Lesson video

Hi, how are you? Good.

I'm feeling really good as well actually, and I'm not sure why I'm in such a good mood.

I think it might have something to do with good weather.

As I look outside right now, there is a blue sky, the sun is shining, and I think, after this lesson has finished, we're going to go and either sit outside for a little while or take a walk as this weather is just far too good not to spend some time in it.

But first, the math lesson.

If you are in a quiet space, free of distractions, then you are ready for the lesson.

If you're not yet, then please press pause and take yourself away somewhere that is quiet and distraction-free, somewhere that you will be able to focus on you and your learning for the next 20 minutes.

Press pause, go and get yourself sorted, come back, and we will start the lesson.

In this lesson, we are developing strategies for both planning and solving problems. We'll start off with match the fractions activity before we spent time exploring the problem for this lesson, responding to the problem for this lesson, and then we will finish up with you independently solving the problem.

Things that you're going to need, a pen or pencil, a ruler, and some paper, or pad, or book.

If you have it, 15 pennies.

Not 15p, but 15 pennies, which of course is 15p, but what I mean is that that 15p must be made up of 15 individual pennies.

Now if you haven't got 15 individual pennies, then just collect 15 items. Hopefully items that are the same or a similar size.

So, for example, 15 pieces of Lego, 15 toy figures, 15 stones.

Press pause, go collect those items. If you're struggling with the 15 pennies or the 15 items, don't worry.

You can perhaps collect some scissors or ask an adult to help you with that, and just cut out or even tear out from some scrap paper 15 small pieces of paper, roll them up into little balls, and then you've got 15 items. Press pause, go and get yourself sorted, and enjoy hunting down and collecting whatever it is that you get for those 15 pennies, then come back and we'll start.

Let's get going then.

A match the fractions activity.

On the screen right now are a series of fractions, and some of them are equivalent.

There will be pairs of equivalent fractions.

Press pause, find those equivalent pairs of fractions, then come back and we will reveal the solutions.

Shall we take a look then? Okay.

So, first of all, a fraction equivalent to 1/2, what did you get? Good, 3/6.

What did you get for 9/12? For 1/5? Good, 2/10.

For 1/4? 2/8.

And finally, 2/5? Good, 4/10.

How would you say 4/10 as a decimal? 0.

4.

How would you say 2/10 as a decimal? Good, 0.

2.

How about 3/4? 0.

75.

And 1/2? 0.

5, good.

Shall we have a look at the problem for this lesson now? Money bags.

Can we give it a read together? One, two, three.

Louise had 15 pennies, which she divided between four bags.

She could then pay any sum of money from 1p to 15p without opening the bags.

How many pennies did Louise put in each of bag? That question in bold at the end is the one you'll be answering through the independent task later on.

Let's break the problem down though and really get to understand it to support you of achieving that later.

So first of all, how many pennies does Louise have in total? Have a quick scan, call out on three.

One, two, three.

Good, Louise had 15 pennies.

Next question.

How many bags is she putting the 15 pennies into? Have a quick scan, tell me on three.

One, two, three.

Good, four bags.

She is dividing those 15 pennies between four bags.

What different amounts of money can she make without opening any bags? So what are we told in the problem? One, two, three.

Good.

Any sum from 1p to 15p.

So that's 1p, 2p, 3p, all the way up to 15p.

She'll be able to make those totals, those sums, using the money bags that she creates.

What coins would you need to make 1p? 1p, it's as simple as that.

How about 2p? Ah, you could use a 2p coin.

But in this problem, which coins is Louise using? Pennies, so how would she make 2p using pennies? Yeah, two of them, 2p.

So with a bag that's holding 1p and a bag that's holding 2p, does that help Louise to make 3p? Well, of course, yeah.

1p and 2p is 3p.

So she's made the sum 3p, and there they are.

A question for you to pause on now.

If Louise put 1p in one bag, 5p in another bag, and 6p in a third bag, what different amounts would she be able to make? Press pause.

Here's a good opportunity to have those coins ready.

So were going to need 12 penny coins or items that you've chosen to represent the coins, and have a play with them.

Represent the 1p, 5p, and 6p, and then explore the totals that she'd be able to make.

Keep going until you found all of them.

Come back again when you're ready to check.

Let's have a look, shall we? So, we must have those amounts of money represented by the money bags.

How many different ways did you find, first of all? Sorry, how many different totals were you able to make? Okay.

Here we go, let me show you what I came up with and compare it to yours.

