Year 4 · Chapter 2

Year 4 Column Addition and Subtraction: worked examples and questions with answers

By the end of this chapter you will be able to

Add numbers with up to 4 digits using the column method, with carrying
Subtract numbers with up to 4 digits using the column method, with exchanging (including numbers with zeros, like 5,003 − 1,847)
Add and subtract in your head by partitioning, bridging, compensating, using near doubles and counting up
Estimate answers by rounding, and check answers using the inverse (opposite) operation
Use bar models (part-whole and comparison) to solve addition and subtraction problems
Solve two-step problems with money and measures, deciding which operations to use and why

You should already know

Adding and subtracting three-digit numbers with the column method
Number bonds to 10, 20 and 100
Place value in four-digit numbers (Chapter 1)
Rounding to the nearest 10, 100 and 1000 (Chapter 1)

Where this leads

Times tables (Chapter 3)
Multiplying and dividing (Chapter 4)
Decimals and money (Chapter 6)
Length, mass and capacity (Chapter 7)
Adding and subtracting numbers with more than 4 digits in Year 5

National Curriculum for England, Key Stage 2 mathematics, Year 4. Content: Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction, Estimate and use inverse operations to check answers to a calculation, Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Printable worksheets. Every lesson in this chapter has a free worksheet and an answer sheet to download and print.

2.1 Column addition: Worksheet (PDF) · Answers (PDF) · lesson page
2.2 Column subtraction: Worksheet (PDF) · Answers (PDF) · lesson page
2.3 Adding and subtracting in your head: Worksheet (PDF) · Answers (PDF) · lesson page
2.4 Estimating and checking your answers: Worksheet (PDF) · Answers (PDF) · lesson page
2.5 Bar models: part-whole and comparison: Worksheet (PDF) · Answers (PDF) · lesson page
2.6 Two-step problems with money and measures: Worksheet (PDF) · Answers (PDF) · lesson page
Check-up and SATs-style questions: Worksheet (PDF) · Answers (PDF) · lesson page

Exercise P Do you remember?

Non-calculator

FWork out 436 + 253.

Done

FWork out 462 − 238.

Done

FRound 3,568 to the nearest 100.

Done

FWhat is the difference between 68 and 100?

Done

FAmira has 250 stickers. Her aunt gives her 175 more stickers. How many stickers does Amira have now?

Done

2.1

Column addition

Year 4
Add numbers with up to 4 digits

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Column additionComing soon

When numbers are big, a written method keeps your working tidy and your answer accurate. In column addition you write one number under the other. Digits with the same value go in the same column: ones under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then you add one column at a time, starting on the right with the ones.

	Th	H	T	O
	3	4	2	5
+	2	3	1	4
	5	7	3	9

3,425 + 2,314 = 5,739. Each column is added on its own: 5 + 4, 2 + 1, 4 + 3 and 3 + 2.

Carrying. Sometimes a column adds up to 10 or more. There is only room for one digit in each column, so we carry. 10 ones are worth 1 ten, so we swap them for a ten and move it to the tens column. We write the carried digit small, under the answer line, so we do not forget it.

10 ones make 1 ten. So when the ones add up to 10 or more, write the ones digit and carry the ten.

Here is 2,468 + 3,375. The ones add up to 8 + 5 = 13. That is 1 ten and 3 ones, so write 3 and carry 1 to the tens column. The same can happen in any column. The carried digit is added in with the next column.

	Th	H	T	O
	2	4	6	8
+	3	3	7	5
	5	8	4	3
		1	1

2,468 + 3,375 = 5,843. The small red digits are the carries.

The answer can have more digits than the numbers you started with. In 6,785 + 5,436 the thousands column makes 12, so the answer is a five-digit number: 12,221. You can also add numbers with different numbers of digits, like 4,073 + 618. Line the digits up on the right, so that ones are under ones. There is nothing to add in the empty spaces.

Key words. The column method is a written way to add or subtract. Carry means to move the tens (or hundreds...) to the next column when a column adds to 10 or more. Sum and total are the answers to an addition.

Key ideas

Write the numbers in columns, with ones under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Add the ones first, then the tens, hundreds and thousands.
If a column adds up to 10 or more, write the ones digit and carry the tens. Add the carried digit in the next column.
Line numbers up on the right, not on the left.
Check with the inverse (opposite) operation: subtract one of the numbers from your answer.

Worked example 2.1.1

Use the column method to work out 3,425 + 2,314.

Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.

Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.

Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O
3 4 2 5
+ 2 3 1 4
Add the ones. Always start with the ones, on the right.
5 + 4 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry.
Th H T O
3 4 2 5
+ 2 3 1 4
9
Add the tens. Now the next column to the left.
2 + 1 = 3
3 is less than 10, so write 3 in the tens column. There is nothing to carry.
Th H T O
3 4 2 5
+ 2 3 1 4
3 9
Add the hundreds. Now the next column to the left.
4 + 3 = 7
7 is less than 10, so write 7 in the hundreds column. There is nothing to carry.
Th H T O
3 4 2 5
+ 2 3 1 4
7 3 9
Add the thousands. Now the next column to the left.
3 + 2 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry.
Th H T O
3 4 2 5
+ 2 3 1 4
5 7 3 9
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
3 4 2 5
+ 2 3 1 4
5 7 3 9

3,425 + 2,314 = 5,739

Check. Use the opposite (inverse) operation: 5,739 − 2,314 = 3,425. ✓
Estimate: 3,000 + 2,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. Start on the right with the ones, not on the left.

Worked example 2.1.2

Use the column method to work out 2,468 + 3,375.

Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O
2 4 6 8
+ 3 3 7 5
Add the ones. Always start with the ones, on the right.
8 + 5 = 13
13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
Th H T O
2 4 6 8
+ 3 3 7 5
3
1
Add the tens. Now the next column to the left. Add the 1 we carried as well.
6 + 7 + 1 = 14
14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
Th H T O
2 4 6 8
+ 3 3 7 5
4 3
1 1
Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
4 + 3 + 1 = 8
8 is less than 10, so write 8 in the hundreds column. There is nothing to carry.
Th H T O
2 4 6 8
+ 3 3 7 5
8 4 3
1 1
Add the thousands. Now the next column to the left.
2 + 3 = 5
5 is less than 10, so write 5 in the thousands column. There is nothing to carry.
Th H T O
2 4 6 8
+ 3 3 7 5
5 8 4 3
1 1
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
2 4 6 8
+ 3 3 7 5
5 8 4 3
1 1

2,468 + 3,375 = 5,843

Check. Use the opposite (inverse) operation: 5,843 − 3,375 = 2,468. ✓
Estimate: 2,000 + 3,000 = 5,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.

Worked example 2.1.3

Use the column method to work out 3,846 + 2,759.

Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O
3 8 4 6
+ 2 7 5 9
Add the ones. Always start with the ones, on the right.
6 + 9 = 15
15 is 1 ten and 5 ones. Write 5 in the ones column and carry 1 to the tens column.
Th H T O
3 8 4 6
+ 2 7 5 9
5
1
Add the tens. Now the next column to the left. Add the 1 we carried as well.
4 + 5 + 1 = 10
10 is 1 hundred and 0 tens. Write 0 in the tens column and carry 1 to the hundreds column.
Th H T O
3 8 4 6
+ 2 7 5 9
0 5
1 1
Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
8 + 7 + 1 = 16
16 is 1 thousand and 6 hundreds. Write 6 in the hundreds column and carry 1 to the thousands column.
Th H T O
3 8 4 6
+ 2 7 5 9
6 0 5
1 1 1
Add the thousands. Now the next column to the left. Add the 1 we carried as well.
3 + 2 + 1 = 6
6 is less than 10, so write 6 in the thousands column. There is nothing to carry.
Th H T O
3 8 4 6
+ 2 7 5 9
6 6 0 5
1 1 1
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
3 8 4 6
+ 2 7 5 9
6 6 0 5
1 1 1

3,846 + 2,759 = 6,605

Check. Use the opposite (inverse) operation: 6,605 − 2,759 = 3,846. ✓
Estimate: 4,000 + 3,000 = 7,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.

Worked example 2.1.4

Use the column method to work out 4,073 + 618.

Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O
4 0 7 3
+ 6 1 8
Add the ones. Always start with the ones, on the right.
3 + 8 = 11
11 is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column.
Th H T O
4 0 7 3
+ 6 1 8
1
1
Add the tens. Now the next column to the left. Add the 1 we carried as well.
7 + 1 + 1 = 9
9 is less than 10, so write 9 in the tens column. There is nothing to carry.
Th H T O
4 0 7 3
+ 6 1 8
9 1
1
Add the hundreds. Now the next column to the left.
0 + 6 = 6
6 is less than 10, so write 6 in the hundreds column. There is nothing to carry.
Th H T O
4 0 7 3
+ 6 1 8
6 9 1
1
Bring down the thousands digit. The other number has no digit in this column, so there is nothing to add.
There is only one digit here, so write 4 in the thousands column.
Th H T O
4 0 7 3
+ 6 1 8
4 6 9 1
1
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
4 0 7 3
+ 6 1 8
4 6 9 1
1

4,073 + 618 = 4,691

Check. Use the opposite (inverse) operation: 4,691 − 618 = 4,073. ✓
Estimate: 4,100 + 600 = 4,700 (rounding to the nearest 100). It is close to the exact answer. ✓

Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.

Worked example 2.1.5

Use the column method to work out 6,785 + 5,436.

Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
Add the ones. Always start with the ones, on the right.
5 + 6 = 11
11 is 1 ten and 1 one. Write 1 in the ones column and carry 1 to the tens column.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
1
1
Add the tens. Now the next column to the left. Add the 1 we carried as well.
8 + 3 + 1 = 12
12 is 1 hundred and 2 tens. Write 2 in the tens column and carry 1 to the hundreds column.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
2 1
1 1
Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
7 + 4 + 1 = 12
12 is 1 thousand and 2 hundreds. Write 2 in the hundreds column and carry 1 to the thousands column.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
2 2 1
1 1 1
Add the thousands. Now the next column to the left. Add the 1 we carried as well.
6 + 5 + 1 = 12
12 is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
2 2 2 1
1 1 1 1
Write the carried digit. There are no digits left in the ten thousands column, but we carried 1 into it.
Nothing to add except the carried digit. Write 1.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
1 2 2 2 1
1 1 1 1
Read the answer. Check the answer has the right number of digits, then write it.
TTh Th H T O
6 7 8 5
+ 5 4 3 6
1 2 2 2 1
1 1 1 1

6,785 + 5,436 = 12,221

Check. Use the opposite (inverse) operation: 12,221 − 5,436 = 6,785. ✓
Estimate: 7,000 + 5,000 = 12,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.

Watch out

Do not forget the carried digit! It is easy to write the carry and then not add it in the next column. Also line the numbers up on the right: if you add 4,073 + 618, the 8 goes under the 3 (ones under ones), not under the 4.

2.2

Column subtraction

Year 4
Subtract numbers with up to 4 digits

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Column subtractionComing soon

In column subtraction the bigger number goes on top. This is the number you start with. You take the bottom number away from it, one column at a time, starting with the ones. Words that mean subtract are take away, minus, less than, fewer than and difference.

	Th	H	T	O
	5	6	8	7
−	2	3	5	4
	3	3	3	3

5,687 − 2,354 = 3,333. Every top digit is big enough, so nothing needs to be exchanged.

Exchanging. Sometimes the top digit is smaller than the bottom digit, like 2 − 7 in the ones column. You cannot take 7 away from 2. So you exchange: swap 1 ten for 10 ones. The tens digit goes down by 1 and the ones digit goes up by 10. Now 12 − 7 = 5. Some people call this borrowing.

Exchange 1 ten for 10 ones. The value of the number does not change.

	Th	H	T	O
	6	34	145	122
−	2	1	8	7
	4	2	6	5

6,452 − 2,187 = 4,265. The ones and the tens both needed an exchange. The red digits are the new digits.

Zeros are tricky. You cannot exchange from a 0, because there is nothing to swap. Go to the next column on the left that is not 0, and pass the exchange along one column at a time. In 5,003 − 1,847, the ones need help (3 − 7), but the tens and the hundreds are both 0. So 1 thousand becomes 10 hundreds, then 1 hundred becomes 10 tens, then 1 ten becomes 10 ones. Each 0 in the middle ends up as a 9.

	Th	H	T	O
	45	90	90	133
−	1	8	4	7
	3	1	5	6

5,003 − 1,847 = 3,156. The thousands digit goes from 5 to 4 and the two zeros become 9s. The ones become 13.

Different lengths. You can take a three-digit number from a four-digit number, like 4,326 − 758. Line the digits up on the right. Where the bottom number has no digit, there is nothing to take away.

Key words. To exchange is to swap 1 of a bigger unit for 10 of the next smaller unit. The difference between two numbers is how far apart they are. It is the answer to a subtraction.

Key ideas

The bigger number goes on top. Line the digits up on the right.
Take away the ones first, then the tens, hundreds and thousands.
If the top digit is smaller than the bottom digit, exchange: take 1 from the column on the left and add 10 to this column.
You cannot exchange from a 0. Go left to the first column that is not 0. Each 0 you pass becomes 9.
Check with addition: the answer plus the number you took away gives the number you started with.

Worked example 2.2.1

Use the column method to work out 5,687 − 2,354.

