### 5 Ways to Explore Place Value Concepts

If you teach intermediate grades, you know that a solid understanding of our place value system is essential.  That being said, many math series focus a great deal on "fill in the blank" place value work...reading and writing big numbers, writing numbers in expanded form, or putting greater than or less than signs between two or more numbers.  Don't get me wrong--these are important.  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 ideas and see what you think!

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 our 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 snack."  The more ridiculous, the better.

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.
 Check out my number line resources for more ideas...
And then take things to an even higher level:

Ask students to identify point outside two numbers on a number line...
Try having students write their own problems for others to solve...

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:

1. The number must be a five digit number.
2. The first digit must be a 1
3. The second digit must be an 8.
4. 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!

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!

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

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!