Lesson video

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Cool! Hello, sorry, I was just doing some measuring.

You see, I want to put up some shelves and decent painting in my room.

But I need to measure it first so I know how much equipment to buy.

It's a good thing you're hear because today's lesson is all about problem solving with decimals.

When I was doing my measuring, I realised that one side of my measuring tape had centimetres, and the other side had metres and so the numbers were really different.

But then I realised with all the math we've been learning, I can convert between the two and even work out how much I have to buy with our fantastic mathematician skills.

So today we're going to be working out some problems with decimals, which is really useful for a real life context.

Let's get started.

Welcome to today's math lesson.

My name is Miss Sew and today we are problem-solving with decimals in context.

When we problem-solve with decimals, we are often looking at units of measure, for example, kilogrammes, litres, metres, and these are great examples of real life maths.

I often have to convert between decimal numbers and integers or whole numbers.

And that's where the strategies that we learned today will be really helpful.

To start with, we're going to do a warm up looking at our units of measure.

Next, we'll examine converting units of measure in more detail.

After that, we'll have a look at some multi-set problems, and at the end of the lesson, you will have an independent task and a quiz.

For today's lesson, you will need a pencil and some paper.

Pause the video and go and get these things now if you don't have them.

Now that you have all the equipment you need, take a moment to check you have a complex space and if you have any apps running, you turn off notifications so that you couldn't concentrate during this lesson.

Let's get started with a warm up converting units of measure.

I'm going to read you the questions and then I want you to pause the video and have a go at answering.

One litre is equal to millilitres, I might use litres to measure water.

One kilometre is equal to mm metres.

one metre is equal to mm centimetres.

one centimetre is equal to mm millimetres.

And I would use this to measure the length of something.

And one kilogramme is equal to mm grammes.

I would use weighing scales in kilogrammes to measure how heavy something is.

Pause the video and write down what you know.

Okay, it's time show you the answers.

If you weren't sure about these, don't worry, I'll be sharing them with you throughout the lesson.

One litre is equal to 1000 millilitres.

One kilometre is equal to 1000 metres.

One metre is equal to 100 centimetres, and one centimetre is equal to 10 millimetres.

One kilogramme is equal to 1000 grammes.

Let's start by looking at our litres which is what I use to measure things like water in this bucket.

One litre is equal to 1000 millilitres.

To convert from one litre to millilitres, I would multiply by 1000.

And to convert the other way, from millilitres to litres, I would divide by 1000.

If we know that one litre is equal to 1000 millilitres, what were two litres be in millilitres? Pause the video and write your answer.

It will be 2000 millilitres.

I'm going to keep showing you some questions and I want you to tell me the answer.

If you need to pause the video and then play it again.

If you can tell me the answer straight away, then keep the video playing.

Six litres is equal to mm millilitres.

6000 millilitres.

1.

4 litres is equal to? 1400 millilitres.

I multiplied by 1000.

3.

7 litres is equal to? 3700 millilitres.

Now let's take a look at measuring length.

If I have one metre, and I convert to centimetres, I multiply by 100.

And if I have centimetres, and I want to convert to metres, I divide by 100.

One metre is equal to 100 centimetres.

Just like before, I'm going to ask you some questions and I want you to pause the video and answer.

If you can do it with me, shout it out when I'm counting down for my three seconds.

Eight metres is equal to? 800 centimetres.

I multiplied by 100.

5.

5 metres is equal to? 550 centimetres.

0.

7 metres is equal to? 70 centimetres.

0.

65 metres is equal to? 65 centimetres.

There are lots of different units of measure, and we need to remember how to convert between them.

When we're using our metric units of measure, we usually have to multiply or divide by a multiple of 10.

Now we're going to have a look at some multi-set problems and use some bar models to help us understand.

When I'm doing problem solving, I find bar models are a really helpful way to help me represent my problem and help me think through the answer.

Bar models don't solve the problem for me, but they represent the different quantities in the question and help me understand what's happening and think about what's missing.

From this bar model, I can see that the hole is 1.

2.

And that below the whole there are three more bars in three parts.

These three parts are worth 0.

4 each.

From this I can see that 0.

4 is equal to 1.

2.

Another way of showing this would be, 0.

4 multiplied by three is equal to 1.

2.

This bar model also shows me that 1.

2 shared into three equal groups, or divided by three is equal to 0.

4.

Lets look at our model to our left first of all.

This bar model shows two parts above a whole.

The two parts are of different values, one part is greater than the other.

So maybe this bar model could represent an additional equation, something like 0.

1 plus 0.

6, is equal to, and then we have a hole underneath.

