Grade by Grade
B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and Dividing

Adding Whole Numbers to 10 000

B2.4 B2.1About 40 minutes
Learning goals
  • I can estimate a sum before I add.
  • I can add 4-digit numbers using the column method (an algorithm).
  • I can regroup ones, tens and hundreds.
  • I can solve story problems with sums up to 10 000.

Words to know

sum
The answer when you add.
algorithm
A set of steps that always works, like the column method.
regroup
Trade 10 of one place for 1 of the next place, like 10 tens for 1 hundred, or 10 hundreds for 1 thousand.
estimate
A close guess that helps you check if an answer makes sense.
thousands
The place to the left of the hundreds. 10 hundreds make 1 thousand.

Remember from Grade 3

In Grade 3 you added 3-digit numbers with the column method: line up the places, add the ones first, and regroup 10 ones as 1 ten when you need to. In Grade 4 the numbers grow to 10 000, so we add a thousands column. The steps stay the same!

Let's start with a story

A hockey arena sold 2475 tickets on Friday and 3860 tickets on Saturday. How many tickets in all?

Before we add, let's estimate. Round each number to the nearest thousand: 2475 is about 2000, and 3860 is about 4000. 2000 + 4000 = 6000. Our exact answer should be close to 6000.

The column method

  1. Estimate first.
  2. Line up the numbers by place: ones under ones, tens under tens, hundreds under hundreds, thousands under thousands.
  3. Add the ones first, then the tens, then the hundreds, then the thousands.
  4. If a column adds up to 10 or more, write the ones digit of that sum and carry 1 to the next column.
  5. Check your answer against your estimate.
Worked example

Example 1: No regrouping

Solve 2346 + 3521.

  1. Estimate: 2000 + 4000 = 6000.
  2. Ones: 6 + 1 = 7.
  3. Tens: 4 + 2 = 6.
  4. Hundreds: 3 + 5 = 8.
  5. Thousands: 2 + 3 = 5.

2346 + 3521 = 5867. That's close to 6000. ✓

Worked example

Example 2: Regrouping in three places

Solve 4678 + 3456.

  1. Estimate: 5000 + 3000 = 8000.
  2. Ones: 8 + 6 = 14. Write 4, carry 1 ten.
  3. Tens: 1 + 7 + 5 = 13 tens. Write 3, carry 1 hundred.
  4. Hundreds: 1 + 6 + 4 = 11 hundreds. Write 1, carry 1 thousand.
  5. Thousands: 1 + 4 + 3 = 8.

4678 + 3456 = 8134. That's close to 8000. ✓

OTHTh11187646543+4318
The column method for 4678 + 3456. The small 1s are the regrouped ten, hundred and thousand.

What does each carried 1 mean?

  • A 1 carried into the tens column means 1 ten (made from 10 ones).
  • A 1 carried into the hundreds column means 1 hundred (made from 10 tens).
  • A 1 carried into the thousands column means 1 thousand (made from 10 hundreds).
Ones: 8 + 6 = 14 ones10 ones1 ten: carry the 14 ones: write 4
In 4678 + 3456, the ones make 14. Ten of them are traded for 1 ten (the carried 1), and 4 ones stay in the ones column.
Worked example

Example 3: A story problem

The library has 3487 books. It gets 1265 new books. How many books now?

  1. Estimate: 3500 + 1300 = 4800.
  2. Ones: 7 + 5 = 12. Write 2, carry 1.
  3. Tens: 1 + 8 + 6 = 15. Write 5, carry 1.
  4. Hundreds: 1 + 4 + 2 = 7.
  5. Thousands: 3 + 1 = 4.

4752 books. That's close to 4800. ✓

Mental math still helps

You don't always need the column method. For 2450 + 1550, think: 450 + 550 = 1000, and 2000 + 1000 = 3000. Together: 4000. Look at the numbers first, then choose your tool.

Neat columns

Write the numbers neatly on grid paper or lined paper turned sideways, one digit in each box. Many mistakes in big sums come from digits drifting into the wrong column.

Just for fun

Q: Why did the little 1 sit on top of the tens column?

A: It got carried away!

Hands-on activity

Closest to 10 000

You need: a deck of playing cards (take out the face cards and the 10s; Ace = 1), paper and a pencil, a partner.

  1. Each player draws 8 cards.
  2. Use them to make two 4-digit numbers. Try to make the sum as close to 10 000 as you can (over or under).
  3. Estimate first, then add with the column method.
  4. Check each other's work. The player whose sum is closer to 10 000 gets a point.
  5. Play 5 rounds.

Math talk: "Where did you put your biggest cards? Why?"

Your turn

1

3214 + 2563 = ?

2

4528 + 1347 = ?

3

2659 + 3283 = ?

4

5806 + 2795 = ?

5

Estimate 3920 + 4105.

6

6000 + 2500 = ?

7

An arena had 2475 fans on Friday and 3860 fans on Saturday. How many fans in all?

More practice: warm-up

1

1000 + 2000 = ?

2

4300 + 500 = ?

3

2000 + 3456 = ?

4

1234 + 1111 = ?

5

5000 + 5000 = ?

More practice: on your own

1

4789 + 2346 = ?

2

1995 + 3005 = ?

3

678 + 2459 = ? (Be careful to line up the ones!)

4

Noor says 3568 + 2721 = 5289. Use an estimate to check.

5

2450 + 1380 + 1550 = ?

Challenge

1

Find the missing digit: 3□56 + 2417 = 6073

2

Three classes collected 2368, 1975 and 3487 cans. Their goal was 8000. Did they reach it?

3

One number is 3725. What number adds to it to make exactly 10 000?

Check your understanding

Quiz

1.

What is 2346 + 3521?

2.

What is 3678 + 2456?

3.

What is the best estimate for 4890 + 3120?

4.

You write 3456 + 278 in columns. Which digit of 3456 goes above the 8?

5.

In the column method, what does a 1 carried into the thousands column mean?

6.

What is 5000 + 3999?

For parents and teachers

Big idea: The curriculum (B2.4) asks Grade 4 students to solve addition problems with whole numbers up to 10 000 using tools and strategies, including algorithms. Your child learned the column algorithm with 3-digit numbers in Grade 3; now it extends to thousands.

Common difficulties:

  • Misaligned digits, especially when one number is shorter (678 + 2459). Use grid paper.
  • Forgetting to add the carried 1, or writing both digits of a column's sum (writing 14 in one column).
  • Not checking for reasonableness. Make "estimate first" a habit; your child should notice when 5289 can't be right for about 6300.

How to help: Add real numbers: kilometres on a road trip, steps on a step counter, points in a game. Ask your child to explain what each carried 1 is worth.