Should students use the technique of Borrowing and Carrying or Regrouping?
Why Words Matter in Math
Some kids understand it better one way or the other, but the “new” way of regrouping is not the way that many of us adults were taught. So, let Mathnasium help be a resource for you as your kids learn the “Common Core” methods.
Consider the following 1st and 2nd-grade Common Core Mathematics Standards:
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as …making ten (e.g., 8+6=8+2+4+10+4=14); decomposing a number leading to a ten (e.g., 13-4=13-3-1=10-1=9)…
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones-called a ‘ten.”
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value…
2.NBT.7 Add and subtract within 1000…using strategies based on place value…understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens , ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Parents and teachers will recognize that these standards apply to place value and regrouping, or, as many of us learned, borrowing and carrying. Does it make a difference if we call the process regrouping or borrowing (subtraction) and carrying (addition)?
The difference could be in the sense that a student makes of the addition or subtraction operation. Once while substitute -teaching in a first -grade class, I was asked by a student if the assignment involved “sticks.” Intrigued, I asked him to show me what he meant. He then proceeded to show me how he, “carried the stick over the ones” in the following problem.
Of course, what he was really doing was regrouping the resulting 12 ones into 1 ten “bundle” (composing) and 2 ones, leaving the ones in the ones place and regrouping the ten to join the other two tens.
In this problem
we regroup the 1 hundred, 2 tens and 3 ones into 11 tens and 13 ones (decomposing-110+13=123). We aren’t borrowing anything (don’t you usually return something you borrow?), we are rewriting the minuend (top number), regrouping (decomposing) the hundreds and tens.
Some may argue that it’s purely semantics; it doesn’t matter what we call the process as long as a student can master it. But for a student having trouble making sense of place value and regrouping, the words borrowing and carrying may not hold as much meaning. The idea of rearranging an addend or minuend to accommodate the operation and calling it what it is, regrouping, may make the steps of the process make more sense.
Since many of the Common Core Standards are forcing kids to Regroup instead of Borrow and Carry, we are seeing many kids come in with a lack of understanding of what they are “doing” when they are “drawing the pictures”. They are going through the motions of drawing the pictures, but they don’t really understand what they are doing. At this critical time in a student’s development, we urge parents to make sure their children really understand WHAT their children are doing by challenging them in new and inventive ways. For fun and creative examples, visit any of our 3 locations…start at Cincymath.com.
Helping your students to make sense of math, whether they excel or need extra help, is our passion. To see if math is making sense for your student, check out questions – Mathnasium.com or click on a grade-specific checkup.