Written Addition And Subtraction
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Written addition and subtraction Some reminders about addition and subtraction. Here are three reminders to help you with written addition and subtraction. Addition vs Subtraction Addition and subtraction are opposites. If you add an amount then take it away again, you will end up at the same place. Similarly, if you take away an amount, then add it back on again, you'll be back where you started. Have a look below to see how this works.
You can use this method to check any addition or subtraction sum A reminder about place value Have a look at the number 623.
• • •
6 is the hundreds digit. 2 is the tens digit. 3 is the units digit.
Estimating then checking To make sure your answer is right when doing a sum, you can estimate before and check after you do the sum. Before - estimate the answer. Do the sum. After- check your answer makes sense.
Have a look at this sum: 82 + 314 Before - estimate. 82 can be rounded up to 100, and 314 can be rounded down to 300. 82 + 314 is approximately 100 + 300, which gives a rough answer of 400. Now do the sum - remembering to start adding with the units.
After - check the answer makes sense:
Now have a look at this sum: 974 + 117 Before - estimate. 974 can be rounded up to 1 000, and 117 can be rounded down to 100. 1 000 + 100 gives a rough answer of 1 100. Now do the sum - remembering to start adding with the units. Don't forget to carry.
After - check the answer makes sense: Estimate: 1 000 + 100 = 1 100 Answer: 974 + 117 = 1 091 - so the answer makes sense! Now have a look at this subtraction sum: 384 - 182 Before - estimate. 384 can be rounded up to 400, and 182 can be rounded up to 200. 400 - 200 gives a rough answer of 200. Now do the sum - remembering to start with the units.
After - check the answer makes sense: Estimate: 400 - 200 = 200 Answer: 384 - 182 = 202 - so the answer makes sense! Find more in the Skillswise Rounding and estimating module.
Traditional addition You may have been taught this addition method at school. When you add any numbers together, it is a good idea to estimate an approximate answer first. Your estimate can then be checked against your actual answer.
Have a look at this sum: 3 437 + 1 242 Before - make an estimate: 3 437 can be rounded up to 3 500, and 1 242 can be rounded down to 1 200. 3 437 + 1 242 is approximately 3 500 + 1 200, which gives a rough answer of 4 700. Now do the sum. Remember to add the units first, then the tens etc.
Estimate: 3 500 + 1 200 = 4 700 Answer: 3 437 + 1 242 = 4 679 so the answer makes sense. Sometimes you will need to carry numbers from one column to the next. Have a look at this sum: 3 437 + 1 275 Before - make an estimate: 3 437 can be rounded up to 3 500, and 1 275 can be rounded down to 1 200. 3 437 + 1 275 is approximately 3 500 + 1 200, which gives a rough answer of 4 700. Now do the sum - remembering to add the units first, then the tens etc. In this sum you will need to do some carrying: • •
Add the units column. 7 + 5 = 12. This means 2 goes into the units column, and 1 is carried into the tens. Now add the tens column. 3 + 7 plus the carried 1 makes 11. So 1 goes into the tens column, and the other 1 is carried to the hundreds.
Estimate: 3 500 + 1 200 = 4 700 Answer: 3 437 + 1 275 = 4 712 - so the answer is close to the estimate. Remember: •
if a column adds to 10 or more, keep the right number in that column, and carry the left hand number to the next column to the left.
Addition by splitting You can split numbers up to make addition easier - splitting the large numbers into hundreds, tens and units. Have a look at the sum 148 + 66. 148 splits into 100, 40, and 8. 66 splits into 60 and 6. This method splits the numbers across the page:
This method splits the numbers down the page:
If you like either of these methods, try them out with some different numbers. Remember: •
With either method, keep the hundreds, tens and units lined up.
Traditional subtraction - borrowing
You may have been taught this subtraction method at school. It involves splitting the sum into hundreds, tens and units, where you sometimes have to borrow from the next column. Have a look at this sum: 192 - 44 Before, get a rough idea: 192 can be rounded up to 200, and 44 can be rounded up to 50. 192 - 44 is approximately 200 - 50, which gives a rough answer of 150. Now do the sum - remembering to start with the units.
Borrowing: If one of the columns has a smaller number on top, the number on top borrows from the number to its left. When working out the units in this sum, as 2 is less than 4, you have to borrow 10 from the tens column. So 2 becomes 12, and in the tens column, 9 becomes 8.
