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Hi.

Have you ever received a gift before that perhaps came in a really large box that you then found yourself spending more time with than the actual gift? Perhaps a parent or carer has complained about the money they've spent on the gift when actually all you're interested in is the box that it came in.

Now, as an adult, I'm no longer playing with the boxes that any gifts I receive come in, however, when those gifts are wrapped with ribbon, my eyes are caught, my attention is drawn.

And I end up keeping that ribbon, perhaps so that maybe one day I'm able to reuse it on a gift that I'm giving to somebody else.

And I have a piece of ribbon here, wrapped quite neatly at the moment.

And this lesson is all about ribbons.

And just look at the length of this one.

It is a really long ribbon, which comes in really handy as the problem that we're about to look at in this lesson is all about really long ribbon.

If you're not in a quiet space at the moment, or there are any distractions around you, can you press pause, take yourself off somewhere else where you will be able to focus and give me your full attention for the next 20 minutes.

Press pause, go and get yourself sorted and press play again when you're ready to start.

In this lesson, we are developing strategies for planning and solving problems. We'll start off with a measurement matching activity before we spend some time exploring the problem, responding to the problem and then in the independent task, solving the problem.

The things that you're going to need: a pen or pencil, a ruler and some paper or a book if your school's provided you with one.

Press pause, go and collect those items and come back and we will start.

Let's get going then.

Here's the matching activity.

Match the equivalent lengths.

One has been completed for you.

500 centimetres is equal to five metres.

The helpful hint, one metre is equal to 100 centimetres.

100 centimetres is equal to one metre.

Can you say both of those for me, starting with one metre? On three, one, two, three.

Good, and the other one.

Excellent, keep that in your mind.

Visualise a metre stick.

Visualise just over three lots of 30-centimeter rulers.

That's how long a metre stick is.

Keep the 30-centimeter ruler in your mind as well just to help you make sense of those equivalent measurements that you're matching up.

Press pause.

Connect the rest of the measurements, come back and we will check.

Shall we take a look? Can you hold up your paper? I'm curious to see how you've laid your work out here.

Hold it up, let me have a look.

Good, okay, so there are some different approaches.

Some writing them side by side, some have tried copying what's on the screen and drawing lines between as well.

Looking really good.

Let's see which of those have been correctly matched.

So keeping that metre in mind.

That's a 30-centimeter ruler in mind visually to help us make sense.

Here's our first correct one then.

1/4 of a metre, 25 centimetres.

Nice connection there to 0.

25.

The equivalent decimal of the fraction 1/4.

Next, 1/2 and 50.

1/2 a metre and 50 centimetres.

Again, connection to the decimal equivalent to the fraction 1/2.

Which decimal is it? 0.

5.

5/10, 50/100.

Well done.

Next, one metre, 100 centimetres.

And 10 centimetres, 0.

1 metres.

0.

1 as a fraction? Good, 1/10.

10 centimetres is 1/10 of a metre.

1/10, 10/100, 0.

1.

Next.

Three metres, 300 centimetres.

0.

5 metres, ah ha, we mentioned that, didn't we? Ribbons.

Let's have a read of the problem together.

Mr. Matthews sold 12 green ribbons and blue ribbons all together.

The total length of the ribbons sold was 12 metres.

Each green ribbon was 80 centimetres long, and each blue ribbon was 1.

4 metres long.

How many green ribbons were sold? How many blue ribbons were sold? Those two questions you will have answered by the end of the session and during the independent task.

Let's slow things down and build our understanding of this problem.

A few questions that we should be able to answer, just using the sentences that are there.

Here's the first question.

How many ribbons has Mr. Matthews sold? Have a quick scan.

And tell me on three.

One, two, three.

Good.

He has sold 12 ribbons all together.

Some blue, some green.

Next question.

How many different colours of ribbon has he sold? Now, this might be a fairly quick answer but give a quick scan to double check the sentences and tell me on three.

One, two, three.