Key words. Column subtraction is a written method. You write the bigger number on top and take away one column at a time. If the top digit is too small, you exchange: swap 1 of the next column for 10 of this column (1 ten for 10 ones, for example). Some people call this borrowing. The difference is the answer to a subtraction.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
5 6 8 7
− 2 3 5 4
Subtract the ones. Always start with the ones, on the right.
7 − 4 = 3
Th H T O
5 6 8 7
− 2 3 5 4
3
Subtract the tens. Now the next column to the left.
8 − 5 = 3
Th H T O
5 6 8 7
− 2 3 5 4
3 3
Subtract the hundreds. Now the next column to the left.
6 − 3 = 3
Th H T O
5 6 8 7
− 2 3 5 4
3 3 3
Subtract the thousands. Now the next column to the left.
5 − 2 = 3
Th H T O
5 6 8 7
− 2 3 5 4
3 3 3 3
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
5 6 8 7
− 2 3 5 4
3 3 3 3

5,687 − 2,354 = 3,333

Check. Use the opposite (inverse) operation: 3,333 + 2,354 = 5,687. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. The bigger number goes on top and the digits are taken away column by column, starting with the ones.

Worked example 2.2.2

Use the column method to work out 6,452 − 2,187.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
6 4 5 2
− 2 1 8 7
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
2 ones is not enough to take away 7. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 2 ones become 12 ones.
12 − 7 = 5
Th H T O
6 4 45 122
− 2 1 8 7
5
Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
4 tens is not enough to take away 8. We need to exchange.
(There were 5 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 4 hundreds become 3 hundreds, and 4 tens become 14 tens.
14 − 8 = 6
Th H T O
6 34 145 122
− 2 1 8 7
6 5
Subtract the hundreds. Now the next column to the left.
(This digit is 3 now, not 4, because we exchanged from this column.)
3 − 1 = 2
Th H T O
6 34 145 122
− 2 1 8 7
2 6 5
Subtract the thousands. Now the next column to the left.
6 − 2 = 4
Th H T O
6 34 145 122
− 2 1 8 7
4 2 6 5
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
6 34 145 122
− 2 1 8 7
4 2 6 5

6,452 − 2,187 = 4,265

Check. Use the opposite (inverse) operation: 4,265 + 2,187 = 6,452. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.

Worked example 2.2.3

Use the column method to work out 7,305 − 1,468.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
7 3 0 5
− 1 4 6 8
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
5 ones is not enough to take away 8. We need to exchange.
The tens has 0, so there is nothing to exchange from there. We start further to the left, at the hundreds.
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 5 ones become 15 ones.
15 − 8 = 7
Th H T O
7 23 90 155
− 1 4 6 8
7
Subtract the tens. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3
Th H T O
7 23 90 155
− 1 4 6 8
3 7
Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
2 hundreds is not enough to take away 4. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 7 thousands become 6 thousands, and 2 hundreds become 12 hundreds.
12 − 4 = 8
Th H T O
67 123 90 155
− 1 4 6 8
8 3 7
Subtract the thousands. Now the next column to the left.
(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 1 = 5
Th H T O
67 123 90 155
− 1 4 6 8
5 8 3 7
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
67 123 90 155
− 1 4 6 8
5 8 3 7

7,305 − 1,468 = 5,837

Check. Use the opposite (inverse) operation: 5,837 + 1,468 = 7,305. ✓
Estimate: 7,000 − 1,000 = 6,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.

Worked example 2.2.4

Use the column method to work out 5,003 − 1,847.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
5 0 0 3
− 1 8 4 7
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
3 ones is not enough to take away 7. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 5 thousands become 4 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 3 ones become 13 ones.
13 − 7 = 6
Th H T O
45 90 90 133
− 1 8 4 7
6
Subtract the tens. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5
Th H T O
45 90 90 133
− 1 8 4 7
5 6
Subtract the hundreds. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 8 = 1
Th H T O
45 90 90 133
− 1 8 4 7
1 5 6
Subtract the thousands. Now the next column to the left.
(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 1 = 3
Th H T O
45 90 90 133
− 1 8 4 7
3 1 5 6
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
45 90 90 133
− 1 8 4 7
3 1 5 6

5,003 − 1,847 = 3,156

Check. Use the opposite (inverse) operation: 3,156 + 1,847 = 5,003. ✓
Estimate: 5,000 − 2,000 = 3,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.

Worked example 2.2.5

Use the column method to work out 6,000 − 2,348.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
6 0 0 0
− 2 3 4 8
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
0 ones is not enough to take away 8. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 8 = 2
Th H T O
56 90 90 100
− 2 3 4 8
2
Subtract the tens. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5
Th H T O
56 90 90 100
− 2 3 4 8
5 2
Subtract the hundreds. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6
Th H T O
56 90 90 100
− 2 3 4 8
6 5 2
Subtract the thousands. Now the next column to the left.
(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3
Th H T O
56 90 90 100
− 2 3 4 8
3 6 5 2
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
56 90 90 100
− 2 3 4 8
3 6 5 2

6,000 − 2,348 = 3,652

Check. Use the opposite (inverse) operation: 3,652 + 2,348 = 6,000. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.

Worked example 2.2.6

Use the column method to work out 4,326 − 758.

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
4 3 2 6
− 7 5 8
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
6 ones is not enough to take away 8. We need to exchange.
Exchange 1 ten for 10 ones: 2 tens become 1 ten, and 6 ones become 16 ones.
16 − 8 = 8
Th H T O
4 3 12 166
− 7 5 8
8
Exchange, then subtract the tens. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
1 ten is not enough to take away 5. We need to exchange.
(There were 2 tens to start with, but we gave one away in an earlier exchange.)
Exchange 1 hundred for 10 tens: 3 hundreds become 2 hundreds, and 1 ten become 11 tens.
11 − 5 = 6
Th H T O
4 23 112 166
− 7 5 8
6 8
Exchange, then subtract the hundreds. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
2 hundreds is not enough to take away 7. We need to exchange.
(There were 3 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 4 thousands become 3 thousands, and 2 hundreds become 12 hundreds.
12 − 7 = 5
Th H T O
34 123 112 166
− 7 5 8
5 6 8
Bring down the thousands digit. The bottom number has no digit in this column, so there is nothing to take away.
(This digit is 3 now, not 4, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 3.
Th H T O
34 123 112 166
− 7 5 8
3 5 6 8
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
34 123 112 166
− 7 5 8
3 5 6 8

4,326 − 758 = 3,568

Check. Use the opposite (inverse) operation: 3,568 + 758 = 4,326. ✓
Estimate: 4,300 − 800 = 3,500 (rounding to the nearest 100). It is close to the exact answer. ✓

Watch out. The bottom digit is always taken from the top digit. Do not turn it round: 3 − 7 is not 4. Exchange instead.

Watch out

Never turn the digits round! In 6,452 − 2,187 it is tempting to write 7 − 2 = 5 in the ones column because 2 − 7 is hard. That gives the wrong answer. The bottom digit is always taken away from the top digit, so exchange instead. And remember: you cannot exchange from a 0.

2.3

Adding and subtracting in your head

Year 4
Mental addition and subtraction

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Adding and subtracting in your headComing soon

A written method always works, but it is not always the quickest. If the numbers are friendly, you can add and subtract in your head. Look at the numbers first, then pick a good strategy. Here are five.

1. Partitioning. Split (partition) the numbers into thousands, hundreds, tens and ones. Add the matching parts, then add the totals. For 346 + 278: 300 + 200 = 500, 40 + 70 = 110, 6 + 8 = 14, and 500 + 110 + 14 = 624. To subtract, keep the first number whole and take away the parts of the second number one at a time.

