Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking you through today's lesson on groups.

I'm really excited to get started on this unit of work because it's one of my favourite areas of maths and I hope that you're going to really enjoy it too.

Before we get started, make sure you've got a pen, and something to write on, and that you're free from distractions.

If possible, make sure you're in a nice quiet area so you can fully concentrate on this lesson.

If you need to pause the video now so you can get anything, then please do but if not, let's get going.

We're starting today's lesson with a try this activity.

You need to decide how many different ways can you put eight apples into two bags.

So for an example, I've got two bags here where I've got five in one bag and three in the other.

When you're finished with that, if you think you've got all the possible ways of doing it, then I want you to have a think about how many different ways could you put eight apples into three bags.

If you feel confident that you know how to get started with this activity, then pause the video now and get going.

When you're ready to go through it, then resume the video.

If you're struggling a bit, just stay tuned and I'm going to give you a couple of hints.

Okay, if you're struggling, that's absolutely fine.

It might help you to get eight things from your house.

So if they're eight of the same thing, then that's great but if not, eight things that can represent our eight apples.

And you're going to split them into two piles and how many different ways can you put those eight things into piles? Pause the video now and have a go at this activity.

I hope you've had a really good go at this try this activity.

How many ways did you get for putting eight applies into two bags? Tell me now.

Tell the screen.

Excellent if you said five ways.

There are five ways to split eight apples into two bags.

So I like to use tables for this kind of thing.

So I've got one bag here and the second bag here.

It doesn't matter which way round they are.

And I'm going to think about a logical way of deciding how many apples go in each bag.

So in the first bag, I could put no apples.

How many does that mean that I have in the other bag? Excellent, eight.

Another way of doing it is to put one apple in a bag.

How many does that mean I have in the other bag? Good, seven.

And I could keep going like this to list all my possibilities and I've done it in a systematic way.

So I could have two and six.

Three and five.

And four and four.

There are no other ways of doing this because they would be repeats of combinations that we've already got.

What about then for the second question? How many different ways can you put eight apples into three bags? I'm not going to go through this because there are loads of ways that you might have thought about it but one way that you could have thought about it was to fix the amount of apples in the first bag, so to say that there's one apple in the first bag and then to write all your combinations that you could have had for bag two and bag three.

So I could have had one, then one, and six.

I could have had one, then two, then five.

I could have had one, then three, then four and so on.

And you could keep going until you've exhausted all the possibilities there.

Moving onto the connect part of the lesson now.

And this is going to link into our main point of the lesson.

So here we've got our two bags from slide one.

Five apples in one bag, three apples in another.

We can show groups using something called ratio notation.

So we can write five apples in one bag, and three apples in the second bag.

We can describe that as five to three.

So we've got five apples in the first bag and three apples in the second bag.

If we had this one, how do you think I could describe that using ratio notation? Pause the video now and tell me.

Excellent, we could describe it as two to six.

Anyone notice another way that we could have described that? One to three, good.

For every one apple that we have in this bag, we have three apples in the second bag.

Those are what we call equivalent ratios and we're going to come on to that in another lesson.

Then finally, we've got these three bags of apples here.

We've got one apple in the first bag, three apples in the second bag and four apples in the third bag.

Tell the screen now how you think we could write that, using ratio notation.

Excellent.

We can write it as one to three to four.

We can have lots of different parts of our ratios, not limited to two.

Here you can see we've got three parts.

We could even go to four, five.

It's not limited.

What I'd like you to do now is have a go at the task that's on the screen.

So draw some sharings of 10 apples between two or more bags and then write them using ratio notation.

Once you've done that, have a think about this tricky question at the bottom.

Can every bag contain an odd number of apples? Pause the video now and have a go at this question.

So I hope you've drawn some really nice diagrams there and then written them with ratio notation.

Can every bag contain an odd number of apples? Did you notice a pattern here? So for our two bags, let's say this is our first bag and this is our second bag, can both our bags contain an odd number of apples if we've got 10? Tell the screen.

