Number bonds: a phrase that can bring confusion to many! What are they? How do they work? How can we help our children with them?
From the time your child starts school you will hear the phrase 'number bonds', possibly from your child but more often from their teacher and in information sent home from school. Surprisingly this information often works on the assumption that we all know what number bonds are! Sadly we don't.
Number bonds are the addition pairs that make a particular number so, for example, if you were looking at the number bonds to 10 you would be looking for all the pairs of numbers that add up to 10:
0 + 10
1 + 9
2 + 8
3 + 7
4 + 6
5 + 5
6 + 4
7 + 3
8 + 2
9 + 1
10 + 0
1 + 9
2 + 8
3 + 7
4 + 6
5 + 5
6 + 4
7 + 3
8 + 2
9 + 1
10 + 0
The most frequently looked at sets of number bonds are the bonds to 10 and 20. Once children have understood and discovered these ones it is assumed that they understand how these patterns work and should be able to work the rest out as and when needed. However, there have been many times when teaching the older primary children when I have brought up the subject of number bonds and I get blank looks from students. This is mainly because number bonds are covered in Infants ( Kindergarten and 1st Grade) and often not revisited as there is so much more curriculum to cover in the older years. As a maths specialist, I feel they should be revised at least once a year, in the later years. The knowledge of these patterns and how to use them in all aspects of number is a brilliant skill to have and many children lack it. You will often find that the first ti e children do this, they write down the sums randomly and it's only when looking at them that they start to understand the patterns involved - the ones that are obvious to us!
As a parent/guardian/ tutor this is one area you can really help your children. It's such a fun topic to teach and can bring amazing rewards, not least your child's confidence with numbers.
So, this week, play with the number bonds and have some fun looking at the patterns and how they link across our number system.
Preschool
What: number bonds to any number up to and including 10 if they're ready. Start with 3 and move on from there.
How: start by using some blocks (or something similar that will do the same job: pencil crayons, cutlery, apples.........) and ask your child to find 3. Once they've done that hold up one block and ask them to find the other blocks you need to make 3. Once they have done this say the sum '1 block and 2 blocks makes 3 blocks'. After making sure your child has understood this and you've repeated it several times then do the same but with 2 + 1. Finally show the two different sums next to each other using the blocks and encourage your child to talk about what he / she sees. He / she might repeat the sums and tell you what each number is. Hopefully the will also notice that the sums are the same but written the opposite way round.
If three is easy then your next step is to progress up the numbers and do something similar to above. I wouldn't do much more than one number and all it's bonds in a session, if you're going to move forward to another number then do it the next day. If you want to write the sums down you can do but it's not essential. The important thing is starting to recognise the bonds for each number and to see the patterns with how they work.
5, 6 and 7 year olds
What: number bonds to 10, 20, some of them may be able to extend this to 30 and 40. Another extension is to do the whole tens number bonds to 100 (10 + 90, 20 + 80.......)
How: start by using some blocks (or something similar that will do the same job: pencil crayons, cutlery, apples..........) and ask your child to find 10. Once they've done that hold up one block and ask them to find the other blocks you need to make 10. Once they have done this say the sum '1 block and 9 blocks makes 10 blocks'. After making sure your child has understood this and you've repeated it several times then do the same but with 2 + 8. Continue doing this until you have all the sums. If you have enough equipment it would be great to have all the sums laid out on the floor / table. If you can't do this then as each one was 'discovered' write it down (or get them to) so they're all written down together. Then encourage your child to talk about what he / she sees. He / she might repeat the sums and tell you what each number is. They need to start to notice that the each number is each sum is one less / more than the previous and some of the sums are the same but the opposite way around. Once you've had a discussion I would finish for the day and let the info sink in. As a follow up activity next day ask your child if they can write all the number bonds to ten. If they can, great. If not, then just briefly go over some of the areas they may find hard. The most common problem in repeating this is children know there's a pattern but can't remember what it is. If they need a nudge then write the first two sums for them and see if they can continue.
If ten is achieved then your next step is to progress up the numbers with number bonds to 20, 30 and higher if you're both enjoying it and it's understood. I wouldn't do much more than one number and all it's bonds in a session, if you're going to move forward to another number then do it the next day.
What: number bonds to 10, 20, 30. Then extend using the 10's and 100's.(10 + 90, 20 + 80..........., 100 + 900, 200 + 800....., 1000 + 9000, 2000 + 8000.........) You may find that you can also start looking at all the number bonds to 100 too.
