Lesson video

Hi there, my name is Mrs. Parnham and I'm going to be your teacher today.

I'm really looking forward to working together with you.

Mrs. Der Ling tells me you're getting really good now at writing repeated addition equations.

She sent you this task in the last lesson.

Did you manage to write a repeated addition equation which matched this number line? Perhaps you decided to draw out the line on right above each jump, water was being added each time.

Did you notice that there were three jumps on the number line? Each one representing 1/10.

So the equation to write to represent this addition equation was, 1/10 plus 1/10 plus 1/10 equals 3/10.

I hope you got it.

Don't worry if not.

You were also asked to try and find the answer to this equation.

Is this true or is this equation false? I always think it's a really good idea to try and explain why you think something is true or false, and explain your thinking.

Did you draw a number line to show your answer? This is what I chose to do.

I drew my number line and divided it into six equal parts.

Because in the question, I knew that I was adding a unit fraction of 1/6 and another 1/6.

I also tried to remember to ensure that my number line contained the zero at the very start.

Then I jumped from zero.

In this jump of 1/6 and that would make me land on number 1/6.

Then I jumped another 1/6.

And this time I would land on the number 2/6.

Therefore I know the answer to 1/6 plus 1/6 is equal to 2/6.

So going back to the original question, I could say that the answer is false.

1/6 and another 1/6 is equal to 2/6, not 2/12.

So the answer is false.

Can you see what mistake might have been made by the person.

And I wonder if you can have a look and explain to someone what mistake do you think that person made.

Pause the video if it helps.

Perhaps the person answering this question simply added up the numerators.

Added the one and the one to create two in two 12 and added the denominators of six plus six, to get the denominator 12.

So perhaps that's what they did.

But we know because of previous work that happened that this can't be true.

When we add a unit fraction and a unit fraction together with the same denominator.

Well done for having a go and extra well done, if you were able to explain your answer.

For today's learning, we're going to be looking at this representation.

We've looked at them before in previous lessons.

They're called Cuisenaire.

And it's likely you've got any at home.

I've not got any at my home either.

We're going to look at them together on this screen.

The important thing to focus on is not the letters on them.

They didn't really much at all.

But to look at the relationship between the rods.

Which is what we're going to do today.

Let's take a look.

If the yellow rod is the whole, then what fraction would one of the white rods be? Pause the video and tell a friend.

or just tell the screen.

Are you back? What fraction do you think one of the white rods would represent? It involves a little bit of our friend visualisation, which I know you've done in other lessons.

Visualising is thinking about in your mind's eye.

How many of those white rods would you be equally length to the yellow rod? I think that would be five.

So with this information you can say that one white rod is worth one.

That's right! You got that.

But we haven't gone one of those white rods.

We have one, two, three of those white rods.

So what would that additional equation look like here? If you've got a pen and paper, see if you can write it down.

Pause the video if you need to.

Have a look.

This is what I wrote.

1/5 plus 1/5 plus 1/5 is 3/5.

But we needed to have that yellow up there to know the volume of the unit fraction to add.

Should we try another one? I think you can do this now.

We're going to look at one more example of this together.

Let's have a look.

This time the blue rod represents the whole.

What faction of the whole is represented using the light green rods? Can we write this representative equation? Let's have a look.

How many light green rods would make the whole? I think that there's enough space for one more likely rod.

Meaning that there will be three green rods making the whole.

We can see two of them.

So, what would one light green rod be worth? And then we need to add another fraction, that's represented by the light green rod.

And then what does that equal? Let's have a look.

Did you write this equation? 1/3 plus 1/3 equals 2/3.

and the denominator and the numerator.

2/3 plus 1/3 equals two 1/3 or 2/3.

I'm so pleased if you got that answer right.

we're getting so good at these now.

Let's have a look at this question.

Let's have a go.

Which representation matches each equation? You can see two representations made with Cuisenaire rods.

The top one has the yellow bar representing the whole.

And on the second representation the orange bar is representing the whole.

On the equations if I look at the denominators, what do you notice? What's the same and what's different? That's right.

I can see that both equations are made up of 1/5.

So this tells me that both representations you must show 1/5.

But how can we match them up? What other information do we know? Well, in the top representation with a yellow and white bars, if one white bar is worth 1/5 how many do we have in the representation? I think I heard you say that we have two of them.

We have 1/5 and another 1/5.

So that would match to the bottom equation.

Wouldn't it? Where it says 1/5 plus 1/5 equals two 1/5 or 2/5.

And let's just having a look at the other rod and check that they match together too.

We're told that these red bars represent 1/5 of the whole.

And we can see that we have three 1/5 here.

So does our remaining equation represent this too? Yes, it does.

It tells us that 3/5 is the same as 1/5 plus 1/5 plus 1/5.

And that is what shown on our representation.

So we've managed to successfully match the Cuisenaire representation with each equation.

Well done if you got those right.

And extra wilds on, if you could explain why.

Can you have a go at completing this equation.

Let's have a look.

This time the blue bar represents the whole.

How many of the white bars would be equivalent to the blue bar? Well, this helps us because the denominator is already written for us in the equation.

It says 2/8 is equal to, I wonder what could go with that.

2/8 is equal to 1/8 plus another 1/8.

Well done.

It's really sad, but it's almost time for me to go now.

However, I'm going to leave you with some practise activity questions as usual.

That's because practise makes progress as any good mathematician will tell you.

There are five equations for you to complete here.

Do you notice that some of them have missing boxes? Just like the practise question that we've just completed together.

And some of them, like the second question just says 4/8 is equal to.

I wonder what we can put in that using learning from the past couple of lessons.

I wonder if you could write some fractions that add up to 4/8 just in the way we've been doing.

And also for 5/8.

And then this question changes a little bit.

Watch out for the symbols, the equal sign and the position of it is really important.

And the last one as well.

I think that will give your brain a good workout.

And then one more question to go to make your brain grow even bigger.

Are you ready for a challenge? This problem, I'd like you to have a go.

You might need your visualising skills that you've been using throughout these lessons.

Stan is making a repeating pattern with some white and some grey cubes.

You can see them in the diagram.

I'd like you to write an addition of a unit fraction to show what fraction of his model is made of grey cubes.

I know you can do that.

Try your very best.

And we'll see you next time.

Thanks for working so hard, bye.