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I can recognise number pairs that total 10 and use them to find the sum of three numbers.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Rearranging the addends identifies the pairs that total 10.
Place value means we can add a single digit to 10.
Representations help us to see the pair that makes 10 and the extra ones number.

Common misconception

Pupils believe a pair to 10 only exists if the addends are next to one another in an equation.

Addition is commutative. Model the use of tens frames to show efficient addition of calculations containing number pairs to 10.

Keywords

Addend - A number added to another.
Commutative - Addition is commutative. This means the order of the addends can be changed without changing the calculation or sum.
Equation - An equation is used to show that one number or calculation is equal to another.
Sum - The sum is the total when numbers are added together.

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Hello.

My name is Mr. Golding and welcome to today's maths lesson.

I'm sure you're going to enjoy it.

And here is our lesson outcome: I can recognise number pairs that total 10 and use them to find the sum of three numbers.

So for today's lesson, it would be helpful to have paper, a pencil, and you might also want to use 10 frames and counters as well.

And here are the keywords for today's lesson.

So the keywords are addend, commutative, equation, sum.

So an addend is a number added to another.

An operation is commutative If the values it is operating on can be written in either order without changing the calculation.

For example, four add three equals seven, three add four equals seven.

So addition is commutative.

An equation is used to show that one number or calculation is equal to another.

The sum is the total when numbers are added together.

And here's our lesson outline.

So in the first part of the lesson, we're going to be finding pairs that total 10.

And in the second part of the lesson, we're going to be using pairs of 10 to find the sum of three numbers.

Let's start with finding pairs that total 10.

Izzy and Alex are going to help you today.

So they're going to ask you some questions and they're going to explain some mathematical ideas to you as well.

How many pieces of fruit are there altogether? Now let's look on the first tree.

We've got seven oranges.

The second tree, we have got five lemons.

And then lying on the ground under the third tree, we have got three apples.

How many pieces of fruit are there altogether? And is there an easy way to add together those three numbers? How can you add seven and five and three together? \"Addition is commutative,\" says Alex.

You can add the numbers in any order.

You can use 10 frames to help you as well.

Here's our 10 frames.

So which number would we start with? Well, we could start with seven.

We've got seven oranges.

What would we add to seven next? We could add three.

So 7 add 3 is a number pair that totals 10.

7 add 3 makes 10.

And then we could add the five.

Here's our five, five lemons.

10 add 5 equals 15.

So altogether, there are 15 pieces of fruit.

Now number pairs that total 10 are helpful.

In addition, here's Alex again and Alex is saying, \"Can you spot the number pair that makes 10?\" Which two tens frames add together to make 10? Which two tens frames have a number pair that totals 10.

You may have spotted we've got a four, a five and a six.

4 and 6 equals 10.

4 add 6 equals 10.

So we could move our six lemons and pop 'em in there, and that makes 10.

4 add 6 equals 10.

4 and 6 are a number pair that totals 10.

Pairs to 10 can help to add numbers together.

So find the number pair that has a sum of 10.

So you're looking for the two numbers that add together to make 10.

Can you spot the two numbers added together to make 10? What have we got? We've got a 5, add 5 equals 10.

So 5 and 5 are a number pair that makes 10, that equals 10.

Let's try another one.

Can you spot the number pair this time? We've got 6 add 4.

6 and 4 equals 10.

So 6 and 4 are another number pair that totals 10.

What can you spot this time? What can you see? We've actually got this time a 0 add 10 equals 10.

So 0 and 10 are also a number pair that totals 10.

And about this time, can you spot the two numbers that add together to make 10? We've got 8, add 2.

8 and 2 equals 10.

And what about this time? This time we've got 3 add 7 equals 10.

Can you find the number pair that has a sum of 10? We've got a nine and a one and a two.

9 add 1 equals 10.

And what about this one? What about this time? So we've got a seven, a four and a three.

And we could do 7 add 3 makes 10.

Alex chooses sets of three number cards.

