Addressing Place Value Misconceptions

When starting a new unit of study, it really helps to know the most common mistakes students tend to make. That way, instruction can address those misunderstandings right from the start — before misconceptions have a chance to settle in.

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One resource I often turn to when thinking about common math errors is Math Misconceptions, PreK–Grade 5: From Misunderstanding to Deep Understanding. It does a great job of highlighting frequent misconceptions and offers practical, classroom-ready suggestions for addressing them.

Place value is one of those foundational skills that really requires deep understanding. Many students can point to the digit in the tens place, for example, but may not understand what that digit actually means — that a 3 in the tens place represents 3 tens, or 30, not just a digit you name.

One sign that students may not truly understand place value is when they misread numbers that include zeros. Zeros are especially tricky and often reveal gaps in students’ understanding of how place value works. With that in mind, instruction and tasks can be intentionally designed to target zeros and help students build stronger place value understanding.

Here’s a simple activity that focuses on working with 6-, 9-, and 12-digit numbers that include zeros. It works well for small-group instruction and can later be moved to a workstation for partner practice. Because the numbers are randomized using dice, the activity can be reused for engaging, meaningful practice.

The activity is set up a bit like a Hangman board, with blanks for each digit. The recording sheet shown is for 6-digit numbers, but versions for 9- and 12-digit numbers are included as well.

To begin, students place zeros in two of the spaces, with one important rule: the number may not start with a zero. To complete the number, they roll a die four times and place each digit as it is rolled. Once the number is complete, students read it aloud and then record it in both word form and expanded notation.

After repeating this process four more times, students order their numbers from greatest to least and find the difference between the greatest and least values. There’s a lot of math packed into this simple activity!

This type of focused practice can go a long way in strengthening place value understanding. You can download the free resource here, and you may also find this post on reading large numbers helpful as you plan instruction.

If you’re looking for a great strategy to help kiddos read large numbers, check out this blog post.