In this video, we will learn how to add a multiple of ten to a multiple of ten and model this with place value equipment.

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### Video Transcript

In this video, we’re going to learn how to add a multiple of 10 to another multiple of 10 and also how to model this using place-value equipment. Each row in this 100 square is made up of 10 smaller squares. And so if we want to use this 100 square to count in 10s, we just need to look at the last number in each row. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. We’ve counted all the way from one 10 through to 10 10s. Did you notice how each of the numbers that we read has a zero on the end? We call these numbers multiples of 10. And in this video, we’re going to learn how to add different multiples of 10 together. So we might add 50 and 20, 30 and 40, or maybe have a go at 70 plus 10. All of these additions show a multiple of 10 being added to another multiple of 10.

Let’s have a think how we can do this. Let’s try finding the total of these two multiples of 10. What’s 60 add 30? To help us find the answer, we could model both numbers using place-value equipment. These are the sorts of maths equipment that we use to help us split up numbers into 10s and ones. What does the number 60 look like? We could model the number 60 by showing six 10s because we know six 10s are the same as 60. 10, 20, 30, 40, 50, 60. Now, let’s model the second number in our addition. How could we show 30? 30 is the same as three 10s. 10, 20, 30. So to find the total of 60 and 30, all we have to do is to add together six 10s and three 10s.

Now, is there a number fact that we could use to help here? We know that six ones or six plus another three ones equals nine ones. And because we know that six plus three equals nine, we know the total of six 10s and three 10s will be nine 10s. Nine 10s are the same as 90. 60 plus 30 equals 90.

Let’s try adding another pair of multiples of 10. What’s the total of 40 and 40? Now, we know that 40 is the same as four 10s. And because we’re adding 40 and 40 together, we need to find the answer to four 10s add another four 10s. Now, can you spot a simpler addition fact that we could use to help us here? What about if we use our place-value equipment to add ones first instead of 10s? Maybe we could use this to help. Four ones plus another four ones equals eight ones. And if we know this, then we also know that four 10s plus another four 10s are going to make eight 10s. And eight 10s is the same as 80. If four plus four equals eight, we know that 40 plus 40 equals 80.

Let’s try answering some questions now where we have to add together pairs of multiples of 10. And to help us, we’ll carry on using place-value equipment.

Add to find the total. Seven plus two equals what. 70 plus 20 equals what.

In this problem, we’re given two additions to work out. We need to find the total of the digits seven and two. And then we’re given a pair of two-digit numbers to add, 70 and 20. These two numbers are multiples of 10. We know this because they both end in a zero. Do you notice anything else about our two additions? They both contain the digits seven and two. These two calculations seem to be linked in some way. The first one looks a little bit easier than the second one. Perhaps we could use it to help us work out the answer to the second one. Let’s begin then by finding the answer to seven plus two.

We can start by modeling the number seven using seven ones cubes, and the two that we’re adding are the same as two more ones. Let’s start with seven and count on another two. Seven, eight, nine. We know that seven ones plus two ones equals nine ones. Seven plus two equals nine. And you know we can use this idea of seven plus two equals nine to help us solve the second addition. We’ve said already that these two numbers are multiples of 10. This means we can model them using 10s blocks. They both are number of 10s. 70 is the same as seven 10s. And the 20 that we need to add on is the same as two more 10s.

And because we know seven plus two equals nine, we know that seven 10s plus two 10s are going to equal nine 10s. And nine 10s are worth 10, 20, 30, 40, 50, 60, 70, 80, 90. We use the first calculation where we were adding ones to help us find the total in this second calculation where we were adding 10s. Seven plus two equals nine. And 70 plus 20 equals 90.

Write the missing number: 10 plus what equals 50.

To help us understand what we need to do to find the answer here, we could draw a part–whole model. Let’s fill in the numbers we know. This is one of those additions where the missing number is one of the numbers we add. So we already know what the total is. This means we can fill in the whole amount, that’s the top number in our part–whole model, as the number 50. We need to add two numbers together to make 50. And if we look at our calculation, we already know what one of those numbers is? One of the parts that makes 50 is 10. Now, it’s our job to find out what the missing part is.

What do we need to add to 10 to make 50? What do you notice about the numbers that we know already in this addition. They both end in a zero, don’t they? This means they’re multiples of 10. We can make them by adding several 10s together. We could even change our part–whole model to show this. 50 is the same as five 10s. And of course, the number 10 is one 10. Now what do we add to one 10 to make a total of five 10s? We know that one plus four more make five. So one 10 plus four more 10s makes five 10s. And so 10 plus 40 equals 50. Our missing number is 40.

Find the two numbers from 10, 20, 60, and zero which add up to 30.

In this question, we’re looking for two numbers that we’re going to add together to give us a total of 30. But we can’t just pick any two numbers. We need to pick two numbers from the numbers that we’re given. And these are 10, 20, 60, and zero. Now, there are two ways we could find the answer here. One of them is a really quick way that we can find the answer. But we’ll go through the other way first and we’ll just mention that at the end.

Now, there’s something interesting about all the numbers in this question. Can you see what it is? Each of the numbers, so that’s the two numbers that we need to add together and also the total that we’re trying to make, ends in a zero. This means they’re all what we call multiples of 10. We can make each number out of an amount of 10s. 10 is the same as one lot of 10. We can make 20 from two lots of 10. 60 is the same as six lots of 10. Zero is no lots of 10. And finally, the number we’re making, 30, is worth three lots of 10.

This is where we should start really. We need to try to make three lots of 10. Which two numbers can you see that we can add together to make three lots of 10? We can use a number fact to help us here. We know that one plus two equals three. And so we can say one 10 plus two 10s equals three 10s. Or to say it another way, 10 plus 20 equals 30.

Now, we did say at the start of this question that there was a really quick way to find the answer. The answer had to be 10 and 20 really. We know that if one of our numbers was zero and we wanted to make 30, then the other number would have to be 30. And we didn’t have 30 as one of our choices. So we could have crossed through the number zero before we started. And also, if we’re making the number 30, another 60 is too large. So we could also have crossed through the number 60 before we started too. Sometimes there’s more than one way to find an answer. The two numbers which add up to 30 are 10 and 20.

So what have we learned in this video? Firstly, we’ve learned what a multiple of 10 is, and also how to describe multiples of 10 as a number of 10s. And then we’ve learned how to add two multiples of 10 together and then model this using place-value equipment.