Which sets include a number pair that totals 10? So there are three sets of number cards.

Let's look at the first one: two, seven, eight.

Is there a number pair that totals 10? Well, 2 add 8 equals 10.

2 add 8 equals 10.

So we have got a number pair that totals 10.

Let's look at the next one.

So we've got nine and three and two.

Have we got a number pair that totals 10? 9 add 1 equals 10, but there's no one.

There's nine, but no one.

3 add 7 equals 10.

There's a three, but no seven.

2 add 8 equals 10.

There's a 2, there's no 8.

There is no number pair that totals 10.

And the last one, we've got four and seven and three.

Have we got a number pair that totals 10? We've got 7 and 3.

7 add 3 equals 10.

Here's one to try on your own.

Which sets of number cards include a pair that totals 10? So have a good look at the numbers in each set.

Can you find a number pair that adds together to make 10? So pause the video and see if you can work out the answers.

Welcome back.

Let's see if you were right.

So the first set of number cards, we've got six, three and four.

We have got a 6 and a 4.

6 add 4 equals 10.

So it's definitely a number pair that totals 10.

Our next set of numbers is eight, three and four.

Is there a pair that totals 10? There is not.

And the last set of numbers is nine, seven and one.

Is there a number pair that totals 10? There is 9 and 1 equals 10.

Well done if you spotted those.

And then we've got some more sets of number cards.

So which sets of number cards include a pair that totals 10? So again, have a good look.

See if you can work out the answers.

Pause the video and have a go at those sets of number cards.

And welcome back.

And let's see if you are right.

So the first set of number cards, we've got two, three, and eight.

We have got a number pair that totals 10.

We've got 2 and 8.

2 add 8 equals 10.

Our next set we've got seven, seven and four.

So a number pair that totals 10.

There's a double, isn't there? There's seven and seven, but there is no number pair that totals 10.

And our last set is three, six and five.

Is there a number pair that totals 10? There's a near double, isn't there? There's five and a six, but there is no number pair that totals 10.

Well done if you've got those ones right.

And here's our task.

In your task, you're going to be looking at which sets of numbers have a pair that totals 10? Which do not? And you're going to place them correctly in the table.

So pairs that totals 10, you're gonna put one side.

And if there's no pair that totals 10, you're gonna put on the other side.

And where a set has a pair that totals 10, can you find the sum of the three numbers? So here are the numbers you're going to sort.

So we've got a six, a five, and a two.

Has that got a pair that totals 10 or is there no pair that totals 10? So you need to put it in the right place on the table.

So pause the video and have a go at that task.

Welcome back and let's look at the answers and see whether you are right.

So here we have pairs, the total 10 on one side, and no pair that totals 10 on the other side.

So we've got on one side we've got a 10, a 5 and a 0 because 10 add 0 equals 10.

And we've got a one, a nine and a three because 9 add 1 equals 10.

On the other side we've got a six, a five, and a two.

There is no pair that totals 10.

So well done if you've got those ones right.

A lot of thinking going on there.

Very well done.

And let's move on to our second part of the lesson and our second part of the lesson, we're going to be using pairs to 10 to find the sum of three numbers.

So we spent a long time looking at pairs that make 10.

Now we're going to be using those to add three numbers together.

So add the pair that totals 10.

Let's start off with that.

First of all, add the pair that totals 10, and then add the remaining addend.

How would you add seven, add six, add three? So look for the pair that makes 10, first of all.

What would that be? So we've got here seven oranges, six apples, and three lemons.

Where's our pair that makes 10? 7 add 3 equals 10.

The number we haven't used so far is 6.

10 add 6 equals 16.

How would you add five, add eight, add two? And again, look for the number pair that makes 10.

So we've got five oranges, eight apples, two lemons.

What would you add together first? 8 add 2 equals 10.

8 and 2 is a number pair that makes 10.

And then all we have to do is to add the five.

So 10 add 5 equals 15.

How would you add four, add nine, add six? Here's our tens frames again.

