We have been through using tally marks to solve problems and using an open number line. Now, on to our next strategy: decomposing.
In decomposing, we are going to be solving combining and separating problems by decomposing, or breaking them down, into groups of tens and ones. In order to work on this strategy with your child, he or she must have a good grasp of place value. He or she will also continue to explore this strategy in multiplication problems in higher grades by using clusters of simpler problems.
Let's look at a combining example for the problem 24 + 12.
1. Decompose both addends into groups of tens and ones, making sure to line up work neatly. The neatly part is harder for most kids at this point than the actual decomposing. ;-)
2. Before finding the partial sums of the tens and ones, I have each student make sure that every number has a "buddy" to combine together. (10+10, 10+2) If not, I have them hold the place with a zero. (4+0) (This step may be skipped, but I stress it in the beginning as they are learning this strategy so they don't get confused as to which numbers to combine.)
3. Find the partial sums of the tens and ones.
4. Combine the partial sums to get the final sum.
Decomposing for subtraction is similar. Let's use the sample problem 24-12.
1. Decompose the minuend (24) and subtrahend (12) into groups of tens and ones.
2. Check for "buddies."
3. Find the difference of each problem. (subtract)
4. Finally, find the sum of the differences. This step (for obvious reasons) confuses children. I explain it to them by saying that we decomposed or broke apart the numbers 24 and 12 so that we could subtract them. Now, we have to put the numbers back together or "recompose" them to get our final answer.
Still confused?Below you will find a quick video clip of Mr. Pinchot (a fifth grade math teacher and coach from our school) explaining the strategy. Thanks Mr. P!