Lesson video

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Yeah, I'm not quite ready for this maths lesson yet.

I'm a bit tangled up with bunting.

This maths lesson, it's about a flagpole problem, where there's a young boy, who's trying to build a flag pole, perhaps to either hang a flag from one maybe to raise some bunting.

I wanted to show you what bunting was.

And I got a bit caught up.

I think it's best that you press pause, so that I can press pause and cut myself free of this bunting and perhaps at the same time, if you've got any distractions around you, you can move away from them, so that you're able to focus on your learning, with a flagpole problem for the next 20 minutes.

Yeah if you could just press pause and I'll be right back.

In this lesson, we will be planning and solving a fraction problem.

We will start off with a quick activity, looking at time durations.

Then we will spend some time both exploring and responding to the problem, which I will leave you to solve for your independent task.

The things that your need for the lesson, are here on the screen, a pen or pencil, a ruler, and something to write onto, a pad, a book or piece of paper.

Press pause, while you collect the items, then come back and we will start.

Okay, a time durations start activity.

Three problems. I'd like you to pause, give them a read, find the missing time durations or end points, then come back and we will review the solutions.

Are you ready to take a look? Okay first one.

A train leaves at 15:35 and arrives at 16:14.

How long was the journey? Could you tell me please, how long the journey was? From you're working out, you've already had a go at it.

How long? Okay, let's have a look at the process taken then.

Compare, how I approached the problem, to how you approached it.

So I thought about the start time being 15:35 and I wanted to work to the next o'clock.

I added on 25 minutes.

I reached 16:00, four o'clock from there, I know that I need another 14 minutes.

I added on 14 minutes to reach 16:14, 14 minutes past four.

I then totaled the 25 and 14 minutes, to reach 39 minutes.

That is the difference, between the starting time and the ending time of the journey, 39 minutes.

How did that compare to your approach? Similar, different? Remember that's where the learning is happening and the reasons for the choices we make there, are really important to reflect upon.

Second one.

A film starts at 18:05, five past six, lasts an hour and 37 minutes.

What time did the film end? Can you tell me what time the film ended? Okay, so again let's compare approaches.

So starting at five past six, 18:05, I added on the hour.

I know the film lasts an hour and 37.

So I added the hour on and reached five past seven, 19:05.

I still need to add on 37 minutes, of the film's duration.

So I did that on to reach 19:42, 18 minutes to eight o'clock.

The film ends at 19:42.

How did that compare to your approach? Again was it similar or different? And if it's different, why did you make those choices? What were you thinking about, while you were solving the problem? Third one.

What time does Isla finish her walk? Okay, let's compare the approaches we've taken.

So I know that 113 minutes, is made up of 60 minutes, that's an hour.

So I added that on first, quarter past two, 14:15 add on 60 minutes, 15:15 quarter past three.

Now I know that I've still got, 53 minutes to add on 60 add 53, is 113 minutes.

So, from quarter past three, 15:15, I worked to the next o'clock by adding 45 minutes and reached 16:00 four o'clock.

So I've not yet added on, 113 minutes in total.

I know there are still eight minutes left, from the 45 to the 53 that once combined with 60 makes 113.

So from four o'clock 16:00 plus eight minutes, I reached the end of her walk's time, 16:08.

I wonder if anyone approached that differently.

So yes, she finishes the walk at 16:08.

Anyone approached it differently? Did anyone do this? Recognising that 113 minutes, is only seven minutes away from two hours, 120 minutes.

So you could add on two hours, quarter past two, quarter past four, 14:15 to 16:15, but because you've increased by too much, seven minutes too much.

You then subtract seven minutes from 16:15 to reach 16:08.

The same answer.

I only thought about that approach after completing it the first time and realised actually that's probably more efficient, smarter.

So there was some learning there for me, when it comes to efficient approaches to solving problems. Let's have a look at the problem we're going to be focusing on for this session.

I am free of my bunting and able to focus on this flagpole problem.

Could you together read with me please? On three, one, two, three.

Ryan is building a flagpole, which is two and a half metres long.

He has a choice of using one metre sticks, half metre sticks and quarter metre sticks.

Some questions for you.

What is Ryan's task? Tell me on three, one, two, three.

To build a flagpole, good.

Next question.

What are the lengths of sticks that Ryan has? Have a scan.

Tell me on three, one, two, three.

One metre, half metre, quarter metre sticks.

