Stories of Discovery

Silent Journey- How Does the Decimal Checker Board Work?

Categories: Faculty insight, Learning through discovery
Date posted: October 23, 2012

The Decimal Checker Board demonstrates the multiplication of decimals.  If you factor out the concept of decimals, it functions exactly like the Checker Board.  For a clearer understanding, I will explain how the Checker Board works with a specific example.

 Let’s consider   34,567 x 9 

 The Board is colour-coded according to place values (units, tens, hundreds, thousands, ten thousands ….)  The horizontal axis along the bottom illustrates the place values for the multiplicand. (34,567)  And the vertical axis along right side illustrates the multiplier. (9)

 We use the colour-coded bead bars to assist us with a concrete presentation.  ( red = 1, green = 2, pink = 3 …)  

 In Casa, the children are taught to multiply by place values.  By lots of repetition, the concept is ingrained.  Referring back to the equation, they would know the process requires them to first multiply 7 units by 9 units (multiplier), then 6 tens by 9 units, then 5 hundreds by 9 units ….  On the board, this is demonstrated by where the place values of each axis meets.  If we were to run a finger going left from the vertical axis, and run another finger upwards from the horizontal axis, they will meet in a square.  This is where the bead bars are placed.  

 

 

In this example, the bead bars will all lie on the bottom row.  This is because our multiplier 9 is a unit, and the unit is the lowest place value on the vertical axis.  So, as we move from right to left, the first square (green) will have 9 white bead bars (white = 7).  The next blue square will have 9 purple bead bars (purple = 6).  The next red square will have 9 light blue bead bars (light blue = 5)….

 

Once the bars are all laid out, we can complete the calculation of each square, beginning at the furthest right (units).  The children should know their multiplication tables by now, so that the manipulation of beads is quick and easy.  9 groups of 7 (white) equals 63.  We exchange the 9 white bars for a purple bar (6), and a pink bar (3).  The pink bar remains in the green units square, and the purple bar moves to the blue tens square.  This is so, because according to its place values, 63 has 3 units and 6 tens.  

 Moving along the axis to the blue tens square, 9 groups of 6 equals 54.  We also have to add the 6 that was “carried” over from the units.  This makes 60.  But it’s not really 60, it’s 600.  Where the bead bars are placed, gives the actual value of the beads.  Because 60 was in the tens place value square, the actual value is 600.  We exchange all those bead bars for a single purple 6 bar, and place it in the red hundreds square.  

We continue this process across the board until there is one bead bar in each square.  These final bars will give us the answer to the equation.  

 

 

 On the Decimal Checker Board, all four sides of the board are considered, opposed to only the two sides discussed above.

 The Checker Board and the Decimal Checker Board essentially serve as a visual and concrete form of a calculator.  If you understand the concept of long multiplication, (multiplying by place values) and know how to use the boards, you will always produce the correct answer.  

 
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