How: If you're starting with the number bonds to 10, which you probably should as revision, then follow what I have written for the 5,6 and 7 year olds.
Once you've covered the basic number bonds to 10, 20 and 30 etc. then you need to move onto the bigger numbers. Initially there is little alternative but to do it with paper and pencil. I try to make this more exciting by either using a white board and pen, or a huge sheet of paper and coloured pens or lots of sheets of paper; one for each sum and then put together in order...........you know what your child likes so use whichever of these works to make it more interesting for them.
By this point your child should have a good idea of what number bonds are and what the patterns are. What you are doing now is showing them how these bonds work across the whole number system and not just with the small numbers. So, maybe using one piece of paper get all the bonds to 10 written down, on the next sheet of paper get your child to write all the (10's) bonds to 100, then on the next sheet, the bonds to 1000 etc. Go as far as your childs knowledge of the number system will let you. Then look at all the sheets of sums and discuss the pattern and how it works.
The next step is to look at all the number bonds to 100. My favourite way of starting this is to give them 3 or 4 sums to work out and then discuss how they're working it out and if there is an easier way. So, ask your child to find what number they need to add to 25 to make 100. Then try 52 and then try 93. While this is happening just watch and see how your child does this. I suspect there will be a lot of finger use! Once they have done these three sums talk to them about how they did them, if they found it difficult or if they found them easy. If they found them difficult you need to show them there is an easy way. Ask them to look at each pair of numbers and for each pair add the units numbers together and then add the tens numbers together. What they should discover is that the units add up to 10 and the tens add up to 90. The next step is to try and encourage your child to explain why this is and then show them how they can use this knowledge to work out the number bonds easily. eg. 45 + ? = 100
So, I need to add something to my units number to make 10 and something to my tens number to make 90.
If I add 5 to the units number I have 10 and if I add 50 to my tens number I have 90. So I need to add 55. Check the sum works :)
Initially your child may need some paper to record these numbers on but as you practice then, hopefully, he / she will be able to do it in their heads. A good way to practice is to every so often just ask 2 or 3 sums or set a nightly challenge of 3 sums one night, 4 the next etc. You could time them and set the challenge of improving their time each night.
What: revision of all number bonds mentioned above. Then moving forward with bigger numbers 10000 + 90000, 20000 + 80000..........., 100000 + 900000, 200000 + 80000.........and then number bonds to 1000.
How: With these children I suspect you will find that a lot of them don't really know the number bonds but with some quick revision they will soon pick up on the patterns. Use the info above and look at all the multiple of 10, 100 and 1000 bonds, they are fun and quick and easy to do and you may be able to get up to and beyond 1000000.
Once you've had fun with the big numbers then revise how they work out the number bonds to 100. Again, you may find they can do it but have never really noticed the pattern mentioned above of the units making 10 and the tens numbers making 90. If they haven't found this, try and help them to discover it. Once these are secure move onto the number bonds to 1000. It's a great skill to be able to find pairs of numbers that make 1000 and, if you know the patterns it's not difficult. As with above, I would give them 3 sums to work out, so ask them to find the number that you add to 295 to make 1000, then 507 and then 989. Once they have done this write the sums down and discuss how they did it and if they can find any patterns that will help them.Hopefully they will notice that the units add to 10, the tens add to 90 and the hundreds add to 900.
eg. 368 + ? = 1000
So, I need to add something to my units number to make 10, something to my tens number to make 90 and something to my hundreds number to make 900. So 8 + 2 makes 10, 60 + 30 makes 90 and 300 + 600 makes 900. So the number I am adding is 632.
As you practice you could turn this into a little competition to try and increase the speed and efficiency of working this out. You could race each other or do sums against own speed or within a certain time.
How: start by using some blocks (or something similar that will do the same job: pencil crayons, cutlery, apples..........) and ask your child to find 10. Once they've done that hold up one block and ask them to find the other blocks you need to make 10. Once they have done this say the sum '1 block and 9 blocks makes 10 blocks'. After making sure your child has understood this and you've repeated it several times then do the same but with 2 + 8. Continue doing this until you have all the sums. If you have enough equipment it would be great to have all the sums laid out on the floor / table. If you can't do this then as each one was 'discovered' write it down (or get them to) so they're all written down together. Then encourage your child to talk about what he / she sees. He / she might repeat the sums and tell you what each number is. They need to start to notice that the each number is each sum is one less / more than the previous and some of the sums are the same but the opposite way around. Once you've had a discussion I would finish for the day and let the info sink in. As a follow up activity next day ask your child if they can write all the number bonds to ten. If they can, great. If not, then just briefly go over some of the areas they may find hard. The most common problem in repeating this is children know there's a pattern but can't remember what it is. If they need a nudge then write the first two sums for them and see if they can continue.