After, check the answer makes sense: Estimate: 200 - 50 = 150 Answer: 192 - 44 = 148 So the answer makes sense! Borrowing because of a zero: This is the same as if one of the columns has a smaller number on top, you borrow from the number to its left.
When working out the units in this sum, as 0 is less than 5, you have to borrow 10 from the hundreds column. So 0 becomes 10. In the hundreds column we now have 1 lots of hundreds.
Remember: • •
If the top number is smaller, borrow from the left. If a zero appears in the top number you will probably need to borrow.
Traditional subtraction - decomposition This is very similar to the 'traditional' method of subtraction, but different words are used to explain how it works. It involves splitting the sum into hundreds, tens and units, where you sometimes have to adjust, or exchange, numbers from the next column. Have a look at this sum: 192 - 44 Before, get a rough idea: 192 can be rounded up to 200, and 44 can be rounded up to 50. 192 - 44 is approximately 200 - 50, which gives a rough answer of 150. Now do the sum - remember to start with the units. Work right to left.
Exchanging: If one of the columns has a smaller number on top, you exchange with the number to its left. When working out the units in this sum, as 2 is less than 4, you have to take one of the tens from the tens column and exchange it for ten units. So 2 becomes 12. In the tens column, as we have exchanged one of the tens for units, we now have 8 tens.
After, check the answer makes sense: Estimate: 200 - 50 = 150 Answer: 192 - 44 = 148 So the answer makes sense! Exchanging because of a zero: This is the same as if one of the columns has a smaller number on top, you exchange with the number to its left.
When working out the units in this sum, as 0 is less than 5, you have to take one of the hundreds from the hundreds column and exchange it for ten lots of tens. So 0 becomes 10. In the hundreds column, as we have exchanged one of the hundreds for tens, we now have 1 lots of hundreds.
Remember: • •
If the top number is smaller, exchange from the left. If a zero appears in the top number you will probably need to exchange.
Subtraction by splitting This method is about splitting up the numbers into hundreds, tens and units, and then looking at the difference between the biggest and smallest number in each column. Have a look at this sum: 277 - 156 Before - get a rough idea: 277 can be rounded up to 300, and 156 can be rounded up to 160. 277 -156 is approximately 300 - 160, which gives a rough answer of 140. Now do the sum - remembering to start taking away with the units. 277 splits into 200, 70 and 7 156 splits into 100, 50 and 6
After - check the answer makes sense: Estimate: 300 - 160 = 140 Answer: 277 - 156 = 121 - so the answer makes sense! Splitting with borrowing Sometimes you may also have to do some borrowing. Have a look at this sum: 237 - 158
Before - get a rough idea: 237 can be rounded up to 240, and 158 can be rounded up to 160. 237 - 158 is approximately 240 - 160, which gives a rough answer of 80. Now do the sum - remembering to start taking away with the units. 237 splits into 200, 30 and 7 158 splits into 100, 50 and 8
In this sum you can see that the tens and units columns have a smaller number on top. In this case, the number on top borrows from the number to its left, starting with the 10s. 30 is less than 50, so you have to borrow 100 from the 100s column. This changes the 200 to 100, and 30 to 130.
Now do the units: 7 is less than 8, so borrow 10 from the 10s column. 7 becomes 17, and 130 becomes 120.
You can now work out the difference between the biggest and smallest number in each column, and then add up the results.
After - check the answer makes sense: Estimate: 240 - 160 = 80 Answer: 237 - 158 = 79 - so the answer makes sense! Remember: • •
If the top number is smaller, borrow from the left. If a zero appears in the top number then you will probably need to borrow.
Subtraction using counting up Some people call this method subtraction using complimentary addition. It is a bit like 'counting on' in the mental methods modules. To answer a subtraction sum, you count up from the smaller number to the higher number. Have a look at this sum: 237 - 158 Before - get a rough idea: 237 can be rounded up to 240, and 158 can be rounded up to 160. 237 - 158 is approximately 240 - 160, which gives a rough answer of 80. Start with the smaller number. Using nearest 10s, then 100s as signposts, count on to the higher number. Now add up the amounts you counted on by. This gives you the difference between the two numbers.
