Year 5: Tables, charts, timetables and bank statements
Part of the Year 5 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Tables, charts, timetables and bank statements
Numbers in real life often come in tables, charts and timetables. Adding and subtracting helps you to find totals and differences. First read the information carefully. Then decide which numbers you need, which operation to use and which method is best.
| Town | Population |
|---|---|
| Ashby | 84,560 |
| Brigg | 126,400 |
| Calder | 47,285 |
| Denby | 91,750 |
Bar charts. Look at the scale on the side. Here every labelled line is 10,000 and there are 5 small steps between them, so each small step is 2,000. A bar that ends two small steps above the 30,000 line is 34,000. Do not just read the nearest number on the scale: count the small steps.
Timetables. Times are written in hours and minutes, with 60 minutes in an hour. To find how long a journey takes, count on from the start time to the end time: first to the next o’clock, then the rest.
| Bus stop | Time |
|---|---|
| School | 08:15 |
| Park | 08:32 |
| Library | 08:47 |
| Station | 09:05 |
| Market | 09:38 |
Bank statements. A bank statement shows money going in (like wages) and money going out (like rent). The balance is the money left in the account. Money in is added. Money out is subtracted.
| What happened | Money in | Money out | Balance |
|---|---|---|---|
| Opening balance | £2,450 | ||
| Wages | £1,865 | £4,315 | |
| Rent | £950 | £3,365 | |
| Gas bill | £185 | £3,180 | |
| Gift | £250 | £3,430 |
Which method? Before you calculate, look at the numbers and ask yourself these questions.
- Are the numbers friendly, or close to round numbers? Mental method (compensate, count up, number bonds).
- Are the numbers big and messy with lots of carrying or exchanging? Column method.
- Do I only need a rough idea? Estimate by rounding.
- Do I need an exact answer, such as for money or a limit? Exact calculation.
Then check your answer with an estimate or the inverse. There is often more than one good method, but you should be able to explain why you chose yours.
Key words. A table shows information in rows and columns. A bar chart uses bars to show amounts. A timetable shows when things happen. A balance is the amount of money in an account.
Key ideas
- Read the table or chart carefully. Find the numbers you need and note the units.
- On a bar chart, work out what each small step on the scale is worth.
- For a timetable, count on to the next o’clock, then add the rest. There are 60 minutes in an hour.
- On a bank statement, money in adds and money out subtracts.
- Choose a method that suits the numbers. Mental for friendly numbers, column for messy ones.
- Check with an estimate or the inverse.
| Town | Population |
|---|---|
| Ashby | 84,560 |
| Brigg | 126,400 |
| Calder | 47,285 |
| Denby | 91,750 |
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 8 4 5 6 0 + 1 2 6 4 0 0 + 4 7 2 8 5 - Add the ones. Always start with the ones, on the right.0 + 0 + 5 = 5
5 is less than 10, so write 5 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.6 + 0 + 8 = 14
14 tens 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.5 + 4 + 2 + 1 = 12 (the red digit is the carry)
12 hundreds is 1 thousand and 2 hundreds. Write 2 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.4 + 6 + 7 + 1 = 18 (the red digit is the carry)
18 thousands is 1 ten thousand and 8 thousands. Write 8 in the thousands column and carry 1 to the ten thousands column. - Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.8 + 2 + 4 + 1 = 15 (the red digit is the carry)
15 ten thousands is 1 hundred thousand and 5 ten thousands. Write 5 in the ten thousands column and carry 1 to the hundred thousands column. - Add the hundred thousands. Now the next column to the left. Add the 1 we carried as well.1 + 1 = 2 (the red digit is the carry)
2 is less than 10, so write 2 in the hundred thousands column. There is nothing to carry. - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 4 5 6 0 + 1 2 6 4 0 0 + 4 7 2 8 5 2 5 8 2 4 5 1 1 1 1
84,560 + 126,400 + 47,285 = 258,245
Check. Use the opposite (inverse) operation: 258,245 − 126,400 − 47,285 = 84,560. ✓
Estimate: 85,000 + 126,000 + 47,000 = 258,000 (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. 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.126,400 − 47,285
- Work it out. Use the column method because the numbers are big.126,400 − 47,285 = 79,115
HTh TTh Th H T O 0 111 216 63 49 010 0− 4 7 2 8 5 7 9 1 1 5 - Write the answer. 79,115 people
Check. Use the opposite operation: 47,285 + 79,115 = 126,400. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
Method. Read the height of each bar using the scale. Then find the difference.