They are the sticks he can choose from.

And how long does the flagpole need to be, that he's building with those sticks? Tell me on three, one, two, three.

Tell me, good.

Two and a half metres long.

Here's a point where I'd like you to pause.

If Ryan uses two, one metre lengths, how many different ways can he make the flagpole? Think about what you know, what you don't know and what skills you have for finding the unknown.

Press pause and come back when you're ready with a solution.

Or two or more, how many solutions will there be? Press pause, come back in a moment.

To take a look.

So we know that he is using two, one metre lengths.

We don't know, what the other lengths are, but we do know the total must be two and a half metres.

So with two metre lengths, that's two metres.

We need to reach two and a half metres, well, what could he have used here? He could have used a half metre, two and a half metres.

Is that the only solution? You have more? Hold up your paper, let me see what else you have.

Of course yes.

So another solution, he has to have two metre sticks, but the half metre could be made of two half metres, fantastic.

Is that the final solution? How do you know it is? It's important, how do we know there aren't any other solutions? There aren't any more we can try? We have to keep those two metres sticks.

The only choice is to make the half metre, or with a half metre stick, or a quarter metre stick two of them.

So we've used, all of the options available.

There are two possible ways.

Next question.

If Ryan uses one metre, how many different ways, can we make the flagpole? So previously the rule was he has to use two metre sticks.

Now, what if he's only using one metre stick, only has to use one metre stick.

How else could the flagpole be built? One metre stick.

What's going to be missing, to make two and a half metres? How could we record our results here? For the last problem, we had two possible ways.

I'd like you to find all the possible ways, for this problem as well.

So how could you record your results? I've got a table to suggest to you.

One metre, half metre, quarter metre and then the box is underneath.

How many, for each of your possible ways, there are of each of those lengths? I've started you off, by filling in one for one metre because you have to have one metre.

But I'm curious about how you will make up, the other metre and a half, using the choices available? Press pause, because that final question, is your independent task for this session.

Complete the task, find all the possible ways of building the flagpole, then come back and share your solutions with me.

Are you ready to take a look? First of all, hold up your paper, let me see all of your mathematical thinking and your reasoning and how you've approached this problem.

Looking so good everyone, really good job well done.

So how many solutions? Hold them up again, let me see if I can count, how many solutions you've come up with.

Okay, just to be sure, hold it up on your fingers for me.

How many solutions? Okay, let's take a look shall we? So using one metre, how many different ways can we make the flagpole, of two and a half metres? One metre? I approached it this way and started off with, three, half metres.

Three, half metres is a metre and a half.

Plus the two and a half metres in total.

Then I thought right, let me keep some things the same and make one change.

So I kept two of the half metres and changed one of the half metres, for two quarter metres.

Two and a half metres in total.

Another way.

Keeping something the same and changing something else.

What might my next length choices be? Definitely one metre, keeping one half metre the same and changing the other half to two quarters as well.

So now I've got my full length made up of one metre, one half, four quarters.

Have I reached all of the solutions yet? There's a change I could make.

What is that? Yes, keep one metre, change the final half into two quarters.

Along with the other quarters, I now have one metre with two, four, six quarters, which is equal to a metre and a half.

Are these all the solutions? You found four? How do we know there aren't anymore? We're not allowed to change the metre stick.

We've used all of our possibilities.

And as we look at it laid out like this, or like this, we can notice patterns, that help us to say yes we found all the possibilities.

We've reduced the half metres by one, until we haven't used any and we've increased the quarter metres from zero, to six, until we can't use anymore.

How did you find this session? Did you enjoy solving the flagpole problem? I'm glad you enjoyed it, now while you were enjoying it, you need to be reflecting on, what you were thinking, what you were doing and why? That's the learning that was happening.

What you see in front of you now, is the process of that learning.

The answer, there are four solutions, is just that the answer, but everything you were doing on your way to that answer, is what we need to celebrate.

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

Thank you so much for joining me for that lesson, I hope you enjoyed it and that you're fully set up and ready to approach any further problems, that you might have today, in any more of your learning.

Now, I still have a problem.

The bunting didn't make it very far, I managed to get it off of the top half, that you can see, but it was still wrapped around my ankles.

So I'm going to go and complete that problem and get the bunting off, once and for all.

Enjoy whatever you're doing next.

And I look forward to seeing you for some more maths learning very soon.