Unitizing - The Foundation of Place Value


As I have worked with fourth and fifth grade students recently it has become extremely painful to me to realize how many of our students do not have place value and base ten understanding.  I see students who still solve problems by counting by one. 
Any idea how long it takes to count 144 dots by one?  A very, very long time.  As I have studied place value, I've come across a new concept, at least it was new for me,  called unitizing.  It is actually the foundatioal skill for students to have before the base ten system will make sense to them.
Unitizing is the preliminary place value understanding that ten can be represented and thought of as one group of ten or ten individual units.  This is a huge shift in thinking for children. 
Example: The number 26 can be represented as 26 units, 1 ten and 16 units, 2 tens and 6 units.

This extends into an understanding that hundred or could be represented as group of hundred, ten groups of ten, or one hundred individual units. 

Kammi (1995) states these ideas require logico-mathematical thinking they cannot just be explained or transmitted.  Children may be able to paraphrase these ideas back if the teacher explains them, but to really understand these ideas, children must infer them on their own, and this requires setting up relationships, generalizing, and understanding why the pattern happens.  This is KEY for number sense to develop. Ten tens is one hundred so thirty tens is three hundred.

Unitizing is a "Big Idea" or critical building block in mathematics.  It is at this point you see a shift in a child's reasoning, perspective, logic, and in mathematical relationships.

Unitizing underlies the understanding of place value and multiplication and division of ten.  Unitizing requires that children use numbers to count not only objects but also groups - and to count them both simultaneously.  For learners, unitizing is a shift in perspective.  Children have just learned to count then objects, one by one.  Unitizing these ten things as ONE thing - one group- requires them almost to negate their original ideas of number.  Unitizing is a huge shift in thinking.  It is important skills for all operations.
We need to get students as early as kindergarten to work with groups of ten, base ten blocks, counting by tens, and shifting from counting by tens to ones.  This needs to continue to grow with the grouping of hundreds, tens, and ones, etc.  

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