If ten is achieved then your next step is to progress up the numbers with number bonds to 20, 30 and higher if you're both enjoying it and it's understood. I wouldn't do much more than one number and all it's bonds in a session, if you're going to move forward to another number then do it the next day.
7, 8 and 9 year olds
What: number bonds to 10, 20, 30. Then extend using the 10's and 100's.(10 + 90, 20 + 80..........., 100 + 900, 200 + 800....., 1000 + 9000, 2000 + 8000.........) You may find that you can also start looking at all the number bonds to 100 too.
How: If you're starting with the number bonds to 10, which you probably should as revision, then follow what I have written for the 5,6 and 7 year olds.
Once you've covered the basic number bonds to 10, 20 and 30 etc. then you need to move onto the bigger numbers. Initially there is little alternative but to do it with paper and pencil. I try to make this more exciting by either using a white board and pen, or a huge sheet of paper and coloured pens or lots of sheets of paper; one for each sum and then put together in order...........you know what your child likes so use whichever of these works to make it more interesting for them.
By this point your child should have a good idea of what number bonds are and what the patterns are. What you are doing now is showing them how these bonds work across the whole number system and not just with the small numbers. So, maybe using one piece of paper get all the bonds to 10 written down, on the next sheet of paper get your child to write all the (10's) bonds to 100, then on the next sheet, the bonds to 1000 etc. Go as far as your childs knowledge of the number system will let you. Then look at all the sheets of sums and discuss the pattern and how it works.
The next step is to look at all the number bonds to 100. My favourite way of starting this is to give them 3 or 4 sums to work out and then discuss how they're working it out and if there is an easier way. So, ask your child to find what number they need to add to 25 to make 100. Then try 52 and then try 93. While this is happening just watch and see how your child does this. I suspect there will be a lot of finger use! Once they have done these three sums talk to them about how they did them, if they found it difficult or if they found them easy. If they found them difficult you need to show them there is an easy way. Ask them to look at each pair of numbers and for each pair add the units numbers together and then add the tens numbers together. What they should discover is that the units add up to 10 and the tens add up to 90. The next step is to try and encourage your child to explain why this is and then show them how they can use this knowledge to work out the number bonds easily. eg. 45 + ? = 100
So, I need to add something to my units number to make 10 and something to my tens number to make 90.
If I add 5 to the units number I have 10 and if I add 50 to my tens number I have 90. So I need to add 55. Check the sum works :)
Initially your child may need some paper to record these numbers on but as you practice then, hopefully, he / she will be able to do it in their heads. A good way to practice is to every so often just ask 2 or 3 sums or set a nightly challenge of 3 sums one night, 4 the next etc. You could time them and set the challenge of improving their time each night.
9, 10 and 11 year olds
What: revision of all number bonds mentioned above. Then moving forward with bigger numbers 10000 + 90000, 20000 + 80000..........., 100000 + 900000, 200000 + 80000.........and then number bonds to 1000.
How: With these children I suspect you will find that a lot of them don't really know the number bonds but with some quick revision they will soon pick up on the patterns. Use the info above and look at all the multiple of 10, 100 and 1000 bonds, they are fun and quick and easy to do and you may be able to get up to and beyond 1000000.
Once you've had fun with the big numbers then revise how they work out the number bonds to 100. Again, you may find they can do it but have never really noticed the pattern mentioned above of the units making 10 and the tens numbers making 90. If they haven't found this, try and help them to discover it. Once these are secure move onto the number bonds to 1000. It's a great skill to be able to find pairs of numbers that make 1000 and, if you know the patterns it's not difficult. As with above, I would give them 3 sums to work out, so ask them to find the number that you add to 295 to make 1000, then 507 and then 989. Once they have done this write the sums down and discuss how they did it and if they can find any patterns that will help them.Hopefully they will notice that the units add to 10, the tens add to 90 and the hundreds add to 900.
eg. 368 + ? = 1000
So, I need to add something to my units number to make 10, something to my tens number to make 90 and something to my hundreds number to make 900. So 8 + 2 makes 10, 60 + 30 makes 90 and 300 + 600 makes 900. So the number I am adding is 632.
As you practice you could turn this into a little competition to try and increase the speed and efficiency of working this out. You could race each other or do sums against own speed or within a certain time.
Whatever you do, have fun :)
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