Adding and Subtracting Fluently Using Standard Algorithms

In third grade, your student added and subtracted within one thousand using strategies based on place value.  This year, we have learned that successful problem-solvers look for shortcuts and are always working toward the most efficient strategy to solve a problem.  Fourth graders are expected to add and subtract fluently (numbers through one million) using standard algorithms.

What are standard algorithms?  They are a processes or steps that when followed correctly in a given situation, will always allow you to arrive at the correct answer.  Translation: it's the way we learned to add and subtract numbers vertically with "borrowing" and "carrying" (which we now call regrouping/renaming).

HOORAY!  Well, at least that would be how I would feel if I was was the parent of a fourth grade Math student.  Finally something you know how to do that isn't taught differently!

Here's the catch--students need to understand what's going on with place value when using these algorithms (as opposed to just crossing out numbers and making them one less, then making the number to the right ten more).  Here's a sample of a think-aloud I will model in class:

Instead of teaching the addition and subtraction algorithms in isolation, I will teach the addition algorithm through using it to check subtraction, as an inverse operation.

So, the think aloud for using the standard addition algorithm to check the subtraction in the example above would sound something like this:

8 ones and 4 ones is 12 ones.  12 ones is 1 ten 2 ones.

8 tens and 4 tens is 12 tens, plus 1 ten from regrouping is 13 tens.  13 tens is 1 hundred 3 tens.

5 hundreds and 5 hundreds is 10 hundreds, plus 1 hundred from regrouping is 11 hundreds.  11 hundreds is 1 thousand 1 hundred.

1 thousand plus 1 thousand from regrouping is 2 thousands.

So, my sum is 2,132, which is the same as the minuend in the subtraction problem, which means I subtracted correctly.

  2,132     minuend
- 1,584     subtrahend
     548     difference (addend when checking with addition)
+1,584     addend
  2,132     sum