Checkerboard

Ah the checkerboard.......It has to be one of my favorite lower elementary materials.  I'm not quite sure why I haven't posted on this yet.  My mother, Gigi, was very kind to make me this checkerboard which can be rolled up and stored like a work rug for the child.  She saved me some precious moolah and also made a decimal checkerboard while she was at it.  It's great to have a supportive grandmother!

The checkerboard has 4 rows and 9 columns of squares arranged in hierarchical colors: green for units, blue for tens, red for hundreds, and green for thousands.  These are the same colors used in previous math materials so the child will be very familiar with them.  The columns range from unit to millions while the individual squares account for units to one billion.  The individual rows not only represent value, they represent the partial products of multi-digit multiplication!  The child can make some large numbers (which Bubs was always excited to do).

Some people are hesitant to start this work for a child if the child has not learned all of his multiplication facts.  However, because the child uses bead bars, there is no need to have the facts memorized.  The child can multiply large numbers while skip counting with the bead bars.  After much use of this material, the facts are mastered. 

Nito has already worked with the checkerboard before.  Today, I presented the 2 digit multiplicand and 2 digit multiplier.  I will walk you through the steps.

The problem is 79 x 12.  He uses the color coded numbers I made for him which correspond to the square on the checkerboard. (Green for unit, blue for ten, etc.)

First, he turns over the ten card for both the multiplicand and the multiplier.  He is focusing on the units first.  He will multiply 9 x 2 which is 18.  He places a brown 8 bar in the units square and a red 1 bar in the tens square.  This now reads "18".  

Second, he turns over the 9 unit card and turn the 7 tens card face up.  Now he is ready to multiply 7 and 2 which is 14.  Now, for the child who is first learning this material, they will focus on the fact that it is 14.  However, as the child progresses, we point out to them that it is really 7 tens and 2 units which makes it 70 x 2.  Therefore the answer is 140, not 14.  This is why you see the yellow 4 bead bar in the tens square and the red 1 bar in the red hundreds square.  The green unit square still only has the brown 8 bar.  

Now the child has successfully multiplied the multiplicand by the unit of the multiplier.  It is time to move on the ten of the multiplier which is the blue 1 card.  The child starts over with the green 9 unit card being flipped over and will now multiply the 9 by the 1.  A blue 9 bar is placed in the ten square above the green unit square.  Remember, we are really multiplying 9 x 10.  This makes the unit have zero and the ten have a 9 bar.

The steps are repeated as before.  The green unit card is flipped over and the blue ten card is face up to now multiply 7 x 1 or really 70 x 10 giving us 700.  We place a white 7 bar in the red hundred square.

The multiplying is complete and now requires us to push all of our beads together.  We do this in an orderly fashion of pushing each column diagonally to the left staying with the same color squares.  For example, the blue 9 bar from the ten square on the second row gets pushed diagonally to the left to end up in the blue 10 square on the bottom row.  Continue with all squares with beads.

Once all of the beads have been pushed to the bottom row, exchanging must begin.  Starting with the units and working left, start exchanging bead bars to end up with one per square. 

The final answer should look like this.  

79 x 12= 948