Addition And Subtraction
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Addition And Subtraction as PDF for free.
More details
- Words: 2,356
- Pages: 26
Addition and Subtraction Mental addition and subtraction 5 ways to add and subtract in your head - "SHARED" Mental methods are about trying to get to the correct answer in the quickest and easiest way!
There are lots of ways to add and subtract numbers in your head. By the time you have looked through the factsheets in this module you will have used 5 different methods for mental addition and subtraction! Try to remember them by using the word "Shared".
• •
When you've read about them, practise the methods you like and can remember most easily. Ask other people about the methods they use - and share your methods too!
•
Keep practising, and HAVE FUN!
Reminders to help you add and subtract Here are three reminders to help you with mental addition and subtraction. 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.
A reminder about adding Have a look at these sums.
Here you can see that the same numbers added together in a different order will give the same answer. Addition and subtraction are opposites. You can check the answer to a subtraction sum by turning the numbers around and adding them up. Have a look below.
Here you've done the sum 25 - 10 and got the answer 15. To check the answer, turn the sum around to 15 + 10 and see if you get 25.
Splitting up numbers Splitting up numbers is a good method to use for both addition and subtraction. It is sometimes called partitioning. Addition Take a look at this addition sum: 80 + 49 To make it easier, split the 49 into 40 + 9. This makes the sum: 80 + 40 + 9 = 129 First, add the first two numbers: 80 + 40 = 120 Then add the result of that sum to the third number to get the answer: 120 + 9 = 129
Subtraction Take a look at this subtraction sum: 150 - 34 To make it easier, split the - 34 into 30 - 4. This makes the sum: 150 - 30 - 4 First, subtract the 30 from 150: 150 - 30 = 120 Then, subtract the 4 from the 120 to get the answer: 120 - 4 = 116
Hundreds, tens and ones
To make addition sums easier, you can separate the hundreds, tens and units and add them up separately. Have a look at how separating works for this sum: 31 + 22
Using this method you can work out that 31 + 22 = 53. Now look at this sum with hundreds as well as tens and units: 125 + 100 + 235 + 132
Using this method you can work out that 125 + 100 + 235 + 132 = 592.
Rounding - addition Rounding is a method for mental addition which is useful in many different situations. Imagine you are in a shop and you have to quickly work out an amount.
£3.70 + £1.00 = £4.70. Taking away 10p gives £4.60 Have a look at how this addition sum can be solved with rounding: 75 + 19
First, round the 19 up to 20 and work out the sum: 75 + 20 = 95 As 20 is 1 more than 19, you then need to subtract 1 from the total. 95 - 1 = 94 Then you can see that: 75 + 19 = 94 Further reading. These tables have some more information to help you with addition by rounding. The first shows methods and examples for adding a number between 11 and 14 to another number.
This table shows methods and examples for adding a number between 15 and 19 to another number.
Rounding - subtraction Rounding is a method for mental subtraction which is useful in many different situations. Imagine you are shopping and need to work out an amount quickly.
£3.70 - £1.00 = £2.70. Adding 10p gives £2.80. Have a look at how this subtraction sum can be solved with rounding: 64 - 17 First, round the 17 up to 20 and work out the sum: 64 - 20 = 44 As 20 is 3 more than 17, you have taken 3 too many from the total. So you need to add 3: 44 + 3 = 47
So you can see that: 64 - 17 = 47 Further reading. These tables have some more information to help you with subtraction by rounding. The first shows you a methods and examples for subtracting a number between 11 and 14 from another number.
This table shows methods and examples for subtracting a number between 15 and 19 to another number.
Empty number line for counting on Counting on using an empty number line is a good method for subtracting numbers mentally.
Use this method to find the difference between 37 and 50. This is the same as the sum 50 - 37.
When you have pictured that line, count on from 37 to 40, which makes 3. Keep that 3 in your head. Then, count from 40 to 50, which is 10. Have a look below to see how this works.
Now all you need to do is add the 3 to the 10. This makes 13. So: The difference between 37 and 50 is 13. Or 50 - 37 = 13
Doubling If you are adding together two numbers that are nearly the same, you can double one of them and then adjust the difference. Imagine you are adding together 38 and 35.
Key words for mental addition 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.
