Year 4: Bar models: part-whole and comparison
Part of the Year 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Bar models: part-whole and comparison
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.
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.
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.
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?
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 4 59 010 0− 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?
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 1 212 314 510 0− 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.
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.
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 3 411 213 30 − 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.Exercise 2E Bar models
Non-calculatorKey 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 2 4 5 0 + 1 3 8 0 - Add the ones. Always start with the ones, on the right.0 + 0 = 0
0 is less than 10, so write 0 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.5 + 8 = 13
13 is 1 hundred and 3 tens. Write 3 in the tens column and carry 1 to the hundreds column. - 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. - Add the thousands. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 2 4 5 0 + 1 3 8 0 3 8 3 0 1
2,450 + 1,380 = 3,830
Check. Use the opposite (inverse) operation: 3,830 − 1,380 = 2,450. ✓
Estimate: 2,000 + 1,000 = 3,000 (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 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 2 7 6 + 4 1 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. - Add the tens. Now the next column to the left. Add the 1 we carried as well.7 + 5 + 1 = 13
13 is 1 hundred and 3 tens. Write 3 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.2 + 1 + 1 = 4
4 is less than 10, so write 4 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.3 + 4 = 7
7 is less than 10, so write 7 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 2 7 6 + 4 1 5 9 7 4 3 5 1 1
3,276 + 4,159 = 7,435
Check. Use the opposite (inverse) operation: 7,435 − 4,159 = 3,276. ✓
Estimate: 3,000 + 4,000 = 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 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 5 0 6 8 + 2 9 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. - 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. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.0 + 9 + 1 = 10
10 is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.5 + 2 + 1 = 8
8 is less than 10, so write 8 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 5 0 6 8 + 2 9 7 5 8 0 4 3 1 1 1
5,068 + 2,975 = 8,043
Check. Use the opposite (inverse) operation: 8,043 − 2,975 = 5,068. ✓
Estimate: 5,000 + 3,000 = 8,000 (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.
- 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 0 0 0 − 1 2 7 5 - 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 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: 4 thousands become 3 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 − 5 = 5 - Subtract the tens. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 7 = 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 − 2 = 7 - Subtract the thousands. Now the next column to the left.(This digit is 3 now, not 4, because we exchanged from this column.)
3 − 1 = 2 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 49 09 010 0− 1 2 7 5 2 7 2 5
4,000 − 1,275 = 2,725
Check. Use the opposite (inverse) operation: 2,725 + 1,275 = 4,000. ✓
Estimate: 4,000 − 1,000 = 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. 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 6 5 0 0 − 2 8 6 0 - Subtract the ones. Always start with the ones, on the right.0 − 0 = 0
- 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 6. We need to exchange.
Exchange 1 hundred for 10 tens: 5 hundreds become 4 hundreds, and 0 tens become 10 tens.
10 − 6 = 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.4 hundreds is not enough to take away 8. We need to exchange.
(There were 5 hundreds to start with, but we gave one away in an earlier exchange.)
Exchange 1 thousand for 10 hundreds: 6 thousands become 5 thousands, and 4 hundreds become 14 hundreds.
14 − 8 = 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 5 614 510 00 − 2 8 6 0 3 6 4 0
6,500 − 2,860 = 3,640
Check. Use the opposite (inverse) operation: 3,640 + 2,860 = 6,500. ✓
Estimate: 7,000 − 3,000 = 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.
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 9 0 0 0 − 5 3 8 5 - 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 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: 9 thousands become 8 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 − 5 = 5 - 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 - 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 8 now, not 9, because we exchanged from this column.)
8 − 5 = 3 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 8 99 09 010 0− 5 3 8 5 3 6 1 5
9,000 − 5,385 = 3,615
Check. Use the opposite (inverse) operation: 3,615 + 5,385 = 9,000. ✓
Estimate: 9,000 − 5,000 = 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.
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 3 4 5 0 − 2 1 7 5 - 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 5. We need to exchange.
Exchange 1 ten for 10 ones: 5 tens become 4 tens, and 0 ones become 10 ones.
10 − 5 = 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 7. 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 − 7 = 7 - 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 - Subtract the thousands. Now the next column to the left.3 − 2 = 1
- Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 3 414 510 0− 2 1 7 5 1 2 7 5
3,450 − 2,175 = 1,275
Check. Use the opposite (inverse) operation: 1,275 + 2,175 = 3,450. ✓
Estimate: 3,000 − 2,000 = 1,000 (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.
- 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 8 − 4 2 6 5 - Subtract the ones. Always start with the ones, on the right.8 − 5 = 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 6. We need to exchange.
The hundreds has 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.
