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Hi, I'm Miss Kidd-Rossiter.

I'm your maths teacher from home.

And I'm going to be taking you through today's lesson on double number lines.

It's going to build on the work that we've already done on ratio.

Really excited to have you on board and to get started.

Before we get going, can you please check that your distraction free, you're in a nice quiet space if you're able to be and you've got something to work with, a pen and paper is ideal, but if not a pencil and exercise book, something along those lines would be great.

If you need to pause the video now to get prepared then please do, but if not, let's get going.

So for today's try this activity, we've got a double number line on the screen and you're told that the markings are equally spaced.

Your job is to figure out how many ways you could complete this double number line, using the number cards that you're given.

If you're confident with this, pause the video now and have a go this activity.

If you're a little bit unsure, just stay tuned and I'll give you a hint.

So, if you need a little bit of help, that's absolutely fine.

That's what I'm here for.

So let's have a think about a times table.

I'm going to go with the three times table.

This box here, would represent our first multiple of three.

So that is three.

The missing one here would be our second multiple of three.

Can you tell me what the second multiple of three is, please? Excellent, it's six.

And then the third box here would represent the third multiple of three, which is nine.

So I can fill that in.

Now we're going to think about a different times table.

So I'm going to go with the fours this time, on the bottom.

So this box here is my first multiple of four, which is four.

This box here, is my second multiple of four, which is eight.

And then I could continue if I wanted to.

So pause the video now and see if you can complete this number line in different ways.

Well done everyone with that try this activity.

We're not going to talk about it too much, because we're going to pull out the key features of a double number line, in the connect.

And you can see on your screen that you've got the same activity.

Can you tell me what you filled in on the top please? Excellent.

And what did you fill in on the bottom? Excellent.

Right, I'm going to give you one of my examples.

Obviously, there's loads of them that you could have come up with.

So I put in one here, three here, four here, and eight here.

What do we notice as we go across the number line? What do we notice as we go across the number line? Pause the video now and think about that.

Excellent.

It is multiples, isn't it? So for the top here, we've got the multiples of one.

Brilliant.

On the bottom, we're still increasing by multiples, but of a different number this time, what are the multiples of this time? Four brilliant.

So we got our first multiple four.

Our second multiple of four.

So you can clearly see that we've got something happening as we go across the number line.

What about though, from here, to here? So from the top of the number line to the bottom of the number line.

Well, to see this a bit better, we might need to fill in the missing numbers.

So this one here, and this one here.

Pause the video now and tell me what you think those missing numbers are.

What did you get for this one? Two? Excellent.

And what did you get for this one? 12.

Excellent.

Now I know that we didn't have a number card with 12 but we're just going to put it there to help us out with this explanation.

So what do we notice about here from one to four? How would we go from one to four? We could add three, couldn't we? So that's an option.

What else could we do? We could multiply by four, couldn't we? Is there any other way? Not sure.

Let us see then.

What about from here to here? How could we get from two to eight? We could add six, couldn't we? Or we could multiply by four.

Interesting.

Are you spotting a pattern? What about here going from three to 12.

Well I could add nine couldn't I? Or I could multiply by four.

So again, I've got a pattern here.

So if we think about these multiplications to go from the top to the bottom, on each one of these, we're multiplying by four.

And this is what's known as a constant of proportionality, so whatever we have on the top of the number line, in this case, we can multiply it by four to get what goes on the bottom of the number line.

So this time, I'm going to have my multiples of two on the top.

So I'm going to have two, four, six.

And I'm going to have my multiples of three on the bottom.

So three, six, nine and so on.

What do I multiply two by to get three? What would I multiply four by to get six? What would I multiply six by to get nine? Pause the video now think about that.

Excellent.

It's 1.

5 isn't it? So this time our constant of proportionality is 1.

5.

Well done, this also helps us if we were given a broken number line.

So let's have a look at one more example together.

So this time, I'm going to have my multiples of three on the top, so three, six, nine and it could continue.

And I'm going to have my multiples of four on the bottom four, eight, 12.

And it could continue.

Pause the video now and work out the constant of proportionality please.

Well done.

This time, it's four over three, so we're going to write it as a fraction.

So this time, our constant of proportionality is four over three.

And this is the same going from any number on the top to any number on the bottom.

So if we've had a broken number line here, we've broken our number line.

We don't know how many equally spaced gaps there's been in between.

And then we're told that 45 is here.

How could we use our constant of proportionality to find the missing number at the bottom? Excellent, we just times don't we by our constant of proportionality.

So we multiply by four thirds.

And this time we get 60.

So hopefully you've understood those double number lines.

We're now going to apply what you've learned to the independent task.

So pause the video now, navigate to the independent task, and then come back when you're ready to go through some answers.

Well done for giving that independent task a go.

There was some quite tricky questions in there.

So I'm sure you've done a really good job of them.

So given the start of these double number lines, what numbers would appear on the top and on the bottom? So what are we looking for here? Well, we know that going along the top are multiples of four.

And going along the bottom are multiples of five.

So we're looking for numbers that are both multiples of four and multiples of five.

So we're looking for common multiples.

What's the first common multiple of four and five? 20.

Brilliant.

So 20 would appear on both.

What about the next one? Excellent.

40 is the next common multiple.

We see a pattern here.

What's our next common multiple of four and five? 60.

Excellent.

So now we can know that any number that's in the 20 times table, so any number that's a multiple of 20 will appear both on the top and the bottom of the number line.

What about for seven and eight? What's our lowest common multiple of seven and eight? Excellent, it's 56.

So 56 is our first common multiple.

So we know that any multiple of 56 will appear on both the top and the bottom of our number line.

So well done if you made those generalisations.

We'll see here that I've given you the answers already.

So if you need to pause the video and check your work.

Excellent.

Here are some more answers.

So for question three, I've given you some of the answers already.

For the second one, let's do this together.

We know that two spaces on our bottom number line give us 9.

6.

So that means that one space must be half of 9.

6, which is 4.

8.

So we've got the multiples of 4.

8 on the bottom of our number line.

On the top, then we've got the multiples of four, haven't we? So four, eight, 12.

And that's how we figured it out.

What would our constant of proportionality be here, from four to 4.

8? Excellent, it's 1.

2.

Well done.

And moving on to the Explore part of the lesson now.

You've got a part of an number line here with equally spaced markings.

Each Mark denotes an integer.

So that's a whole number value.

How many ways can you fill the boxes? Pause the video now and have a go at this task.

If you're struggling, one way that you could fill in this box here is 24.

So what are we increasing by from 24 to 36? Well, we're increasing by 12.

Well done.

And what's our constant of proportionality? What's our constant of proportionality here? Two.

Well done.

So that means to get from 36 to our missing box here, we will be multiplying by two.

So this box here would be 72.

That's one way of doing it.

Pause the video now and have another go.

Excellent work.

Well done.

So we've gone through one answer that you could have had.

There are two other answers that you could have got.

Can you tell me what they were? You could have had 27 and 64 here.

Or you could have had 32 and 54.

That's the end of today's lesson.

So thank you so much for all your hard work on double number lines.

I hope you've enjoyed the lesson.

Don't forget to go and do the quiz now to show me what you've learned.

And hopefully I'll see you again soon.

Bye.