2. Bridging. Jump to the next round number (10, 100 or 1000), then add or subtract what is left. For 396 + 47, add 4 to reach 400, then add the other 43.

Bridging through 100: 396 + 4 = 400, and 400 + 43 = 443.

3. Compensating. If you are adding or subtracting a number just below or above a round number (like 9, 99, 199 or 301), use the round number and then fix the answer. 546 + 99: add 100 (a bit too much) to get 646, then take away 1 to get 645. To take away 298, take away 300 and put 2 back.

4. Near doubles. If two numbers are very close, double the smaller number and add the small difference. 350 + 351: double 350 is 700, plus 1 is 701.

5. Counting up. To find the difference between two numbers that are close, start at the smaller and count up to the bigger. For 5,002 − 4,987, count from 4,987 up to 5,000 (13) and then on to 5,002 (2). The difference is 13 + 2 = 15.

Counting up from 4,987 to 5,002: 13 + 2 = 15.

Key words. To partition is to split a number into parts. To bridge is to jump to a round number. To compensate is to make up for a change you made. A double is a number added to itself.

Key ideas

Partition: split the numbers into thousands, hundreds, tens and ones, then add the matching parts.
Bridge: jump to the next 10, 100 or 1000, then do the rest.
Compensate: add or take away a round number, then fix the answer (add 99 = add 100, take away 1).
Near doubles: double the smaller number and add the difference.
Count up to find the difference when the numbers are close.

Worked example 2.3.1

Work out 346 + 278 in your head by partitioning.

Key words. To partition a number is to split it into parts, one part for each digit (for example 345 = 300 + 40 + 5).

Method. Split (partition) both numbers into thousands, hundreds, tens and ones. Add the parts that match, then add the totals.

Partition both numbers. Write each number as the value of its digits.
346 = 300 + 40 + 6
278 = 200 + 70 + 8
Add the matching parts. Thousands with thousands, hundreds with hundreds, and so on.
hundreds: 300 + 200 = 500
tens: 40 + 70 = 110
ones: 6 + 8 = 14
Add the totals together. Start with the biggest and keep a running total.
500 + 110 = 610
610 + 14 = 624
Write the answer.
346 + 278 = 624

Check. Use the opposite operation: 624 − 278 = 346. ✓

Watch out. Do not forget a part. Count the parts: every digit that is not 0 must be added.

Worked example 2.3.2

Work out 745 − 278 in your head by partitioning the second number.

Key words. To partition a number is to split it into parts, one part for each digit.

Method. Keep the first number whole. Split (partition) the number you are taking away, then take the parts away one at a time, biggest first.

Partition the number you take away. Only the second number is split up.
278 = 200 + 70 + 8
Take the parts away one at a time. Start with the biggest part. Use the new number as the start of the next step.
745 − 200 = 545
545 − 70 = 475
475 − 8 = 467
Write the answer. The last number is the answer.
745 − 278 = 467

Check. Use the opposite operation: 467 + 278 = 745. ✓

Watch out. Take the parts away from the first number, one after another. Do not take them away from each other.

Worked example 2.3.3

Work out 396 + 47 by bridging through 100.

Key words. To bridge through 100 is to use a jump that lands exactly on a multiple of 100, then jump again.

Method. Bridge through 100. Add enough to reach the next 100, then add what is left.

How far is 396 from the next 100? 400 is the next multiple of 100.
400 − 396 = 4
Split 47 into 4 and 43. The first part takes us exactly to 400.
47 = 4 + 43
Add the first part to reach 400. This is the bridge.
396 + 4 = 400
Add the second part. This is easy because we are on a round number.
400 + 43 = 443
Show it on a number line.

Check. Use the opposite operation: 443 − 47 = 396. ✓

Watch out. Make sure the two parts add back to 47: 4 + 43 = 47.

Worked example 2.3.4

Work out 1,203 − 8 by bridging through 100.

Method. Bridge through 100. Take away enough to land on the 100 below, then take away what is left.

How far is 1,203 above the 100 below it? 1,200 is the multiple of 100 just below 1,203.
1,203 − 1,200 = 3
Split 8 into 3 and 5. The first part takes us exactly to 1,200.
8 = 3 + 5
Take away the first part to reach 1,200. This is the bridge.
1,203 − 3 = 1,200
Take away the second part. This is easy because we start from a round number.
1,200 − 5 = 1,195
Show it on a number line. We count back from the right.

Check. Use the opposite operation: 1,195 + 8 = 1,203. ✓

Watch out. Make sure the two parts add back to 8: 3 + 5 = 8.

Worked example 2.3.5

Work out 546 + 99 by compensating.

Key words. To compensate is to make up for a change. You use an easier number, then correct the answer.

Method. Compensate: add the nearby round number 100 instead, then fix the answer.

Spot a nearby round number. 100 is much easier to work with than 99.
99 is 1 less than 100: 99 = 100 − 1
Add 100 instead of 99. Round numbers are easy.
546 + 100 = 646
Fix the answer. We added 1 too many, so we must take 1 away.
646 − 1 = 645

Check. Use the opposite operation: 645 − 99 = 546. ✓

Watch out. Do not forget the last step. You changed the number you add or take away, so the answer needs fixing.

Worked example 2.3.6

Work out 1,204 − 298 by compensating.

Key words. To compensate is to make up for a change. You use an easier number, then correct the answer.

Method. Compensate: take away the nearby round number 300 instead, then fix the answer.

Spot a nearby round number. 300 is much easier to work with than 298.
298 is 2 less than 300: 298 = 300 − 2
Take away 300 instead of 298. Round numbers are easy.
1,204 − 300 = 904
Fix the answer. We took away 2 too many, so we must put 2 back.
904 + 2 = 906

Check. Use the opposite operation: 906 + 298 = 1,204. ✓

Watch out. Do not forget the last step. You changed the number you add or take away, so the answer needs fixing.

Worked example 2.3.7

Work out 350 + 351 using a near double.

Key words. A double is a number added to itself. A near double is a sum of two numbers that are almost the same.

Method. Near doubles: if two numbers are close, double the smaller one, then add the small difference.

Spot the near double. The numbers are very close together.
351 is 1 more than 350, so 351 = 350 + 1
Double 350. Double each part of the number, then add.
double 300 = 600
double 50 = 100
600 + 100 = 700
Add the extra 1. 351 is 1 more than 350, so the total is 1 more than the double.
700 + 1 = 701

Check. Use the opposite operation: 701 − 351 = 350. ✓

Watch out. Double the SMALLER number and add the difference. Do not add it to the bigger number.

Worked example 2.3.8

Work out 5,002 − 4,987 by counting up.

Key words. The difference between two numbers is how far apart they are. Counting up is a good way to find a difference when the numbers are close.

Method. To find the difference between two numbers that are close, start at the smaller number and count up to the bigger one. Add up the jumps.