- Read the scale. The labelled lines go up in 10,000s. There are 5 small steps between them, so each small step is 10,000 ÷ 5 = 2,000.10,000 ÷ 5 = 2,000
- Read the Thursday bar. It ends 3 small steps above the 40,000 line: 3 × 2,000 = 6,000.40,000 + 6,000 = 46,000
- Read the Wednesday bar. It ends 1 small step below the 30,000 line: 30,000 − 2,000.30,000 − 2,000 = 28,000
- Find the difference. Take the smaller number from the bigger number.46,000 − 28,000 = 18,000
TTh Th H T O 3 416 60 0 0 − 2 8 0 0 0 1 8 0 0 0
Check. 28,000 + 18,000 = 46,000. ✓
Watch out. Do not read the nearest label on the scale. Count the small steps.
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value.
HTh TTh Th H T O 3 4 0 0 0 + 4 2 0 0 0 + 2 8 0 0 0 - Add the ones. Always start with the ones, on the right.0 + 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.0 + 0 + 0 = 0
0 is less than 10, so write 0 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.0 + 0 + 0 = 0
0 is less than 10, so write 0 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.4 + 2 + 8 = 14
14 thousands is 1 ten thousand and 4 thousands. Write 4 in the thousands column and carry 1 to the ten thousands column. - Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.3 + 4 + 2 + 1 = 10 (the red digit is the carry)
10 ten thousands is 1 hundred thousand and 0 ten thousands. Write 0 in the ten thousands column and carry 1 to the hundred thousands column. - Write the carried digit. There are no digits left in the hundred thousands column, but we carried 1 into it.There is only one digit here, so write 1 in the hundred thousands column.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 3 4 0 0 0 + 4 2 0 0 0 + 2 8 0 0 0 1 0 4 0 0 0 1 1
34,000 + 42,000 + 28,000 = 104,000
Check. Use the opposite (inverse) operation: 104,000 − 42,000 − 28,000 = 34,000. ✓
Estimate: 34,000 + 42,000 + 28,000 = 104,000 (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.
| What happened | Money in | Money out | Balance |
|---|---|---|---|
| Opening balance | £2,450 | ||
| Wages | £1,865 | ? | |
| Rent | £950 | ? | |
| Gas bill | £185 | ? | |
| Gift | £250 | ? |
Key words. A bank statement lists the money going in and out of an account. The balance is the amount of money in the account.
Method. The balance is the money in the account. Start with the opening balance. Add money that comes in and take away money that goes out, one line at a time.
- Start with the opening balance. This is the first number.Opening balance = £2,450
- Wages come in. Money in is added to the balance. Money out is taken away.2,450 + 1,865 = 4,315
Th H T O 2 4 5 0 + 1 8 6 5 4 3 1 5 1 1 - Rent goes out. Use the new balance from the step before.4,315 − 950 = 3,365
Th H T O 3 412 311 15 − 9 5 0 3 3 6 5 - Gas bill goes out. Use the new balance from the step before.3,365 − 185 = 3,180
Th H T O 3 2 316 65 − 1 8 5 3 1 8 0 - A gift comes in. Use the new balance from the step before.3,180 + 250 = 3,430
Th H T O 3 1 8 0 + 2 5 0 3 4 3 0 1 - Write the final balance. It is the last balance.£3,430
Check. Check the total: £2,450 + money in − money out = £2,450 + £2,115 − £1,135 = £3,430. ✓
Watch out. Money out (a payment) makes the balance smaller. Money in (a deposit or wages) makes it bigger.
| Bus stop | Time |
|---|---|
| School | 08:15 |
| Park | 08:32 |
| Library | 08:47 |
| Station | 09:05 |
| Market | 09:38 |
Method. Count on from the earlier time to the later time. Jump to the next whole hour first, then add the rest. Add up the jumps.