So we've got a four, a nine and a six.

Where's our number pair that makes 10? 4 add 6 equals 10.

And then 10 add 9 equals 19.

Find the sum of this bar model.

So our sum is the number that goes to the top.

So we've got to add together a six, a seven and a four.

How would you add together six, add seven, add four? How would you find the sum of six, add seven, add four? We've got a six.

We have the 4, that makes 10.

So 6 add 4 equals 10.

And then we have to add the seven.

10 add 7 equals 17.

Can you find the sum of these bar models? There are three bar models on there.

Can you find the sum? So pause the video, add the three addends together and think carefully about how you're going to add them together.

Welcome back.

Let's see if you were right.

So in our first bar model, we've got the numbers three, five and seven.

3 add 7 equals 10.

3 and 7 are a number pair that makes 10.

So our answer would be 15.

3 add 7 equals 10.

10 add 5 equals 15.

Let's look up next bar model.

So we've got two, four, and six.

Where's our number pair that makes 10? So we've got a six and a four.

6 and 4 equals 10.

Add the 2 equals 12.

And our last bar model, one, seven and nine, 1 add 9 equals 10.

Then we add the 7.

10 add 7 equals 17.

Well done if you've found the sum for those three bar models.

Find the missing addend from this bar model.

So this time we've gotta work out what number is missing, which addend is missing.

So we've got 8, add something, add 5 equals 15.

This is where tens frames can be very useful.

So 15 is made out of 10 and 5 and we've got a five as one of our addends.

So our other two addends must add up to make 10.

10 add 5 equals 15.

One of the addends is 8.

What do you need to add to 8 to get to 10? 8 add 2 equals 10.

So our missing addend is two.

Now here's three to try on your own.

They're a bit tricky, these ones.

You have to think about these carefully.

Really use those (indistinct) to help you.

Find the addends missing from these bar models.

So again, look carefully at those addends.

Look carefully at the sum.

See if you can work out which addend is missing.

Pause the video and see if you can find those missing addends.

Welcome back.

Let's see if you were right.

So in our first one, we've got a three and a seven and a missing number, and they add up together to make 14.

But 7 add 3 makes 10.

7 add 3 equals 10.

They're a number pair that equals 10.

So our missing number must be four because 10 add 4 equals 14.

Our next one we've got a 10, a missing number and a four.

10 add 4 equals 14.

So our missing number must be 0.

And our last one, you may have actually seen this problem already, the numbers in a slightly different order.

Can you work out the missing number? So we've got something add 5, add 8 equals 15.

Well, 10 add 5 equals 15.

So the 8 and the missing addend must add up to 10.

So what number added to 8 makes 10? What number added to 8 equals 10? Missing number must be two.

Very well done if you've got those ones right.

Find different ways to complete this equation.

So we've got a missing number, add a missing number, add 4 equals 14.

What do you notice about the two missing addends? So we've got a missing number, add a missing number, add 4 equals 14.

Now you may have spotted that 14 has a one's number of 4.

14 is made up of 10 and 4, which means our two missing addends must have a total of 10.

So what we're looking for are two numbers that add together to make 10 'cause 10 add 4 equals 14.

So our two missing numbers must have a total, must have a sum of 10.

So which numbers have a sum of 10? How could you complete this equation? Well, you could do 9, add 1, add 4 equals 14.

Or you could swap the numbers around, of course, 'cause addition is commutative.

So you could also do 1 add 9, add 4 equals 14, or you could do 8 add 2, add 4 equals 14, 7 add 3, add 4 equals 14.

Are there any more ways? Can you think of any more? Well, there are.

You could also do 6 add 4, add 4 equals 14.

6 add 4 equals 10.

Add another 4 equals 14.

5 Add 5 also equals 10.

So 5 add 5, add 4 equals 14 and 10 add 0 equals 10.

So 10 add 0, add 4 equals 14.

Can you find different ways to complete this equation? So this time, you've got the missing number, add seven, add another missing number equals 17.