Start at the smaller number. The difference is how far we have to count up.
Start: 4,987. Finish: 5,002.
Count up in easy jumps. Jump to a round number first, then add the rest.
4,987 + 13 = 5,000
5,000 + 2 = 5,002
Add up the jumps. The total of all the jumps is the difference.
13 + 2 = 15

Check. Use addition: 4,987 + 15 = 5,002. ✓

Watch out. Add up the jumps. The answer is the size of the jumps, not the number you finish on.

Watch out

Compensating has two steps. People often do the first step (add 100) and then forget to fix the answer. 546 + 99 is not 646. Also be careful with the direction: when you take away too much, you must put some back.

2.4

Estimating and checking your answers

Year 4
Estimate, Inverse operations

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Estimating and checking your answersComing soon

Before you do a calculation, it helps to estimate the answer. An estimate is a good guess that is close to the real answer. To estimate, round the numbers to the nearest 10, 100 or 1000, then do the easy calculation. For 3,874 + 2,129, round to the nearest 1000: 4,000 + 2,000 = 6,000. We write 3,874 + 2,129 ≈ 6,000. The sign ≈ means “is about equal to”.

3,874 is closer to 4,000 than to 3,000, so 3,874 rounds up to 4,000.

An estimate tells you if your answer is sensible. If your exact answer is not close to your estimate, you have made a mistake somewhere. Rounding to the nearest 100 gives a closer estimate than rounding to the nearest 1000, but it is a bit harder.

Checking with the inverse. Addition and subtraction are inverse (opposite) operations. They undo each other. If 4,644 + 2,486 = 7,130, then 7,130 − 2,486 should take us back to 4,644. The four numbers make a fact family.

The whole is 7,130 and the two parts are 4,644 and 2,486.

The fact family: 4,644 + 2,486 = 7,130 2,486 + 4,644 = 7,130 7,130 − 2,486 = 4,644 7,130 − 4,644 = 2,486.

Missing numbers. To find a missing number in a sum like ? + 2,486 = 7,130, think of a bar model. The whole is 7,130. One part is 2,486. The other part is the missing number, so take the part away from the whole: 7,130 − 2,486.

Key words. An estimate is a close answer. Inverse operations are opposites. Sensible means that the answer is the right sort of size.

Key ideas

To estimate, round each number (to the nearest 10, 100 or 1000), then do the easy calculation.
≈ means “is about equal to”.
An exact answer should be close to the estimate. If not, check your working.
Addition and subtraction are inverses: if a + b = c, then c − b = a.
Use a bar model to find a missing number: find a part by subtracting, find a whole by adding.

Worked example 2.4.1

Estimate 3,874 + 2,129 by rounding to the nearest 1000.

Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.

Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.

Round 3,874 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.
3,874 ≈ 4,000 (the hundreds digit is 8, so round up)
Round 2,129 to the nearest 1,000. Do the same for the second number.
2,129 ≈ 2,000 (the hundreds digit is 1, so round down)
Do the easy calculation. Rounded numbers are easy to add or subtract.
4,000 + 2,000 = 6,000

Check. The exact answer is 6,003. It is close to the estimate of 6,000. ✓

Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).

Worked example 2.4.2

Estimate 6,548 − 2,891 by rounding to the nearest 100.

Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.

Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.

Round 6,548 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.
6,548 ≈ 6,500 (the tens digit is 4, so round down)
Round 2,891 to the nearest 100. Do the same for the second number.
2,891 ≈ 2,900 (the tens digit is 9, so round up)
Do the easy calculation. Rounded numbers are easy to add or subtract.
6,500 − 2,900 = 3,600

Check. The exact answer is 3,657. It is close to the estimate of 3,600. ✓

Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).

Worked example 2.4.3

Jack says that 5,423 − 2,687 = 3,264. Use an estimate to show that his answer is not sensible. Then find the correct answer.

Method. Estimate the answer by rounding. If Jack’s answer is nowhere near the estimate, it cannot be right.

Round both numbers. Round to the nearest 100 so the sum is easy.
5,423 ≈ 5,400 (the tens digit is 2, so round down)
2,687 ≈ 2,700 (the tens digit is 8, so round up)
Work out the estimate.
5,400 − 2,700 = 2,700
Compare with Jack’s answer. Jack got 3,264. The estimate says the answer should be close to 2,700.
3,264 is a long way from 2,700, so it is not sensible.
Find the correct answer. Use the column method carefully.
Th H T O
45 134 112 133
− 2 6 8 7
2 7 3 6

5,423 − 2,687 = 2,736

Check. The correct answer 2,736 is close to the estimate 2,700. ✓

Watch out. Always ask: is my answer about the right size? An estimate takes a few seconds and can catch big mistakes.

Worked example 2.4.4

Sam says that 4,518 + 2,787 = 7,205. Use the inverse operation to check if he is right.

Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.

Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.

Write Sam’s answer as an inverse calculation. The opposite operation should take us back to the first number.
4,518 + 2,787 = 7,205 so 7,205 − 2,787 should be 4,518
Work it out. Use the column method.
7,205 − 2,787 = 4,418
Th H T O
67 112 90 155
− 2 7 8 7
4 4 1 8
Compare. We should get 4,518.
We got 4,418. 4,418 is not 4,518, so Sam is wrong.
Find the correct answer. Do the original calculation again.
4,518 + 2,787 = 7,305
Th H T O
4 5 1 8
+ 2 7 8 7
7 3 0 5
1 1 1

Check. The correct answer is 7,305. 7,305 − 2,787 = 4,518. ✓

Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.

Worked example 2.4.5

Find the missing number. ? + 2,486 = 7,130

Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.

Look at the number sentence. The box stands for the number we want to find.
? + 2,486 = 7,130
Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
Choose the operation. To find a missing part, take the part we know away from the whole.
7,130 − 2,486
Work it out. Use the column method if the numbers are big.
7,130 − 2,486 = 4,644
Th H T O
67 101 123 100
− 2 4 8 6
4 6 4 4
Check in the number sentence. Put the answer back in the box.
4,644 + 2,486 = 7,130 ✓

Check. Read the whole number sentence with your answer in the box. It must be true. ✓

Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.

Worked example 2.4.6

Find the missing number. 5,000 − ? = 3,276

Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.

Look at the number sentence. The box stands for the number we want to find.
5,000 − ? = 3,276
Draw a bar model. The whole is the first number. The missing number is one of the parts.
Choose the operation. To find a missing part, take the part we know away from the whole.
5,000 − 3,276
Work it out. Use the column method if the numbers are big.
5,000 − 3,276 = 1,724
Th H T O
45 90 90 100
− 3 2 7 6
1 7 2 4
Check in the number sentence. Put the answer back in the box.
5,000 − 1,724 = 3,276 ✓

Check. Read the whole number sentence with your answer in the box. It must be true. ✓

Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.

Watch out

An estimate is not the exact answer, so do not expect it to match exactly. It should only be close. And when you check with the inverse, use the opposite sign: check an addition by subtracting, and check a subtraction by adding.

