Post # 11 The Decimal Place Value System

The early days of the class focus on what we believe is the core deficit in math disabilities, numeracy.  The automatic recognition of quantity and quantity relationships is incredibly important.   Using manipulatives and simultaneous processing as a strategy, we help children create multi-modal memories to support applications.  Early addition and subtraction skills rely on these representations and as we extend them across place value we help students to prepare for more complex computations.  In reading we would say the child moves from learning to read to reading to learn.  In math we build the tools for later calculations and problem solving by building fluency with number awareness and facts. 

One early activity I like to use with young students is building  place value concepts without counting.  Ask pairs of students to build tally marks with craft sticks on a place value mat.  One student builds the tallies and quickly passes two sets of tallies to a partner who bundles them into a ten.  We time them to see how many tens they can build in two minutes.  On day two we bundle more tens.  On day three we make tallies with ten bundles and build one hundred with our tens.  They quickly learn how our system of quantity bundling builds our awareness of the place value system.  And, they learn the purpose of our place value system is to be able to recognize quantities without counting.  It is a higher order of subitizing.   

When we get to place value as a concept, we must utilize the quantity awareness built in early subitizing activities and apply it across greater magnitudes.  Thus, 3 + 2 = 5 becomes 30 + 20 = 50.    On day two of the course, we explored the place value system first with craft sticks and then transitioned to base ten blocks.  You may notice that the third section of the course after lunch is quite short.  It was at this point that the class went into the hall and built the place value system to the ten million rod.  

Using 10 cm x 10 cm boxes from the craft store which are the identical size of the one thousand cube, we build the ten thousand rod and outlined the hundred thousand flat.  Then using yellow cord from the dollar store knotted at every meter, we constructed the outlines of the one million cube.  We held the cord out at one meter lengths and outlined the ten million rod.  Children often do this in class and in a previous post I included some pictures from the summer program in which the children constructed quantities from one to twelve thousand. 

One thing I have been emphasizing lately is the use of the term "proper number" and "improper number."  Think of proper numbers that conform to the rules of place value, no more than nine in any place.  Think of improper numbers as those which need to be "simplified." They are numbers that occur as the result of an operation such as adding seven and eight...or which we create in by decomposing  or regrouping in order to subtract.  If we begin talking to students about improper numbers when they are learning place value concepts, we are setting the stage for fractions ahead of time.  We are also emphasizing the order and symmetry of the place value system.  It really is quite elegant.  

Finally, I want to add that for many students the use of the craft sticks is a game changer.  I noted this summer in my program that older elementary students who were practicing subtraction with decomposing a ten did not understand regrouping as "unbundling" the ten.  As they sought to subtract they would try to reach into the bag of sticks for a "ten" because they were used to trading...the ten rod for unit cubes.  Even for older students, that task of bundling and unbundling must come before we transition to the place value blocks which are indeed more efficient for many concepts.