How to make it
- Choose the digitsPick 1 to 5 digits for the top number and 1 to 4 for the bottom one; tick three numbers for a third addend.
- Decide on carryingRegrouping None keeps every column under ten, Always forces at least one carry, and Mixed lets the sheet include both kinds.
- Print the sheet and keyChoose vertical or horizontal, set 1 to 40 problems, then print or save a PDF with the answer key page after it.
The settings behind each sum
Top number and Bottom number fix the size of every problem. A one-digit choice means any number from 0 to 9, while two digits or more always gives a number of exactly that length, so a 3-digit top number runs from 100 to 999. Mixing sizes is allowed: a 4-digit top number over a 1-digit bottom number, such as 2,368 + 7, is a good check that a child lines up the ones and does not slide the 7 under the thousands.
Three numbers adds a third row with the same number of digits as the bottom one. With regrouping set to None, the generator makes sure neither the first sum nor the second needs a carry. Always means the first two numbers carry at least once, which is the setting to use when a lesson is specifically about regrouping. Mixed draws freely, so some problems carry and some do not, and the child has to notice which is which.
The default is 20 two-digit problems in vertical layout, four to a row. Very long answers drop the sheet to three columns to keep digits readable, and the Bigger print box removes one more column for children who write large. In rows, the number of problems across follows the widest sum: three for two-digit numbers, two once five-digit numbers need the room.
Teaching regrouping in the column method
Take 47 + 38. Start with the ones: 7 + 8 = 15. Fifteen ones is one ten and five ones, so write 5 in the ones column and a small 1 above the tens. Then add the tens, including the carried one: 4 + 3 + 1 = 8. The answer is 85. American classrooms usually call this regrouping or carrying; many UK teachers say column addition and talk about exchanging ten ones for a ten.
Children understand the small 1 better if they first see it happen with real objects. Many teachers build 47 and 38 with base-ten blocks or bundles of straws, push the loose ones together, and swap ten of them for a rod before writing anything. Once the swap makes sense, the written method is a record of it, not a trick.
Move through the settings in order. Begin with two digits and None, so the column routine is solid without carrying. Switch to Always for a lesson or two, then to Mixed, which is closest to real problems. Three-digit sums add a second possible carry, from tens into hundreds, and are worth a separate step before four and five digits.
Addition settings by grade
These are common starting points, not rules; one class can span two rows of this table. On US and Canadian sheets (those that open on Letter) the footer code changes with the digit settings, so a sheet of two-digit sums shows CCSS 2.NBT.B.5, three digits show CCSS 3.NBT.A.2, and four or five digits show CCSS 4.NBT.B.4, the standard for fluent use of the standard algorithm. Single-digit facts are labeled CCSS 1.OA.C.6. Three numbers keep the code of the digit setting, although three two-digit addends can pass 100, a step past what CCSS 2.NBT.B.5 describes.
In England, column addition with formal carrying is usually met in Year 3 and extended to four digits in Year 4. In Australia, written methods for two- and three-digit numbers often appear around Year 3, after a lot of mental work with tens and ones. If your child's school uses a different order, follow the school; matching the method they see in class saves confusion at home.
| Settings | US grade | England | Australia |
|---|---|---|---|
| 1 digit + 1 digit, horizontal | Grade 1 | Year 1 to Year 2 | Year 1 |
| 2 digits + 1 digit, no regrouping | Grade 1 to grade 2 | Year 2 | Year 1 to Year 2 |
| 2 digits + 2 digits, regrouping mixed | Grade 2 | Year 3 | Year 2 to Year 3 |
| 3 digits + 3 digits, vertical | Grade 3 | Year 3 to Year 4 | Year 3 to Year 4 |
| 4 or 5 digits, vertical | Grade 4 | Year 4 to Year 5 | Year 4 to Year 5 |
Vertical columns or horizontal rows
Vertical layout stacks the numbers right-aligned with a plus sign and a rule, ready for the column method. Horizontal layout writes 36 + 9 = on one line, which invites mental strategies instead: making ten (36 + 4 + 5), using a near double, or counting on from the larger number. A sensible rhythm is horizontal for one-digit and small two-digit facts, vertical once numbers reach three digits.