It could represent two ingredients going into a salad that I'm adding up and weighing together.

Let us look at our bar model on our right.

This bar model shows two equal parts that equal a whole.

This could be something like, I might have two pencil cases that have the exact same number of pencils, how many pencils are there in total? So our bar models don't solve the equation for us, but they represent the problem.

And this can be really helpful when we want to decide our next step.

Take a look at this bar model.

What is this bar model telling us? And what do we know? This bar model has a hole which is worth 6.

25 and two parts.

But do the two parts equal the whole? No, they don't.

We still have a missing part here.

And we want to find out what that is.

I want you to have a go using what you know already about bar models to solve what this missing part is.

Pause the video and have a go now.

Let's have a look at the answer.

So, from this bar model, I can tell that I will have to subtract.

I have two parts here that do not equal the whole and the whole is 6.

25.

To find out what this missing part is, I need to subtract both of these parts from the whole.

There are two ways I could have done that.

6, now I'm going to show you two different strategies you could have used to get to the answer.

And I want you to think about which one you would want to use or which one you did use to try and solve this equation.

I could add both part or subtract from the whole, or I could subtract them each one by one from the whole.

To do the first method, I would have to 2.

75, which is 4.

65 and subtract it from the whole to get 1.

6.

Or I could subtract 2.

9 from the whole and then subtract 1.

75 from that number.

I would probably go with my subtraction strategy here.

Because adding both these parts together doesn't really make it any easier.

These two numbers added together isn't a very easy equation.

And so I might as well just subtract them one by one.

It's time for a quiz.

Which bar model represents this problem.

Let me read the word problem for you, and then I want you to choose whether bar Model A or bar model B represents the word problem.

To create a poster, I found a large piece of paper and folded it half.

Each equal partners 0.

4.

Bar Model A or bar model B? Pause the video.

The answer was bar Model B.

0.

4 and 0.

4 are my two halfs, added together they make 0.

8.

Which bar moreover it presents this problem? To make two litres of lemonade I need 1.

6 litres of water and the rest is lemon juice.

How much lemon juice will I need? Is it bar Model A or bar Model B.

It is bar Model A.

We are making two litres of lemonade which is our whole.

We have 1.

6 litres of water and the rest would be lemon juice.

Bar model a represents this problem.

Have a go at this word problem using this bar model to help you.

Miss Sew is painting her classroom.

The wall is 2.

8 metres in length, on Monday she paints 1.

2 metres, on Tuesday, she paid 0.

6 metres.

How much does she have left to paint? Pause the video and work out your answer.

To do this, I added up both my parts here and subtracted them from the whole.

I could have also done 2.

8 metres subtract 1.

2 and then 1.

6 metres, subtract 0.

6 metres, my answer would have also been one metre.

Hopefully from these examples, you've seen how bar models can represent our thinking and help us solve problems. Let's read this problem together and then try and draw our own bar model.

Stephen has a plank of wood three metres long, he cuts off 1.

2 metres, then 75 centimetres, and then another half metre.

How much wood is left? We don't have a bar model for this.

Can you have a go drawing one? Pause the video and have a go.

Let as see the bar model that I created for this problem.

So, Stephen has a plank of wood that is three metres long, that's the whole.

He cuts off 1.

2 metres, so I've drawn a bar here.

Then he cuts off 75 centimetres.

And then another half a metre.

So I've represented the whole and drawn the bars to represent how much has been cut off.

How much wood is left? Now we have our bar model, I want to work out what this missing part would be, I will have to subtract these three quantities from three metres.

But something seems a bit strange.

This is a fraction, and 75 has 10s, and then this is a decimal number.

I need to subtract all of these are three metres.

With this sort of decimal word problem that uses a real life context, I will have to convert all my measures into the same unit.

I think it would be better if we converted all of these into metres first.

So to convert everything into metres, if something isn't centimetres, I need to divide it by 100.

I want you to pause the video and write what all of these measurements are in metres.

Let's take a look at the answers.

Now we have all our measurements in metres, it's much easier to work out.

I'm to subtract all of these measurements from our whole to work out what this missing part is.

Pause the video and have a go doing that yourself now.

Let's take a look.

I know if I added all of these together, I would get 2.

45 metres.

three metres subtract 2.

45 metres is equal to 0.

55 metres.

55 metres.

That's how much wood is left.

Thank you so much for joining in with our math lessons today and helping me solve lots of different word problems. Now it's time for your independent task.

Each question: Draw a bar model, label it, convert any units if you need to, and then solve it.

Read both of these word problems and complete all the tasks above.

If you need help here's a support sheet with the converted units.