Key words for mental subtraction 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. Difference The difference between 8 and 5 is 3. 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.
'Mental addition and subtraction' tutor notes This module can be used as a starting point for: learning different methods of mental 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/E3.2 - add and subtract using three-digit whole numbers. N1/E3.3 - recall addition and subtraction facts to 20. N1/L1.8 - approximate by rounding. 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: Mental addition and subtraction factsheets There are ten sheets in this section which can be printed out and kept. • • • • • • • • • •
Factsheet 1 - SHARED - An overview of 5 methods for mental addition and subtraction. Factsheet 2 - Reminders to help the students with mental addition and subtraction. Factsheet 3 - Method 1 - splitting up numbers. Factsheet 4 - Method 2 - hundreds, tens and units. Factsheet 5 - Method 3 - rounding (addition). Factsheet 6 - Method 3 - rounding (subtraction). Factsheet 7 - Method 4 - empty number line. Factsheet 8 - Method 5 - doubling. Factsheet 9 - Key words for mental addition. Factsheet 10 - Key words for mental subtraction.
Mental addition and subtraction games There are seven games for practising mental addition and subtraction. Game 1: The Change Game - no timer In this game you are working on a till serving customers. You have 5 customers to serve. The till shows the cost of the items the customer is buying, and the customers hand appears with a note, £5, £10 or £20. You must give the correct change, by dragging conis and notes from the cash drawer into the customers hand. You have 3 chances each time. There are 3 levels to choose from. Level 1: Customer pays with a £5 or £10 note. Giving correct change requires whole pounds and 50p pieces only.
Level 2: Customer pays with a £5 or £10 note. Giving correct change requires whole pounds and multiples of 10p only. Level 3: Customer pays with a £5, £10 or £20 note. Any price can come up so all coins and notes may be needed in giving change. This game has sound effects. (Listen out for when you give too much change!) Game 2: The Change Game - with timer This is the same game but with a time limit. The object is to serve as many customerse as you can before the time runs out. Game 3 and Game 4: Mental Maths Fridge Magnet Games In these games the learner can practice mental addition and subtraction skills by filling blanks in sums written out in fridge magnets. At the start of the game, the learner can choose whether to answer questions by finding the answer or filling a blank in the question (eg. 35 - ? = 20). They can also choose whether to have a time limit (60 seconds) on each question. At the end they are given a score out of 10. With a score of 8 or more a bonus screen is available, on which there is a random selection of fridge magnet letters to re-arrange and play about with. Game 5: Bargain Hunt This is a mental addition game which is based on the BBC Bargain Hunt programme and features David Dickinson. The student has to add up the prices of the antiques on the cards. The student can select to add up two or three numbers. There are 3 levels, A, B and C with A being the easiest and C the hardest. At level A the numbers are easier to add up as the units don't carry over and there is more time to calculate the sum. At level C units and tens carry over and there is less time to calculate the sum. Game 6 and Game 7: Mental Maths Conveyor Belt Games In these games, the learner can practice mental addition and subtraction skills by answering questions relating to items which appear on a conveyor belt. At the start of the game, the learner can choose whether to answer questions by clicking on one of three choices, or by typing in their answers and clicking 'check' or hitting the return key. If they answer any question incorrectly, they get the choice of a second chance or just to see the correct answer. At the end they are given a summary of the questions, the answers they gave and their score. If the learner answers more than 8 out of 10 questions correctly, they will be given the option of a bonus 'tennis' game, which is played using the mouse. TOP TIP! To see any of the games 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!
Mental 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. Mental addition and subtraction worksheets There are five printable worksheets in this section, for learners to carry on the work done online. • • • • •
Worksheet 1 - Some practise for method 1 - splitting up numbers. Worksheet 2 - Identify which numbers add up to a certain amount, using hundreds, tens and units. Worksheet 3 - Some sums to practise addition and subtraction by rounding. Worksheet 4 - An empty number line worksheet. Worksheet 5 - A worksheet to practise doubling.
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 that you might find useful resources that you can adapt for teaching mental addition and subtraction. •
•
BBC KS2 Bitesize Maths Bitesize is aimed at children at the end of Key Stage 2, but it still has useful activities you can try with your students. AAA Math - addition
•
AAA Math - subtraction An American site containing many pages demonstrating different addition and subtraction skills, with interactive activities and games.
