How to Explain Addition and Subtraction to Third Graders

Your third grader can probably add 25 + 13. But what about 256 + 178?

Third grade is when addition and subtraction grow up. Numbers get bigger, regrouping becomes essential, and mental math strategies become increasingly important.

Here's how to help your child master these skills.

What's New in Third Grade

In second grade, students worked mainly with two-digit numbers. Third grade expands to:

• Three-digit numbers (up to 1,000)
• Multiple regroupings in a single problem
• Mental math strategies for efficiency
• Inverse operations (using addition to check subtraction)

The algorithms stay the same, but the numbers demand more careful place value attention.

Addition with Regrouping: The "Carrying" Concept

Why We Regroup

Let's trace through 347 + 285:

Ones column: 7 + 5 = 12

• We can't write 12 in one column
• 12 = 1 ten + 2 ones
• Write 2 in ones, carry the 1 ten to the tens column

Tens column: 4 + 8 + 1 (carried) = 13 tens

• 13 tens = 1 hundred + 3 tens
• Write 3 in tens, carry the 1 hundred

Hundreds column: 3 + 2 + 1 (carried) = 6 hundreds

Answer: 632

Making It Concrete

Use base-10 blocks to show why regrouping works:

1. Build 347 (3 hundreds, 4 tens, 7 ones)
2. Build 285 (2 hundreds, 8 tens, 5 ones)
3. Combine the ones: 12 ones
4. Trade 10 ones for 1 ten: now you have 2 ones and an extra ten
5. Combine tens: 4 + 8 + 1 = 13 tens
6. Trade 10 tens for 1 hundred: now 3 tens and an extra hundred
7. Combine hundreds: 3 + 2 + 1 = 6 hundreds
8. Read the result: 632

When kids physically make these trades, regrouping stops being magic and starts being logical.

The Expanded Form Method

Some children understand better when numbers are broken apart:

  347 = 300 + 40 + 7
+ 285 = 200 + 80 + 5
        ---------------
        500 + 120 + 12
        500 + 130 + 2  (10 ones become 1 ten)
        600 + 30 + 2   (100 tens become 1 hundred)
        = 632

This method makes the regrouping visible and connects directly to place value.

Subtraction with Regrouping: The "Borrowing" Concept

Why Borrowing Works

Let's trace 532 - 278:

Ones column: 2 - 8 = ?

• We can't take 8 from 2
• Borrow 1 ten from the tens place
• Now we have 12 ones: 12 - 8 = 4

Tens column: 2 (was 3, borrowed 1) - 7 = ?

• We can't take 7 from 2
• Borrow 1 hundred from the hundreds place
• Now we have 12 tens: 12 - 7 = 5

Hundreds column: 4 (was 5, borrowed 1) - 2 = 2

Answer: 254

The "Hotel" Analogy for Borrowing

Remember the place value hotel? Borrowing is like this:

"We need more ones, but we only have 2. Let's ask the tens floor to send down a group of 10. Now the tens floor has one fewer group, but we have 12 ones to work with."

This makes borrowing a reasonable transaction, not a mysterious procedure.

Subtracting Across Zeros

The trickiest problems involve zeros: 500 - 247

Step by step:

• Ones: 0 - 7 = can't do. Borrow from tens.
• Tens: 0 tens—nothing to borrow! Go to hundreds.
• Borrow 1 hundred (now 4 hundreds left)
• That hundred becomes 10 tens
• Borrow 1 ten for the ones (now 9 tens left)
• That ten becomes 10 ones

Now solve: 10 - 7 = 3, 9 - 4 = 5, 4 - 2 = 2. Answer: 253

Alternative: Counting Up

Some students prefer "counting up" for subtraction:

500 - 247:

• Start at 247
• Add 3 to reach 250
• Add 50 to reach 300
• Add 200 to reach 500
• Total added: 3 + 50 + 200 = 253

This method avoids borrowing entirely and builds number sense.

Mental Math Strategies

Third graders should develop mental math flexibility. Here are key strategies:

Breaking Apart Numbers

For 68 + 45:

• Break 45 into 40 + 5
• 68 + 40 = 108
• 108 + 5 = 113

Making Friendly Numbers

For 298 + 156:

• 298 is close to 300
• 300 + 156 = 456
• But we added 2 too many: 456 - 2 = 454

Compensation

For 52 - 19:

• 19 is close to 20
• 52 - 20 = 32
• But we subtracted 1 too many: 32 + 1 = 33

Left-to-Right Addition

For 347 + 235:

• Add hundreds: 300 + 200 = 500
• Add tens: 40 + 30 = 70
• Add ones: 7 + 5 = 12
• Combine: 500 + 70 + 12 = 582

This mirrors how we naturally think about numbers.

Using Inverse Operations

Third graders learn that addition and subtraction are related:

• If 347 + 285 = 632, then 632 - 285 = 347
• Subtraction "undoes" addition

Checking Work

Teach your child to check subtraction with addition:

Problem: 532 - 278 = 254
Check: 254 + 278 = ?

If the check equals 532, the answer is correct. This builds confidence and catches errors.

Common Mistakes (And How to Fix Them)

Mistake 1: Forgetting to Regroup

Error: 347 + 285 = 5212 (just adding digits: 7+5=12, 4+8=12, 3+2=5)

Fix: Practice with base-10 blocks. When you have 12 ones, you must trade for a ten. The physical constraint makes the rule concrete.

Mistake 2: Regrouping When Not Needed

Error: Automatically carrying on every problem

Fix: Ask "Is this column 10 or more?" Only regroup when the answer is yes.

Mistake 3: Borrowing Errors

Error: 532 - 278, borrowing incorrectly and getting 354

Fix: Use the "cross out and rewrite" method clearly. When you borrow, physically show the changed numbers.

Mistake 4: Not Checking Reasonableness

Error: 347 + 285 = 132 (place value confusion)

Fix: Estimate first. 347 is about 350, 285 is about 300. The answer should be around 650. 132 doesn't make sense.

Practice Strategies for Home

Estimation First

Before solving, estimate:

• "347 + 285... that's about 350 + 300 = 650"
• Solve the exact problem
• Check: "632 is close to 650. That makes sense!"

Number of the Day

Pick a target number. Ask:

• "What two numbers add to get 500?"
• "What's 500 minus 137?"
• "How many ways can you make 500 using addition?"

Shopping Math

Use receipts or pretend shopping:

• "These items cost $3.47 and $2.85. What's the total?"
• "You have $10. You spent $6.32. How much is left?"

Fact Family Triangles

        632
       /   \
    347  +  285

From this triangle, generate four facts:

• 347 + 285 = 632
• 285 + 347 = 632
• 632 - 285 = 347
• 632 - 347 = 285

Error Analysis

Show problems with mistakes. Ask your child to find and fix the error:

    347
  + 285
  -----
    5212  ← What went wrong?

This builds critical thinking about the process.

Building Fluency

Speed Comes From Understanding

Don't rush to timed tests. Children who understand place value and regrouping will naturally get faster. Children who memorize procedures without understanding will make more errors under pressure.

Flexible Thinking

Encourage multiple approaches:

• "Solve 400 - 156 using the algorithm."
• "Now solve it by counting up."
• "Which way felt easier?"

Flexibility is the sign of true mathematical understanding.

The Bottom Line

Addition and subtraction with regrouping are skills your child will use forever. The key is connecting procedures to understanding:

• Regrouping works because of place value
• Mental math strategies show number sense
• Checking with inverse operations builds confidence

When your third grader can solve 500 - 247 and explain why the borrowing works, they've mastered more than a procedure—they've developed mathematical thinking.