Lesson video

Hello, I'm Miss Brinkworth, I'm going to going through this maths lesson with you today.

So shall we look at the learning objectives together? Today, what we're going to be doing is using the inverse operation to find missing numbers.

Now, the inverse operation that we're talking about here is the relationship between multiplication and division.

And what's really great about today's lesson is we're using facts that you already know and we're just applying them to new situations.

So it's a lovely trick to be able to use your multiplication facts and apply them to division questions.

Often, people feel very confident with their multiplications and less confident with their division, but actually we use all the same facts, we just have to recognise that that's what we're doing.

So should we look at today's lesson agenda? What we're doing today is we're going to start with arrays, that's probably a way that you're quite used to representing multiplication and division.

So we're going to start there and we're going to think about applying, looking at those arrays slightly differently to see that relationship between multiplication and division.

We're then going to relate arrays to fact families.

These are groups of numbers which come together, three numbers, and if we can remember their relationship, which is just some times tables knowledge, it really helps us with any division question we might come across.

It's then, like I say, about applying that known fact, that information that you already know and just recognising when you can use it in new situations.

Finally, at the end of the lesson, there'll be time for independent work, which is a chance for you to take your time with some work on your own and really embed today's learning.

And then, at the end, there's the exit quiz, which is a nice bit of fun to just see how much of today's learning's gone in.

Okay, all you're going to need is a pen or pencil and some paper, a smile would be wonderful as well.

So pause the video and get what you need.

Okay, let's get started then.

So we've got a lovely warm up in today's lesson, and this is about the question six times three.

And what you need to think about for this warmup is which of these representations show six times three and which ones don't.

But think carefully because they might not show them in a way that you're used to, but work out what six times three is and think is that showing the answer to six times three? Pause the video and then come back together for our thoughts when you're ready.

Let's get through them together.

So hopefully the first thing that you did was say, right, six times three is, well, let's have a check, six times three or three times six, whichever way you want to look at it, six, 12, 18.

We're looking for 18.

Do these different different representations show 18? Well, if we start with that yellow rectangle, it's got 18, it's got three columns and it's got six rows.

So that one here with the circle around it does represent 18, it does represent xix times three.

The next one, this nice picture here which looks like marbles or balloons in bags, there are six groups and there are three in each group, which is a lovely representation of what we're talking about when we mention multiplication, and division actually is groups, equal groups, that's multiplication and division.

So that one also represents six times three.

This one up here is kind of a sort of traditional array, probably a way that you've seen multiplication or maybe division represented before.

And again, that one does represent six times three.

We've got six across the top, three down the sides, so there are 18 blue dots there.

What about this one then? This one's a little bit different, a tally.

You might've seen tallies before when you've done pictograms. Tallies are little lines that we use when we're recording data.

And when we get to five, we put that diagonal line through it.

So we've got five, 10, 15, 16, 17, 18, we do have 18 there shown as a tally.

So that's quite a different way of representing it, but it does show 18.

So again, that one does represent six times three.

What else have we got? We've got this one down the bottom, which is repeated addition.

We've got three add three six times, we've got six lots of three.

So that one also represents 18.

And hopefully you can remember that multiplication is just repeated addition, but, as you can see there, it becomes quite long.

It becomes quite complicated to write out and there's room for us to make mistakes when we're writing out lots and lots of plus three plus three plus three.

So it's much quicker, more efficient for us to use a multiplication.

What else have we got here? We've got this one here as well with the smiley faces.

Now, it's in quite a strange shape and maybe one that we're not used to, but there are 18 smiley faces there, so that does represent six times three as well.

We then get onto this one, six add three.

Six add three is not the same as six times three, so that one does not represent six multiplied by three.

And then the last one, I wasn't quite sure about whether to put a cross by this one or not, I wonder what you thought? It is showing the three times tables, we've got three, six, nine, 12, etc.

And it does go up to six lots of three, but then it goes one further and it goes up to seven times three.

So I decided to split across by it, but I'll give you the benefit of the doubt and let you have that one if you decided not to put a cross.

Okay, so arrays, what are we talking about when we look at arrays? You've seen them before and they're a great way of showing what we mean by multiplication and division.

They're really simple to draw out and they're really simple to understand.

All we have to do is count our rows, and we've got five here, and then our columns, and then we can see that we've got our multiplication facts.

Five times by thee is 15.

Five equal groups of three means that I've got 15 dots in total on that array.

Here, we've got multiplication facts drawn from these next arrays.

We've got four lots of three.

And when I shift that array onto its side, I've got three lots of four.

What is the answer to four times by three or three times by four? Well, it's the same answer because that array is exactly the same.

It's got the same number of dots in it.

I just shifted it.

So four times by three, do you know? Is 12, let me just check.

I'm just going to check with my three times tables.

Three, six, nine, 12, yep.

And then with my four times tables, four, eight, 12, wonderful.

So there is an array showing multiplication.

And we know that we can shift the order of multiplication around in that four times three is the same as three times four.

What are we talking about when we do division then? Well, hopefully you could see, if we just go back to that multiplication, there are three numbers there which are being used, four, three and 12.

They have that relationship, four times three is 12, three times four is 12.

When we come onto division, we're using the same knowledge, the same numbers.

There is one number missing from these division questions, and it's the same number that we were using for the multiplication questions.

So this time, instead of starting with the parts, like we do with the multiplication question, because these are division, we're sharing out, we're starting with the whole.

So we're starting with the larger number and we're going to share it out.

So 12, the whole, the large number comes at the start of our division questions.