After - check the answer makes sense:
Estimate: 240 - 160 = 80 Answer: 237 - 158 = 79 - so the answer makes sense!
Addition Glossary Here are some of the words which will crop up when doing addition sums.
Have a look below to see how they can be used in the simple sum 3 + 4 = 7. Add 3 add 4 is 7. Altogether Altogether, 3 and 4 make 7. Increase If you increase 3 by 4 you get 7. More 7 is 3 more than 4. Plus 3 plus 4 is 7. Sum The sum of 3 and 4 is 7. Total The total of 3 and 4 is 7.
Subtraction Glossary Here are some of the words which will crop up when doing subtraction sums.
Have a look below to see how they can be used in the simple sum 8 - 5 = 3. Decrease If you decrease 8 by 5 you get 3. Decomposition A method of subtraction. Difference The difference between 8 and 5 is 3. Exchange You can exchange one lot of tens, for ten lots of units. Fewer than 3 is 5 fewer than 8. Less than 3 is 5 less than 8. Minus 8 minus 5 is 3. Reduce If you reduce 8 by 5 you get 3. Subtract 8 subtract 5 is 3. Take away 8 take away 5 is 3.
'Written addition and subtraction' tutor notes This module can be used as a starting point for: learning different methods of written addition and subtraction. Please let us know what you think of the factsheets, worksheets, quiz and games at [email protected]
How does this tie in with the new curriculums? •
• • •
England N1/L1.3 - Add, subtract, multiply and divide using efficient written methods. N1/L1.8 - Approximate by rounding. N1/L1.9 - Estimate answers to calculations. Wales As England. Northern Ireland As England. Scotland See www.aloscotland.com for details of the Scottish curriculum.
In the Skillswise module you'll find: Written addition and subtraction factsheets There are ten sheets in this section which can be printed out and kept. • • • • • • • • • •
Factsheet 1 - Some reminders about addition and subtraction. Factsheet 2 - Checking the sum before and after. Factsheet 3 - Traditional addition. Factsheet 4 - Addition by splitting. Factsheet 5 - Traditional subtraction - borrowing. Factsheet 6 - Traditional subtraction - decomposition. Factsheet 7 - Subtraction by splitting. Factsheet 8 - Subtraction using complementary addition. Factsheet 9 - Addition Glossary. Factsheet 10 - Subtraction Glossary.
The Amoeba Addition and Subtraction Games In these games the learner can practise the 'splitting numbers' methods shown in the factsheets. There are two games: one for addition and another for subtraction. Learners fill gaps by typing in. At each stage they are shown where they went wrong and get a second try. At the end of the game they are given a summary of how they got on in each section and an overall score. If they get 75% or more, they get a bonus game - 'Shoot the Amoebas'
TOP TIP! To see the game completely full screen, press the F11 key on the keyboard. This takes away the distraction of the top browser bar. To bring the browser bar back, just press F11 again! Written addition and subtraction quiz The learner can choose their level. Level A is the easiest, level C the hardest. Students can print out a certificate if they score 50% or more in the quiz. This will appear as a link on the results page - click on the link and the certificate will appear in a new window. Once printed students can write their name on the certificate. Written addition and subtraction worksheets There are six printable worksheets in this section for learners to carry on the work done online. •
• • • • •
Worksheet 1 - Some questions to practise written addition using different methods. There are examples and separate answersheets covering each of the written methods. Worksheet 2 - Some questions to practise written subtraction using different methods. Worksheet 3 - Addition puzzle 1. Worksheet 4 - Addition puzzle 2. Worksheet 5 - Subtraction puzzle 1. Worksheet 6 - Subtraction puzzle 2.
Technical help: To get the most out of this topic area you need the following 'plug-ins': •
Flash The game in this topic section uses Flash. This is free to download and should only take a few minutes. You can follow the BBC WebWise instructions to download it to your machine. Find out more.
If you don't have Flash the same learning points are covered in the quiz and in the worksheets and factsheets. If you are new to the web, why not try the BBC WebWise online course, Becoming WebWise? It's free, you can do it in your own time from any computer and it will take you through everything you need to know to use the web successfully in your teaching. Get WebWise. You can find out more about the technical requirements for Skillswise in our Help - Technical Information section.
Taking it further: Here are a few suggestions of other places on the web where you might find useful resources that you can adapt for teaching written addition and subtraction.
