Year 4 Column Addition and Subtraction: check-up and SATs-style questions

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.

1. 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	7
   +	2	5	9	6

2. Add the ones. Always start with the ones, on the right.
   7 + 6 = 13
   13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   4 + 9 + 1 = 14
   14 is 1 hundred and 4 tens. Write 4 in the tens column and carry 1 to the hundreds column.
4. Add the hundreds. Now the next column to the left. Add the 1 we carried as well.
   8 + 5 + 1 = 14
   14 is 1 thousand and 4 hundreds. Write 4 in the hundreds column and carry 1 to the thousands column.
5. 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.
6. Read the answer. Check the answer has the right number of digits, then write it.

   	Th	H	T	O
   	3	8	4	7
   +	2	5	9	6
   	6	4	4	3
   	1	1	1

   
   3,847 + 2,596 = 6,443

Check. Use the opposite (inverse) operation: 6,443 − 2,596 = 3,847. ✓
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.

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.

1. 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	2	1	4
   −	3	6	5	8

2. 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.
   4 ones is not enough to take away 8. We need to exchange.
   Exchange 1 ten for 10 ones: 1 ten become 0 tens, and 4 ones become 14 ones.
   14 − 8 = 6
3. 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.
   0 tens is not enough to take away 5. We need to exchange.
   (There were 1 tens to start with, but we gave one away in an earlier exchange.)
   Exchange 1 hundred for 10 tens: 2 hundreds become 1 hundred, and 0 tens become 10 tens.
   10 − 5 = 5
4. 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.
   1 hundred is not enough to take away 6. We need to exchange.
   (There were 2 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 1 hundred become 11 hundreds.
   11 − 6 = 5
5. Subtract the thousands. Now the next column to the left.
   (This digit is 6 now, not 7, because we exchanged from this column.)
   6 − 3 = 3
6. Read the answer. Check the answer has the right number of digits, then write it.

   	Th	H	T	O
   	67	112	101	144
   −	3	6	5	8
   	3	5	5	6

   
   7,214 − 3,658 = 3,556

Check. Use the opposite (inverse) operation: 3,556 + 3,658 = 7,214. ✓
Estimate: 7,000 − 4,000 = 3,000 (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.

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.

1. 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	4
   −	2	7	8	5

2. 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.
   4 ones is not enough to take away 5. 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 4 ones become 14 ones.
   14 − 5 = 9
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 − 8 = 1
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 − 7 = 2
5. 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
6. Read the answer. Check the answer has the right number of digits, then write it.

   	Th	H	T	O
   	56	90	90	144
   −	2	7	8	5
   	3	2	1	9

   
   6,004 − 2,785 = 3,219

Check. Use the opposite (inverse) operation: 3,219 + 2,785 = 6,004. ✓
Estimate: 6,000 − 3,000 = 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.

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 200 instead, then fix the answer.

1. Spot a nearby round number. 200 is much easier to work with than 199.
   199 is 1 less than 200:  199 = 200 − 1
2. Take away 200 instead of 199. Round numbers are easy.
   3,456 − 200 = 3,256
3. Fix the answer. We took away 1 too many, so we must put 1 back.
   3,256 + 1 = 3,257

Check. Use the opposite operation: 3,257 + 199 = 3,456. ✓

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

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.

1. Round 4,918 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.
   4,918 ≈ 5,000  (the hundreds digit is 9, so round up)
2. Round 3,076 to the nearest 1,000. Do the same for the second number.
   3,076 ≈ 3,000  (the hundreds digit is 0, so round down)
3. Do the easy calculation. Rounded numbers are easy to add or subtract.
   5,000 + 3,000 = 8,000

Check. The exact answer is 7,994. It is close to the estimate of 8,000. ✓

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

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

1. Look at the number sentence. The box stands for the number we want to find.
   ? + 1,756 = 4,000
2. Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
3. Choose the operation. To find a missing part, take the part we know away from the whole.
   4,000 − 1,756
4. Work it out. Use the column method if the numbers are big.
   4,000 − 1,756 = 2,244
   

   	Th	H	T	O
   	34	90	90	100
   −	1	7	5	6
   	2	2	4	4

5. Check in the number sentence. Put the answer back in the box.
   2,244 + 1,756 = 4,000 ✓

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.

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.