And then we share it.

So if we've got 12 and we're sharing it between three people or three groups, how many does each group get? The number missing here is four, we used 12, three and four in our multiplication questions, just in a different order.

So for 12 divided by three, it's still my three times tables that I'm thinking of.

How many threes are there in 12? I count in my three times table until I get to 12.

Three, six, nine, 12, there are four.

So division questions are multiplication questions, they use the same information, it's all about you understanding your multiplication, your times tables.

And then you can apply those to division questions.

Here again for the next missing one, I start with my whole, 12.

I've got four, what number is missing? It's three.

So when I divide 12 by four, how many fours are there in 12? Four, eight, 12 is my four times tables, there are three.

Okay, I'm going to give you the questions, and I just need you to think what is the missing number in this relationship? Now, that wasn't too hard, this is just a way of getting us to understand these relationships between multiplication and division.

So there's just the one missing number, it's the same number that comes up the whole time.

The three numbers come up through all of these.

So four times by three is 12, we have the parts and we're looking for the whole.

We've got four groups and there's three in each group.

The whole is 12.

And then for the division question and the multiplication question, we're using those same three numbers, it is our multiplication known facts that we're applying to division questions here.

Okay, here, we've got a similar thing, but instead of being in an array, it's on a bead string.

So how many groups have I got? I've got one, two, three groups of beads.

And how many is in each group? Well, I've got five in each group.

So I've got five times by three is 15.

Okay, I've got a division question here now though, something divided by three.

Well, I need the whole for a division question, we're going to start with the big number.

So 15 goes at the start, 15 divided by three, the missing number from my other question is five.

And now three times by something gives me, well, I've got a part, I times it by the other part to give me a whole, and this same number comes up here again for my inverse division question.

So hopefully this makes it clear that there is a very, very close relationship between division and multiplication.

Your turn then, pause the video here, have a good at the bead string and see if you can find the three numbers that are being used, the two parts and the whole, and then put them in the right order for multiplication and division.

Let's see how you got on.

So you were given one, there's three, there's three beads in each group.

How many groups are there? One, two, three, four, five.

There are five groups.

So hopefully you can see again that these are the same, this is the same facts that we used in the last question.

Five times by three is 15.

I'm hoping you will know that through your confidence with your five or your three times tables, hopefully both.

But look how many different ways you can apply that one fact.

For each of these, you can get two multiplication and two division questions out of them.

So that's a long way to go with one simple multiplication fact.

Okay, just a little different way of looking at it.

What's missing here? Three, something, four equals that array, have I multiplied or have I divided three to get that array at the end? Well, hopefully you can see that at the end, I've got a larger number.

I've got a large array at the end of that question, at the end of that calculation.

I've got the whole at the end of the question.

So three has got bigger.

Three has got bigger by a multiple of four, so it's three times by four.

Your turn, what's missing here? Well done, hopefully you can see, we have the whole at the start of this question.

We've got the large number, the large array at the start of the question.

It's then got smaller, so I must have divided it, so 12 divided by four gives me three.

Okay, so what we've been talking about this whole lesson are these fact families.

It's about being able to see two numbers and thinking about what the relationship between those two numbers is.

So I've got six and three here, what do you think the missing number might be with six and three? Now, there's a few correct answers, I suppose, because you might think that it's two, for example, two times three is six, or three times six is 18.

So they appear in different relationships.

Have a go at this one.

What do you think the missing number might be here? It could be three times three is nine.

And if you got that, that's great.

It could be, it could be that it was, let me think.

Nine, 18, 27, it could be three times nine is 27.

So that could be a missing number as well.

Okay, here, there could be a few different numbers that we could have, nine and 27.

Okay, so time to pause the video here and have a go at your independent task.

It's just practising the same things that we've been doing throughout the lesson, but come back when you've finished and we'll go through the answers together.

Well done, let's have a look through.

I'm hoping you found that independent task okay.

Let's look at how you got on.

So this was one of those questions where we're just thinking about what's happened to 10? Has it got bigger or smaller? Have we got the whole at the beginning or at the end of the question? So is it a multiplication or a division question being shown with these arrays? Well, 10 times by three gives me 30, and then, if you look at the stars, that number has got smaller, so we are dividing, okay.

Here on these questions at the bottom, you're just looking for that missing number in the fact family.

So what's happened to 27? I've divided it.

What have I divided 27 by if I've got three? I've divided it by nine.

So it's about seeing that relationship and knowing that 27 is in the three times table, how many threes makes 27? It's nine.

So just thinking about those relationships, about what times tables you already know.

What times by three equals 30? Well done if you could see that was 10.

Three times by something is 33.

Well done if you knew that was 11.

And for the last questions, something divided by three is seven.

What's the missing number? Well, you can use that inverse to help you because it's seven times by three.

Seven times by three, 21, so 21 divided by three is seven.

Here's this fact families again where you've been given the two numbers, what's the one that's missing.

So here they are, so we've got three and 10 gives us 30.

One and three gives us three, six and three gives us 18.

Nine and three gives us 27, we've got 12, four and three, we've got five to give us 15, so we've got 18, six and three, 21 for three and seven, three for eight and 24, and nine there for three and 27.

Well done, everybody, I would love to see your working out for today's lesson, so if there's any work you'd like to share with us, please ask a parent or carer to share it on Instagram, Facebook or Twitter, tagging @oaknational and #learnwithoak.

But before you go, please have a go at the final knowledge quiz and see how well you got on with today's learning.

Really great work, everybody, please enjoy the rest of your day, buh-bye.