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, like decimals).
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 the conceptual understanding, they help students who might otherwise flounder build strategies and experience success until their conceptual understanding catches up with their procedural abilities.
Easy ways to teach converting numbers & place value to struggling students
These tips for teaching place value are perfect for working with your struggling learners. They 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.
Teaching students to convert place value between standard and expanded form
Expanded form can be really tricky for students. It requires them to break down numbers and keep track of the value of each digit while they write a series of very large numbers.
So many students seem to really struggle going back and forth between standard and expanded form that I prepare in advance by having graph paper ready when I teach this lesson.
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.
When it comes to teaching my struggling students to convert from standard to expanded form, I like to teach them to use visual cues. 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.
Then they cross off the first digit and repeat the same process with all the rest.
I also find that many times students rush through the process of converting the numbers from one form to the other. They also 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 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 to help.
This 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. We use a highlighter to make sure the commas stand out and help students really pay attention to them.
If a student still struggles after I give them this tip, I teach them to box the word “thousand”. We underline and read the number before the box. Then we put a comma in place of “thousand”. Then they write the number after the box.
Get the Place Value Cheat Sheet
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Assessing place value mastery – the most important piece of the puzzle
One of the most important things I do with my struggling students is use formative assessments, or quick checks.
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 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:
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.
Differentiating place value lessons using formative assessment data
I have a set of 12 of the formative assessments – 2 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:
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.
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.