1. Write Tom’s answer as an inverse calculation. The opposite operation should take us back to the first number.
   5,208 + 3,897 = 9,005  so  9,005 − 3,897 should be 5,208
2. Work it out. Use the column method.
   9,005 − 3,897 = 5,108
   

   	Th	H	T	O
   	89	90	90	155
   −	3	8	9	7
   	5	1	0	8

3. Compare. We should get 5,208.
   We got 5,108. 5,108 is not 5,208, so Tom is wrong.
4. Find the correct answer. Do the original calculation again.
   5,208 + 3,897 = 9,105
   

   	Th	H	T	O
   	5	2	0	8
   +	3	8	9	7
   	9	1	0	5
   	1	1	1

Check. The correct answer is 9,105. 9,105 − 3,897 = 5,208. ✓

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

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.

1. Draw a comparison bar model. The two bars let us see which amount is bigger and what the difference is.
2. Choose the operation. We want the difference between the two amounts, so we take the smaller from the bigger.
   2,070 − 1,425
3. Work it out. Use the column method if the numbers are big.
   2,070 − 1,425 = 645
   

   	Th	H	T	O
   	12	100	67	100
   −	1	4	2	5
   		6	4	5

4. Write the answer.
   645 members

Check. Use the opposite operation: 1,425 + 645 = 2,070. ✓

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

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.

1. Draw a bar model. The whole bar is £5,000. It is split into the two amounts used and the part that is left.
2. Step 1: add the two amounts used. Put the two parts together.
   £1,875 + £2,340 = £4,215
   

   	Th	H	T	O
   	1	8	7	5
   +	2	3	4	0
   	4	2	1	5
   	1	1

3. Step 2: take the total away from the start. What is left is the whole minus the parts that were used.
   £5,000 − £4,215 = £785
   

   	Th	H	T	O
   	45	90	90	100
   −	4	2	1	5
   		7	8	5

4. Write the answer.
   £785

Check. Add everything back: £1,875 + £2,340 + £785 = £5,000, 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.

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.

1. Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, £650.
2. Step 1: find how many Her brother has. Her brother has £650 fewer, so we subtract.
   £2,300 − £650 = £1,650
   

   	Th	H	T	O
   	12	123	100	0
   −		6	5	0
   	1	6	5	0

3. Step 2: find the total. Add the two amounts: Priya and Her brother.
   £2,300 + £1,650 = £3,950
   

   	Th	H	T	O
   	2	3	0	0
   +	1	6	5	0
   	3	9	5	0

4. Write the answer.
   £3,950

Check. The difference between the two amounts should be £650: £2,300 − £1,650 = £650. ✓

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

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.

1. 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	3	2	5
   +	2	4	6	8

2. Add the ones. Always start with the ones, on the right.
   5 + 8 = 13
   13 is 1 ten and 3 ones. Write 3 in the ones column and carry 1 to the tens column.
3. Add the tens. Now the next column to the left. Add the 1 we carried as well.
   2 + 6 + 1 = 9
   9 is less than 10, so write 9 in the tens column. There is nothing to carry.
4. Add the hundreds. Now the next column to the left.
   3 + 4 = 7
   7 is less than 10, so write 7 in the hundreds column. There is nothing to carry.
5. Add the thousands. Now the next column to the left.
   4 + 2 = 6
   6 is less than 10, so write 6 in the thousands column. There is nothing to carry.
6. Read the answer. Check the answer has the right number of digits, then write it.

   	Th	H	T	O
   	4	3	2	5
   +	2	4	6	8
   	6	7	9	3
   			1

   
   4,325 + 2,468 = 6,793

Check. Use the opposite (inverse) operation: 6,793 − 2,468 = 4,325. ✓
Estimate: 4,000 + 2,000 = 6,000 (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.

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.

1. 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

2. 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
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
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
5. 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
6. 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.

Method. Round both numbers, work out an easy estimate, then find the choice that is closest.

1. Round the numbers to the nearest 1,000. Rounded numbers are quick to add or subtract.
   7,096 ≈ 7,000  (the hundreds digit is 0, so round down)
   1,894 ≈ 2,000  (the hundreds digit is 8, so round up)
2. Work out the estimate.
   7,000 + 2,000 = 9,000
3. Choose the closest answer. The choices are very different sizes, so only one can be close.
   A: 900
   B: 9,000  (close to the estimate)
   C: 5,000
   D: 90,000

Check. The exact answer is 8,990, which is close to 9,000. ✓

Watch out. You do not need the exact answer. Round, work out the easy sum, and look for the closest choice.

