Add and subtract within 1,000

What is this skill?

In third grade, children are expected to add and subtract within 1,000 fluently, which means accurately, efficiently and with flexible strategies. Problems include 458 + 367 and 803 − 256. Children use the written column method with regrouping, but also mental strategies like adding hundreds, then tens, then ones, or counting up from the smaller number.

The most challenging problems are subtractions across zeros, such as 803 − 256. There are no tens to break apart, so a hundred is regrouped into 10 tens, and then one of those tens is regrouped into 10 ones. Seeing 803 as 7 hundreds, 9 tens and 13 ones is a sign of strong place value understanding. Checking a subtraction by adding the answer back is a habit third graders are encouraged to build.

Why it matters

Fluency with three-digit addition and subtraction is a foundation for the rest of elementary math. Multi-digit multiplication involves adding partial products, long division involves subtracting at every step, and measurement and money problems in later grades rely on it too. If these calculations are slow or error-prone, the new ideas become harder to learn.

Being flexible matters as much as being accurate. For 500 − 298, counting up from 298 to 300 and then to 500 is much quicker than regrouping twice. Children who can choose a strategy that fits the numbers are developing real number sense rather than only following steps.

Common mistakes

• Subtracting the smaller digit from the larger in each column regardless of which is on top. Ask "Is the top digit big enough?" for each column.
• Getting lost when regrouping across a zero, as in 803 − 256. Building it with base-ten blocks or money, trading a hundred for ten tens and a ten for ten ones, makes the steps make sense.
• Forgetting to carry in addition when a column adds to 10 or more, especially in the tens or hundreds column.
• Not estimating. A quick estimate, like 800 − 250 is about 550, catches answers that are far off.

How to help at home

• Use real numbers: the cost of two items, the distance of two legs of a trip, or how many points are needed to reach a goal in a game.
• Ask your child to solve one problem two ways, such as with the column method and by counting up, and to compare the answers.
• Practice checking. After a subtraction, add the answer and the number subtracted and see if the original number comes back.
• Talk about which strategy is easiest for a particular problem and why. "Would you count up for 600 − 295? Why?"

Worked examples

These are real questions from the Tutorsaurus add and subtract within 1,000 practice, with the answers worked out.

1. Example 1

   448 + 398 = ?

   Answer: 846. 448 + 398 = 846.

2. Example 2

   660 − 386 = ?

   Answer: 274. 660 − 386 = 274. Check: 274 + 386 = 660.

3. Example 3

   808 − 429 = ?

   Answer: 379. 808 − 429 = 379. Check: 379 + 429 = 808.