Comparing 2-Digit and 3-Digit Numbers Worksheets

Compare place by place

Start with the biggest place. If the hundreds are different, the number with more hundreds is greater, whatever the other digits are: 506 > 489. If they are the same, move right and compare the tens, then the ones. Many of the problems on these sheets share the first digit on purpose, so children have to look further along.

• Comparing 2-digit numbers (grade 1, 1.NBT.B.3).
• Comparing 3-digit numbers (grade 2, 2.NBT.A.4).
• Ordering 2-digit and 3-digit numbers both ways.

Comparing 2 and 3 digit numbers worksheets: what is in the set

There are 6 comparing 2 and 3 digit numbers worksheets on this page, and every one has an answer key except for any cut-out games. The first four sets compare pairs of 2-digit and 3-digit numbers, and the last two put four numbers in order. These greater than less than 2nd grade worksheets use the signs >, < and =, and they are also useful for grade 1 and grade 3 children.

Comparing 2 digit numbers: how often does the tens digit decide?

Most pairs of numbers are decided at the first place. Of the 8,100 ordered pairs of 2-digit numbers, the tens digit gives the answer for 88.9%, and the ones digit is needed only when the tens are the same, which happens in 11.1% of the pairs. Here is how the pairs divide for 2-digit and 3-digit numbers:

This is why the comparing 2 and 3 digit numbers worksheets include many pairs that share the first digit: if they did not, children would never need to look beyond it. A pair such as 47 and 74 uses the same digits, so it is a good test of whether a child compares the value of the digits, or the digits themselves.

Comparing 3 digit numbers worksheets: look from the left

The rule for comparing 3 digit numbers worksheets is to start on the left and stop at the first place where the numbers differ. For 3-digit pairs, the hundreds decide in 88.9% of the cases, the tens in 10.0%, and the ones in 1.0%. The table shows eight pairs and the place that decides each one:

The Common Core asks grade 1 children to compare 2-digit numbers (1.NBT.B.3) and grade 2 children to compare 3-digit numbers (2.NBT.A.4). The Common Core standards for grade 2 number and operations in base ten describe the second standard, and the signs are explained in Wikipedia’s article on inequality.

Greater than less than 2nd grade: comparing 2-digit and 3-digit numbers

In greater than less than 2nd grade work, children also compare numbers with different lengths. Any 3-digit number is greater than any 2-digit number. There are 81,000 such pairs, and each is decided by the number of digits alone, so no place-by-place check is needed. A child who knows this can compare 99 and 101 in a second, but a child who compares the first digits will say 99 is greater.

Digit reversals: why 47 is not 74

A pair of numbers with the same digits is a good test. When the digits are reversed, the tens decide, and the ones do not matter. These are the first six pairs of numbers with two different digits, other than zero:

There are 36 such pairs among the 2-digit numbers. They are a good warm-up for comparing 2 and 3 digit numbers, and for the place value worksheets and for the base ten blocks diagrams on this page.

Ordering 3 digit numbers: four numbers, two directions

Ordering 3 digit numbers is comparing several times. The usual method is to find the least number, write it down, and repeat with the numbers that are left. Here are six examples, three with 2-digit numbers and three with 3-digit numbers, as they might appear on a worksheet:

Compare numbers to 1000: landmarks on the number line

To compare numbers to 1000, it helps to picture the number line. Numbers on the left are less, and numbers on the right are greater. This table shows five landmarks, and which numbers are on each side of them. You can print a number line from the number line tool:

Making the greatest and least numbers from digits

A good extension is to make the greatest and least 3-digit number from three digits. Put the biggest digit in the hundreds place for the greatest number, and the smallest non-zero digit there for the least. The table shows six sets of digits:

Common mistakes when comparing 2 and 3 digit numbers

Mistakes in comparing 2 and 3 digit numbers are often about which digit to look at. The table shows five of them and what the child did:

Comparing 2 and 3 digit numbers word problems

Word problems ask children to compare real quantities. Ask which is more or fewer, and write the sign:

Games and activities for comparing 2 and 3 digit numbers

Children learn comparing 2 and 3 digit numbers best when they play with it. These games use things that are found at home or in a classroom:

• Digit cards: draw three cards and make the greatest number you can, then the least
• Place value war: each player makes a 3-digit number from cards, and the greater number wins the round
• Higher or lower: one player thinks of a number and the other guesses, with “higher” and “lower” as clues
• Number line walk: put number cards on the floor in order, with one missing, and let the child find the gap
• Base ten blocks: build two numbers with blocks and compare the flats first
• Sort the lineup: give five children number cards and ask them to line up

Extra support and extra challenge with comparing 2 and 3 digit numbers

For children who need more support: use base ten blocks, and build both numbers. Compare the flats, then the rods, then the cubes. Say what is the same: “both have 2 hundreds”. Do not mix 2-digit and 3-digit numbers until each is secure.

For children who need more challenge: ask for the number that is between two given numbers, for how many numbers are between 347 and 352, and for the greatest number that is less than 400. Add a question about how many 3-digit numbers can be made from three digits.

How to tell that a child is ready to move on from comparing 2 and 3 digit numbers

1. The child compares two 2-digit numbers by the tens, then the ones.
2. The child compares two 3-digit numbers from the left, and stops at the first place that differs.
3. The child knows that a 3-digit number is greater than a 2-digit number.
4. The child orders four numbers from least to greatest and back, with few mistakes.

When all four are true, move on to comparing large numbers. Many children are ready for this at the end of grade 2 or the start of grade 3.

A 20-minute lesson on comparing 2 and 3 digit numbers

A short lesson is the best way to introduce comparing 2 and 3 digit numbers. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where comparing 2 and 3 digit numbers fits across the grades

No skill stands alone. This table shows what children learn before and after comparing 2 and 3 digit numbers, with the standard that goes with each step:

This page covers the step from grade 1 to grade 3. If a child needs a step back, go to the page on comparing numbers to 20.

Helping at home with comparing 2 and 3 digit numbers

Parents do not need to be experts to help with comparing 2 and 3 digit numbers. These suggestions work well, and each takes only a few minutes:

• Ask “which is more, 47 or 74?” at the shop with the prices on the labels.
• Use a deck of number cards: deal three, and make the greatest and the least number.
• Look at house numbers on your street and put them in order.
• Ask the child to explain how they know, instead of just checking the answer.
• Keep sessions short, about 10 minutes, and stop when the child is tired.

How to check progress in comparing 2 and 3 digit numbers

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for comparing 2 and 3 digit numbers

Most children need about a week of short sessions for comparing 2 and 3 digit numbers. This plan follows the order of the worksheets on this page:

When the plan is complete, move on to comparing large numbers. The whole sequence is on the comparing numbers worksheets page, and the place value worksheets page has the place value background.