• •
AAA Math - addition AAA Math - subtraction An American site with many pages demonstrating different addition and subtraction skills, with interactive activities and games.
You can use this method to check any addition or subtraction sum A reminder about place value Have a look at the number 623.
• • •
6 is the hundreds digit. 2 is the tens digit. 3 is the units digit.
Estimating then checking To make sure your answer is right when doing a sum, you can estimate before and check after you do the sum. Before - estimate the answer. Do the sum. After- check your answer makes sense.
Have a look at this sum: 82 + 314 Before - estimate. 82 can be rounded up to 100, and 314 can be rounded down to 300. 82 + 314 is approximately 100 + 300, which gives a rough answer of 400. Now do the sum - remembering to start adding with the units.
After - check the answer makes sense:
Now have a look at this sum: 974 + 117 Before - estimate. 974 can be rounded up to 1 000, and 117 can be rounded down to 100. 1 000 + 100 gives a rough answer of 1 100. Now do the sum - remembering to start adding with the units. Don't forget to carry.
After - check the answer makes sense: Estimate: 1 000 + 100 = 1 100 Answer: 974 + 117 = 1 091 - so the answer makes sense! Now have a look at this subtraction sum: 384 - 182 Before - estimate. 384 can be rounded up to 400, and 182 can be rounded up to 200. 400 - 200 gives a rough answer of 200. Now do the sum - remembering to start with the units.
After - check the answer makes sense: Estimate: 400 - 200 = 200 Answer: 384 - 182 = 202 - so the answer makes sense! Find more in the Skillswise Rounding and estimating module.
Traditional addition You may have been taught this addition method at school. When you add any numbers together, it is a good idea to estimate an approximate answer first. Your estimate can then be checked against your actual answer.
Have a look at this sum: 3 437 + 1 242 Before - make an estimate: 3 437 can be rounded up to 3 500, and 1 242 can be rounded down to 1 200. 3 437 + 1 242 is approximately 3 500 + 1 200, which gives a rough answer of 4 700. Now do the sum. Remember to add the units first, then the tens etc.
Estimate: 3 500 + 1 200 = 4 700 Answer: 3 437 + 1 242 = 4 679 so the answer makes sense. Sometimes you will need to carry numbers from one column to the next. Have a look at this sum: 3 437 + 1 275 Before - make an estimate: 3 437 can be rounded up to 3 500, and 1 275 can be rounded down to 1 200. 3 437 + 1 275 is approximately 3 500 + 1 200, which gives a rough answer of 4 700. Now do the sum - remembering to add the units first, then the tens etc. In this sum you will need to do some carrying: • •
Add the units column. 7 + 5 = 12. This means 2 goes into the units column, and 1 is carried into the tens. Now add the tens column. 3 + 7 plus the carried 1 makes 11. So 1 goes into the tens column, and the other 1 is carried to the hundreds.
Estimate: 3 500 + 1 200 = 4 700 Answer: 3 437 + 1 275 = 4 712 - so the answer is close to the estimate. Remember: •
if a column adds to 10 or more, keep the right number in that column, and carry the left hand number to the next column to the left.
Addition by splitting You can split numbers up to make addition easier - splitting the large numbers into hundreds, tens and units. Have a look at the sum 148 + 66. 148 splits into 100, 40, and 8. 66 splits into 60 and 6. This method splits the numbers across the page:
This method splits the numbers down the page:
If you like either of these methods, try them out with some different numbers. Remember: •
With either method, keep the hundreds, tens and units lined up.
Traditional subtraction - borrowing
You may have been taught this subtraction method at school. It involves splitting the sum into hundreds, tens and units, where you sometimes have to borrow from the next column. Have a look at this sum: 192 - 44 Before, get a rough idea: 192 can be rounded up to 200, and 44 can be rounded up to 50. 192 - 44 is approximately 200 - 50, which gives a rough answer of 150. Now do the sum - remembering to start with the units.
Borrowing: If one of the columns has a smaller number on top, the number on top borrows from the number to its left. When working out the units in this sum, as 2 is less than 4, you have to borrow 10 from the tens column. So 2 becomes 12, and in the tens column, 9 becomes 8.