So, I, first of all, totaled 1p, 5p, and 6p.

So I could make 12p using those bags.

I could just use the 1p and the 5p to make, yeah, 6p.

Or I could use the 1p and the 6p to make 7p.

Have I found all of the options? So I've used all three.

I've used the one and the five.

I've used the one and the six.

What have I not used? Good, the 5p and the 6p together to make 11p.

So how many totals were there that we could make? Good, four totals based on those amounts in the bags.

So, I said at the beginning, the question you would be answering through the independent task is, how many pennies did Louise put in each bag if she's able to make each of those sums from 1p to 15p? How are we going to organise our thinking though? I have a suggestion for you that you might like to use.

Of course, have a representation of those money bags.

Ideally, have the 15 pennies or something to represent them, so that you can explore, move around, and manipulate, making changes, maybe starting off with a certain number of pennies in each bag, but realising you've got to make a change.

So it's a good idea to be practical with this.

In terms of the recording, I suggest a table like this.

So, for example, if across those four bags, you've decided to put one coin in one, two coins in another, five, and then seven.

That's really clearly represented in the top parts of the table.

Then we know we need to make each sum from one to 15.

So working in an organised way, which sums can we make and can we then record on the table like this? Now I know straight away I can make 1p, 2p, 5p, and 7p, because I've got those values already in the bags.

In terms of now using those bags to make the other amounts up to 15, I'm going to work in order and answer yes or no for each of those values.

So three, 3p, can I make 3p? Yes, using two and one, using those money bags.

How about four? No, I can't make 4p? 6p? I could use five and one.

8p? Five, two, and one.

I'm using three bags.

9p? Yes, with two of the bags holding 7p and 2p.

10p? Yes, with those three, and so on.

11? No, I can't.

12? Yes, with those two.

13, 14, and 15p? Yes, I can make each of those.

However, because to solve the problem, I need to be bale to make every value from 1p to 15p every sum, this is not the solution because I'm unable to make 4p and 11p.

So I'm going to try again.

I'm going to change the amount in each bag, test to see if I can make each of those sums to 15.

If I can, I'd solve the problem.

If I can't, I stop, I try again, but this table I can keep on using to represent the changes I've made to the money in each bag and then the values I can make.

Press pause, go and have a go at solving the money bags problem, and come back when you've got a solution.

There is a solution.

It is possible.

So keep on trying, persevere, look at the changes you're making, work with the actual items or pennies, be practical, and it will help you to achieve and be successful.

Come back when you're ready.

So how did you get on? Were you successful? Have you solved the problem? How did you solve it? Think, think now, reflect.

What were you doing that helped you to achieve success? Because as much as solving the problem is important, what's more important is the process you were taking.

That's when the learning was happening.

So, focus in on that, think.

What were you doing? What were you saying, writing? How were you making changes? What was going through your mind? What connections were you making? How were you deciding what to do next? All of that is really powerful learning.

And focusing on that more than the answer is going to help you with future learning, with future problems. There may have been something you did with this one that you can use in future problems in maths and beyond.

So focus on that process just as much as you focused on the answer if not more.

In terms of a solution, this was one that we had tried, I shared before you got busy.

I tested some more, until I reached a solution.

It took me more than one go and more than one change to make money bags, but the solution, well, you tell me.

What did you have in each of the bags to help you solve the problem? Again, let's slow it down.

Tell me what you had in the first money bag? The second? The third? And the fourth? Fantastic.

1p, 2p, 4p, 8p.

And with those bags, with those pennies in the bag, and let's just check.

Eight plus four is 12, plus two is 14, plus one is 15.

Yes, we used all 15 pennies, and we were able to make, first of all, those totals using just the bags that had those coins in, and then working through the rest.

We're able to make each of those values through to 15 by combining two or three or four in the case of 15p money bags.

I hope that you've enjoyed this lesson and solving the problem money bags.

If you had to collect 15 items to use as pennies, make sure you return those now.

I hope that you've enjoyed solving the problem money bags.

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

Thank you for joining me for this lesson.

I hope you enjoyed solving the problem money bags.

If you had to collect items to represent those pennies, be sure to put them away as we finish the session.

If it was Lego, if it were toy figures, if they were counters from board games, put them all the way in the places they came from.

As for the pennies, if they're yours, well, pop them back safely in wherever you keep your own money.

And if you borrowed them, make sure you return those as well.

If you've got any more learning lined up for the day, I hope that you enjoy it, and I look forward to seeing you again soon for some more maths learning.

Bye.