Learning place value can sometimes be a challenge for young math students. This is because they are moving from a concrete counting system of objects that they can manipulate or can imagine manipulating to a counting system that is bigger than their concept of reality.
Chanting your numbers is a form of rote memorization that is unattached to the real world. Learning to count actual objects is tangible to a child and it is but a short bridge for children to connect the chanted numbers with actual objects. In fact, this is their first experience with the idea of ratio. There is a one to one correspondence between the the word I say, the number of objects I see and the symbol I write. The child camps in this corner of math for some time, and even though they may learn the number system from one to a hundred, we often are making a mistake if we assume they understand place value. They are still thinking in that same ratio of one object to one word to one symbol and a hundred objects is still within the realm of their experience. They may easily own a hundred small cars, a hundred blocks, a hundred books, for instance
In fact, many children can learn to rote count by hundreds or by thousands, ten thousands, hundred thousands, and on up to our boys favorite – the mystical googol plex. But just as very young children can count to ten easily without yet grasping the relationship between ‘seven’ and seven objects let alone the symbol ‘7’; older children may experience similar struggles when trying to connect the location of a digit in a numeral with its intrinsic value. (This is a separate struggle than the struggle to imagine what exactly is a thousand, ten thousand, a million? Even as adults we struggle to conceive of large numbers like a billion, trillion, etc even though we understand the notation for such large numbers.)
It is often quite a leap for children to move from this stage of the 1:1 ratio to the 10:1 ratio or the 100:1 ratio. It is very important that children should be allowed amble time to explore, play and practice with this new idea of one digit representing a group of objects; and that the location of that digit determines exactly how many objects it stands for. There are many ways of encouraging this kind of ‘play practice’ and manipulatives play a key role.
In our home we have begun playing the card game war using multiple cards to battle with larger numbers. Children must be able to ‘read’ the number but also determine the value of the number – which is greater? I got the idea for this game from Crewton Ramone’s House of Math page Teach Math With Playing Cards. Below is a video that we recorded to show you how we play:
If you have a link or idea for a fun way to practice or play with the idea of place value leave a comment. If you found this post interesting or helpful take a moment to like us on Face Book or sign up for our newsletter in the sidebar!