What Is Regrouping in Math?

Regrouping in math is trading 10 ones for 1 ten, or 1 ten for 10 ones, so that a column can be added or subtracted. It is what most parents learned as carrying and borrowing. In 46 + 37, the ones make 13, so ten of them become one ten, written as a small 1 over the tens, and the answer is 83. Nothing is carried or borrowed: the 13 ones are only rewritten as 1 ten and 3 ones, which is why schools say “regroup”.

Children start making a new ten in first grade, and second graders add with regrouping within 100 and then within 1,000. Adding with regrouping, step by step, once called carrying, has its own guide, as does subtracting with regrouping, once called borrowing. Each comes with a free worksheet and answer keys.

What is regrouping in math?

Regrouping in math is rewriting a number with its places grouped differently, without changing its value. Ten ones are one ten, and ten tens are one hundred, so a number can trade between its places in either direction. In addition, a child regroups when a column adds up to 10 or more. In subtraction, a child regroups when a column has too few to take away from.

The small 1 on a homework sheet is that ten, and it is worth 10, not 1.

Regrouping is the same as carrying and borrowing: regrouping in addition is what was called carrying, and regrouping in subtraction is what was called borrowing. Homework may also call it trading, renaming, or composing and decomposing a ten. The old words hide what happens. “Carry the 1” hides that the 1 is a ten, and “borrow” suggests the ten is paid back, when it is only traded. The Common Core does not use carry, borrow, or even regroup: second-grade standard 2.NBT.B.7 says that “sometimes it is necessary to compose or decompose tens or hundreds”.

Regrouping is place value at work. A child who regroups correctly knows that the 4 in 46 is 40, and the same trade later works between tens and hundreds. With base ten blocks, the trade is ten small cubes swapped for one rod.

Regrouping in subtraction (borrowing)

Regrouping in subtraction means trading one ten for ten ones when a column has too few ones to take away from, which is what used to be called borrowing. In 52 − 27, the 2 ones cannot give 7, so one of the 5 tens becomes 10 ones. The 52 is now 4 tens and 12 ones, still 52. Then 12 − 7 = 5 and 4 − 2 = 2, for 25.

Addition makes a new ten out of ones, and subtraction opens a ten up into ones. Subtraction also has mistakes of its own, such as taking the smaller digit from the larger in every column, and subtracting across a zero, as in 403 − 158. Subtraction with regrouping, step by step covers two-digit and three-digit problems and subtracting across zeros, with its own worksheet.

What grade do kids learn regrouping?

Children start regrouping in first grade, regroup within 100 and then 1,000 in second grade, and learn the standard algorithm by name in fourth grade.

Grade	What children do	Common Core	Texas (TEKS)
1st grade	Add a two-digit and a one-digit number, or a multiple of 10, with models or drawings; “sometimes it is necessary to compose a ten”	1.NBT.C.4	1.3(A), a multiple of 10 and a one-digit number, with models
2nd grade	Add and subtract within 100 fluently; add up to four two-digit numbers; add and subtract within 1,000 with models or drawings, related to a written method; explain why the strategies work	2.NBT.B.5, 2.NBT.B.6, 2.NBT.B.7, 2.NBT.B.9	2.4(B), 2.4(C)
3rd grade	Add and subtract within 1,000 fluently, “using strategies and algorithms based on place value”	3.NBT.A.2	3.4(A)
4th grade	The standard algorithm, by name	4.NBT.B.4	4.4(A)

The new ten first appears in first grade’s 1.NBT.C.4, and third grade’s 3.NBT.A.2 asks for fluency within 1,000. Subtraction with regrouping starts in second grade, alongside the addition.

Texas asks second graders to add up to four two-digit numbers and subtract two-digit numbers “using mental strategies and algorithms based on knowledge of place value” (2.4(B), TEKS grade 2). Third graders work within 1,000 “with fluency” (3.4(A), TEKS grade 3). A second grader who still draws blocks for a three-digit sum is on time, because 2.NBT.B.7 asks for models or drawings at that stage. Regrouping comes after the addition strategies kids learn first, such as counting on and making ten.

Do kids still learn to carry and borrow?

Yes. The column method parents call carrying and borrowing is the standard algorithm, and the Common Core requires it by name for adding and subtracting in fourth grade (4.NBT.B.4). Texas requires it in fourth grade too (4.4(A)), and it asks for “algorithms” from second grade (2.4(B)). What changed is the order and the words. In first and second grade, children add “using concrete models or drawings” and “relate the strategy to a written method” (1.NBT.C.4 and 2.NBT.B.7). Third graders add “using strategies and algorithms based on place value” (3.NBT.A.2). In all three grades, the class says regroup.

Homework in those grades may show one addition, 46 + 37, in up to three ways before the column method:

• With base ten blocks. Four rods and 6 units plus 3 rods and 7 units make 7 rods and 13 units. Ten units are traded for a rod, leaving 8 rods and 3 units, so 83. The base ten blocks guide shows the trade beside the written method.
• Tens and ones separately. First 40 + 30 = 70, then 6 + 7 = 13, and 70 + 13 = 83. The Common Core Standards Writing Team’s progressions document for base ten calls this “recording newly composed units in separate rows”, and it keeps the new ten in view.
• On an open number line. Start at 46, jump 30 to 76, then jump 7 to 83, as the number line guide shows.

None of these replaces the column method; they are the reasons behind its marks. Mathematics educators Karen Fuson and Sybilla Beckmann describe the order in the NCSM Journal: students explain the reasoning in a written method “with visual models. Then, in a later grade, students move to using the standard algorithm fluently with no visual models.” Regroup is a classroom word, not a standard’s: Eureka Math lists “bundle, unbundle, regroup, rename, change” among the familiar terms of its second-grade Module 4. Showing your child how to carry the 1 is not wrong. A sheet that asks for the drawing still wants the drawing, though, because that is the stage being marked. New math explained for parents covers why math is taught in this order.

Going further: regrouping in your head

Regrouping also works in the head, by moving an amount from one number to the other before adding. For 398 + 529, take 2 from the 529 and give it to the 398: 400 + 527 = 927. For 38 + 47 + 93 + 62, pair the numbers with round sums: 38 + 62 = 100 and 47 + 93 = 140, so the total is 240. Both are examples from the Common Core Standards Writing Team’s progressions document, which calls them special strategies for particularly easy computations. It keeps second grade’s main focus on the methods that work for all numbers, so these shortcuts come once the columns make sense. They are regrouping done mentally. The pairing relies on adding in any order, one of the properties of addition, and both moves belong to mental math.