Free Grade 2 Math Worksheets

A teacher's guide to Grade 2 math worksheets

Something quietly dramatic happens in second grade. For two years, children have worked with small numbers, usually ones they could picture in a handful of objects. Now they are asked to add and subtract numbers like 47 and 38, which cannot be pictured as a pile of counters, and which cannot be worked out by counting. They have to use the structure of the number system. They have to know that 47 is four tens and seven ones, and that ten ones can be traded for a ten. This is called place value, and it is the single biggest idea of the year.

This page gathers the Grade 2 worksheets: two-digit addition and subtraction without regrouping, the same with regrouping, a mixed-review page, and an introduction to multiplication and division. This guide explains what each is for, how regrouping really works, how to teach it so that it makes sense, and how to use the new multiplication and division pages as a gentle first look at ideas that become central in Grade 3.

A Grade 2 subtraction page, with the title and instruction stating exactly what it practices. Every problem here needs regrouping.

What changes at Grade 2

Two things change at once.

Addition and subtraction move to two digits, and introduce regrouping. Regrouping is what many of us still call "carrying" and "borrowing." It is the step in which ten ones are exchanged for one ten, or one ten for ten ones.

Multiplication and division appear. They come in gently, as ideas about equal groups, rather than as full tables to be memorized.

In many US state standards, Grade 2 asks children to know their single-digit sums from memory, to add and subtract within 100 fluently using strategies based on place value, to add and subtract within 1,000 using concrete models and drawings, and to work with equal groups and arrays as a foundation for multiplication. Standards differ, so check your own. But the picture is broadly this: Grade 2 is where children learn to work with tens and ones.

What the pages cover

Addition, no regrouping. Two-digit addition. The instruction line on the page reads "Regroup if you need to," so it is worth glancing at a page before handing it over. If a child needs strictly carry-free problems, choose the problems yourself or check each page, because some sums on these pages may still need a carry.

Subtraction, no regrouping. Two-digit subtraction in which each digit of the bottom number is no larger than the digit above it, so nothing has to be borrowed. These are the "easy" subtraction problems, such as 83 − 72.

Addition with regrouping. Two-digit addition in which every problem needs a carry, as the title and instruction say: "Every problem needs regrouping."

Subtraction with regrouping. Two-digit subtraction in which every problem needs a borrow.

Mixed review. Addition and subtraction on the same page, with and without regrouping.

Multiplication, intro facts. The easiest families: the 2s, 5s and 10s, along with zero and one.

Division, intro facts. The reverse of those multiplication facts, such as 40 ÷ 10 and 18 ÷ 2.

Each of the seven has thirty numbered pages, with fresh numbers on every page.

Place value: the big idea

Before regrouping makes sense, a child has to see that a two-digit number is made of tens and ones. The number 47 is not "four" and "seven" standing side by side. It is 4 tens and 7 ones, or 40 and 7. That simple fact is what regrouping depends on.

The best way to teach it is with real objects.

• Base-ten blocks. Small cubes for ones, long rods for tens, flat squares for hundreds. A rod is worth ten cubes, and the child can check by lining them up.
• Bundles of sticks. Ten craft sticks tied with a rubber band make a ten.
• Coins. Dimes and pennies are a natural model: a dime is worth ten pennies.
• Place value charts. A simple two-column chart with "tens" and "ones."
• Expanded form. 47 = 40 + 7. Writing numbers this way makes the structure visible.

A child who can build 47, trade ten ones for a ten, and say what happened has understood the big idea. Everything else is practice.

The number sense pages for Grade 2 build place value and skip counting in exactly this spirit, and they are a good companion to the pages here.

Regrouping in addition

Here is 38 + 47, worked in a way that shows the idea.

1. Add the ones. 8 ones + 7 ones = 15 ones.
2. Regroup. 15 ones is the same as 1 ten and 5 ones. Write the 5 in the ones place, and carry the 1 ten to the tens column.
3. Add the tens. 3 tens + 4 tens + the carried 1 ten = 8 tens.
4. The answer. 8 tens and 5 ones: 85.

A child with base-ten blocks can do exactly this. Put out 3 rods and 8 cubes, and 4 rods and 7 cubes. Push the cubes together: 15. Trade ten of them for a rod. Count: 8 rods and 5 cubes. The paper method records what the hands did.

Two more examples to illustrate the pattern:

When a child can explain why the 1 is carried, not just where to write it, they are ready for the harder cases that come in Grade 3.

Regrouping in subtraction

Subtraction regrouping is harder, and it is where most children stumble. Here is 62 − 36.

1. Look at the ones. 2 ones minus 6 ones. You cannot take 6 from 2.
2. Regroup. Take 1 ten from the 6 tens, leaving 5 tens. Trade it for 10 ones, giving you 12 ones.
3. Subtract the ones. 12 − 6 = 6.
4. Subtract the tens. 5 − 3 = 2.
5. The answer. 26.

With base-ten blocks, the child can see it happen: there are not enough cubes, so they trade a rod for ten cubes, and now they have enough.