Excellent, yes, they can.

I could have, for example, three apples in here and seven apples in here.

That works, doesn't it? Three is an odd number, seven is an odd number.

What about if I have three bags? Can I have an odd number of apples in each of these bags? Let's try.

So I could have three apples in here.

I could have three apples in here.

But how many does that mean I have to have in my last bag to make 10? Excellent, four.

So that is not every bag containing an odd number of apples.

Let's just try it again with three and make sure that it's just not a fluke.

Give me another odd number.

You try it.

If you need to, pause the video and have a go.

I'm going to go with five in the first bag and then three in the second bag because I know that they are both odd numbers.

How many does that give me all together? Well, that's eight.

So that means I need two in my final bag and two is not an odd number.

Can we notice a pattern here? Is there a relationship between the number of bags that we're using and whether we can get an odd number of apples in each bag? Pause the video now and have a think about that.

If you came up with an idea there, that's what we call a conjecture.

So you're starting to make an educated guess about what you think the relationship is between the number of bags and the odd and even number of apples.

So well done with that.

We're going to move on now and you're going to apply your learning so far to an independent task.

So pause the video now, navigate to the worksheet.

When you're ready to go through some of the answers, resume the video.

Excellent work, well done for persevering through this independent task.

Let's go through some of the answers.

Some of them I'm going to explain and some of them I'm just going to give you the answer and you can check your work.

How many sweets are there in the group? Well, we can see quite clearly that there's seven.

If they make 10 of the same groups, how many sweets will Asif put in? So Asif is putting in two sweets each time.

So if he puts two sweets into 10 groups, how many sweets has he put in all together? Tell me now.

Excellent, 20.

If they make 24 of the same groups, how many sweets will Sally put in? So we've got 24 of the groups and Sally is putting in five each time.

So how many has she put in? Tell the screen now.

Excellent, 120.

And then finally, if they make 50 of the same groups, how many sweets will they put in together? So we know we've got seven sweets in the group all together and we're making 50 of those groups.

So that means we will have 350 sweets.

I really like this question, especially because it's getting you to explain your answers.

So what I'm going to do is I'm going to tell you whether it can go in or not and then I want you to read out your explanation to the screen.

So first one, two to nine could be the ratio of green to yellow counters.

Can you read out your explanation now? Excellent, we could have two green counters and nine yellow counters and that makes 11 counters in total.

The second one cannot be the ratio of green counters to yellow counters.

Can you read out your explanation to me now? Excellent explanation there.

If this is how many green counters we have, and this is how many yellow counters we have, that means we've got 11 green and one yellow, which means all together, we've got 12 counters.

So this can't be our ratio.

Next one's tricky, so I'm going to come back to that one at the end.

This next one, I think you can actually talk about this one either way.

So read out your explanation to me now.

Excellent, so we have got 11 counters in total here 'cause zero green and 11 yellow but the question does say that we make a group of green and yellow counters.

So does that mean we need some of each? I'm not sure, I'll let you decide what you think the question's asking there.

And the last one could be a ratio of green counters to yellow counters because I could have seven green and four yellow and all together that makes 11.

What about this one to one then? That means for every one green counter we have, we have one yellow counter.

So if I had two green counters, how many yellow counters would I have? Tell me now.

Excellent, two, so that's four counters in total.

If I had three green counters, then I'd have three yellow counters, which is how many counters in total? Tell me now.

Excellent.

If I had four green counters, and four yellow counters, then that would be eight counters in total.

Let's keep going.

If I had five green and five yellow, I'd have 10 counters in total and if I had six green and six yellow, then I have 12 counters in total.

So can you see that there's no way here that I can get 11 counters.

So this one cannot be a possible ratio of green counters to yellow counters.

So question three, let's write this as a ratio.

We've got Antoni to Binh to Cala.

And Antoni saves four pounds a month.

Binh saves nine pounds a month.

And Cala saves seven pounds a month.

How many months are in the year? Just remind me.

Excellent, 12.

