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Hi everyone.

It's Mr. Whitehead here for your math lesson.

What do you think of the setup behind me? Does it look good? So this lesson is called flag pole.

In case you hadn't noticed, that's not a flag pole.

That is a broom from my kitchen.

However, it is helping me to hang some bunting along the back of the room.

This is lesson 15 of 15.

Maybe you are joining for the first time, but maybe you have been here for more than just the one.

Lesson 15 of 15 is quite an accomplishment.

So the bunting is up.

Now turn into link to the flag pole problem.

We'll look at in this lesson, but also to celebrate all of the learning that's happened across this unit.

If you are free of distractions and in a quiet space, then you are ready for us to start.

But if you need to press pause and take a moment to find somewhere to work where you will be able to give me your undivided attention for the next 20 minutes, then please press pause now and start again when you're ready.

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

We're going to start off with a time durations activity before we spend time exploring the problem, responding to the problem, leaving you ready to independently solve the problem at the end of the session.

Some things you're going to need, a pen or pencil.

Something to write on, a pad or book or piece of paper and a ruler.

Press pause, if you need to go and collect those things, then come back when you're ready to start.

So time duration activity.

Three problems for you to read and respond to.

Some of them you are looking for a time duration as the solution.

Some of them you're using the time duration to find an end time.

Press pause, complete this task and come back when you're ready to look at the solutions.

Okay, let's take a look.

Now I know I said ready to look at the solutions, but really I want you to focus on the process that's been taken to reach those solutions.

First of all, hold up your paper.

Let me see the solutions.

Let me see any mathematical thinking that you have shown on your paper to give me an idea as to how you reach that solution.

Hold them up, hold them steady.

Okay, good.

Now those, the process you've taken compare it to what I described now.

The first one.

So one thing that I noticed if the start time is 14:25, the end time is almost three hours later.

It's one minute away from 17:25.

So I added on three hours.

The journey time is three hours minus one hour, because 17:25 is one minute later than the journey actually ends.

So three hours subtracts one minute, two hours 59 minutes.

How did that compare to the process you took? We may have reached the same solution, but what were our journeys like for getting there.

Second one.

Film starts at 17:05 and lasts an hour and 45 minutes.

Tell me what time it ended? Okay.

And let's see how I approached it.

Compare it to yours.

17:05 I added an hour on an hour of the film.

18:05 45 minutes still to add on.

From 18:05 adding 45 minutes brings us to 18:50.

10 to seven is when the film ends.

Again, compare the approaches.

Were they the same? Did you do something slightly different? Perhaps you added on two hours and subtracted 15.

Let's look at the last one.

Jenny goes for a walk at two o'clock, 14:00 hours, for 98 minutes.

At what time does she finish her walk? Tell me the time she finishes her walk.

Good.

And let's see how we get there.

Two o'clock, 14:00 hours.

I added on 60 of those 98 minutes to get to three o'clock.

I know I still have 38 minutes to add on, because 60 and 38 is 98.

So from three o'clock, 38 minutes later, 3:38, 15:38, 22 minutes to four.

Comparing those solutions.

Did anyone solve the last one in a different way? Brilliant! And we just compare the efficiency of these journeys taken.

The connections that have been made to reach that same solution.

Let's take a look at the problem that we're focusing on for this session.

Flag pole.

Let's give the problem a read.

This is the problem that we're going to focus on for this session.

Some of you may recognise it from a previous session, but look out for the difference.

Let's read it together.

Ryan is building a flag pole which is two and a half metres long.

If he has a choice of using one metre, half metre, and quarter metre sticks, how many different ways can he make the flag pole? Ryan's flag pole is not a broom like mine is.

By the end of the session, you will have solved this problem telling me how many different ways there are to solve it with those metre sticks, half metre sticks, quarter metre sticks on offer.

But let's break this down and build up to that slowly.

Some questions.

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

One, two, three to build a flag pole.

Good.

Tell me what are the lengths of sticks that Ryan has? Tell me on three.

One, two, three.

He has half metre sticks, quarter metre sticks, and one metre sticks.

Good.

How long does the flag pole needs to be? Tell me on three.

One, two, three.

It has to be two and a half metres long.

I've got a question here that you can pause on.

If Ryan uses one metre length, how many different ways can we make the flag pole using the half and the quarter metres that are available? Press pause and give this problem a go, come back, when you're ready to share.