- Write the two times. The journey starts at the earlier time and ends at the later time.Start 08:32, finish 09:05
- Count on in jumps. Jump to the next o’clock first, because it is easy to count from there.08:32 + 28 minutes = 09:00
09:00 + 5 minutes = 09:05 - Add up the jumps. The total of the jumps is the number of minutes.28 + 5 = 33 minutes
Check. 08:32 + 33 minutes = 09:05. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not use column subtraction on clock times.
| Stage | Distance (km) |
|---|---|
| London to New York | 5,570 |
| New York to Los Angeles | 3,940 |
| Los Angeles to Tokyo | 8,830 |
| Tokyo to Delhi | 5,840 |
Method. Plan the steps. Find the total distance, find the distance already flown, then subtract. (There is a quicker way too: add the stages still to fly.)
- Add all four stages. This gives the whole journey.5,570 km + 3,940 km + 8,830 km + 5,840 km = 24,180 km
TTh Th H T O 5 5 7 0 + 3 9 4 0 + 8 8 3 0 + 5 8 4 0 2 4 1 8 0 2 3 1 - Add the first two stages. This is the distance Dev has already flown.5,570 km + 3,940 km = 9,510 km
Th H T O 5 5 7 0 + 3 9 4 0 9 5 1 0 1 1 - Subtract. Whole journey minus the distance flown is the distance left.24,180 km − 9,510 km = 14,670 km
TTh Th H T O 1 213 411 18 0 − 9 5 1 0 1 4 6 7 0 - Check the quicker way. The distance left is also the last two stages added together.8,830 km + 5,840 km = 14,670 km
TTh Th H T O 8 8 3 0 + 5 8 4 0 1 4 6 7 0 1 1
Check. 9,510 + 14,670 = 24,180 km. ✓
Watch out. Both ways give the same answer. Choose the one that needs fewer steps.
4,999 + 3,001 45,368 + 27,594 70,000 − 69,994 306,040 − 148,975
Method. For each calculation, look at the numbers first. Friendly numbers suit a mental method. Messy numbers suit the column method.
- 4,999 + 3,001. Mental method. 3,001 + 5,000 = 8,001, then take 1 away.8,000
- 45,368 + 27,594. Column method. Lots of carrying, so a written method is safer.72,962
- 70,000 − 69,994. Mental method. The numbers are very close, so count up: 69,994 + 6 = 70,000.6
- 306,040 − 148,975. Column method. Zeros and exchanges, so use columns.157,065
- Check the choices. There can be more than one good method, but you must be able to explain why you chose it.Each answer can be checked with the inverse operation.
Check. 8,000 − 3,001 = 4,999 ✓; 72,962 − 27,594 = 45,368 ✓; 69,994 + 6 = 70,000 ✓; 157,065 + 148,975 = 306,040. ✓
Watch out. Do not use a column method for 4,999 + 3,001 just because it is an addition. A mental method is quicker and less likely to go wrong.
Watch out
Read bar charts carefully: a bar that is between two labelled lines is not equal to the nearest label. Count the small steps. On a bank statement do not add money out: money out is subtracted from the balance. And do not use column subtraction for clock times, because there are 60 minutes in an hour, not 100.Exercise 2G Tables, charts, timetables and bank statements
Non-calculator| Town | Population |
|---|---|
| Ashby | 84,560 |
| Brigg | 126,400 |
| Calder | 47,285 |
| Denby | 91,750 |
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value.
HTh TTh Th H T O 8 4 5 6 0 + 4 7 2 8 5 - Add the ones. Always start with the ones, on the right.0 + 5 = 5
5 is less than 10, so write 5 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.6 + 8 = 14
14 tens 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.5 + 2 + 1 = 8 (the red digit is the carry)
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.4 + 7 = 11
11 thousands is 1 ten thousand and 1 thousand. Write 1 in the thousands column and carry 1 to the ten thousands column. - Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.8 + 4 + 1 = 13 (the red digit is the carry)
13 ten thousands is 1 hundred thousand and 3 ten thousands. Write 3 in the ten thousands column and carry 1 to the hundred thousands column. - Write the carried digit. There are no digits left in the hundred thousands column, but we carried 1 into it.There is only one digit here, so write 1 in the hundred thousands column.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 4 5 6 0 + 4 7 2 8 5 1 3 1 8 4 5 1 1 1
84,560 + 47,285 = 131,845
Check. Use the opposite (inverse) operation: 131,845 − 47,285 = 84,560. ✓
Estimate: 85,000 + 47,000 = 132,000 (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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 1 2 6 4 0 0 − 9 1 7 5 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 5. We need to exchange.
