Approaches to teaching place value differ depending upon grade level. In the primary grades, place value is taught using many techniques; one of the most-effecive is using base-10 manipulatives, which come in different shapes for different place values.
After the focus of the early grades, in general, students possess an understanding of place value by the time they arrive in the intermediate grades.
As a result, we are no longer focusing on identifying 1's, 10’s, or 100’s places in a number; instead, we focus on applying place-value understanding for everyday applications and solving problems.
Simple games for repetition
All students need to understand how to apply place value to verbally say a large number. This is tough for students and takes a lot of repetition and practice.
But repetition can be fun! Here's how I handle it in my classroom.
This “game” is simple and can be fit in between other elementary math activities. I write a large number on the board, something in the millions or even higher if I feel they need more of a challenge.
Then in the morning, as they're putting their personal whiteboards away after number strings, they must file by me and read the number correctly. If they don't read it correctly, they go to the end of the line and come back through.
The children love it! It’s a fun challenge, but most importantly they get a little bit of that one-on-one time with their teacher, which is always a huge motivator.
Video tips: teaching place value
Place value in intermediate grades really comes into play when we are comparing two numbers. For example, when comparing the number 400,000 with the number 400, students need to be able to express how much bigger the “4” is in the first number than it is in the second number (it’s 1,000 times bigger).
I often mix in other numbers just to confuse them, such as having to compare 435,672 with 419. Of course, the answer is the same.
When teaching place value, we are trying to instill an awareness of size versus an awareness of digits. The digits are simply mathematical symbols that must be placed within the context of their position.
Place value and algorithms
And not just multiplication or division algorithms, but all algorithms — even addition and subtraction. They are all place-value dependent. When children understand place value, they are much more successful in applying these standard approaches to resolving mathematical problems.
There are a lot of place value games on the Internet. If you simply search for “interactive place value games third grade” (without the quotes), you’ll find a lot of opportunities for your children to practice.