2-Digit Addition Without Regrouping Worksheets

2-digit addition without regrouping worksheets to print (PDF)

These 2-digit addition without regrouping worksheets show what the generator prints: a page of 20 vertical problems with no carrying, a horizontal page for mental math, a missing-number page and the answer key. Click a picture for the PDF, or use the generator above to make a new set.

About 2-digit addition without regrouping

In these 2-digit addition without regrouping worksheets the ones add up to 9 or less and so do the tens, so children never need to carry. That lets them focus on the big idea of place value: add the ones to the ones, then the tens to the tens. The Common Core standards for grade 1 number and operations in base ten begin this work in grade 1 (1.NBT.C.4), and it builds on positional notation, the idea that the position of a digit gives its value.

How to add 2-digit numbers without regrouping

Take 34 + 25:

1. Line up the numbers so the ones are under the ones and the tens are under the tens.
2. Add the ones: 4 + 5 = 9.
3. Add the tens: 3 + 2 = 5.
4. The answer is 59.

The grid paper worksheet puts every digit in its own box, which is the easiest way to keep columns straight.

2 digit addition without regrouping worksheets: how many problems qualify?

Most pairs of 2-digit numbers need regrouping, so a worksheet that has none must be chosen with care. Of all 8,100 ordered pairs of 2-digit numbers, only 1,980 have no regrouping, which is 24.4%. The reason is simple: the ones digits must add up to 9 or less, and so must the tens digits. In the generator, the “No carrying or borrowing” setting picks only those problems, so every problem on the page is a 2-digit addition without regrouping problem. Here is how the ones digits can add up:

There are 55 ordered pairs of ones digits with a sum of 9 or less. The tens digits are the digits 1 to 9, since a 2-digit number cannot start with 0, so there are fewer pairs:

That gives 36 pairs of tens digits. Multiply 55 by 36 and you get the 1,980 problems that never regroup, and that is the pool that the worksheets draw from.

Double digit addition without regrouping: four ways to think about 34 + 25

Double digit addition without regrouping is the first place where children use place value to add. These four problems show three ways to add, and all of them work with the generator’s worksheets:

Each method says the same thing in a different way: the tens and the ones can be added separately, because 34 + 25 is 30 + 4 + 20 + 5.

Two digit addition worksheets: 30 practice problems with answers

Here are 30 problems from the pool of 1,980, with the working. Use them as a quick test, or cover the last column and let a child solve each problem. They show that two digit addition worksheets with no regrouping still need careful work, since the tens and ones are added separately:

2 digit addition no regrouping: adding a multiple of ten

A good first step is to add a multiple of ten to a 2-digit number. In 2 digit addition no regrouping problems of this kind, only the tens digit changes and the ones digit stays the same, which helps children to see the pattern:

Addition without carrying: estimating and checking

Addition without carrying is the right place to teach children to estimate and check their work, because the numbers are small and the answers are easy to verify. Round each number to the nearest ten to get an estimate, and check the answer by subtracting one addend:

The check by subtracting also shows the link between addition and subtraction, which is a key idea for grade 2 (2.NBT.B.5).

2-digit addition without regrouping word problems

Word problems show why children need 2-digit addition without regrouping. These six stories can be solved with one addition. Ask children to write the number sentence first and then to say what the answer counts:

Common mistakes in 2-digit addition without regrouping

Because there is no carrying, the mistakes in 2-digit addition without regrouping are different from those in problems with regrouping. This table shows what the wrong answers look like, so a teacher can see what the child has misunderstood:

A child who adds every digit has not understood place value, and a child who leaves out the ones may have lined up the numbers wrongly. Grid paper, where each digit has its own box, prevents both mistakes.

Where 2-digit addition without regrouping fits in the addition sequence

Children do not learn addition in one step. This table shows the order in which the skills are usually taught, with the grade level and the matching worksheets on this site:

Fact families for 2-digit addition without regrouping

Every addition problem belongs to a fact family of four number sentences. When children write the family for a 2-digit addition without regrouping problem, they see that subtraction undoes addition. This is also a good way to check an answer:

The hundred chart and 2-digit addition without regrouping

A hundred chart is a picture of 2-digit addition without regrouping. To add the tens, move down one row for each ten, and to add the ones, move right one square for each one. Since there is no regrouping, the child never has to go past the end of a row. The same five problems on a hundred chart look like this:

You can print a chart from the hundreds chart tool and let children trace each move with a counter.

Number bonds for the ones column

In every problem with no regrouping, the ones digits add up to 9 or less. Children who know the number bonds for 5 to 9 can find these sums at once, so a few minutes with the bonds is a good warm-up before the worksheets:

How to use the 2-digit addition without regrouping worksheets in a lesson

1. Show the idea with blocks for two or three problems, and say the tens and the ones aloud.
2. Solve one problem together on the board with the numbers lined up in columns.
3. Give the vertical worksheet for independent work, with the grid paper layout for children who need it.
4. Check with the answer key, and let children find their own mistakes.
5. End with a few word problems to link the written method to real situations.

A five-day plan for 2-digit addition without regrouping

Most children need about a week of short sessions before they are fluent. This plan goes from adding a multiple of ten to word problems:

When a child gets 9 out of 10 right on two days in a row, move on to 2-digit addition with regrouping. The whole sequence is in the addition worksheets section.

Tips

• Use base-ten blocks or bundles of 10 straws to show tens and ones.
• Always start with the ones column, even when there is no carrying, to build the habit for later.
• Estimate first: 34 + 25 is about 30 + 30 = 60.
• When children are ready, move on to 2-digit addition with regrouping.