Good, say it again, how many? Because some of you were saying the colours as well.

So tell me the number.

Good, two.

You can tell me the colours now if you want as well, of course.

There we are.

Green and blue.

Not 12, that's the number of ribbons sold.

Of course, the number of colours, the different colours on choice, on offer, two.

How long is each green ribbon? Quick scan.

Ready to tell me? One, two, three.

Good, 80 centimetres long.

How could we say that in metres? It's 80/100, 8/10.

Tell me as a decimal.

0.

8 metres.

Good.

And how long is each blue ribbon? Have a quick scan.

Get ready to tell me on three.

One, two, three.

Good, 1.

4 metres.

Can you tell me that in centimetres? Good, 140 centimetres.

What is the total length of all the ribbons sold? Have a scan.

Tell me on three.

One, two, three.

12 metres.

The total length of all ribbons sold was 12 metres.

If Mr. Matthews had sold one blue ribbon and one green ribbon, what would the total length of the two ribbons be? For this one, I'd like you to pause.

There's going to be a little bit more thinking needed.

So press pause and think about how you could represent your thinking and your solution as you answer this problem.

Come back when you're ready.

Shall we take a look? Can you hold your paper up? Let me see how you've represented the maths or your findings related to this part of the problem.

Looking good, really smart, well done.

Look, I say smart, looking efficient in how you've been representing your thinking.

So tell me then, what will the length be? Okay, and we could or we will have pulled this part of the problem out to help us answer.

So we identify green, 80 centimetres, blue, 1.

4 metres.

And then in terms of what we do next, there are a few options.

We need to combine the two.

If we combine 80 and 1.

4 and say 81.

4, we've missed something.

Of course, they are in different units.

80 centimetres, 1.

4 metres.

Always helpful to work in the same unit.

So we could work with 80 and 140, 220 centimetres or we could work with 0.

8, 1.

4, 2.

4 metres.

Either of those final answers is correct.

They are equivalent, of course, but helpful.

In measurement problems, work in the same unit.

And if you are given different units in the problem, make a conversion first.

Next question.

If Mr. Matthews had sold one blue ribbon and two green ribbons, what would be the total length of the three ribbons be? What do you notice has changed in this problem, in this question, compared to the previous question? Last time we had one of each.

This time, we've still got one blue but we've got one more green.

That might influence how you answer this question.

As you press pause, find a solution for me.

Maybe make some connections to the last question you answered.

Come back when you're ready to share.

Let's take a look.

So again, this part of the problem is going to help us, the information with the lengths of each ribbon.

Hold up your paper, let me see how you approached it.

Nice, good, I can see someone that has connected to the question before and I can see lots of you as well who have kind of started from scratch as such.

You've taken the information about the lengths of each ribbon and combined enough to represent one blue and two green.

Like this, for example.

80 and 80 for the two green.

And 1.

4 or 140, converting to the same units.

Centimetres, 300 centimetres or keeping them all in metres.

Two lots of 0.

8 and 1.

4.

Three metres.

Now imagine Mr. Matthews sold six green ribbons and six blue ribbons.

What would the total length of the 12 ribbons be? Press pause, have a go at solving this part of the problem.

Then come back and we'll take a look.

Let's have a look.

Can you hold up your paper for me? Let me see how you've been recording your mathematical thinking and your solutions.

Well, this is interesting.

Look, hold that steady because as I compare the last few questions, I'm noticing some of you are continuing to organise your work in the same way but some of you are changing.

And perhaps becoming a little bit more organised and systematic in your approach.

Really good to see and that will be really important for what comes next.

But first, let's review the question.

So we're still using this part of the main problem, the description of this ribbon's situation.

Each green, 80 centimetres.

Each blue, 1.

4 metres.

We need six of each.

Six lots of 80.

Six lots of 1.

4.

Perhaps six lots of 0.

8 and six lots of 140, depending on any conversions you've used.

So I've represented 80 centimetres six times using eight multiplied by six is 48, so 80 multiplied by six is 480.

