Lesson video

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Hi everyone it's Mr Whitehead here, ready for your maths lesson.

Before we get started, I want you to do something for me.

You just need to think of one vegetable and one fruit.

Think of them now.

Now I'm fairly confident that the vegetable you were thinking of was a carrot.

And that the fruit you were thinking of was an Apple or an orange, maybe a banana.

Of course, you may have been thinking of different vegetables or fruits, but typically I bet you were thinking of a fairly common one like the ones I named.

In this lesson, we are going to be thinking about fruit as the context for our problem.

And one of the pieces of fruits will be an orange.

but look out for what the other piece of fruit is, not a very common one and not one that many of you would have been thinking of, when I asked you to think of one just now.

Before we get going and discover what this second fruit is, I'd like you to make sure that you're able to give me your full attention for the next 20 minutes.

And if you need to take yourself off into a quieter place, free from distractions, where you can focus, press pause, while you get yourself sorted and play again when you're ready to continue.

In this lesson, we are planning and solving a money problem using a guess and check strategy.

We'll start the lesson off with some practise, at column addition.

Before we spend time exploring the problem, responding to the problem, which will lead you ready to solve the problem independently to end the lesson.

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

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

Let's get going then with some column addition practise.

six sets of add ends, six sets of numbers to add together.

I need you to find the sum the sum of the two known parts is unknown.

The sum of the two known add ends is unknown.

Find the unknown sums. Press pause, come back when you're ready to check the solutions.

Oh, and I suggest that for each of those pairs, you estimate as well.

We'll be looking at estimations as well as the sums, when we look at the solutions.

So do give each of them an estimate first.

Come back when you're ready to check.

Let's take a look.

So estimates first by rounding the add ends, depending on the size of them.

I think in most of these cases to the nearest thousand, and then adding those thousands, those multiples of thousand that you end up with to get an estimated sum.

So if I just give one example that of that very last one, I would round those two add ends to 4,000 and 3000, which is 7,000.

Once we've got our estimates, as we start to calculate, we're able to compare the calculated sums to the estimates and they should be fairly close.

If they're not, it indicates that perhaps our calculated sums has an error somewhere in there.

So it's a nice way of being able to spot any errors that we make for ourselves and correct them.

Here are those unknown sums once calculated.

Take a look and give yours a mark.

When you're ready, hold up your paper for me so I can see how hard you've worked on this first task.

And I'm happy to see of course, where we've got six found sums, and you've correctly calculated, but I'm also happy to see where there are any errors, that you have been able to spot and fix for yourselves.

And even if now you've got a few of them that aren't yet correct, if you're able to pause and fix them, then there's learning happening there too.

So all around, I'm feeling really positive about to start to this lesson.

Let's have a read of the problem.

A market stall is selling oranges and lychees.

Oranges cost 45P each or 45 hundreds of a pound, and lychee fruit cost 25P each or 25 hundreds of a pound.

Reena buys some oranges and lychees, which cost a total of six pounds 35.

How many oranges and lychees could she have bought? Now, the question is what you will answer by the end of the session.

And you will independently find the solution to that question as part of the task.

Let's break the problem down and build our understanding of it to help you achieve that by the end of the lesson.

First question then.

What has Reena bought from the market stall? You ready to tell me, go on one, two, three, fantastic.

Some oranges and some lychees.

How much does one lychee cost? Tell me, good, 25P.

And how much does one orange cost? Tell me, good, 45P.

How much did she spend in total? Scan the text, get ready to tell me one, two, three, good, six pound 35 that's the total cost of what she bought.

And now a point at which you might want to pause two questions.

How much would three lychees and three oranges cost? Then how much would 10 lychees and 10 oranges cost? Press pause and have a go at working on those two questions.

Then come back when you're ready to share.

Are you ready to take a look? First of all, could you hold up your paper so I can see how you've laid out your thinking and your solutions to these two questions.

Keep them steady.

I can't see them when they're waving around that's better.

Good, let's have a look through them, shall we? Focusing on that first question to begin with, three lychees three oranges.

So using what I know from the problem about oranges costing 45P each, I can either calculate 0.

453 three times, 1.

35, or 45 multiplied by three, 135.

