February 16, 2014

Place Value Disks - A Valuable Tool?

I was just reading through a mathematics module from EngageNY and saw multiple references to "place value disks." I had never heard of them, so I did a quick search. Here's what they look like:

These seem pretty cool at first glance... the student can put the disks in a place value mat and show how a number can be decomposed.

HOWEVER I have 2 major concerns about these:

1. They don't show the meanings or relationships of the values. Each value (1, 10, 100, 1000, etc) is exactly the same except for color. To be mathematically accurate, the 10 discs should be 10 times larger than the 1 disc, and the 100 disc should be 10 times larger than the 10 disc.
Interestingly, I did find this teacher-made version:
Better, but it doesn't look like they are accurate. Could 10 of those yellow discs really fit inside the red one?

2. They are misleading when used in a place value chart. Take this image, for example:

Many people would agree that this chart shows 446. However, it actually shows 40,406. How? Look in the Tens column. Since each disk is labeled "10," then each disk represents 10 tens. Therefore, there are actually 4 x 10 Tens in the chart and 4 x 100 Hundreds. So the chart shows 400 Hundreds, 40 Tens, and 6 ones.
This is the same reason why the common practice of bundling sticks is troublesome:
This is NOT 126. Since each stick is one, and there are 100 sticks in the hundreds column, that means the 100 x 100 in the hundreds column alone.

To use a place value chart properly, simply record the number of times that value is used. Like these:
These are better because you simply count the number in each column. If there are 2 blocks in the tens column, that is 2 tens or 20.

The problem with place value disks in a chart is that they show value, rather than simply counting how many one, tens, hundreds, etc you have.

So how CAN you use place value disks?

This is a great use for place value disks. Since they aren't in a chart, they really do show the number represented. The benefit here is that they require less drawing/writing for the student. They are a short-cut.

I suggest using place value disks only after the students have a strong understanding of number and place value. They don't really represent their value and can lead to confusion when used with place value charts.

~ Amanda