Exchange 1 hundred for 10 tens: 4 hundreds become 3 hundreds, and 0 tens become 10 tens.
10 − 5 = 5 - 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.3 hundreds is not enough to take away 7. We need to exchange.
(There were 4 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 3 hundreds become 13 hundreds.
13 − 7 = 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 − 1 = 4 - Exchange, then subtract the ten thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.2 ten thousands is not enough to take away 9. We need to exchange.
Exchange 1 hundred thousand for 10 ten thousands: 1 hundred thousand become 0 hundred thousands, and 2 ten thousands become 12 ten thousands.
12 − 9 = 3 - Bring down the hundred thousands digit. The bottom number has no digit in this column, so there is nothing to take away.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away in this column, so the digit stays: 0.
We do not write a 0 at the front of an answer, so leave this space empty. - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 0 112 25 613 410 00 − 9 1 7 5 0 3 4 6 5 0
126,400 − 91,750 = 34,650
Check. Use the opposite (inverse) operation: 34,650 + 91,750 = 126,400. ✓
Estimate: 126,000 − 92,000 = 34,000 (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 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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value. The numbers have different lengths, so line them up on the right.
HTh TTh Th H T O 8 4 5 6 0 + 1 2 6 4 0 0 + 4 7 2 8 5 + 9 1 7 5 0 - Add the ones. Always start with the ones, on the right.0 + 0 + 5 + 0 = 5
5 is less than 10, so write 5 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.6 + 0 + 8 + 5 = 19
19 tens is 1 hundred and 9 tens. Write 9 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.5 + 4 + 2 + 7 + 1 = 19 (the red digit is the carry)
19 hundreds is 1 thousand and 9 hundreds. Write 9 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.4 + 6 + 7 + 1 + 1 = 19 (the red digit is the carry)
19 thousands is 1 ten thousand and 9 thousands. Write 9 in the thousands column and carry 1 to the ten thousands column. - Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.8 + 2 + 4 + 9 + 1 = 24 (the red digit is the carry)
24 ten thousands is 2 hundred thousands and 4 ten thousands. Write 4 in the ten thousands column and carry 2 to the hundred thousands column. - Add the hundred thousands. Now the next column to the left. Add the 2 we carried as well.1 + 2 = 3 (the red digit is the carry)
3 is less than 10, so write 3 in the hundred thousands column. There is nothing to carry. - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 8 4 5 6 0 + 1 2 6 4 0 0 + 4 7 2 8 5 + 9 1 7 5 0 3 4 9 9 9 5 2 1 1 1
84,560 + 126,400 + 47,285 + 91,750 = 349,995
Check. Use the opposite (inverse) operation: 349,995 − 126,400 − 47,285 − 91,750 = 84,560. ✓
Estimate: 85,000 + 126,000 + 47,000 + 92,000 = 350,000 (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.
Method. Read the height of the Thursday bar using the scale.
- Find the value of a small step. Between two labelled lines there are 5 small steps.10,000 ÷ 5 = 2,000
- Read the bar. The bar ends 3 small steps above 40,000.40,000 + 3 × 2,000 = 46,000
Check. Count down 4,000 from 50,000: 46,000. ✓
Watch out. Count the small steps. Do not read the nearest label.
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.42,000 − 38,000
- Work it out. Use the column method because the numbers are big.42,000 − 38,000 = 4,000
TTh Th H T O 3 412 20 0 0 − 3 8 0 0 0 4 0 0 0 - Write the answer. 4,000 people
Check. Use the opposite operation: 38,000 + 4,000 = 42,000. ✓
Watch out. “More than” does not always mean add. Draw the bars first, then think about which bar you are finding.
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value.
TTh Th H T O 3 4 0 0 0 + 4 2 0 0 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.0 + 0 = 0
0 is less than 10, so write 0 in the tens column. There is nothing to carry. - Add the hundreds. Now the next column to the left.0 + 0 = 0
0 is less than 10, so write 0 in the hundreds column. There is nothing to carry. - 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. - Add the ten thousands. Now the next column to the left.3 + 4 = 7
7 is less than 10, so write 7 in the ten thousands column. There is nothing to carry. - Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 3 4 0 0 0 + 4 2 0 0 0 7 6 0 0 0
34,000 + 42,000 = 76,000
Check. Use the opposite (inverse) operation: 76,000 − 42,000 = 34,000. ✓
Estimate: 34,000 + 42,000 = 76,000 (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.
