This video is of me introducing teen numbers to my 4 year old. She already knew how to count past 20, but that doesn't mean she knows what those numbers actually mean or that she understands place value! Cuisenaire rods help children see the structure in our number system. They are visual and kinesthetic, therefore, information learned while using them is stored more easily in the brain.
This video shows me combining the rods with numerals into the teens and then we go on to name the "tens" (20, 30, 40, etc.) This was her first experience with this idea of place value. We'll be going over this many times before it really sinks in.
This video shows another way to introduce the concept of place value in the decimal system. This is a more traditional way to do it. People usually use Base Ten blocks, but Cuisenaire Rods work perfectly well, too!
Notice that I don't tell her the English name for every single number. It is more important at this point that she understand the "tens and ones" concept than that she attach each quantity to a particular name. Eventually it will all come together in her mind that "ten and three" and "thirteen" and "13" are all the same thing.
Let me repeat: It is much more important that children first understand "tens and ones" than that they be able to say "thirteen" when they see "13."
This is an important concept to get down, especially for when it comes time to do long multiplication or division. Lots of practice in giving the "real" names for a certain number of tens or telling how many tens is in a number is essential for understanding more complex elementary school math.
Cuisenaire Rods help make the concept of place value, which is often very abstract for children, more concrete and understandable. They can visualize it. They can feel it. They can much more easily internalize the concept.
This concept is slightly easier than talking about tens because we call numbers in the hundreds place, hundreds. This is not the case with the tens place. We say "twenty," not "two-ten" or "thirty," not "three-ten" as they do in other countries. Working on naming a certain number of hundreds when they add up to more than one thousand is the important concept here.