Video: Making 6 and 7

In this video, we will learn how to use pictures and addition equations to show all the ways to make the numbers 6 and 7.

12:24

Video Transcript

Making Six and Seven

In this video, we’re going to learn how to use pictures and addition equations to show all the ways to make the numbers six and seven.

Here we have seven birds sitting on a wire. At the moment, they’re all on the right-hand side of the wire. At this end, there are no birds or zero. And all seven of the birds are huddled up together at the other end. We can write the number of birds at either end of our wire as an addition. And it’s going to make a total of seven. Zero plus seven equals seven. You know, we can record this number fact in lots of different ways, as a number bond in this part–whole diagram. If we like the idea of birds on a wire, we could use counting beads on a piece of string. We could also write out the addition as a number sentence.

How else could we make seven? Well, let’s imagine that one of our birds gets fed up being part of a large group and wants to hop off to the other end of the wire on his own. There we go. We could model this by pushing one of our beads along the string. What addition can we see now? We now have one bird at this end of the wire. And although we did have seven birds on the other end, we now have one less. We have six birds, but we still have seven birds altogether. We can say that one plus six equals seven. It’s another way of making the same total.

What if another bird decides to move? This shows another way to make seven. Two and five make seven too, so do three and four. You know, changing one thing at a time, whether it’s a bird on a wire or a bead on a string, is a good strategy that we can use to make sure we find all the possible ways to make a number. And if we look carefully at our number sentences, we could spot some patterns.

Firstly, we can see that the answer each time is seven. This is because we’re finding different ways to make seven. If we think about beads on a string, the number of beads aren’t going to change. What pattern can we see with the first number in each number sentence? Zero, one, two, three. These numbers are increasing by one each time. What number would you expect to come next? Zero, one, two, three, four.

If we look at the second number in each number sentence, we have seven, six, five, four. These numbers are going down, and they’re decreasing by one each time. Seven, six, five, four, three. We’d expect the next number to be three. Four plus three equals seven. And we can continue that pattern. Five and two make seven. Six and one make seven. And finally, if we move all the beads to the other side, seven and zero make seven too. We found eight different ways to make the number seven. Let’s have a go at answering some questions now. We can use this strategy in some different models and answer some questions how to make six and seven.

Find the missing addition sentence. Zero plus six is six. One plus five is six. Two plus four is six. Three plus three is six. Four plus two is six. What? And we have four possible answers. Four plus one is six. Four plus two is five. Five plus one is six. And four plus one is five.

In this question, we’re given some addition sentences. These are written using numbers, but they’re also modeled using cubes. And we can see both orange and green cubes here. The first line of cubes shows no green cubes and six orange cubes. That’s where we get our number sentence zero plus six from. We can think of the first number as being the number of green cubes that we can see and the second number as being the number of orange cubes that we can see. And because the length of each line of cubes is the same each time, these are always going to make six. Zero plus six is six.

We can also see that one plus five is six. Two green cubes and four orange cubes make six. If we add together three of each type of cube, we get six. Four plus two make six. But then we come to a missing addition sentence. And the question asks us to find out what it is. What can we say about this missing addition sentence? Well, firstly, we can say that we’re looking for two numbers that we need to add together, just like all the other addition sentences. We can also say that we’re looking for a number sentence that gives the answer six.

If we look at our line of cubes, we can see that there are six cubes just like all the others. So which two numbers can we find that make six? If we look at the numbers in each addition, we can see some patterns. The first number in each addition, which is the number of green cubes, increases by one each time. If we read each of the first numbers, we can see zero, one, two, three, four. If we’re increasing by one each time, what’s going to come after four? We’d expect to see the number five. Should we count our green squares to see whether that’s correct? One, two, three, four. Yes, there are five green squares.

And if we look at the second number in each addition, which is the number of orange squares, we can see that these decrease by one each time. They get smaller. Six, five, four, three, two. What comes after two? One. How many orange squares are in our line of cubes? One. So we would expect our missing addition sentence to say five and one is six. Can you see that as one of our possible choices? Yes, here it is. Five plus one is six.

Using cubes like this is a really good way to model all the possible ways to make a number. In fact, there is only one other way that isn’t shown. A line of just green cubes would show us that six plus zero is six too. But we don’t need to know this to answer the question. The missing addition sentence from the picture that we were shown is five plus one is six.

Which of these has a different answer? Three plus three. One plus five. Three plus four. Or two plus four.

We can see that these four different additions are also shown as a model using both blue and orange rectangles. Can you see what the first number in each addition represents? It’s the number of blue rectangles, isn’t it? For example, in the first addition sentence or equation, we have three blue rectangles. That’s why our first number is three. And we also have three orange rectangles. That’s why the second number in our equation is three. So what is three plus three? Let’s start by saying the first number and then counting on another three. So we’ll say three, four, five, six. There are six rectangles in our first model. Three plus three equals six.

In our second model, we can see that we have one blue rectangle and five orange rectangles, so we can start with the number one and count on another five. One, two, three, four, five, six. Our second number sentence also shows six. And if we compare the length of our models, we can see they’re both the same length. They both contain six rectangles, don’t they?

What about our next number sentence, three plus four. We’ll start with three and count on four. Three, four, five, six, seven. This number sentence has an answer of seven. And if we look at the length of the model, we can see that this is longer than the rest. The number sentence with a different answer is three plus four. We know this because if we start on two and count on another four, we’re going to arrive at six. Two, three, four, five, six. The addition that has a different answer is the one that shows three plus four.

There are six cats. Three plus three is six. Find out the missing numbers to have another way to get six. What plus what is six.

We’re told in this question that there are six cats, and this question is all about different ways to make six. To begin with, we’re shown a number sentence made out of pictures. In the first picture, we can see three cats. And in the second picture, we can see another three cats. Then, in the final picture, we can see six cats. This shows us that three plus three is six. We could actually draw a line across our group of six cats to show us that three and three make six.

But then we’re shown another picture number sentence. This time we’ve got some missing numbers, and we’re told to find out the missing numbers to have another way to get six. How else could we make six? Well, if we look carefully at our first picture, we can see that, instead of three cats, this now shows two cats. Let’s write the number two above that picture. Two plus what make six. But if we want to make the same total, which is six, we need to do something with the cat that’s walked away. Instead of three cats to begin with, we have two. So the cat that’s gone away is gonna have to join the second group to keep the answer the same.

If you remember, we did have a group of three cats as a second group. We now need to have a group with one more cat in it. Let’s count them to see whether there are four cats in our second group. One, two, three. Yes, there are. There are four cats in our second group. Two plus four is six. And again, we can draw a line on our group of six just to show that two and four make six. We know that three plus three is six, and we can use this to help us find that two plus four is six too.

What have we learned in this video? We’ve learned how to use pictures and equations or number sentences to show all the ways to make the numbers six and seven.

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