional guided practice and support after a few days.
Depending on my class I've used these in two ways:
Option 1: Place Value Pre-Post Assessments
When I have a group that is really at different levels, I give one of these assessments before I teach the lesson to those students who are likely to have already mastered the concept.
This lets me know who has already mastered the skill so I can give them a project that requires them to apply their knowledge. This is a great way to build project-based learning into my math. This also allows me to teach the skill to a smaller group of students without boring the students who have already mastered it.
Option 2: Place Value Post-test & Retest
When I use the formative assessments in this way, I give one as a quick check after I teach each lesson. This is typically how I do it when my whole class has weaker place value skills and there aren't students who have already mastered the unit objectives.
Once I see how students do on the formative assessment after the lesson, I build small groups and do re-teach. The small groups take the alternative version a few days later after they've had additional opportunities to learn and practice the skill.
More Printable Activities and Classroom Resources to Help with Teaching Place Value?
While the strategies I mentioned above are not designed to replace the lessons you teach on the conceptual level, they can make a big difference for struggling learners in upper-grade levels. They will help students build procedural fluency while they continue to work through the abstract nature of learning place value.
If you're needing more support for your place value unit, I've created several resources and fun activities to help you out.
Click on the images to check them out now in my store.