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Subtraction Algorithms An algorithm is a procedure used to solve a math computation problem. The algorithms you probably used as a child are still being taught in our schools. What we know from research and experience tells us that the “traditional” algorithm didn’t always work for students. The focus of the learning was on the process and not on the concept. We learned the catchy phrase of “Does McDonalds Sell Cheese Burgers to help us remember the steps of long division: divide, multiply, subtract, check and bring down. The focus was on the steps without regard to the conceptual understanding of taking a whole and breaking it into parts. In today’s classrooms, students will learn many algorithms. The goal is for the student to find one what they
can be secure, efficient, and accurate with. If they have more than one of these algorithmic “tools” mastered they can use the one that best fits the problem they are working on. There are 5 algorithms used in subtraction: Trades-First, Counting Up, Left-to-Right, Same-Change Rule, and Partial-Differences. Example: Trades-First Subtraction In this algorithm all the trading is done before the subtraction, allowing the children to concentrate on one thing at a time. This is similar to the one we have traditionally used in the US.
Examine the columns. You want to make trades so that the top number in each column is as large as or larger than the bottom number.
To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number is the ones column becomes 13, and the top number in the tens column becomes 3.  To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 13, and the top number in the hundreds column becomes 7. Now subtract column by column in any order. Counting Up To subtract using the counting-up algorithm, start with the number you are subtracting (the subtrahend), and "count up" to the number you are subtracting from (the minuend) in stages. Keep track of the amount you count up at each stage. When you are finished, find the sum of the amounts. Example: Counting Up To find 843 - 248, start with 248 and count up to 843. 248 Add 2 to count up to the nearest 10 250 Add 50 to count up to the nearest hundred 300 Add 500 to count up to the largest possible 100 800 Add 43 to count up to 843 843 Now find the sums of the numbers you added. 2 50 + 500 595 Partial-Differences The partial-differences subtraction algorithm is a fairly unusual method but one that appeals to some children, The procedure is fairly simple: Write partial differences for each place, record them, then add them to find the total difference. A complication is that some of the partial differences may be negative.
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