The trickiest case is a zero in the ones place, as in 50 − 14. Here the child has no ones at all, so a ten must be traded for ten ones: 4 tens and 10 ones. Then 10 − 4 = 6, and 4 − 1 = 3. The answer is 36. A child who has worked this out with blocks will rarely forget it. A child who has only learned "cross out the 5 and make it 4" often makes mistakes.

A few more for practice:

Mental strategies that go with the paper method

Paper methods are important, but they should not be the only tool. Good second graders also use mental strategies, and the page can be a place to practice them.

• Count up by tens. 56 + 30 is 66, 76, 86.
• Add tens first. 38 + 47: 38 + 40 = 78, then 78 + 7 = 85.
• Make a friendly number. 29 + 35: add 1 to 29 to make 30, then 30 + 34 = 64.
• Count up to subtract. 62 − 36: from 36 to 40 is 4, from 40 to 60 is 20, from 60 to 62 is 2. 4 + 20 + 2 = 26.
• Use an open number line. Jump by tens and ones, and record the steps.

These strategies strengthen number sense, and a child who has them can check a written answer by thinking: "56 + 35 is about 90. My answer was 91. That makes sense."

Estimating and checking

A few habits will save a lot of errors.

• Estimate first. Round both numbers to the nearest ten. 56 + 35 is about 60 + 40 = 100. The answer should be near 100.
• Check with the opposite operation. To check 62 − 36 = 26, add: 26 + 36 = 62.
• Look at the size of the answer. Subtraction should give a smaller number than the start. Addition should give a larger one.
• Reread the problem. Is the sign what you thought?

A child who gets in the habit of asking "Does that make sense?" will catch many of their own mistakes.

An introduction to multiplication and division

Most state standards put formal multiplication and division facts in Grade 3. In Grade 2, the aim is to lay the foundation: to understand that multiplication means equal groups, and division means sharing or grouping equally. The pages here preview the easiest facts, to give a child a first taste.

Grade 2 multiplication intro facts: the 2s, 5s and 10s, along with zero and one.

Why the 2s, 5s and 10s? They are the easiest families, because they connect to skip counting and to things a child already knows. Counting by 2s gives even numbers. Counting by 5s follows the pattern of a clock face or a hand. Counting by 10s is the pattern of place value. A child who skip counts can find any of these products.

Equal groups. 3 × 5 means 3 groups of 5. Draw three circles with five dots in each. Count the dots: 15. Or skip count by 5s: 5, 10, 15.

Arrays. An array is a rectangle of rows and columns. 3 × 5 is 3 rows of 5, and a child can count it as 15. Turn it on its side, and it is 5 rows of 3, and the answer is the same. That is the commutative property, and it halves the number of facts to learn.

Zero and one. 0 × 5 = 0, because zero groups of five is nothing. 1 × 2 = 2, because one group of two is two. These special cases are good to teach explicitly.

Division as the reverse. 10 ÷ 2 asks "How many groups of 2 are in 10?" or "If 10 is shared between 2, how many each?" Both give 5. A child who knows 2 × 5 = 10 has what they need.

Grade 2 division intro facts: the reverse of the 2s, 5s and 10s, such as 40 ÷ 10 and 18 ÷ 2.

Fact families. The same three numbers give four facts: 2 × 5 = 10, 5 × 2 = 10, 10 ÷ 2 = 5, 10 ÷ 5 = 2. A child who sees the family can use multiplication to solve division.

Don't rush. A child who has seen the ideas, drawn the arrays and skip counted the answers has done what Grade 2 asks. Memorizing the facts is the work of Grade 3.

A routine that works

A short, regular routine suits the Grade 2 page. Here is a pattern:

1. Oral warm-up. Three minutes of mental math: "What's 30 + 40? What's 56 + 10? What's 70 − 20?"
2. Show a method. Use blocks or a drawing for one problem, and say each step.
3. Try two or three with the method. Let the child do the talking.
4. Do half a page on paper. Six problems, with care.
5. Check. Estimate, then use the opposite operation.
6. Look at one mistake. Ask what happened, and fix it.
7. Finish with a game. Cards or dice.

Fifteen minutes is plenty. If the child is frustrated, stop, and come back tomorrow.

Word problems in second grade

By Grade 2, children are expected to solve one- and two-step word problems, and the pages here are most useful when they are paired with stories. A story tells the child which operation to use, which is the harder part.

• Add to. "Maya had 38 stickers. Her friend gave her 47 more. How many does she have?" (38 + 47 = 85)
• Take from. "A shop had 62 apples. It sold 36. How many are left?" (62 − 36 = 26)
• Put together. "There are 29 red pencils and 35 blue pencils. How many pencils in all?" (29 + 35 = 64)
• Compare. "A tree is 83 inches tall, and another is 44 inches. How much taller is the first?" (83 − 44 = 39)
• Equal groups. "There are 4 bags with 5 oranges in each. How many oranges?" (4 × 5 = 20)
• Sharing. "Share 18 crayons equally between 2 children. How many each?" (18 ÷ 2 = 9)

A useful routine is: read the story, say it in your own words, draw a picture, write the equation, solve it, and check that the answer makes sense in the story. A child who does this is doing real mathematics.