One pound 35 or 135P for three oranges.

Lychees, will the lychees three lychees, going to cost more or less than the three oranges? They're going to cost less.

And we would know that before we even calculated.

Why would we know that before we completed the calculation? Yes, oranges one range is 45P, one lychee is 25P.

If I've got three of each of them, then of course the one that was more expensive for one would be more expensive for three.

So the lychees will be cheaper.

And again I can calculate 0.

25 three times or 25 three times 0.

75 of a pound or 75P.

Combining those two costs of course, because we're looking at the total of these six items, two pounds 10, 2.

10, 210P for three oranges and three lychees.

The second part just reminds me again, hold up your paper so I can see your calculations here.

Good, so this time we're multiplying the cost for one that's cost we're multiplying by 10.

And again, which of the fruits would be most expensive if we're buying 10 of them? Oranges, because that is the most expensive fruit for one.

And we're buying the same number of each.

So multiplying by 10, 0.

45 10 times 4.

5, 450P four pound 50.

Compared to, you tell me what it was for lychees? Good, two pounds 50 for 10 lychees, 2.

5 or 250P.

Combining the costs a total of seven pounds.

So we just had a go at finding the total of three of each type of fruit and 10 of each type of fruit.

Now looking at those total costs, do you notice anything about those answers? Thinking about the original problem, we're trying to find out which fruit was bought at a total cost of six pound 35.

So I wonder now how this might have helped and what's your next guess might be.

Shortly I'm going to leave you to finish off solving the problem.

We've had a start together and I think you're confident and ready to continue independently.

So we're looking to find out which items or how many, so we know which items or she doesn't like lychees, but how many of each were bought at a total cost of six pounds 35.

I've got suggestion again of how you might record the results.

I asked you earlier to hold up your paper so I could take a look at how you were starting with your recording.

And it will be helpful if you use something like this, to keep a record of each of your guesses.

We're going to make a guess and check.

And if we need to take another guess and check.

So for example, we've tried three of each and ten of each.

And in this table you can see the total cost for the oranges and lychees and the total combined cost.

Then importantly, was that too little or too much? Our first guest was too little, our second guest was too much.

So the next try that we have should be based on and influenced by what's already happened.

It wouldn't make sense for example, to now try 11 of each or 12 of each if we know that 10 of each was too much.

Don't forget the number of each type of fruit doesn't have to be the same.

Press pause make use of that table, and continue solving the problem.

There is a solution, and I'll tell you that this time there are at least three ways to solve the problem.

So if you find one challenge yourself and find another.

And if you're struggling to find one we know that there are three at least, so keep on trying and aim to reach that goal of finding the solution and think about the decisions you're making, why you're making them, what you've tried already, what you might try next to help you with that learning in the moment.

Press pause and come back when you're ready to share.

How did you get on? How many solutions did you find? One, hold your fingers up two, three, fantastic.

Again, the answer is important, but it's what you were doing to reach that solution that is the most important thing for you to reflect on right now.

In terms of the solutions, let's take a look.

These were the two that we had tried already together.

What I show you next are the solutions.

I'm not showing you each of my guesses and, and the progress I was making towards them.

So just showing you what the final selections could have been.

So there we have it, we could have bought three oranges and 20 lychees.

We could have bought eight oranges and 11 lychees, 13 oranges and two lychees.

Each of those options would have totaled to six pound 35 would have been correct.

Like I said, I had other attempts as well that were coming out as too little.

How did you approach the problem though? That is what's most important.

How did you decide which guess would come next? What changes to make to the number of oranges or lychees that you were suggesting? That is the most important part.

And did you find all the solutions? So if we thinking that that was a go, how would you know when you had found them all? There's some challenge in there.

So it's not just about finding them all, but knowing you have found them all or knowing that there are more to find.

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

So oranges and lychees.

The next time you are asked to name a fruit, think of a type of fruit, maybe lychee will be there somewhere in your memory to add to your list as well as the common types of fruits, oranges, apples, and bananas.

Thank you so much for joining me for this lesson.

I hope you enjoyed and achieved, as we worked through the fruit problem.

Enjoy any more learning that you've got lined up for the day as well.

And I look forward to seeing you again soon for some more maths, take care, bye.