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

1. Look at the number sentence. The box stands for the number we want to find.
   ? − 2,365 = 4,500
2. Draw a bar model. The missing number is the whole. It is made of the two parts we know.
3. Choose the operation. To find the whole, add the two parts together.
   4,500 + 2,365
4. Work it out. Use the column method if the numbers are big.
   4,500 + 2,365 = 6,865
   

   	Th	H	T	O
   	4	5	0	0
   +	2	3	6	5
   	6	8	6	5

5. Check in the number sentence. Put the answer back in the box.
   6,865 − 2,365 = 4,500 ✓

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.

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

1. Draw a bar model. A picture shows what we know and what we need to find.
2. Choose the operation. We are putting two amounts together, so we add.
   2,865 + 3,478
3. Work it out. Use the column method if the numbers are big.
   2,865 + 3,478 = 6,343
   

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

4. Write the answer.
   6,343 tickets

Check. Use the opposite operation: 6,343 − 3,478 = 2,865. ✓

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

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.

1. 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.
2. Step 1: find the total cost. Add the prices.
   £185 + £97 = £282
   

   	H	T	O
   	1	8	5
   +		9	7
   	2	8	2
   	1	1

3. Step 2: find the change. Take the total cost away from the money we started with.
   £300 − £282 = £18
   

   	H	T	O
   	23	90	100
   −	2	8	2
   		1	8

4. Write the answer.
   £18 change

Check. Add the cost and what is left: £282 + £18 = £300, 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.

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.

1. Write Sam’s answer as an inverse calculation. The opposite operation should take us back to the first number.
   7,000 − 2,468 = 5,632  so  5,632 + 2,468 should be 7,000
2. Work it out. Use the column method.
   5,632 + 2,468 = 8,100
   

   	Th	H	T	O
   	5	6	3	2
   +	2	4	6	8
   	8	1	0	0
   	1	1	1

3. Compare. We should get 7,000.
   We got 8,100. 8,100 is not 7,000, so Sam is wrong.
4. Find the correct answer. Do the original calculation again.
   7,000 − 2,468 = 4,532
   

   	Th	H	T	O
   	67	90	90	100
   −	2	4	6	8
   	4	5	3	2

Check. The correct answer is 4,532. 4,532 + 2,468 = 7,000. ✓

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

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.

1. Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, 1,865.
2. Step 1: find how many Team B has. Team B has 1,865 fewer, so we subtract.
   2,540 − 1,865 = 675
   

   	Th	H	T	O
   	12	145	134	100
   −	1	8	6	5
   		6	7	5

3. Step 2: find the total. Add the two amounts: Team A and Team B.
   2,540 + 675 = 3,215
   

   	Th	H	T	O
   	2	5	4	0
   +		6	7	5
   	3	2	1	5
   	1	1

4. Write the answer.
   3,215 points

Check. The difference between the two amounts should be 1,865: 2,540 − 675 = 1,865. ✓

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

Key words. To work backwards is to start from the answer and use the inverse of each step in reverse order.

Method. Work backwards. Use the inverse (opposite) of each step, starting from the last one.

1. Write the steps in order. Mei did: start → add 1,475 → subtract 2,300 → 3,950.
   ? → + 1,475 → − 2,300 → 3,950
2. Undo the last step. The last step was − 2,300. The inverse is + 2,300.
   3,950 + 2,300 = 6,250
   

   	Th	H	T	O
   	3	9	5	0
   +	2	3	0	0
   	6	2	5	0
   	1

3. Undo the first step. The first step was + 1,475. The inverse is − 1,475.
   6,250 − 1,475 = 4,775
   

   	Th	H	T	O
   	56	112	145	100
   −	1	4	7	5
   	4	7	7	5

4. Write the number.
   4,775

Check. Go forward: 4,775 + 1,475 = 6,250 and 6,250 − 2,300 = 3,950. ✓

Watch out. 3 marks: 1 for undoing the subtraction, 1 for undoing the addition and 1 for the correct answer. Work backwards, not forwards.