Method. Read each bar first. Then look for the two bars that add to 74,000. Use the tens of thousands and the ones to cut down the choices.
- Read each bar. Count the small steps of 2,000 on each bar.Mon 34,000, Tue 42,000, Wed 28,000, Thu 46,000, Fri 38,000
- Look for the pair. There are only 10 pairs of days, so we can try them all.Mon + Tue: 34,000 + 42,000 = 76,000
Mon + Wed: 34,000 + 28,000 = 62,000
Mon + Thu: 34,000 + 46,000 = 80,000
Mon + Fri: 34,000 + 38,000 = 72,000
Tue + Wed: 42,000 + 28,000 = 70,000
Tue + Thu: 42,000 + 46,000 = 88,000
Tue + Fri: 42,000 + 38,000 = 80,000
Wed + Thu: 28,000 + 46,000 = 74,000 (74,000!)
Wed + Fri: 28,000 + 38,000 = 66,000
Thu + Fri: 46,000 + 38,000 = 84,000 - Check no other pair works. We checked every pair: only one adds to 74,000.Only Wednesday and Thursday.
Check. 28,000 + 46,000 = 74,000. ✓
Watch out. Check every pair, not just the first one that looks right.
| What happened | Money in | Money out | Balance |
|---|---|---|---|
| Opening balance | £2,450 | ||
| Wages | £1,865 | ? | |
| Rent | £950 | ? | |
| Phone bill | £48 | ? | |
| Shopping | £215 | ? | |
| Gift | £150 | ? |
Key words. A bank statement lists the money going in and out of an account. The balance is the amount of money in the account.
Method. The balance is the money in the account. Start with the opening balance. Add money that comes in and take away money that goes out, one line at a time.
- Start with the opening balance. This is the first number.Opening balance = £2,450
- Wages come in. Money in is added to the balance. Money out is taken away.2,450 + 1,865 = 4,315
Th H T O 2 4 5 0 + 1 8 6 5 4 3 1 5 1 1 - Rent goes out. Use the new balance from the step before.4,315 − 950 = 3,365
Th H T O 3 412 311 15 − 9 5 0 3 3 6 5 - Phone bill goes out. Use the new balance from the step before.3,365 − 48 = 3,317
Th H T O 3 3 5 615 5− 4 8 3 3 1 7 - Shopping goes out. Use the new balance from the step before.3,317 − 215 = 3,102
Th H T O 3 3 1 7 − 2 1 5 3 1 0 2 - A gift comes in. Use the new balance from the step before.3,102 + 150 = 3,252
Th H T O 3 1 0 2 + 1 5 0 3 2 5 2 - Write the final balance. It is the last balance.£3,252
Check. Check the total: £2,450 + money in − money out = £2,450 + £2,015 − £1,213 = £3,252. ✓
Watch out. Money out (a payment) makes the balance smaller. Money in (a deposit or wages) makes it bigger.
| What happened | Money in | Money out |
|---|---|---|
| Wages | £3,200 | |
| Rent | £1,450 | |
| Car repair | £875 | |
| Holiday | £2,230 | |
| Refund | £640 |
Method. Add up all the money that went in. Add up all the money that went out. Then find the difference.
- Money in. Add the lines in the “Money in” column.£3,200 + £640 = £3,840
Th H T O 3 2 0 0 + 6 4 0 3 8 4 0 - Money out. Add the lines in the “Money out” column.£1,450 + £875 + £2,230 = £4,555
Th H T O 1 4 5 0 + 8 7 5 + 2 2 3 0 4 5 5 5 1 1 - Find the difference. Take the smaller total from the bigger total.£4,555 − £3,840 = £715
Th H T O 3 415 55 5 − 3 8 4 0 7 1 5 - Write the answer. £715 more went out
Check. £3,840 + £715 = £4,555. ✓
Watch out. Add the money in and the money out separately. Do not mix them up.
| Bus stop | Time |
|---|---|
| School | 08:15 |
| Park | 08:32 |
| Library | 08:47 |
| Station | 09:05 |
| Market | 09:38 |
Method. Count on from the earlier time to the later time. Jump to the next whole hour first, then add the rest. Add up the jumps.