2.5

Bar models: part-whole and comparison

Year 4
Solve addition and subtraction problems

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Bar models: part-whole and comparisonComing soon

A bar model is a picture that helps you see what a word problem is asking. You draw a bar and label it with the numbers you know and a question mark for the number you want. There are two main kinds of bar model.

Part-whole bar models show a whole that is made of parts. A farm has 1,246 hens and 835 ducks. The whole is the number of birds. The parts are the hens and the ducks. If you know the parts, add to find the whole. If you know the whole and one part, subtract to find the other part.

Part-whole: the two parts (hens and ducks) make the whole (all the birds). Whole = 1,246 + 835.

Comparison bar models show two amounts side by side. The longer bar is the bigger amount. The dashed part is the difference: how much more the bigger amount is. Ben has 2,350 stamps and Cara has 1,875. To find how many more Ben has, subtract: 2,350 − 1,875.

Comparison: Ben has more than Cara. The dashed part is the difference.

Which operation?

You know both parts and want the whole: add.
You know the whole and one part, and want the other part: subtract.
You want the difference between two amounts: subtract the smaller from the bigger.
“5 more than” the smaller amount gives the bigger amount: add. “5 fewer than” the bigger amount gives the smaller amount: subtract.

Always read the question twice, draw the bars, then think about which bar you are finding. The words “more” or “fewer” alone do not tell you whether to add or subtract.

Key words. A bar model is a drawing of the numbers in a problem. The whole is the total. A part is one piece of the whole. The difference is how much bigger one amount is than another.

Key ideas

Draw a bar model. Put a question mark on the number you want.
Part-whole: parts + parts = whole. Whole − part = other part.
Comparison: the dashed gap is the difference. Bigger − smaller = difference.
Bigger = smaller + difference. Smaller = bigger − difference.
Check your answer by using the inverse operation.

Worked example 2.5.1

A farm has 1,246 hens and 835 ducks. How many birds are there altogether?

Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.

Draw a bar model. A picture shows what we know and what we need to find.
Choose the operation. We know both parts and want the whole, so we add.
1,246 + 835
Work it out. Use the column method if the numbers are big.
1,246 + 835 = 2,081
Th H T O
1 2 4 6
+ 8 3 5
2 0 8 1
1 1
Write the answer.
2,081 birds

Check. Use the opposite operation: 2,081 − 835 = 1,246. ✓

Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?

Worked example 2.5.2

A theatre has 3,500 seats. 2,175 seats have been sold. How many seats are empty?

Method. Draw a bar model to see what is happening. Decide whether to add or subtract, then use a written method.

Draw a bar model. A picture shows what we know and what we need to find.
Choose the operation. We know the whole and one part, and want the other part, so we subtract.
3,500 − 2,175
Work it out. Use the column method if the numbers are big.
3,500 − 2,175 = 1,325
Th H T O
3 45 90 100
− 2 1 7 5
1 3 2 5
Write the answer.
1,325 seats

Check. Use the opposite operation: 1,325 + 2,175 = 3,500. ✓

Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?

Worked example 2.5.3

Ben has 2,350 stamps. Cara has 1,875 stamps. How many more stamps does Ben have than Cara?

Key words. A comparison bar model shows two amounts side by side. The difference is how much longer one bar is than the other.

Method. Draw a comparison bar model. The longer bar is the bigger amount. The dashed part is the difference. Then decide whether to add or subtract.

Draw a comparison bar model. The two bars let us see which amount is bigger and what the difference is.
Choose the operation. We want the difference between the two amounts, so we take the smaller from the bigger.
2,350 − 1,875
Work it out. Use the column method if the numbers are big.
2,350 − 1,875 = 475
Th H T O
12 123 145 100
− 1 8 7 5
4 7 5
Write the answer.
475 stamps

Check. Use the opposite operation: 1,875 + 475 = 2,350. ✓

Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.

Worked example 2.5.4

Ben has 1,875 stamps. Cara has 640 more stamps than Ben. How many stamps does Cara have?

Key words. A comparison bar model shows two amounts side by side. The difference is how much longer one bar is than the other.

Method. Draw a comparison bar model. The longer bar is the bigger amount. The dashed part is the difference. Then decide whether to add or subtract.

Draw a comparison bar model. The two bars let us see which amount is bigger and what the difference is.
Choose the operation. Cara has 640 more than Ben, so we add.
1,875 + 640
Work it out. Use the column method if the numbers are big.
1,875 + 640 = 2,515
Th H T O
1 8 7 5
+ 6 4 0
2 5 1 5
1 1
Write the answer.
2,515 stamps

Check. Use the opposite operation: 2,515 − 640 = 1,875. ✓

Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.

Worked example 2.5.5

Cara has 4,230 marbles. Dev has 1,650 fewer marbles than Cara. How many marbles does Dev have?

Key words. A comparison bar model shows two amounts side by side. The difference is how much longer one bar is than the other.

Method. Draw a comparison bar model. The longer bar is the bigger amount. The dashed part is the difference. Then decide whether to add or subtract.

Draw a comparison bar model. The two bars let us see which amount is bigger and what the difference is.
Choose the operation. Dev has 1,650 fewer than Cara, so we take away.
4,230 − 1,650
Work it out. Use the column method if the numbers are big.
4,230 − 1,650 = 2,580
Th H T O
34 112 133 0
− 1 6 5 0
2 5 8 0
Write the answer.
2,580 marbles

Check. Use the opposite operation: 2,580 + 1,650 = 4,230. ✓

Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.

Watch out

The word “fewer” does not always mean subtract, and “more” does not always mean add. In “Cara has 640 more than Ben” you add to find Cara, but you subtract to find the difference. Draw the bars first and decide which bar you are finding.

2.6

Two-step problems with money and measures

Year 4
Two-step problems, Money and measures

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Two-step problems with money and measuresComing soon

A two-step problem needs two calculations. The answer to the first calculation helps you do the second. These problems are often about money and measures (length, mass and capacity).

Use these five steps every time:

Read the problem twice. What do you know? What do you need to find?
Draw a bar model.
Plan your two steps. What do you find first?
Calculate with a written or mental method.
Check that your answer makes sense and answers the question.

A school has 6,000 stickers. 1,850 and 2,375 are used. Step 1: add the two used amounts. Step 2: take the total from 6,000.

Money. Use the same units all the way through. £1 is 100p, so £10 is 1,000p. If a problem mixes pounds and pence, change them to the same unit first. Change is the money left over when you pay with more than the cost. Measures. Do the same with length (cm, m, km), mass (g, kg) and capacity (ml, l): all the amounts must be in the same unit before you add or subtract. Write the unit in your answer.

Many two-step problems follow one of these patterns:

Add, then subtract: add up the amounts used, then take them from the start (stock, money left, distance still to go).
Subtract, then add: follow a story where some leave and some join.
Compare, then total: use “more than” or “fewer than” to find the second amount, then add both.
Total, then compare: add two amounts, then find the difference from a third.

Key words. Change is the money you get back. Pence (p) are the small units of money. A unit is a measurement word such as cm, kg or ml.

