Have you ever been teaching your place value  unit and been feeling pretty good?  Your kids can label the place value chart, build numbers with base ten blocks….and then things come to a screeching halt when teaching expanded form?  Maybe your kids can only write the expanded form when they can “count the zeroes” for each place? Or get confused when asked what the value of each digit is?

That is usually because the kids are learning by rote memory, rather than an understanding of what each place value really means.

Digits vs. Numbers

First, kids need to understand the difference between a digit and a number. Digits are symbols used to write numbers.  They can be 0-9.  A number is an amount of something and is written using digits. For example, the number 345 is written using the digits 3, 4, and 5. This is the first lesson in my Place Value Interactive Notebook and More! pack with interactive, projectable mini lessons.

Embedding Value of a Digit

How can you help kids really understand the value of each digit and the meaning of place value? One way is to embed the concept of value of a digit very early so that kids hear the term and have time to develop an understanding of the meaning. When I introduce the term value, I introduce with the base ten blocks.  We discuss the value, or what each block is “worth,” as soon as the base ten blocks come out.  This can help kids be exposed to the term very early.

From then on nearly every place value concept I teach is centered on the concept of the value of each digit. How do I embed this in everything?

One trick is to allow students to see how each place value on the chart is related.  In one of my first small group lessons, students actually build a ten using ones blocks, a hundreds flat using only tens (I would do ones as well, but that would take forever! LOL) and introduce the thousands cube. You can see how I model this here, in this video. It is also a lesson found in my  Easy Prep: Place Value pack.

It is important that students see how the places are related, because they need to realize that numbers can be built different ways.  For efficiency, we use as few hundreds, tens, and ones by trading in. However, 18 could be represented by 18 ones or 1 ten and 8 ones- the value is the same. We called this “funny numbers” in our classroom, because they looked funny when they were built on the mats.

Why in the world would I encourage kids to build numbers in all crazy ways?  Don’t we WANT them to build the numbers efficiently so they can easily write them in standard form and expanded form? Well, yes and no.  I do want students to be able to build them so they can easily write them in standard form and expanded form.

However, if students can think flexibly then this will make more advanced concepts much smoother.  Think about it when we subtract with REGROUPING. Students are trading in a ten and breaking up the ones to make them able to subtract, right?  Well, what does that number look like now?  A funny number! So the VALUE of 36 3 tens and 6 ones OR 2 tens and 16 ones…which will help kids later on when subtracting with grouping!

Looking for more practice for “funny numbers?’ Check out this pack, Funny Numbers on the Funny Farm! Want to try this out with a freebie? Just click on the picture below for a FREEBIE!

Clear as mud or does this make sense? Want more tips for teaching place value? Check out this post! How do you teach place value?