And again, what do you notice about the two missing addends? So have a good look at that equation.

See if you can work out what the missing numbers could be.

And can you find more than one answer? Can you find all the different answers? So again, pause the video and have a go.

See if you can work out the answers.

Welcome back.

So what do you notice about the two missing addends? Well, 7 add 10 equals 17 or 10 add 7 equals 17.

So our two missing addends must add up to make 10.

So you're looking for two numbers that add together to make 10.

And if you have those two numbers to 7, you would get the answer 17.

So you could have done 9 add 7, add 1 equals 17.

9 add 1 equals 10.

So add the 7 would equal 17.

You could have done 8 add 7, add 2 equals 17, or 7 add 7, add 3 equals 17.

You may have also found 6 add 7, add 4 equals 17, or 5 add 7, add 5 equals 17, or 10 add 7, add 0 equals 17.

And of course, you can reverse those numbers, well, change those numbers around.

So you could instead have 0 add 7, add 10 equals 17.

So well done if you found some of those ways.

Very, very well done if you found lots and lots of different ways.

And here is your practise task.

So for the first practise task, you're looking to find the numbers missing from these bar models.

So in the first three bar models, it's the sum that is missing.

So you're looking for the sum.

And in the three bar models underneath, you're looking for a missing addend.

So you're looking for one of the numbers that adds together to make the sum.

And here's task number two.

So you've gotta find the missing numbers.

So you've got missing numbers in those equations.

And task number three, how many ways can you complete this equation? So there's lots and lots of different ways you could find the answer.

How many different ways can you find the answer? So have a get at those tasks.

Again, pause the video and we'll have a look at those answers later.

Welcome back.

Let's see how you got on.

So here's our answers for the bar models.

So those are the numbers that are missing for the bar models.

So we've got the sums 14, 17, and 13.

And then the missing addends were eight and five and seven.

And then we've got task two, find the missing numbers.

So we've got the answers there.

And then for task three is a sum of the answers.

It's not all of them 'cause there are lots and lots of different answers.

That is just some of the answers.

You might have some answers that are different to those ones or you might have some where the numbers are reversed.

So instead of having 1 add 9, add 6 equals 16, you could have had 9 add 1, add 6 equal 16.

And again, very well done if you found lots and lots of different ways of making 16.

So fantastic work today.

Very well done and you should now be really confident at using those pairs to 10 to find the sum of 3 numbers.

Here's our lesson summary.

So addition is commutative.

So remember, that means you can do it in any order.

You can swap around the addends and add 'em up in any order you want.

So whichever way is easiest.

Number pairs to 10 can help you add addends together.

So looking for those number pairs to 10 is a really useful strategy to use when you're adding numbers together.

So find and add number pairs to 10 first.

Excellent work today.

Very well done.