Some children copy horizontal problems into columns and lose track of place value on the way. Squared paper fixes this: one digit per square, ones under ones. Print a page of half-inch graph paper for rough work, or move to place value worksheets if the real issue is not knowing which digit is the tens. When the same class is ready for the reverse operation, the subtraction worksheet generator uses the same layouts and keys.
Common addition mistakes and how the key catches them
The classic error is the forgotten carry: 47 + 38 written as 75. The ones digit is right and the tens digit is one short, which is easy to spot against the key. A close cousin is writing the whole 15 in the ones column, giving 715. Others include adding the carried 1 to the wrong column, starting from the left, and, in horizontal problems with uneven lengths, adding the 7 of 2,368 + 7 to the 2.
The key shows final sums in pink in the same positions as the problems, so a parent can compare digit by digit rather than just marking right or wrong. Look at which column went wrong. Errors always in the tens point to carrying; errors scattered everywhere point to basic facts, and a short sheet of one-digit sums or the mixed facts generator for a week will help more than more column work.
How many sums: warm-up, homework, test
For a warm-up, six to ten problems at a level the child can already do. Homework usually sits at 15 to 20, the default, which is one page for two-digit vertical sums. For a test of regrouping, use Mixed with 20 to 30 problems so you see whether the child decides correctly when to carry, not only how. Four- and five-digit sums take longer each, so 12 to 16 is plenty.
New variant keeps all settings and deals new numbers, so you can print a different sheet for each table group or a second attempt the following day. If a child was absent, the copied link rebuilds the old sheet exactly; so does its footer number entered in the Sheet number box under More options, with the settings unchanged.
A homeschool example: a second grader who has just met carrying might do ten two-digit sums with Always on Monday and Tuesday, ten with Mixed on Wednesday, and a 20-problem Mixed sheet on Friday that a parent marks with the key while the child watches. Any problem marked wrong goes back to the child to redo in the margin, with the blocks out if needed. Keeping the Friday sheet's link means the same page can be tried again two weeks later to see what stuck.
Questions
How do you teach addition with regrouping?
Start with objects: build both numbers with base-ten blocks, combine the ones, and trade ten ones for a ten. Then show the written version, adding ones first and writing the carried 1 above the tens. Use the None setting until the column routine is easy, then Always, then Mixed.
What does no regrouping mean on an addition worksheet?
It means no column adds up to ten or more, so nothing has to be carried; 42 + 35 needs no regrouping, 47 + 38 does. Choose None under Regrouping and every problem on the sheet, including three-number sums, is built that way. It is the usual first step with two-digit numbers.
Can I make addition worksheets with three numbers?
Yes. Tick Three numbers and each problem gets a third addend with the same number of digits as the bottom number. Three-number sums are good practice for looking for pairs that make ten, and in vertical layout they show that a column total can reach 20 or more.
Can I make a horizontal addition worksheet?
Choose Horizontal under Layout. Problems are written on one line, such as 58 + 7 =, with an answer line, up to three to a row and fewer when the numbers are long. Horizontal layout works well for facts and for mental strategies; for three digits and up, vertical is easier to work in.
What grade learns two-digit addition with regrouping?
In the US it is usually second grade, and US sheets show CCSS 2.NBT.B.5 in the footer. In England column addition with carrying commonly arrives in Year 3, and in Australia written methods often begin around Year 3. Many children meet the idea earlier with blocks before the written method.
Can I make a worksheet mixing addition and subtraction?
This page makes addition only, so a child can focus on one written method. For a sheet that mixes both operations, open the mixed facts generator on the main math page and choose Addition and subtraction; for column subtraction with borrowing, use the subtraction generator.
Common Core State Standards: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.