Powerful mathematicians have many different strategies at their fingertips that they can use to solve problems.  They can choose which strategy will be the most efficient for the problem at hand and not just use the one strategy that is most familiar.

Importance of a Math Tool Box

To illustrate this idea, consider the story of Dustin.  Dustin was a third grader in a very traditional math class.  Every morning his class would practice many problems using the standard algorithm for subtraction.  Due to all this practice, he had gotten quite good at the standard algorithm. 

When I came to visit, Dustin and I played a game.  In this game we were going to movies and we had $5 to spend at the snack bar.  We flipped over a card and totaled our purchases - $4.99.  I asked Dustin how much change we would get and he was unsure.  He asked to get a piece of paper.  He came back and wrote “500 - “ then his pencil broke and he had to get a new pencil.  Finally, he wrote “500 – 499” and started borrowing from the five.  After about two minutes he told me that we would get 1¢ change.  I asked him if he had any other strategies to use for this problem and he said, “No, this is the only way I know how to do subtraction.”  I suggested we could use counting 497,498, 499, 500.  It’s one step from 499 to 500.  He was incredulous.  That was so much easier than using the standard algorithm.  Unfortunately, he only had one strategy in his toolbox and wasn't used to choosing from a variety of strategies to fit the problem at hand.

Constant Difference Strategy

To broaden your own toolbox of subtraction strategies, I want to share the Constant Difference Strategy.  It is one of my favorites.  Though it is not useful for every problem, when it is used, it makes a problem so much easier to solve. 

The big idea is that we are finding the difference or the space between two numbers.  Where the numbers are located on the number line does not matter as long as the size of the space stays the same. We can shift up or down the number line to make the problem easier to solve.

  

Consider 92-46=__.  At first glance this problem does not lend itself easily to mental math.  However, with a bit of shifting up or down the number line we can make it much easier.

Let’s add four to each number.  Then we have 96-50=__.  This is much easier to solve!

Alternately, we could also subtract two from each number leaving us with 90-44=___.  Again the problem is so much easier to solve mentally.  

It doesn’t matter whether we add or subtract but we have to do the same thing to both of the numbers in the problem.  If you add or subtract to/from one number, do the same for the other side and the difference will remain the same. 

Try Some on Your Own

Take a look at the problems below.  Which ones would work well with the Constant Difference Strategy?  Which ones would be better to solve another way? You can use the Math Learning Center's Number Line App to show your thinking.

141 – 56 =

232-67=

433-196=

In order to be proficient with this strategy, children need to have strong number sense.  They also need to be comfortable moving up and down a number line.  If your child is not ready for this strategy yet, try a more concrete one here. After more time working with concrete models, they will build their skills and then be ready for the Constant Difference Strategy.