Tag Archives: partial sums

Creative Subtraction for the Very Young

OK, this is far from a revolutionary idea, but I was impressed with my eldest daughter’s approach to a subtraction problem. What I present may already be used by others, but it was new to me.

She was interested a few months ago in learning what negative numbers were and what caused them.  Of course, I dove right in and explained.  From time-to-time she’s asked for more, but mostly I thought it was an idea that had gone fallow.  Then she wrote the following last night.

\begin{array}{ccc} &7&0 \\ -&4&2 \\\hline &3&0 \\ &-&2 \\\hline &2&8 \end{array}

I had learned column subtraction from right to left with “borrowing.”  It was an algorithm that I understood; many classmates struggled.  My daughter worked left to right by column/place value.  So, she computed 70-40 and wrote 30.  Then she used her knowledge of negative numbers and asked me, “So 0 minus 2 is -2, right?”.  She then wrote -2.  The rest was easy.  What impressed me was her adaptation of an algorithm she had been using for partial sums. If a student understands negative numbers, I wonder if this might be a cleaner approach.  The thinking is also similar to what one might use when calculating using an abacus.  Cool.