- Write the two times. The journey starts at the earlier time and ends at the later time.Start 08:32, finish 09:05
- Count on in jumps. Jump to the next o’clock first, because it is easy to count from there.08:32 + 28 minutes = 09:00
09:00 + 5 minutes = 09:05 - Add up the jumps. The total of the jumps is the number of minutes.28 + 5 = 33 minutes
Check. 08:32 + 33 minutes = 09:05. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not use column subtraction on clock times.
Method. Count on from the earlier time to the later time. Jump to the next whole hour first, then add the rest. Add up the jumps.
- Write the two times. The journey starts at the earlier time and ends at the later time.Start 08:47, finish 09:38
- Count on in jumps. Jump to the next o’clock first, because it is easy to count from there.08:47 + 13 minutes = 09:00
09:00 + 38 minutes = 09:38 - Add up the jumps. The total of the jumps is the number of minutes.13 + 38 = 51 minutes
Check. 08:47 + 51 minutes = 09:38. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not use column subtraction on clock times.
Method. Count on from the earlier time to the later time. Jump to the next whole hour first, then add the rest. Add up the jumps.
- Write the two times. The journey starts at the earlier time and ends at the later time.Start 08:15, finish 09:38
- Count on in jumps. Jump to the next o’clock first, because it is easy to count from there.08:15 + 45 minutes = 09:00
09:00 + 38 minutes = 09:38 - Add up the jumps. The total of the jumps is the number of minutes.45 + 38 = 83 minutes = 1 h 23 min
Check. 08:15 + 83 minutes = 09:38. ✓
Watch out. There are 60 minutes in an hour, not 100. Do not use column subtraction on clock times.
| Stage | Distance (km) |
|---|---|
| London to New York | 5,570 |
| New York to Los Angeles | 3,940 |
| Los Angeles to Tokyo | 8,830 |
| Tokyo to Delhi | 5,840 |
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value.
TTh Th H T O 5 5 7 0 + 3 9 4 0 + 8 8 3 0 + 5 8 4 0 - Add the ones. Always start with the ones, on the right.0 + 0 + 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.7 + 4 + 3 + 4 = 18
18 tens is 1 hundred and 8 tens. Write 8 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.5 + 9 + 8 + 8 + 1 = 31 (the red digit is the carry)
31 hundreds is 3 thousands and 1 hundred. Write 1 in the hundreds column and carry 3 to the thousands column. - Add the thousands. Now the next column to the left. Add the 3 we carried as well.5 + 3 + 8 + 5 + 3 = 24 (the red digit is the carry)
24 thousands is 2 ten thousands and 4 thousands. Write 4 in the thousands column and carry 2 to the ten thousands column. - Write the carried digit. There are no digits left in the ten thousands column, but we carried 2 into it.There is only one digit here, so write 2 in the ten thousands column.
- Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 5 5 7 0 + 3 9 4 0 + 8 8 3 0 + 5 8 4 0 2 4 1 8 0 2 3 1
5,570 + 3,940 + 8,830 + 5,840 = 24,180
Check. Use the opposite (inverse) operation: 24,180 − 3,940 − 8,830 − 5,840 = 5,570. ✓
Estimate: 5,600 + 3,900 + 8,800 + 5,800 = 24,100 (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.
Method. Add the first and the last stage. (You can check by taking the middle two stages from the total.)
- Add the first and last stages. These are the stages we want.5,570 km + 5,840 km = 11,410 km
TTh Th H T O 5 5 7 0 + 5 8 4 0 1 1 4 1 0 1 1 1 - Check with the total. Total minus the middle two stages should give the same answer.24,180 − (3,940 + 8,830) = 24,180 − 12,770 = 11,410 km
Check. 11,410 + 12,770 = 24,180. ✓
Watch out. The stages you do not want are the middle two, so you can also subtract them from the total.
| Day | Sales |
|---|---|
| Monday | £12,450 |
| Tuesday | £9,875 |
| Wednesday | £15,320 |
| Thursday | £11,690 |
Method. This is a multi-step problem. Add the sales to find the total. Then take the costs away.
- Add the four days of sales. We need the total sales.£12,450 + £9,875 + £15,320 + £11,690 = £49,335
TTh Th H T O 1 2 4 5 0 + 9 8 7 5 + 1 5 3 2 0 + 1 1 6 9 0 4 9 3 3 5 1 2 2 - Take away the costs. Money left = total sales minus costs.£49,335 − £27,500 = £21,835
TTh Th H T O 4 8 913 33 5 − 2 7 5 0 0 2 1 8 3 5 - Write the answer. £21,835
Check. £21,835 + £27,500 = £49,335. ✓
Watch out. Read what the question asks. Total sales is not the final answer.