Then I've kept 1.

4 as it was.

1.

4 six times, six lots of 1.

4.

Well, one six times is six.

The one from 1.

4.

Then the 0.

4 multiplied by six, well, I'm using four times six to help me.

Four six is 24.

So 0.

4 multiplied by six, 2.

4.

Six add 2.

4 is 8.

4 metres.

So I've got my two lengths, totals.

480 centimetres of, which colour was that? That was green, and 8.

4 metres of blue but we need to give the total length.

So now combining.

I can't combine 480 and 8.

4.

488.

4 would not be correct.

Let's get the units the same.

So 480 add 840.

Well, that's 1,320 metres, centimetres, sorry.

Did anyone answer by combining in metres, with metres as your unit? And what did you get? And is that equivalent to 1,320 centimetres? Yes, yes, it is.

4.

8 add 8.

4 is equal to 13.

2 metres.

Would anyone improve my recording there in any way? How would you improve it? Yes.

On that second line, 480 add 840, 1,320 centimetres.

I could out in there, edit it to improve it, is equal to if I'm using words, is equal to 1,320 centimetres.

Really good spot.

Always important to look out for any ways to edit and improve in maths, just the same as in English.

So we just tried six of each.

Six green, six blue.

13.

2 metres, 1,320 centimetres in total.

But in this problem, we are looking for a total of 12 metres or how many centimetres? 1,200.

So six of each gave us too much or too little? Too much, sorry, too much.

So which combination of green and blue, how many of each might you try next? And why? Really important to think about that because it's what you're going to do.

But a question, I commented on this when you held your work up.

How could we organise our results.

We tried six and six.

It was too much.

We're going to try another amount now.

It might also be too much.

It might be too little.

But we're going to keep on trying different amounts of green and blue until we make 12 metres in total.

So I'm just thinking our organisation here is really important to help us keep track of what we've tried, what we might try next and why we might try that next.

Important that we'll be able to see any patterns as we make changes to the number of green and blue ribbons that we try.

So here's a table that I suggest you use.

A table that allows you to record the number of green ribbons and the length, the number of blue ribbons and the length.

The total length of green and blue.

And then is it too long or too short? You can see there for our six of each, the recording.

I might try next five green and six blue.

Then I'll fill the table in.

And identify whether or not I've got too much or not enough.

Press pause.

Have a go at completing the activity.

I'm really interested to see the approach you take and of course, what the solution is because there is one.

There is a number of green and a number of blue that will total 12 metres.

Press pause and come back once you've found your solutions.

How did you get on? Frustrating? Did you make it? Often, solving problems like this does get me feeling a little bit agitated.

When I know there is a solution, I feel better because at least I know I'm working towards one and there will be that final puzzle piece to find.

Although sometimes in maths, there isn't a solution.

But I hope because you knew there was one, you persevered, continued and reached a solution in the end.

So I continued to use the table.

I said I was going to try different combinations of five and five, five and six, six and five, all either too long or too short.

Eventually, there were a few more to try after this one before I reached the solution.

But eight green and four blue totaled 1,200 centimetres, 12 metres.

So the solution was there in the end.

Just hold up your work for me.

Let me compare my table here.

Although this is shorter than it really was, of course.

But let me see how you got on.

Did you maintain a systematic approach and organised approach to your work? Looking good, everyone, well done.

Thank you so much for joining me for the lesson, all about ribbons.

I hope that you're feeling like you've achieved something, having solved the problem about the green and blue ribbons by the end.

If you would like to share any of your learning from this session with Oak National, please ask a parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you so much for joining me for this maths lesson, everyone.

I hope you enjoyed it as much as I did.

If you've got anymore learning lined up for the day, then approach it with that same confidence and resilience that you have shown throughout this maths lesson.

I look forward to seeing you again soon for some more maths but first, I need to get this ribbon rolled up again and put away.

Thanks again and see you soon.

Bye.