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" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137325%2Fl5qmi968o1xiizktrwqj.png&w=384&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/433b2d51f42712190773081788e04d5b.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137329%2Fbtoqedfobveatn1a7wll.png&w=384&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/ff7bd7445be6831e1a0d8f10d5dffe45.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137325%2Fl5qmi968o1xiizktrwqj.png&w=384&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/433b2d51f42712190773081788e04d5b.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137332%2Fb2n5e64u135z3vfhbtdu.png&w=640&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/68738538f9a056472ed3e4dc48ededf5.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137329%2Fbtoqedfobveatn1a7wll.png&w=384&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/ff7bd7445be6831e1a0d8f10d5dffe45.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137322%2Fxip3p8oemvnb0620v2g2.png&w=384&q=75", "imageKey": "a007431b-ac2d-2ca7-0ce5-b1c0af77457d/question/c9fa6b29db2439b3da79cc28cd4d2ec8.png" } ], "id": "3487bae8-981a-8865-48b4-21f5a2478fff", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" } ], "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Review strategies for adding and subtracting across 10", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Add three addends by finding pairs that total 10" } }, { "id": "c4617635-83c9-4c5b-178a-7daa5e28de6d", "type": "Resource", "resourceType": "Quiz", "title": "Add three addends by finding pairs that total 10", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "What equation do the tens frames represent? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137330%2Frjzjtttzcov1qapsrtrt.png&w=1920&q=75", "imageKey": "c4617635-83c9-4c5b-178a-7daa5e28de6d/question/575446b140d4e61a009ca671a0f187fc.png" }, "questionType": "Multiple choice", "correct": [ { "text": "6 + 4 + 3 = 13" } ], "choices": [ { "text": "5 + 5 + 3 = 13" }, { "text": "7 + 3 + 3 = 13" }, { "text": "5 + 4 + 4 = 13" }, { "text": "6 + 4 + 3 = 13" } ], "id": "39e05bf5-5f4a-74b2-9cfd-dd8537758243", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" }, { "type": "Question", "question": { "text": "Which calculations include number pairs that total 10? " }, "questionType": "Multiple choice", "correct": [ { "text": "3 + 7 + 2" }, { "text": "8 + 1 + 2" } ], "choices": [ { "text": "5 + 4 + 4" }, { "text": "6 + 3 + 2" }, { "text": "3 + 7 + 2" }, { "text": "8 + 1 + 2" } ], "id": "20a7bd58-d088-9075-cfe1-aefef6d795fc", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" }, { "type": "Question", "question": { "text": "Match the equation to the correct sum. " }, "questionType": "Matching", "pairs": [ { "left": { "text": "8 + 2 + 1" }, "right": { "text": "11" } }, { "left": { "text": "8 + 2 + 4" }, "right": { "text": "14" } }, { "left": { "text": "2 + 3 + 8" }, "right": { "text": "13" } }, { "left": { "text": "2 + 8 + 2" }, "right": { "text": "12" } } ], "id": "7b5477ab-eaf5-957f-7323-e0f48d3c8c85", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" }, { "type": "Question", "question": { "text": "What is the sum of the numbers in the bar model?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137328%2Fdp87sszzq0vf0lpboy5l.png&w=750&q=75", "imageKey": "c4617635-83c9-4c5b-178a-7daa5e28de6d/question/335941a8594756b01f859e95d53a2a19.png" }, "questionType": "Multiple choice", "correct": [ { "text": "16" } ], "choices": [ { "text": "15" }, { "text": "16" }, { "text": "18" }, { "text": "19" } ], "id": "1771560a-f0c1-2075-5f09-c06ace1ec414", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" }, { "type": "Question", "question": { "text": "Find the missing addend in the equation. ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137305%2Fifvmfitbg4jgqbhhaelk.png&w=1080&q=75", "imageKey": "c4617635-83c9-4c5b-178a-7daa5e28de6d/question/2d4127d8f40207cc72b963c7c79676e3.png" }, "questionType": "Multiple choice", "correct": [ { "text": "4" } ], "choices": [ { "text": "4" }, { "text": "5" }, { "text": "6" }, { "text": "11" } ], "id": "f3a576f8-f831-aa57-5460-962d32842014", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" }, { "type": "Question", "question": { "text": "What addend is missing from this bar model? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698137332%2Fcvqu38q2kgxi9fkbsxhk.png&w=750&q=75", "imageKey": "c4617635-83c9-4c5b-178a-7daa5e28de6d/question/f123d1f1454ae032a4b3bf2ed04618be.png" }, "questionType": "Multiple choice", "correct": [ { "text": "7" } ], "choices": [ { "text": "3" }, { "text": "7" }, { "text": "9" }, { "text": "12" } ], "id": "60c2e54c-9d13-7446-1f17-acbd8b5cefc7", "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5" } ], "lessonId": "d9804574-baff-cbfa-1516-a7333e7c76b5", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Review strategies for adding and subtracting across 10", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Add three addends by finding pairs that total 10" } }, { "id": "dc11e265-b048-bb73-c8b5-f89f463061e7", "type": "Content", "contentType": "Additional material", "content": { "text": "

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