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 5,000 instead, then fix the answer.
- Spot a nearby round number. 5,000 is much easier to work with than 4,999.4,999 is 1 less than 5,000: 4,999 = 5,000 − 1
- Add 5,000 instead of 4,999. Round numbers are easy.3,001 + 5,000 = 8,001
- Fix the answer. We added 1 too many, so we must take 1 away.8,001 − 1 = 8,000
Check. Use the opposite operation: 8,000 − 4,999 = 3,001. ✓
Watch out. Do not forget the last step. You changed the number you add or take away, so the answer needs fixing.
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 to the next column. The sum or total is the answer to an addition.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, hundreds and so on. 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 so on, so every digit is added to digits of the same value.
TTh Th H T O 4 5 3 6 8 + 2 7 5 9 4 - Add the ones. Always start with the ones, on the right.8 + 4 = 12
12 ones is 1 ten and 2 ones. Write 2 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 + 9 + 1 = 16 (the red digit is the carry)
16 tens is 1 hundred and 6 tens. Write 6 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.3 + 5 + 1 = 9 (the red digit is the carry)
9 is less than 10, so write 9 in the hundreds column. There is nothing to carry. - Add the thousands. Now the next column to the left.5 + 7 = 12
12 thousands is 1 ten thousand and 2 thousands. Write 2 in the thousands column and carry 1 to the ten thousands column. - Add the ten thousands. Now the next column to the left. Add the 1 we carried as well.4 + 2 + 1 = 7 (the red digit is the carry)
7 is less than 10, so write 7 in the ten thousands column. There is nothing to carry. - Read the answer. Check that the answer has a sensible number of digits, then write it.
TTh Th H T O 4 5 3 6 8 + 2 7 5 9 4 7 2 9 6 2 1 1 1
45,368 + 27,594 = 72,962
Check. Use the opposite (inverse) operation: 72,962 − 27,594 = 45,368. ✓
Estimate: 45,000 + 28,000 = 73,000 (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. 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, 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: 69,994. Finish: 70,000.
- Count up in easy jumps. Jump to a round number first, then add the rest.69,994 + 6 = 70,000
- Add up the jumps. The total of all the jumps is the difference.6 = 6
Check. Use addition: 69,994 + 6 = 70,000. ✓
Watch out. Add up the jumps. The answer is the size of the jumps, not the number you finish on.
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. The difference is the answer to a subtraction.
Method. Write the bigger number on top. Take away the ones first, then the tens, hundreds and so on. 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 so on.
HTh TTh Th H T O 3 0 6 0 4 0 − 1 4 8 9 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: 4 tens become 3 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.3 tens is not enough to take away 7. We need to exchange.
(There were 4 tens to start with, but we gave one away in an earlier 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: 6 thousands become 5 thousands, and 0 hundreds become 10 hundreds.
Exchange 1 hundred for 10 tens: 10 hundreds become 9 hundreds, and 3 tens become 13 tens.
13 − 7 = 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 − 9 = 0 - Exchange, then subtract the thousands. The top digit is smaller than the bottom digit, so we cannot take it away yet. We swap 1 from the next column.5 thousands is not enough to take away 8. We need to exchange.
(There were 6 thousands to start with, but we gave one away in an earlier exchange.)
The ten thousands has 0, so there is nothing to exchange from there. We start further to the left, at the hundred thousands.
Exchange 1 hundred thousand for 10 ten thousands: 3 hundred thousands become 2 hundred thousands, and 0 ten thousands become 10 ten thousands.
Exchange 1 ten thousand for 10 thousands: 10 ten thousands become 9 ten thousands, and 5 thousands become 15 thousands.
15 − 8 = 7 - Subtract the ten thousands. 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 hundred thousands. Now the next column to the left.(This digit is 2 now, not 3, because we exchanged from this column.)
2 − 1 = 1 - Read the answer. Check that the answer has a sensible number of digits, then write it.