Key ideas

Two steps means two calculations. Do them in a sensible order.
Draw a bar model first.
Make sure all amounts are in the same unit (£ with £, p with p, cm with cm).
Change = money paid − total cost.
Check your answer with the inverse, and ask: does it make sense?

Worked example 2.6.1

A school has 6,000 stickers. Reception use 1,850 stickers and Year 1 use 2,375 stickers. How many stickers are left?

Method. This is a two-step problem. First add up everything that was used. Then take that total away from the amount at the start.

Draw a bar model. The whole bar is 6,000. It is split into the two amounts used and the part that is left.
Step 1: add the two amounts used. Put the two parts together.
1,850 + 2,375 = 4,225
Th H T O
1 8 5 0
+ 2 3 7 5
4 2 2 5
1 1
Step 2: take the total away from the start. What is left is the whole minus the parts that were used.
6,000 − 4,225 = 1,775
Th H T O
56 90 90 100
− 4 2 2 5
1 7 7 5
Write the answer.
1,775 stickers

Check. Add everything back: 1,850 + 2,375 + 1,775 = 6,000, which is the start amount. ✓

Watch out. Do not take away just one of the amounts. Both amounts were used, so take away the total of both.

Worked example 2.6.2

Aisha buys a book for 695p and a pen for 249p. She pays with a £10 note. How much change does she get? Give your answer in pence.

Key words. Change is the money you get back when you pay with more than the cost. Pence (p) are the small units: 100p = £1.

Method. This is a two-step problem. First add up how much everything costs. Then take the cost away from the money we have. What is left is the answer.

Make the units the same. £1 is the same as 100p, so we change the £10 note to pence.
£10 = 10 × 100p = 1,000p
Draw a bar model. The whole bar is the money we start with (or pay). It is split into the cost of each thing and what is left.
Step 1: find the total cost. Add the prices.
695p + 249p = 944p
H T O
6 9 5
+ 2 4 9
9 4 4
1 1
Step 2: find the change. Take the total cost away from the money we started with.
1,000p − 944p = 56p
Th H T O
01 90 90 100
− 9 4 4
5 6
Write the answer.
56p change

Check. Add the cost and what is left: 944p + 56p = 1,000p, which is the money we started with. ✓

Watch out. Do not take away just one price. Both things were bought, so take away the total cost. The units must match: pounds with pounds, or pence with pence.

Worked example 2.6.3

Ben scores 2,350 points in a game. Cara scores 640 more points than Ben. How many points do they score altogether?

Method. This is a two-step problem. First use the comparison to find the second amount. Then add the two amounts to find the total.

Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, 640.
Step 1: find how many Cara has. Cara has 640 more, so we add.
2,350 + 640 = 2,990
Th H T O
2 3 5 0
+ 6 4 0
2 9 9 0
Step 2: find the total. Add the two amounts: Ben and Cara.
2,350 + 2,990 = 5,340
Th H T O
2 3 5 0
+ 2 9 9 0
5 3 4 0
1 1
Write the answer.
5,340 points

Check. The difference between the two amounts should be 640: 2,990 − 2,350 = 640. ✓

Watch out. A common mistake is to stop after step 1. The question asks for the total of BOTH amounts.

Worked example 2.6.4

A charity wants to raise £3,000. In May it raises £1,245. In June it raises £1,380. How much more money does it need?

Method. This is a two-step problem. First find the total. Then compare it with the other amount by finding the difference.

Step 1: find the total. Put the two amounts together.
£1,245 + £1,380 = £2,625
Th H T O
1 2 4 5
+ 1 3 8 0
2 6 2 5
1
Draw a comparison bar model. The dashed part is the difference we want.
Step 2: find the difference. Take the smaller amount from the bigger one.
£3,000 − £2,625 = £375
Th H T O
23 90 90 100
− 2 6 2 5
3 7 5
Write the answer.
£375

Check. Add the difference to the smaller amount: £2,625 + £375 = £3,000. ✓

Watch out. Take the SMALLER amount from the BIGGER amount to find the difference.

Worked example 2.6.5

The table shows how many people came to a fair on three days.

Day	People
Friday	2,845
Saturday	4,160
Sunday	3,925

How many more people came on Saturday and Sunday together than on Friday?

Method. This is a two-step problem. First add the people on Saturday and Sunday. Then compare with Friday by finding the difference.

Step 1: find the total for Saturday and Sunday. Put the two days together.
4,160 + 3,925 = 8,085
Th H T O
4 1 6 0
+ 3 9 2 5
8 0 8 5
1
Draw a comparison bar model. One bar is Saturday and Sunday together. The other is Friday. The dashed part is what we want.
Step 2: find the difference. Take the smaller amount from the bigger amount.
8,085 − 2,845 = 5,240
Th H T O
78 100 8 5
− 2 8 4 5
5 2 4 0
Write the answer.
5,240 more people

Check. Add the difference to Friday: 2,845 + 5,240 = 8,085. ✓

Watch out. Read the question carefully. It asks about Saturday and Sunday together, so add those two days first.

Watch out

Check the units before you calculate. £5 and 250p cannot be added until they are both in pounds or both in pence. And remember that two-step problems have two answers on the way: the answer to step 1 is not the final answer.

Exercise 2F Two-step problems

Non-calculator

FA farm shop has 5,000 eggs. It sells 1,265 eggs on Saturday and 1,840 eggs on Sunday. How many eggs are left?

Done

FMr Ali has £9,000 in the bank. He pays £2,485 for a holiday and £1,350 for a sofa. How much money does he have left in the bank?

Done

FA laptop costs £385 and a mouse costs £27. Kofi pays with £500. How much change does he get?

Done

FLeo has 1,850 stickers. Mei has 475 more stickers than Leo. How many stickers do they have altogether?

Done

FA lorry carries 3,640 kg of potatoes. A van carries 1,275 kg fewer than the lorry. How many kilograms do the lorry and the van carry altogether?

Done

FAmira cycles 1,250 m to the park and then 875 m to the shop. Her whole route is 3,000 m. How much further does she have to cycle?

Done

PSDev flies 1,865 km and then 2,740 km. Mia flies 3,980 km. How much further does Dev fly than Mia?

Done

PSThere are 840 passengers on a train. At the next station 365 passengers get off and 278 passengers get on. How many passengers are on the train now?

Done

PSA cafe records how much milk it uses.

Day	Milk used (ml)
Monday	1,750
Tuesday	2,395
Wednesday	1,860

How much more milk is used on Monday and Wednesday together than on Tuesday?

Done

PSDev has £12. He buys a comic for 475p and a sticker book for 360p. How much money does he have left? Give your answer in pence.

Done

RA baker makes 2,450 rolls. She sells 1,380 rolls in the morning and 645 rolls in the afternoon. Which two calculations show how many rolls are left? Tick two boxes.
A 2,450 + 1,380 + 645
B 2,450 − 1,380 − 645
C 2,450 − 1,380 + 645
D 2,450 − (1,380 + 645)

Done

RAisha scores 3,450 points. Ben scores 1,275 more points than Aisha. How many points do Aisha and Ben score altogether? Ravi says the answer is 4,725. What mistake did Ravi make? What is the correct answer?