After, check the answer makes sense: Estimate: 200 - 50 = 150 Answer: 192 - 44 = 148 So the answer makes sense! Borrowing because of a zero: This is the same as if one of the columns has a smaller number on top, you borrow from the number to its left.
When working out the units in this sum, as 0 is less than 5, you have to borrow 10 from the hundreds column. So 0 becomes 10. In the hundreds column we now have 1 lots of hundreds.
Remember: • •
If the top number is smaller, borrow from the left. If a zero appears in the top number you will probably need to borrow.
Traditional subtraction - decomposition This is very similar to the 'traditional' method of subtraction, but different words are used to explain how it works. It involves splitting the sum into hundreds, tens and units, where you sometimes have to adjust, or exchange, numbers from the next column. Have a look at this sum: 192 - 44 Before, get a rough idea: 192 can be rounded up to 200, and 44 can be rounded up to 50. 192 - 44 is approximately 200 - 50, which gives a rough answer of 150. Now do the sum - remember to start with the units. Work right to left.
Exchanging: If one of the columns has a smaller number on top, you exchange with the number to its left. When working out the units in this sum, as 2 is less than 4, you have to take one of the tens from the tens column and exchange it for ten units. So 2 becomes 12. In the tens column, as we have exchanged one of the tens for units, we now have 8 tens.
After, check the answer makes sense: Estimate: 200 - 50 = 150 Answer: 192 - 44 = 148 So the answer makes sense! Exchanging because of a zero: This is the same as if one of the columns has a smaller number on top, you exchange with the number to its left.
When working out the units in this sum, as 0 is less than 5, you have to take one of the hundreds from the hundreds column and exchange it for ten lots of tens. So 0 becomes 10. In the hundreds column, as we have exchanged one of the hundreds for tens, we now have 1 lots of hundreds.
Remember: • •
If the top number is smaller, exchange from the left. If a zero appears in the top number you will probably need to exchange.
Subtraction by splitting This method is about splitting up the numbers into hundreds, tens and units, and then looking at the difference between the biggest and smallest number in each column. Have a look at this sum: 277 - 156 Before - get a rough idea: 277 can be rounded up to 300, and 156 can be rounded up to 160. 277 -156 is approximately 300 - 160, which gives a rough answer of 140. Now do the sum - remembering to start taking away with the units. 277 splits into 200, 70 and 7 156 splits into 100, 50 and 6
After - check the answer makes sense: Estimate: 300 - 160 = 140 Answer: 277 - 156 = 121 - so the answer makes sense! Splitting with borrowing Sometimes you may also have to do some borrowing. Have a look at this sum: 237 - 158
Before - get a rough idea: 237 can be rounded up to 240, and 158 can be rounded up to 160. 237 - 158 is approximately 240 - 160, which gives a rough answer of 80. Now do the sum - remembering to start taking away with the units. 237 splits into 200, 30 and 7 158 splits into 100, 50 and 8
In this sum you can see that the tens and units columns have a smaller number on top. In this case, the number on top borrows from the number to its left, starting with the 10s. 30 is less than 50, so you have to borrow 100 from the 100s column. This changes the 200 to 100, and 30 to 130.
Now do the units: 7 is less than 8, so borrow 10 from the 10s column. 7 becomes 17, and 130 becomes 120.
You can now work out the difference between the biggest and smallest number in each column, and then add up the results.
After - check the answer makes sense: Estimate: 240 - 160 = 80 Answer: 237 - 158 = 79 - so the answer makes sense! Remember: • •
If the top number is smaller, borrow from the left. If a zero appears in the top number then you will probably need to borrow.
Subtraction using counting up Some people call this method subtraction using complimentary addition. It is a bit like 'counting on' in the mental methods modules. To answer a subtraction sum, you count up from the smaller number to the higher number. Have a look at this sum: 237 - 158 Before - get a rough idea: 237 can be rounded up to 240, and 158 can be rounded up to 160. 237 - 158 is approximately 240 - 160, which gives a rough answer of 80. Start with the smaller number. Using nearest 10s, then 100s as signposts, count on to the higher number. Now add up the amounts you counted on by. This gives you the difference between the two numbers.
After - check the answer makes sense:
Estimate: 240 - 160 = 80 Answer: 237 - 158 = 79 - so the answer makes sense!
Addition Glossary Here are some of the words which will crop up when doing addition sums.