HTh TTh Th H T O 2 39 015 69 013 410 0− 1 4 8 9 7 5 1 5 7 0 6 5
306,040 − 148,975 = 157,065
Check. Use the opposite (inverse) operation: 157,065 + 148,975 = 306,040. ✓
Estimate: 310,000 − 150,000 = 160,000 (rounding to the nearest 10,000). 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. Work out what each small step is worth, then count the small steps.
- Find the value of a small step. Between 40,000 and 50,000 there are 5 small steps.10,000 ÷ 5 = 2,000
- Count the steps on the Thursday bar. The bar ends 3 small steps above 40,000.40,000 + 3 × 2,000 = 46,000
- Find Leo’s mistake. 45,000 is halfway between 40,000 and 50,000. That would be 2.5 small steps, which is not a line on the chart.Leo guessed. He should have counted the small steps.
Check. Each small step is 2,000, so bars can only end at even thousands. 45,000 cannot be right. ✓
Watch out. On a chart, only read exact values where a bar ends on a line. Count the lines.
| Town | Population |
|---|---|
| Ashby | 84,560 |
| Brigg | 126,400 |
| Calder | 47,285 |
| Denby | 91,750 |
Method. Round the numbers to the nearest 10,000 and compare. Then add the exact numbers to be sure.
- Round the populations. The nearest 10,000 gives easy numbers.Ashby 84,560 ≈ 80,000
Calder 47,285 ≈ 50,000
Brigg 126,400 ≈ 130,000 - Estimate. 80,000 + 50,000 = 130,000. That is the same as Brigg, so the estimate is too close to decide.130,000 compared with 130,000
- Work out the exact total. The estimate is too close, so use the exact numbers.84,560 + 47,285 = 131,845
HTh TTh Th H T O 8 4 5 6 0 + 4 7 2 8 5 1 3 1 8 4 5 1 1 1 - Compare. 131,845 compared with 126,400.131,845 is more than 126,400, so Zainab is right.
Check. 126,400 − 131,845 = −5,445. Brigg has 5,445 fewer. ✓
Watch out. When an estimate is very close, you cannot decide. Work out the exact answer.
A 20,000 + 12,500 B 50,000 − 17,500 C 16,250 + 16,250 D 40,000 − 7,000
Method. Work out each answer in your head. The odd one out has an answer that is different from the other three.
- Work out A. Add the thousands, then the hundreds.20,000 + 12,500 = 32,500
- Work out B. Take away 17,500 from 50,000. 50,000 − 17,500 = 32,500 (since 17,500 + 32,500 = 50,000).50,000 − 17,500 = 32,500
- Work out C. A double. Double 16,000 is 32,000 and double 250 is 500.16,250 + 16,250 = 32,500
- Work out D. Take away 7,000 from 40,000.40,000 − 7,000 = 33,000
- Find the odd one out. A, B and C all give 32,500. D gives 33,000.D
Check. 32,500 + 17,500 = 50,000 ✓ and 33,000 + 7,000 = 40,000. ✓
Watch out. Do all four calculations before you decide.
| Adults | Children | Total | |
|---|---|---|---|
| Saturday | 12,450 | ? | 20,100 |
| Sunday | ? | 9,850 | 18,300 |
| Total | ? | ? | ? |
Method. Each row and each column must add up to its total. Find the missing numbers one at a time, using a row or column where only one number is missing.
- Saturday children. The Saturday row is adults + children = total, so subtract.20,100 − 12,450 = 7,650
TTh Th H T O 1 29 010 110 00 − 1 2 4 5 0 7 6 5 0 - Sunday adults. The Sunday row has one number missing, so subtract.18,300 − 9,850 = 8,450
TTh Th H T O 0 117 812 310 00 − 9 8 5 0 8 4 5 0 - Total adults. The Adults column is Saturday + Sunday.12,450 + 8,450 = 20,900
TTh Th H T O 1 2 4 5 0 + 8 4 5 0 2 0 9 0 0 1 1 - Total children. The Children column is Saturday + Sunday.7,650 + 9,850 = 17,500
TTh Th H T O 7 6 5 0 + 9 8 5 0 1 7 5 0 0 1 1 1 - Grand total. Add the two totals along the bottom row.20,900 + 17,500 = 38,400
TTh Th H T O 2 0 9 0 0 + 1 7 5 0 0 3 8 4 0 0 1
Check. Check the other way: 20,100 + 18,300 = 38,400. ✓
Watch out. Work in an order where only one number is missing each time.