Are you ready to take a look? So there's a rule here.

One metre, one one metre stick has to be used, but the total length of two and a half metres needs to be made up using the other two options the half and the quarter metre.

So how many options are there? How many possible ways are there for Ryan to complete his flag pole? Just show me with your fingers.

Okay.

That's what you found.

And I wonder how you found that.

I wonder how you approached this problem.

Randomly trying different approaches or perhaps being more systematic, making it's one way and then making a slight change for the next way and the next way.

Look at this systematic approach that I've taken here.

So one metre and the rest of the flag pole could be made up of three half metre sticks.

That's two and a half metres in total.

Didn't use any quarter metres.

My slight change now must still include a one metre stick.

I'm going to keep two of the half metre sticks and then change one of the half metres for two quarter metres.

What would the next one be? Now, anyone that was part of the previous lesson has worked on this part of the problem already.

So I hope is thinking already more systematically and can tell me what my next guess is going to be.

You tell me what it will be.

Definitely a one metre.

Good.

A half metre and then the rest quarter metres.

Are there any more options? Of course, there's a change I can still make.

Notice, look, we've gone from three half metres to two half metres to one half metre.

There must be another option.

No half metres, all quarter metres.

Now have we found all the possibilities? There isn't anything else we can change.

We've used all the options.

There are four ways to solve this problem.

Now you told me earlier how many ways there were that you had found, but we've really talked through there the approach to solving the problem, the systematic approach.

And if you'd seen this part of the problem previously, I hope that your systematic working has progressed from last time.

Now, I think you're ready to have a go at the rest of the problem independently.

So we just had this rule of you must have a one metre stick, but of course, for the main problem the only rules are that it must total two and a half metres.

And you are hunting for all of the possible ways of building that flag pole.

I recommend a systematic approach like I've just shown you.

Important for us to consider how to record our results and organise our thinking.

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

Really simple.

One metre, half metre, quarter metre, and underneath that how many of each we're using.

I've started it off with the solutions that we came up.

Some of the solutions that we came up with from our little go into it together, but there are some missing there, but do you notice one thing changes, one thing stays the same? Slight changes as you move through.

The table here can really help you keep a track of your systematic approach.

Press pause, have a go at solving the problem and come back when you have found all of the solutions for how to build this flag pole and importantly, how do you know you have found them all.

So how did you get on? How many solutions did you find? Tell me the number.

There's a lot of solutions here.

Lots of possible ways of building this flag pole.

Now, fantastic that you've reached a solution.

You found the total number of solutions, but as always, it's the process you've taken, the steps you've followed, the thinking, the decisions that's most important.

Let me show you the table completed with all of the options for building the flag pole.

And I want you to look and notice how have I been systematic.

How does this help me to say, yes, I have found them all.

Look at the top.

Starting with two metres.

Two one metre sticks means I can then complete the flag pole with zero half metres and two quarter metres or one half metre and zero quarter metres.

They're the only options, if I've got two metre sticks.

Then I make a change.

I'm going to use one one metre stick and keep that the same while I change my half metres and quarter metres.

And look at the patterns in the numbers, three, two, one, zero, zero, two, four, six.

As I reduced the number of half metres by one, I increased the number of quarter metres by two.

The same when I make the change to zero metre sticks.

Look at that pattern starting with all half metres at five.

Then as I reduced by one half metre, how does my quarter metre change? It increases by two.

Really supporting a systematic approach to finding all the possibilities and knowing when all have been found.

How does this compare to your table? Can I take a look? Hold your table up or however you've been recording your results.

How did that help you to know you had found all the possible ways of solving the problem? Is there anything you would change based on how I've shown you and talked you through my approach? Slightly more systematic working, looking for patterns, connections.

Good.

I hope you've enjoyed the session and solving the flag pole problem.

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

Thank you so much for joining me for lesson 15 of 15 in this money and measures problem solving unit.

I don't know about you, but I do quite like the bunting and my broom handle flag pole up behind me.

I might leave it there for a little while longer before taking it down just to enjoy the celebrations of completing this unit a little bit further.

As I said, some of you may only have joined for this one session and, of course, you've been very welcomed, just as welcome as anyone that's been here for a little longer.

With whatever you have lined up for the rest of the day, I hope you enjoy it and complete it with a smile.

I look forward to seeing you again soon for some more math learning.

Take care.

Bye.