There are lots of ways to add and subtract numbers in your head. By the time you have looked through the factsheets in this module you will have used 5 different methods for mental addition and subtraction! Try to remember them by using the word "Shared".
• •
When you've read about them, practise the methods you like and can remember most easily. Ask other people about the methods they use - and share your methods too!
•
Keep practising, and HAVE FUN!
Reminders to help you add and subtract Here are three reminders to help you with mental addition and subtraction. 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.
A reminder about adding Have a look at these sums.
Here you can see that the same numbers added together in a different order will give the same answer. Addition and subtraction are opposites. You can check the answer to a subtraction sum by turning the numbers around and adding them up. Have a look below.
Here you've done the sum 25 - 10 and got the answer 15. To check the answer, turn the sum around to 15 + 10 and see if you get 25.
Splitting up numbers Splitting up numbers is a good method to use for both addition and subtraction. It is sometimes called partitioning. Addition Take a look at this addition sum: 80 + 49 To make it easier, split the 49 into 40 + 9. This makes the sum: 80 + 40 + 9 = 129 First, add the first two numbers: 80 + 40 = 120 Then add the result of that sum to the third number to get the answer: 120 + 9 = 129
Subtraction Take a look at this subtraction sum: 150 - 34 To make it easier, split the - 34 into 30 - 4. This makes the sum: 150 - 30 - 4 First, subtract the 30 from 150: 150 - 30 = 120 Then, subtract the 4 from the 120 to get the answer: 120 - 4 = 116
Hundreds, tens and ones
To make addition sums easier, you can separate the hundreds, tens and units and add them up separately. Have a look at how separating works for this sum: 31 + 22
Using this method you can work out that 31 + 22 = 53. Now look at this sum with hundreds as well as tens and units: 125 + 100 + 235 + 132
Using this method you can work out that 125 + 100 + 235 + 132 = 592.
Rounding - addition Rounding is a method for mental addition which is useful in many different situations. Imagine you are in a shop and you have to quickly work out an amount.
£3.70 + £1.00 = £4.70. Taking away 10p gives £4.60 Have a look at how this addition sum can be solved with rounding: 75 + 19
First, round the 19 up to 20 and work out the sum: 75 + 20 = 95 As 20 is 1 more than 19, you then need to subtract 1 from the total. 95 - 1 = 94 Then you can see that: 75 + 19 = 94 Further reading. These tables have some more information to help you with addition by rounding. The first shows methods and examples for adding a number between 11 and 14 to another number.
This table shows methods and examples for adding a number between 15 and 19 to another number.
Rounding - subtraction Rounding is a method for mental subtraction which is useful in many different situations. Imagine you are shopping and need to work out an amount quickly.
£3.70 - £1.00 = £2.70. Adding 10p gives £2.80. Have a look at how this subtraction sum can be solved with rounding: 64 - 17 First, round the 17 up to 20 and work out the sum: 64 - 20 = 44 As 20 is 3 more than 17, you have taken 3 too many from the total. So you need to add 3: 44 + 3 = 47
So you can see that: 64 - 17 = 47 Further reading. These tables have some more information to help you with subtraction by rounding. The first shows you a methods and examples for subtracting a number between 11 and 14 from another number.
This table shows methods and examples for subtracting a number between 15 and 19 to another number.
Empty number line for counting on Counting on using an empty number line is a good method for subtracting numbers mentally.
Use this method to find the difference between 37 and 50. This is the same as the sum 50 - 37.
When you have pictured that line, count on from 37 to 40, which makes 3. Keep that 3 in your head. Then, count from 40 to 50, which is 10. Have a look below to see how this works.
Now all you need to do is add the 3 to the 10. This makes 13. So: The difference between 37 and 50 is 13. Or 50 - 37 = 13
Doubling If you are adding together two numbers that are nearly the same, you can double one of them and then adjust the difference. Imagine you are adding together 38 and 35.
Key words for mental addition 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.
Key words for mental subtraction 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. Difference The difference between 8 and 5 is 3. 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.