Have a look below to see how they can be used in the simple sum 3 + 4 = 7. Add 3 add 4 is 7. Altogether Altogether, 3 and 4 make 7. Increase If you increase 3 by 4 you get 7. More 7 is 3 more than 4. Plus 3 plus 4 is 7. Sum The sum of 3 and 4 is 7. Total The total of 3 and 4 is 7.
Subtraction Glossary Here are some of the words which will crop up when doing subtraction sums.
Have a look below to see how they can be used in the simple sum 8 - 5 = 3. Decrease If you decrease 8 by 5 you get 3. Decomposition A method of subtraction. Difference The difference between 8 and 5 is 3. Exchange You can exchange one lot of tens, for ten lots of units. Fewer than 3 is 5 fewer than 8. Less than 3 is 5 less than 8. Minus 8 minus 5 is 3. Reduce If you reduce 8 by 5 you get 3. Subtract 8 subtract 5 is 3. Take away 8 take away 5 is 3.
'Written addition and subtraction' tutor notes This module can be used as a starting point for: learning different methods of written addition and subtraction. Please let us know what you think of the factsheets, worksheets, quiz and games at [email protected]
How does this tie in with the new curriculums? •
• • •
England N1/L1.3 - Add, subtract, multiply and divide using efficient written methods. N1/L1.8 - Approximate by rounding. N1/L1.9 - Estimate answers to calculations. Wales As England. Northern Ireland As England. Scotland See www.aloscotland.com for details of the Scottish curriculum.
In the Skillswise module you'll find: Written addition and subtraction factsheets There are ten sheets in this section which can be printed out and kept. • • • • • • • • • •
Factsheet 1 - Some reminders about addition and subtraction. Factsheet 2 - Checking the sum before and after. Factsheet 3 - Traditional addition. Factsheet 4 - Addition by splitting. Factsheet 5 - Traditional subtraction - borrowing. Factsheet 6 - Traditional subtraction - decomposition. Factsheet 7 - Subtraction by splitting. Factsheet 8 - Subtraction using complementary addition. Factsheet 9 - Addition Glossary. Factsheet 10 - Subtraction Glossary.
The Amoeba Addition and Subtraction Games In these games the learner can practise the 'splitting numbers' methods shown in the factsheets. There are two games: one for addition and another for subtraction. Learners fill gaps by typing in. At each stage they are shown where they went wrong and get a second try. At the end of the game they are given a summary of how they got on in each section and an overall score. If they get 75% or more, they get a bonus game - 'Shoot the Amoebas'
TOP TIP! To see the game completely full screen, press the F11 key on the keyboard. This takes away the distraction of the top browser bar. To bring the browser bar back, just press F11 again! Written addition and subtraction quiz The learner can choose their level. Level A is the easiest, level C the hardest. Students can print out a certificate if they score 50% or more in the quiz. This will appear as a link on the results page - click on the link and the certificate will appear in a new window. Once printed students can write their name on the certificate. Written addition and subtraction worksheets There are six printable worksheets in this section for learners to carry on the work done online. •
• • • • •
Worksheet 1 - Some questions to practise written addition using different methods. There are examples and separate answersheets covering each of the written methods. Worksheet 2 - Some questions to practise written subtraction using different methods. Worksheet 3 - Addition puzzle 1. Worksheet 4 - Addition puzzle 2. Worksheet 5 - Subtraction puzzle 1. Worksheet 6 - Subtraction puzzle 2.
Technical help: To get the most out of this topic area you need the following 'plug-ins': •
Flash The game in this topic section uses Flash. This is free to download and should only take a few minutes. You can follow the BBC WebWise instructions to download it to your machine. Find out more.
If you don't have Flash the same learning points are covered in the quiz and in the worksheets and factsheets. If you are new to the web, why not try the BBC WebWise online course, Becoming WebWise? It's free, you can do it in your own time from any computer and it will take you through everything you need to know to use the web successfully in your teaching. Get WebWise. You can find out more about the technical requirements for Skillswise in our Help - Technical Information section.
Taking it further: Here are a few suggestions of other places on the web where you might find useful resources that you can adapt for teaching written addition and subtraction.
• •
AAA Math - addition AAA Math - subtraction An American site with many pages demonstrating different addition and subtraction skills, with interactive activities and games.
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