Place Value Cups

I'm going to devote today's blog to a topic I struggle greatly with: Place Value. In our elementary math class, we have learned of a few different number systems: Egyptian, Babylonian, and Mayan, to name a few. Understanding these numbers systems greatly enhanced my understanding of our number system and its use of place value. It also helped me understand the struggle students may undergo when trying to comprehend our own Base 10 system. Although I won't look at these other number systems in today's blog post, I highly recommend examining them and sharing them with your students.

Minnesota's Math Standards regularly refer to the importance of understanding place value. This basic understanding, which feels not-so-basic when you're new to it, is crucial in efficiently undergoing mathematical operations. A student must understand place value in order to truly understand and utilize common short algorithms used for addition, subtraction, multiplication, and division.

The following tool is a neat manipulative to help to students understand place value (from http://suedowning.blogspot.com):

Sue Downing cites many uses of the cups:

"We use the cups to:
        understand place value
        practice counting forward and backward
        learn the names of large numbers
        decompose numbers to expanded form"

I made my own set of cups to try this out, and I found they were most useful for decomposing numbers to expanding form, which allows for a greater understanding of relationship between digits and their place value. By pulling out the thousands cup, I understood that a 1 in the thousands place is not 1 but rather 1,000.

However, the cups do not permit students to experiment with different representations of the same numbers as readily as other manipulatives do.

For example, we know that ten ones are equivalent to one ten. Twelve tens are the same as one hundred and two tens. Four hundred can also be expressed as 40 tens. Base 10 blocks are far more useful for demonstrating this than place value cups, as students are able to actually, physically "trade in" ten ones for one ten (or whatever the exchange is). Developing this knowledge is necessary for understanding and using algorithms.

With the cups, once students reach "10," they have to change the tens digit to 1 and the ones digit to 0. We know that ten ones is the same as one ten, but students may not understand this relationship. Nor are they able to understand and explore more abstract representations of numbers that base ten blocks allow.

Thoughts? Does anyone know of other unique manipulative for learning about place value? Have those manipulatives been effective with students?

"The day i passed maths"

A boy who has long struggled with math shares his passing grade with his father. He knew his father would be happy, so he set up a camera to catch his reaction. So incredibly uplifting. Every child and parent should feel this kind of joy through success in school!