Effective teaching and intervention for place value require a deep understanding of numbers in their mathematical contexts, including the relationship between numbers and counting. Knowing how to represent numbers in different contexts, as well as why they are used in certain ways, is part of this task.
Due to the abstract nature of the numbers, students may have more difficulty understanding these concepts when we begin looking at extremely large and extremely small numbers. This post explains how to identify students' gaps in knowledge and how to address their needs when it comes to these more difficult place value concepts.
Understanding Place Value Concepts
Making meaning can be a challenge when it comes to numbers. Many students struggle because they lack the conceptual understanding of what place value really is and how it can help them break apart and reconstruct numbers.
When we consider the math concept in its entirety, there are several key things students should be able to do. First, they need to be able to understand that all numbers have an order or sequence. Second, they must know that each number has a position within this sequence. The foundations of this are laid before students ever enter school.
As the numbers get larger, students need to understand that each digit has value and that these values have a relationship to one another. This is where the standards related to Powers of 10 come in. They also need to be able to read and write the numbers in multiple formats. The same is true when numbers begin to get smaller – such is the case with decimals.
Finally, they need to be able to compare and order these numbers. This means they need to be able to determine if two numbers are equal or not, whether one is bigger or smaller than the other.
Gaps in Knowledge Related to Place Value Concepts
The first step towards addressing a gap in knowledge about place value is identifying exactly what the problem area is. Students often don't realize that they aren't grasping some aspect of place value until someone points out the issue.
One reason for this is because it can be more difficult to recheck their work, unlike addition and subtraction where they can use the inverse to determine if their answer is correct. There are several common areas where elementary students struggle with place value learning tasks.
In my own classrooms, these were the major areas I found to be difficult for my learners:
- Converting between different forms, especially from standard to word form and to and from expanded form when zeros were involved.
- Ordering 3 or more 5-digit or 6-digit numbers
- Comparing larger numbers
The value of formative assessment for place value concepts
When it comes to intervention efforts, the goal is always to focus on data-based decision-making. Formative assessments, exit tickets, or quick checks are all great tools. They allow you to gather this data quickly and easily to ensure that you're targeting the learner's needs.
With place value, this can include evaluating students' understandings through forms that are paper-based or even digital assessments that are self-correcting.
You'll likely want to target specific skills with each assessment. This helps make sure you have a clear idea of who has mastered the learning and who hasn't, including examining whether students may be following inaccurate procedures or have conceptual misunderstandings that need to be addressed.
In my classroom, I found that it was helpful to have two versions of each of the quick checks that I could use to assess important place value concepts quickly and easily as well as monitoring growth.
The main skills I liked to assess as part of my formative assessment included:
- converting to word form
- standard form conversions
- converting to expanded form
- mixed conversion – all three formats
- ordering numbers
- comparing numbers using <, >, and =
Therefore, I created two formative assessments for each skill. to be sure that I had an idea of A) who was showing difficulties in understanding the concepts and B) how students were responding to my place value interventions.
Here's an example of one of the assessment probes I created:
I recently added digital versions in Google Forms that are self-correcting and great for a digital learning environment. Here's an example of what it looks like.
While it can be trickier to provide online interventions to learners, these assessments are a great way to identify learning gaps and ensure you've got a good handle on class learning. I've included these, and their paper-based counterpart, as part of my Place Value Intervention Kit to simplify the process of tracking who needs extra support.
Using Intervention Activities to Help Struggling Learners
In the classroom, intervention plans often take place in a small group as a reteach of the lessons covered in class. This is typically in addition to things like differentiated worksheets offered during regular instruction. These may be documented on an intervention planning sheet to share with your campus SST committee.
Or you might not even consider them interventions at all!
However, when you notice a student is struggling and you're having to consistently reteach the skills most of your class is mastering, it is time to start documenting your efforts as part of their Tier 1 intervention time.
When it comes to place value, intervention activities need to focus on skill and knowledge gaps. Some learners with conceptual misunderstandings will need to go back to the hands-on stage to make things concrete and help them visualize larger numbers.
Using place value disks or the hands-on place value tiles included in my Place Value Intervention Kit can begin to clarify the meaning of large numbers and help students better understand how they break apart to create expanded form.
Other students may just need more proficient procedures or a set of steps. This can help them develop a mental map of the process. Thus, it allows them to fluently work through converting numbers between forms and making comparisons between them.
One common issue is that students are slow or inefficient in working through the process. These students have the foundation of the mathematical understanding of place value concepts. They just aren't fluent quite yet.
In this case, the next step in the learning progressions is to help them built automaticity. Giving clear steps or a mental checklist can be a great way to boost individual student learning in this instance.
Where to find math intervention materials for place value
As a teacher, it can be hard to find intervention materials. You need things that can fit into your already limited instructional time and give struggling students concrete strategies. However, classroom interventions must offer more than just a reteach in the exact same format as your original instruction.
This Place Value Intervention kit is easy to prep while targeting key skills needed in an easy-to-use format. In other words, it addresses common misconceptions and supports growth.
The benefit of this resource is it gives struggling learners a clear approach for handling this abstract concept. It also includes multiple progress monitoring probes in several formats. This lets you know you're targeting the right students. You'll feel confident that you have what you need to ensure that all students can achieve success with the standards.
The Place Value Intervention Kit includes:
- 5 gradual release mini-lessons with step-by-step strategies, guided practice, and independent practice included (available in worksheet and foldable formats)
- 12 skill-based progress monitoring probes (print & self-grading digital)
- Hands-on Value Modeling Tiles
- Student Place Value Strategy Chart & Organizers
- Data collection and tracking sheets to monitor progress
- A summative assessment
- Answer keys for easy grading
Unlike many teaching resources that only include cute crafts or games, these step-by-step lesson plans ensure elementary students show skill growth during Tier 1 intervention held in their mathematics classrooms.
If your students aren't understanding foundational concepts of place value with multi-digit numbers (4-digit, 5-digit, or 6-digits), you can rest assured that this resource will help you plan and implement intervention sessions that make a big difference.
Just click the button to get these handy intervention resources now.