'Mental addition and subtraction' tutor notes This module can be used as a starting point for: learning different methods of mental 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/E3.2 - add and subtract using three-digit whole numbers. N1/E3.3 - recall addition and subtraction facts to 20. N1/L1.8 - approximate by rounding. 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: Mental addition and subtraction factsheets There are ten sheets in this section which can be printed out and kept. • • • • • • • • • •
Factsheet 1 - SHARED - An overview of 5 methods for mental addition and subtraction. Factsheet 2 - Reminders to help the students with mental addition and subtraction. Factsheet 3 - Method 1 - splitting up numbers. Factsheet 4 - Method 2 - hundreds, tens and units. Factsheet 5 - Method 3 - rounding (addition). Factsheet 6 - Method 3 - rounding (subtraction). Factsheet 7 - Method 4 - empty number line. Factsheet 8 - Method 5 - doubling. Factsheet 9 - Key words for mental addition. Factsheet 10 - Key words for mental subtraction.
Mental addition and subtraction games There are seven games for practising mental addition and subtraction. Game 1: The Change Game - no timer In this game you are working on a till serving customers. You have 5 customers to serve. The till shows the cost of the items the customer is buying, and the customers hand appears with a note, £5, £10 or £20. You must give the correct change, by dragging conis and notes from the cash drawer into the customers hand. You have 3 chances each time. There are 3 levels to choose from. Level 1: Customer pays with a £5 or £10 note. Giving correct change requires whole pounds and 50p pieces only.
Level 2: Customer pays with a £5 or £10 note. Giving correct change requires whole pounds and multiples of 10p only. Level 3: Customer pays with a £5, £10 or £20 note. Any price can come up so all coins and notes may be needed in giving change. This game has sound effects. (Listen out for when you give too much change!) Game 2: The Change Game - with timer This is the same game but with a time limit. The object is to serve as many customerse as you can before the time runs out. Game 3 and Game 4: Mental Maths Fridge Magnet Games In these games the learner can practice mental addition and subtraction skills by filling blanks in sums written out in fridge magnets. At the start of the game, the learner can choose whether to answer questions by finding the answer or filling a blank in the question (eg. 35 - ? = 20). They can also choose whether to have a time limit (60 seconds) on each question. At the end they are given a score out of 10. With a score of 8 or more a bonus screen is available, on which there is a random selection of fridge magnet letters to re-arrange and play about with. Game 5: Bargain Hunt This is a mental addition game which is based on the BBC Bargain Hunt programme and features David Dickinson. The student has to add up the prices of the antiques on the cards. The student can select to add up two or three numbers. There are 3 levels, A, B and C with A being the easiest and C the hardest. At level A the numbers are easier to add up as the units don't carry over and there is more time to calculate the sum. At level C units and tens carry over and there is less time to calculate the sum. Game 6 and Game 7: Mental Maths Conveyor Belt Games In these games, the learner can practice mental addition and subtraction skills by answering questions relating to items which appear on a conveyor belt. At the start of the game, the learner can choose whether to answer questions by clicking on one of three choices, or by typing in their answers and clicking 'check' or hitting the return key. If they answer any question incorrectly, they get the choice of a second chance or just to see the correct answer. At the end they are given a summary of the questions, the answers they gave and their score. If the learner answers more than 8 out of 10 questions correctly, they will be given the option of a bonus 'tennis' game, which is played using the mouse. TOP TIP! To see any of the games 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!
Mental 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. Mental addition and subtraction worksheets There are five printable worksheets in this section, for learners to carry on the work done online. • • • • •
Worksheet 1 - Some practise for method 1 - splitting up numbers. Worksheet 2 - Identify which numbers add up to a certain amount, using hundreds, tens and units. Worksheet 3 - Some sums to practise addition and subtraction by rounding. Worksheet 4 - An empty number line worksheet. Worksheet 5 - A worksheet to practise doubling.
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 that you might find useful resources that you can adapt for teaching mental addition and subtraction. •
•
BBC KS2 Bitesize Maths Bitesize is aimed at children at the end of Key Stage 2, but it still has useful activities you can try with your students. AAA Math - addition
•
AAA Math - subtraction An American site containing many pages demonstrating different addition and subtraction skills, with interactive activities and games.
Related Documents
Written Addition And Subtraction
November 2019 14
Addition And Subtraction
November 2019 17
Addition And Subtraction Equations
June 2020 6
Introducing Addition & Subtraction
December 2019 21