Done

RTom had some money. He spent £1,250 on a bike and £385 on a helmet. He now has £2,365 left. How much money did Tom have at the start?

Done

Chapter summary

Skill	Method
Column addition	Line up ones under ones. Add from the right. If a column makes 10 or more, write the ones digit and carry the tens.
Column subtraction	Bigger number on top. Subtract from the right. If the top digit is smaller, exchange 1 from the next column (10 more in this column).
Zeros in the top number	You cannot exchange from a 0. Go left to the first column that is not 0. Each 0 you pass becomes 9.
Mental strategies	Partition; bridge through 10, 100 or 1000; compensate (add 99 = add 100, take away 1); near doubles; count up to find a difference.
Estimating	Round each number to the nearest 10, 100 or 1000, then do the easy calculation. Use ≈.
Checking	Use the inverse: check an addition by subtracting and a subtraction by adding. Compare the answer with your estimate.
Part-whole bar models	Parts added together make the whole. Whole − one part = the other part.
Comparison bar models	The gap between the bars is the difference. Bigger − smaller = difference.
Two-step problems	Read, draw a bar model, plan two steps, calculate, check. Use the same units all the way through.

Can you…?

I can add numbers with up to 4 digits using the column method, with carrying.
I can subtract numbers with up to 4 digits using the column method, with exchanging.
I can subtract when there are zeros in the top number, like 5,003 − 1,847.
I can add and subtract in my head by partitioning, bridging, compensating, using near doubles and counting up.
I can estimate an answer by rounding.
I can check an answer with the inverse operation.
I can use part-whole and comparison bar models.
I can solve two-step problems with money and measures and choose the right operations.

Key terms

Column method: A written way to add or subtract. Numbers go one under the other with the same place values lined up.
Carry: When a column adds to 10 or more, you write the ones digit and move the tens to the next column.
Exchange: In subtraction, swapping 1 of the next column for 10 of this column (for example 1 ten for 10 ones). Also called borrowing.
Sum / total: The answer to an addition.
Difference: How far apart two numbers are. It is the answer to a subtraction.
Inverse: The opposite operation. Addition and subtraction undo each other.
Estimate: A close answer found by rounding the numbers first.
Partition: To split a number into parts, such as 346 = 300 + 40 + 6.
Bridging: Jumping to the next round number (10, 100 or 1000) and then doing the rest.
Compensate: To use an easier number and then fix the answer, such as adding 100 and taking away 1 to add 99.
Double: A number added to itself.
Bar model: A drawing of bars that shows the numbers in a problem. Part-whole models show parts and a whole. Comparison models show two amounts side by side.
Change: The money you get back when you pay more than the cost.
Two-step problem: A problem that needs two calculations to solve.

Total 18 marks. Allow about 18 minutes.

Exercise 2X SATs-style questions

Non-calculator

FWork out 4,325 + 2,468.[1 mark]

Done

FWork out 6,000 − 2,357.[1 mark]

Method. Write the bigger number on top. Take away the ones first, then the tens, the hundreds and the thousands. If a top digit is too small, exchange 1 from the next column.

Line up the digits in columns. The bigger number goes on top. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands.
Th H T O
6 0 0 0
− 2 3 5 7
Exchange, then subtract the ones. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.
0 ones is not enough to take away 7. We need to exchange.
The tens and hundreds have 0, so there is nothing to exchange from there. We start further to the left, at the thousands.
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 0 tens become 10 tens.
Exchange 1 ten for 10 ones: 10 tens become 9 tens, and 0 ones become 10 ones.
10 − 7 = 3
Subtract the tens. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 5 = 4
Subtract the hundreds. Now the next column to the left.
(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6
Subtract the thousands. Now the next column to the left.
(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3
Read the answer. Check the answer has the right number of digits, then write it.
Th H T O
56 90 90 100
− 2 3 5 7
3 6 4 3

6,000 − 2,357 = 3,643

Check. Use the opposite (inverse) operation: 3,643 + 2,357 = 6,000. ✓
Estimate: 6,000 − 2,000 = 4,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓

Watch out. You cannot exchange from a 0. Look left for the first column that is not 0, then pass the exchange along one column at a time. Each 0 in the middle becomes 9.

Done

FWhich is the best estimate for 7,096 + 1,894? Tick one box. A 900 B 9,000 C 5,000 D 90,000[1 mark]

Done

FWrite the missing number. ? − 2,365 = 4,500[1 mark]

Done

FA theatre sells 2,865 tickets on Friday and 3,478 tickets on Saturday. How many tickets does it sell altogether? Show your working.[2 marks]

Done

PSA coat costs £185. A hat costs £97. Mrs Jones pays with £300. How much change does she get?[2 marks]

Done

RSam says that 7,000 − 2,468 = 5,632. Use addition to show that Sam is wrong. Then write the correct answer.[2 marks]

Done

PSIn a quiz, Team A scores 2,540 points. Team B scores 1,865 fewer points than Team A. How many points do the two teams score altogether?[2 marks]

Done

RMei thinks of a number. She adds 1,475. Then she subtracts 2,300. Her answer is 3,950. What number did Mei think of first? Show how you know.[3 marks]

Done

PSThe table shows the heights of three mountains.

Mountain	Height (m)
Mount Everest	8,849
K2	8,611
Kangchenjunga	8,586

[3 marks]

(a)How much higher is Mount Everest than K2?

(b)Aisha climbs K2 and then Kangchenjunga. What is the total height she climbs? (2 marks)

Done

← Chapter 1: Place value to 10,000 Chapter 3: Times tables to 12 × 12 →

Year 4 Column Addition and Subtraction: worked examples and questions with answers

By the end of this chapter you will be able to

You should already know

Where this leads

Exercise P Do you remember?

Column addition

Key ideas

Watch out

Exercise 2A Column addition

Column subtraction

Key ideas

Watch out

Exercise 2B Column subtraction

Adding and subtracting in your head

Key ideas

Watch out

Exercise 2C Mental strategies

Estimating and checking your answers

Key ideas

Watch out

Exercise 2D Estimating, inverse operations and missing numbers

Bar models: part-whole and comparison

Key ideas

Watch out

Exercise 2E Bar models

Two-step problems with money and measures

Key ideas

Watch out

Exercise 2F Two-step problems

Chapter summary

Can you…?

Key terms

Exercise 2Z Check-up (non-calculator)

Exercise 2X SATs-style questions

	TTh	Th	H	T	O
		6	7	8	5
+		5	4	3	6

	TTh	Th	H	T	O
		6	7	8	5
+		5	4	3	6
					1
				1

	TTh	Th	H	T	O
		6	7	8	5
+		5	4	3	6
				2	1
			1	1

	TTh	Th	H	T	O
		6	7	8	5
+		5	4	3	6
			2	2	1
		1	1	1