So if Antoni saves four pounds a month for a full year, how much does he save in total? Tell me now.

Excellent, 48 pounds.

If Binh saves nine pounds a month for a full year, how much does she save in total? Tell me know.

Excellent, 108 pounds.

And if Cala saves seven pounds a month for a whole year, how much does she save in the full year? Tell me now.

Excellent, 84 pounds.

So how much do they have all together? So what does this word all together mean? It means we need to add them up.

So we've got 48, add 108.

Add 84 and you might be much quicker at mental arithmetic than I am.

I need to write it in the columns, check I'm doing it correctly.

Eight add eight is 16, add my four is 20, four add eight is 12, add my two is 14.

And then one add one is two.

So my final answer is 240 pounds.

And remember that you need to include your units here.

Tricky question this one.

So well done for persevering with it if you got there.

A bowl of fruit contains three apples, two oranges and six bananas.

Maja sells n bowls like this at the market.

How many bananas did she sell? So n here is representing any number.

So she sells six bananas multiplied by n bowls.

So n groups.

So she sells 6n.

If she sold n apples, how many bowls did she sell? There are three apples in each bowl, so that means that n divided by three gives us the number of bowls that she sold.

If she sold n bowls, how many pieces of fruit did she sell in total? Well, there's 11 pieces of fruit in each bowl, so that must be 11n.

Well done if you got those.

They were really tricky.

Right, last part of today's lesson then is the explore task.

In this bag, there are plums and three satsumas.

The greengrocer is choosing a label for the bag.

You've got the four different labels there on your screen.

What's the same and what's different about the labels? And which label should the greengrocer choose to put on the bag? What do you think? If you raced through that part, then I've got a challenge question here for you, which says which of these is still true if the greengrocer doubles the amount of fruit in each bag? And what about if she added two more of each fruit to a bag? Pause the video now and have a go at this activity.

Right, let's have a think about this then.

We're going to, first of all, decide what's the same and what's different about the labels.

So can you tell me what you came up with there? Excellent, well done.

What did you decide was the best label for the greengrocer to put on the bag? Okay, nice decision.

Right, I'm going to talk you through some of my thinking here.

You might have thought about it differently and that is absolutely fine.

This is one of those tasks that we want you to be thinking mathematically and making those conjectures that we talked about earlier.

So the first one contains eight fruit.

Is that true? Yeah, it is true, isn't it? It contains eight fruit but it doesn't tell us what fruit is contained within the bag.

Will that label still be true if I double the amount of fruit in each bag? No, it won't, will it? And what about if I add two more of each fruit into the bag? No, exactly, still not true.

So although that's true for this, it's not true if I change the amount of fruit.

There are two more plums than satsumas.

Again, that one's true.

Will it be true if I double the amount of each fruit in there? So that would give me 10 plums and six satsumas.

No, it wouldn't, would it? What about if I added two more of each into there? Would it be the same then? Yes, it would.

Good, really well done.

Let's talk about this one then.

The ratio of plums to satsumas is five to three.

If I doubled the amount of fruit in that bag, does this ratio change? What would it change to? Excellent, 10 to six.

What do we know about this ratio in comparison to this ratio? Excellent, this one is two groups of this one, isn't it? So we can say that this one is always going to be true if we double it so long as we increase by a multiple of five for the plums and a multiple of three for that satsumas and it's the same multiple, then this one will always be true.

Is it true if I add two more of each fruit to the bag? So that would give me seven plums and five satsumas.

Is this ratio the same as this ratio? Is it more than one group of this ratio? No, it's not, well done.

And 3/8 of the fruit in the bag are satsumas.

I'm going to leave that one with you to think about.

Is that true or not? What happens when we double it? What happens when we add two more into each bag? That's the end of today's lesson.

So thank you so much for all your hard work.

Please remember to navigate to the quiz now so that you can show me what you've learnt, which I know will be loads.

Thanks again for everything.

I hope you have a really great day and I hope to see you again soon.

Bye.