5 Place Value Activities for Deep Understanding

If you teach upper elementary math, you know that a solid understanding of our place value system is essential. Unfortunately, many math series focus a great deal on “fill in the blank” place value work. This could involve reading and writing big numbers, writing numbers in expanded form, or putting greater than or less than signs between two or more numbers rather than deeper, more meaningful place value activities. Don’t get me wrong–these are important.

Place value lessons and activities: A blog post

Unfortunately, students can be successful at these tasks with very minimal understanding of our place value system. Want to kick it up a notch? Check out these five place value activities and see what you think!

Place Value Lesson #1

Study the names of the different “periods” of numbers. Students LOVE to learn about big numbers…and even if your curriculum only goes up to 6 digits like mine, exposing students to the patterns of our place value system helps build understanding and interest. Reading books like Steven Kellogg’s “How Much is a Million” and other big number books can add to the fun. Students LOVE to see not just millions…but billions…and trillions… and…

Having students read and write these huge numbers helps them see how we work in sets of “three” digits…and once you learn the pattern and the names of these different places, you can read any number! We even make up ridiculous statements like, “I think I’ll eat 4 quadrillion, 247 trillion, 723 billion, 924 million, 429 thousand, 294 doughnuts for a snack.” The more ridiculous, the better.

Encourage students to write and read numbers in partners and make up their own crazy tales with these huge numbers. Stress the importance of the commas to show the different “periods” and how they are clues when writing and reading large numbers. Practice in small dose often–it’s a great warm up activity. I also love to try to fool students by using numbers that have lots of the same digits so they really need to concentrate. The number “10,010,110” takes more concentration than “53,623,678”. Mix it up!

Place Value Lesson #2

One of the most important ways we can build students’ understanding of numbers is to work extensively with number lines. Often, we ask students to place numbers on a number line or ask them to identify a point on a number line…like the problem below.

When asking students to solve problems like this, encourage them to show their thinking by adding other “benchmark” numbers rather than simply guessing. Better yet, have them share their thinking so others can learn from different strategies. This is a great time to identify and clear up place value misconceptions. Also, this is SO much more powerful than simply filling in the blank on a number line in a workbook!

Check out my number line resources for more ideas…

And then take things to an even higher level:

Start with numbers lines that do not begin at zero…
Ask students to identify points outside two numbers on a number line…
Try having students write their own problems for others to solve…
Ask students to write about their thinking, not just talk about it…

Place Value Lesson #3

A third way to dig into place value is to experiment with mystery numbers. I start my place value unit with some of these with smaller numbers and gradually make them more and more complex. Some of them might have only one answer–and others might have tons of answers…all of them can lead to GREAT discussions about how they can tell what numbers will fit the rules! For example, the problem below should lead to some of the following conclusions:

The number must be a five digit number.
The first digit must be a 1
The second digit must be an 8.
The ones place must be a 1, 3, 5, 7, or 9–until they realize that the tens place number is double the ones place (ruling out the 5, 7, and 9)

You get the idea. What WONDERFUL math talks. And the best part? Ask students to try writing their own!

Place Value Lesson #4

Another element of place value that is often overlooked is the idea of being flexible with numbers…being able to manipulate numbers in the different places. If a student sees the number 15,273, they should easily be able to tell you what number is 400 more…or 30 less…or 6 more…or 40,000 more. Whether this be with mental math exercises, games, or other “number play”, I did a bunch of these problems with my students and it was fascinating to watch their different strategies and struggles!

For some students, this really took awhile to make sense. We actually did some addition problems to “prove it”. What’s 500 more than 5,267? Let’s add the 500 and see what happens. When students study and NOTICE, the connections in their brain grow so much stronger than if we simply TELL them. Or worse yet–never expose them to this type of thinking!

Check these cards out as a part of a place value pairing in my store!

Place Value Lesson #5

Finally, big numbers are amazing and very “real world”. Students love to know that we have about 30 trillion red blood cells at any one time. Our best estimate as to how many stars are in the universe? 100 billion. There are over 900,000 different types of insects in the world. Encourage students to find big numbers in the books they read…in the newspaper…related to your subject areas. Maybe even create a “big number museum” where you record their findings!

So…have FUN with place value. Don’t let the scope and sequence of your pacing guide or math textbook get in the way of helping students develop their natural wonder for numbers in their world!