Place Value Relationships: Teaching Ideas and Place Value Activities
When Texas changed their math standards years ago, one of the TEKS stood out to me. Even now, 8 years after I’ve said farewell to my 4th grade classroom, I still remember TEKS 4.2A: Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left.
The way this was worded left me scratching my head when trying to figure out how to get 9-year-olds to understand it. But when I realized it’s simply describing relationships within the base-ten system, that helped it click for my students. But it wasn’t easy, and it took a lot of trial and error to explain it in a way that made it make sense.
Here are some strategies and activities that worked for me teaching place value relationships in my 4th grade classroom and with my own kids at home.
Place Value Relationships: Make It Visual
Most of the kids easily understood the “Interpret the value of each place-value position as 10 times the position to the right.” They understood that each place was just ten times the one before it. But it was the “one-tenth” part that threw them off. While kids are familiar with fractions by 4th grade, looking at place value in this way is very new, and a little bit abstract at first.
I can’t stress this enough: kids need to see how it works. They need to physically hold the place values, move them around, and experience this concept for it to stick. This is why now, I always bring out the base-ten blocks before I begin any kind of explanation.
We start with the little ones block and hold it up against the tens rod to show how it looks like a fraction model with one-tenth shaded. We then line up a tens rod on top of the hundreds square to show the same idea.
You could also print out a tens rod and ask students to shade one-tenth of the rod. Then ask “How much did you color in?” When they say “one,” you can connect this to the place value relationships. Then repeat with the hundreds square and tens rod.
Place Value Interactive Notebook
Once kids have a good understanding of this, I like to have them solidify it with an interactive notebook activity. Not only does this have them bring the concept to paper, but it creates a resource for them to look back on if they need a refresher.
I created this Interactive Notebooking Activity because I want them to have a reminder of what place value relationships look like with base ten blocks by treating them like fraction models. This is a great place to get the fraction blocks back out so they can visualize it as they fill in the place value block section on their interactive notebook page.
Then for the number line section, we fill in the number for each place value, then we start by drawing arrows showing how each larger place to the left is ten times the value of the place to the right. Normally, we would explain the opposite as each place value being divided by ten. I do introduce this idea as well, but since the standards specifically use the fraction one-tenth, I bring it back to fractions here and remind students that each decreasing place value is one-tenth the value of the place to the left.
Whew! That’s a lot of words, and the explanation can feel heavy. But if they have a visual to connect with as they learn this, it really helps.
This Place Value Relationships Interactive Notebook Activity and Quick Check Assessment works great for us, because it gives them that number line for reference, some practice problems to refer back to if they need to see an example, and the Quick Check is my exit ticket so I can quickly see which kids still need help understanding this.
Get Moving!
The whole left/right wording of this TEKS is what always tripped up some of my students. So to help practice this in a fun way, I would give each student their own “place” on a notecard, like ones, tens, hundreds, thousands, and so on. Depending on the number of students, you might need to split them into a few groups for this. Once each student has their place value, they line up in order. Then, I give some simple instructions:
Turn to face the place on your left
Turn to face the place on your right
(If you have any left/right stories, this is a fun time to use one!)
Then, I hand each kid an object. I’ll say: “Pass this to the place that is 10 times your value.” Then, “Pass this to the place that is one-tenth your value.” (You’ll have to repeat each instruction a few times, otherwise the kids just keep passing it back and forth!)
We do this slowly at first, then as the kids get more confident, I speed up. Sometimes we’ll see how fast we can go, until it erupts into chaos and laughs!
This is one of those standards that feels “serious,” so approaching it in this fun, lighthearted way helps lower the intimidation factor for the more math-wary kiddos!
Place Value Relationships: Wrapping Up
If you use our Place Value Relationships Interactive Notebook Activity, there’s a really handy quick check assessment in there that makes a great exit ticket. It lets you know who totally gets it, and who might need a little extra practice. For the first bit, I let them use their interactive notebooks with the number line for reference too.
As always, when it comes to new skills, I believe in taking time to really break it down. Place value relationships is one of those things that is good to really understand while young, because it gives them a stronger math foundation later on.
And if you're not ready to introduce the one-tenth concept yet, check out the version below that only shows increasing place value relationships!
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