Why is place value so hard?  

Place value is the understanding that the place of the digit determines its value. So a 2 in the ones place is far different from a 2 in the tens place. It is one of the most important concepts to understand in math because it is the root of number sense; the basis from which all calculations with larger numbers are made; and crucial for comparing and ordering numbers, which is an important  life skill. To read more about the importance of place value, click here.

But place value is one of the most difficult things for students to comprehend. Why? Because it is abstract. Students can’t visualize, let alone comprehend, what these large numbers look like; so how can they represent them abstractly in standard form?

Another reason why place value is so hard for students to master, is because place value is a base 10 system, which means that digits to the left are 10 times bigger and digits to the right are 10 times smaller. But how can we expect students to understand that, when they haven’t even mastered multiplication and division????? We expect them to be able to read and write and represent large numbers long before they have a solid understanding of multiplicative thinking!

How can you make place value easy?

There are two things you can do in primary to help students develop a solid understanding that will prepare them to deal with bigger numbers better. First: since the concept is abstract, make it concrete. Any physical  groupable model such as rekenreks, ten frames, and most importantly base 10 blocks, should be featured in all your lessons. You want students to practice and complete bundling of 10 and trading for 1.

Understanding that 10 of one thing can be 1 of another thing is your focus. But don’t forget to go the other way…show that 1 of something can be broken up into 10 smaller units as well. Often teachers forget this, which is detrimental to the development of fractional parts and decimal numbers later on. Just like we should be linking addition and subtraction, so to, should we be linking grouping and ungrouping.

Second, concentrate on the additive property of place value (expanded form).  Primary students don’t fully understand multiplication and division and thus the base 10 system, but they do know how to add. Do substantial work demonstrating to your students that numbers are made up of different place values. For example,  23 is actually 20 + 3. This will not only help them decompose numbers in different ways (build number sense), it will also give meaning to the different place values. 2 isn’t just a digit, it means 20 or 2 tens and is completely different from a 2 in the ones place.

Here is an example of Rory using the additive property to understand numbers. As you can see, I thought it was “amazing!” (apparently I need to cut down on my use of that word!).

For more do’s and don’t about teaching place value, read my earlier post found here.

Using place value cards

Place value cards are very underutilized in the primary classroom; however, they are a great way to bridge the gap between concrete models and abstract representations. The benefit of using a colour-coded set is that students quickly see the patterns and similarities. They begin to recognize which colour relates to which place value. These cards are a great transition for those needing a bigger challenge and who have mastered bundles of ten. Students quickly learn how to use them (stack the smaller place on top of the larger). The cards also make it easy for kids to read the numbers into the thousands because they can just spread them out: 9875 becomes 9000 + 800 + 70 +5. If they can recognize that, they can read the number while reinforcing the additive property at the same time.

Still not sure how to use them in a class? First, look at the patterns within each place value. Then practice composing and decomposing some numbers. Give them challenges about what to create: largest odd number, smallest 3 digit number, etc. Play some games that require ordering and comparing numbers. Use the cards to help them play. If they’re ready, move on to some addition questions and have the students add by decomposing the numbers first into their place values, grouping them and then recomposing the new number (the sum).  Here is an example of Rory and I playing a game using the place value cards and a number line. He loved it!

All of these ideas can be done individually, at a station, or as a whole class. Have more ideas of how to use them, I’d love to hear them! Leave your ideas in the comments below!

See? It’s not so hard to make place value easy!