A sample fifteen-minute session

A session with a seven-year-old, working on addition with regrouping.

1. Minute 0 to 3. Build 38 + 47 with base-ten blocks. Count the ones: 15. Trade ten of them for a rod. Count the rods: 8. Read the answer: 85.
2. Minute 3 to 5. Write the same problem in columns. Point to where each block step shows up on paper.
3. Minute 5 to 11. Turn to the worksheet. Do the first four problems. For each, say "ones first, then tens," and say aloud when a ten is carried.
4. Minute 11 to 13. Pick one problem and estimate first. Does the answer fit?
5. Minute 13 to 15. Finish with a game of "Race to 100" with two dice.

The blocks do the thinking, the page records it, and the estimate checks it. That is what a good lesson on this topic looks like.

Common mistakes and what they mean

Mistakes in two-digit arithmetic have clear patterns, and knowing them lets you fix the cause.

• Forgetting to carry. 38 + 47 = 715, because 8 + 7 = 15, and 3 + 4 = 7. The child has written both. Show the carried ten with blocks.
• Carrying but forgetting to add it. 38 + 47 = 75. The child carried the 1 but did not add it to the tens. Make it visible: write the small 1 above the tens column.
• Subtracting the smaller from the larger. 62 − 36 = 34. The child did 6 − 2 = 4 and 6 − 3 = 3. Go back to blocks, and show why you cannot take 6 from 2.
• Borrowing but forgetting to reduce. 62 − 36 = 36, because the child made 12 − 6 = 6 but then did 6 − 3 = 3. The tens digit should have become 5.
• Zero trouble. 50 − 14. The child writes 4 − 0 = 4 in the ones. Return to blocks.
• Misaligned digits. 8 + 23 written so that the 8 sits under the 2. Use squared paper or a place value chart.
• Multiplication confusion. 3 × 5 = 8. The child added. Draw equal groups.
• Division confusion. 10 ÷ 2 = 20. The child multiplied. Use sharing language and drawings.

Whenever a mistake repeats, go back to objects. It nearly always works.

Games that build fluency

• Race to 100. Roll two dice, form a two-digit number, and add it to a running total.
• Place value war. Each player flips two cards to make a two-digit number. The higher number wins.
• Hundred chart hop. Put a counter on 36. Hop 10 forward. Where are you? Hop 5 back.
• Skip counting songs. By 2s, 5s and 10s, forward and backward.
• Arrays with snacks. Arrange crackers in rows. How many in all?
• Fair shares. Share 20 grapes between 5 people. How many each?
• Number of the day. Write all the ways you can make the number, using addition and subtraction.
• Estimation jar. Guess how many, then count by tens.

A few minutes of games a day builds fluency without the pressure of a page.

How to know a child is ready for Grade 3

A child is ready for Grade 3 when two-digit addition and subtraction are secure, when they understand place value, and when they can work with equal groups. Signs include:

• They can add and subtract two-digit numbers accurately, with and without regrouping.
• They can explain the steps, not just do them.
• They know the sums of single digits from memory.
• They can skip count by 2s, 5s and 10s.
• They can show multiplication as equal groups or arrays.
• They are curious about larger numbers.

If those are in place, three-digit regrouping and the full multiplication and division facts are the next step.

For teachers

A second-grade classroom has a wide range, and these pages help to meet it.

• Differentiate. Some children need the no-regrouping pages, and others the regrouping ones. Use the numbered pages for variety.
• Use for centers. With blocks, a place value chart and a partner, a page becomes a hands-on station.
• Assess. A single page, done independently, shows who has mastered which skill.
• Warm-ups and exit tickets. A few problems make a quick, focused routine.
• Homework. A half page a night.
• Class sets. Print different pages to avoid copying.

The Grade 2 math bundles collect ten pages of each skill into a single download, which is useful for a week of practice or a take-home pack.

For parents

You do not need to be a mathematician to help a second grader.

• Use real things. Coins are perfect for place value. Pennies and dimes are base-ten blocks in your pocket.
• Ask "why." "Why did you carry the 1?" The explanation matters.
• Keep it short. Ten to fifteen minutes.
• Let the child teach you. Explaining is the best test of understanding.
• Avoid shortcuts. Tricks that skip understanding can cause trouble later.
• Be patient. Regrouping is hard, and it takes time.

Questions that come up

My child's school teaches a different method. That is common. Ask the teacher, and use the method your child's school uses. The page is just a place to practice.

Why do some pages say "regroup if you need to"? The instruction line is a general reminder. Look at the problems on the page, and choose the page that fits your child.

Should my child memorize multiplication facts now? Not necessarily. Grade 2 is about understanding equal groups. The memorization comes in Grade 3.

My child makes careless mistakes. Slow down, estimate first, and check with the opposite operation.

My child hates borrowing. It is the hardest idea in the year. Go back to blocks, and do one problem at a time.

How many pages a week? Two to four, a few problems at a time, with games in between.

Grade 2 is the year in which numbers become structures, with tens and ones that can be traded and rearranged. A child who sees this has taken the biggest step in elementary arithmetic.