10 − 6 = 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 − 2 = 7 - Subtract the thousands. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 4 = 0
We do not write a 0 at the front of an answer, so leave this space empty. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 4 59 010 08 − 4 2 6 5 7 4 3
5,008 − 4,265 = 743
Check. Use the opposite (inverse) operation: 743 + 4,265 = 5,008. ✓
Estimate: 5,000 − 4,000 = 1,000 (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. 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 7 0 0 0 − 3 8 4 6 - 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 6. 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: 7 thousands become 6 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 − 6 = 4 - 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 - 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 - 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 - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 6 79 09 010 0− 3 8 4 6 3 1 5 4
7,000 − 3,846 = 3,154
Check. Use the opposite (inverse) operation: 3,154 + 3,846 = 7,000. ✓
Estimate: 7,000 − 4,000 = 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. 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. Bigger has 450 more than Smaller, so we add.2,145 + 450
- Work it out. Use the column method if the numbers are big.2,145 + 450 = 2,595
Th H T O 2 1 4 5 + 4 5 0 2 5 9 5 - Write the answer. 2,595
Check. Use the opposite operation: 2,595 − 450 = 2,145. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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. Smaller has 1,875 fewer than Bigger, so we take away.6,300 − 1,875
- Work it out. Use the column method if the numbers are big.6,300 − 1,875 = 4,425
Th H T O 5 612 39 010 0− 1 8 7 5 4 4 2 5 - Write the answer. 4,425
Check. Use the opposite operation: 4,425 + 1,875 = 6,300. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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. Bigger has 1,992 more than Smaller, so we add.3,008 + 1,992
- Work it out. Use the column method if the numbers are big.3,008 + 1,992 = 5,000
Th H T O 3 0 0 8 + 1 9 9 2 5 0 0 0 1 1 1 - Write the answer. 5,000
Check. Use the opposite operation: 5,000 − 1,992 = 3,008. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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 are putting two amounts together, so we add.3,486 + 2,759
- Work it out. Use the column method if the numbers are big.3,486 + 2,759 = 6,245
Th H T O 3 4 8 6 + 2 7 5 9 6 2 4 5 1 1 1 - Write the answer. 6,245 books
Check. Use the opposite operation: 6,245 − 2,759 = 3,486. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
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.1,345 m − 1,085 m
- Work it out. Use the column method if the numbers are big.1,345 m − 1,085 m = 260 m
Th H T O 1 2 314 45 − 1 0 8 5 2 6 0 - Write the answer. 260 m
Check. Use the opposite operation: 1,085 m + 260 m = 1,345 m. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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 (all the beads) and one part (the blue beads), so we subtract to find the other part.7,500 − 3,264
- Work it out. Use the column method if the numbers are big.7,500 − 3,264 = 4,236
Th H T O 7 4 59 010 0− 3 2 6 4 4 2 3 6 - Write the answer. 4,236 red beads
Check. Use the opposite operation: 4,236 + 3,264 = 7,500. ✓
Watch out. Read the question again at the end. Does your answer make sense, and does it answer what was asked?
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 5,000. 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.1,250 + 2,075 = 3,325
Th H T O 1 2 5 0 + 2 0 7 5 3 3 2 5 1 - Step 2: take the total away from the start. What is left is the whole minus the parts that were used.5,000 − 3,325 = 1,675
Th H T O 4 59 09 010 0− 3 3 2 5 1 6 7 5 - Write the answer. 1,675 green beads
Check. Add everything back: 1,250 + 2,075 + 1,675 = 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. Decide if the question is about a whole and its parts, or about comparing two separate amounts.
- Read the question. Mia and Noah each have their own stickers. We are not putting them together. We are comparing them.Question: “How many more does Mia have than Noah?”
- Choose the bar model. Model A has two bars side by side, with the difference marked. Model B puts the two amounts together into a total, which is not what the question asks.Model A matches.
- Answer the question. The difference is the bigger amount minus the smaller amount.2,400 − 1,350 = 1,050
Th H T O 2 3 410 00 − 1 3 5 0 1 0 5 0
Check. 1,350 + 1,050 = 2,400. ✓
Watch out. Model B would be right for “How many stickers do Mia and Noah have altogether?”
Method. Look at the comparison bar model. The difference is the gap between the two bars, so adding it to the smaller amount gives the bigger amount.
- Use Priya’s method. The missing number is the gap that is added to 4,175 to reach 6,000.4,175 + ? = 6,000, so ? = 6,000 − 4,175
- Work out the gap. Subtract in columns.6,000 − 4,175 = 1,825
Th H T O 5 69 09 010 0− 4 1 7 5 1 8 2 5 - Check the other way. Add the gap to the smaller amount.4,175 + 1,825 = 6,000
Th H T O 4 1 7 5 + 1 8 2 5 6 0 0 0 1 1 1 - Answer. Yes, Priya is right. Both ways give 1,825.
Check. The gap added to the smaller amount gives the bigger amount: 4,175 + 1,825 = 6,000. ✓
Watch out. Finding the difference by counting up and by subtracting are both correct. They always give the same answer.
Method. Look at the comparison bar model and try some numbers.
- Look at the picture. The difference is the dashed part. It is only a part of the longer bar, not all of it.The dashed part is shorter than the whole top bar.
- Try some numbers. The shorter bar is more than 0, so some of the long bar is used up by the short bar.2,350 − 1,875 = 475 and 475 < 2,350
9,000 − 8,999 = 1 and 1 < 9,000 - Decide. The difference is always smaller than the bigger number (when both numbers are more than 0).Always
Check. Bigger − smaller = difference, so bigger = smaller + difference. The smaller number is more than 0, so the bigger number is more than the difference. ✓
Watch out. If the smaller number was 0, the difference would be the same as the bigger number, not smaller.
Method. Take the difference away from the total. What is left is two equal bars. Share it equally, then put the difference back on the bigger number.
- Look at the bar model. If we cut the dashed part off the long bar, both bars are the same size.Total = 9,000. Difference = 1,200.
- Take the difference away from the total. This leaves two equal parts.9,000 − 1,200 = 7,800
Th H T O 8 910 00 0 − 1 2 0 0 7 8 0 0 - Share the two equal parts. Each part is half of 7,800.7,800 ÷ 2 = 3,900 (the smaller number)
- Find the bigger number. The bigger number is the smaller number plus the difference.3,900 + 1,200 = 5,100
Check. 3,900 + 5,100 = 9,000 ✓ and 5,100 − 3,900 = 1,200. ✓
Watch out. Check your answer with BOTH facts: the total and the difference.