Lesson video

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How are we doing today? Welcome to today's math lesson with me Ms. Jones.

Today, I am super excited because we get to do some reasoning problems together.

Let's have a look at what we're going to be doing today.

In today's lesson, we're going to be applying what you know with fractions to reasoning problems. This lesson has a slightly different structure because we've got three tasks hidden figures, fraction pyramid and mystery numbers.

And for each one, I'll show you an example.

And then you'll pause the video to do each task one by one.

Finally, you've got a quiz where you can apply your knowledge to a mixture of fraction problems. You'll need today, a pencil and a piece of paper to jot down your answers.

If you haven't got one, go and get one now.

But if you have, let's get started with the first problem.

Hidden figures.

Hmm, I wonder what this could be about.

Let's have a look.

Hidden figures example.

Which bar is longer? Okay.

So we've got here a sort of sheet covering up for the rest of the diagram, So you can't see the whole of each bar.

Which do you think is the longest? Explain how you know and convince me.

So what I might do here is try and sketch what I think each one would look like alongside each other.

So we know that each of these bars has been divided into three equal parts because we've got them labled here.


We can see how big one, one the third is.

So if we were to draw the complete box, they might look like this.

This one, one third is smaller than the top one.

So if we were to draw another two thirds, this bottom bar would end up being shorter than the top bar.


So I've drawn an example, I've also tried to explain it in words.

Which is what you'll need to do.

Convince me with an explanation and draw an example.


It's time to remove the sheet and see if we were right.

Oh, we were right.

The top bar is longer than the bottom bar.


This time, it's your turn to have a go.

Here we've got some different bars.

One is labelled with one quarter and one, one third.

What would the rest of the bar look like? Which bar is longer? Explain how you know and convince me.

Pause the video now to complete your first task.

When you're done, come back to the video to go over the answers and look at task two and task three.


Let's look at the solution together.

Which bar is longer? I asked you to think of an explanation and a quick sketch to show your thinking.

Here's my explanation.

A quarter of the top bar is the same size as a third of the bottom bar.

The top bar will have four parts of this size, and the bottom bar will have three parts of this size.

Therefore, the top bar will be longer.

And here's my sketch to show what I mean.

Let's reveal to see if we were right.


The top bar was the longer bar.

Task two.

Fraction pyramid.

What do you think that this one could be about? Let's look at an example first.

Place the fractions in the pyramid so that each fraction is the sum of the two fractions just below it.

I'll let you read through that again to make sense of what we need to do.


So two bricks such as these two need to total together to be equivalent to this one above it.

So at the moment I can't work out a brick like this, because we've got no fractions around it.

So in this example, I'm going to start off with this top brick because I've got the two below it.

And these two need to total to equal this one.

One plus eight tenths is equal to one and eight tenths.

Which other ones can I work out next? Well, I've got these two bricks.

One tenth added to two tenths is equal to three tenths.


Which one can I work at next? Well, this time I haven't got two bricks below something.

But I have got two bricks here near each other.

I know that three tenths plus something is equal to eight tenths.

Or eight tenths takeaway three tenths would give me this one.

I know that this has to be five tenths, because five and three make eight.

So five tenths and three tenths would make eight tenths.

Now I can work out this one.

Got one whole which I know is the same as ten tenths.

So this one must also be five tenths, because five tenths added to five tenths here would equal one whole.

Now I can think about these bottom.

I'll still come work out this one, because I've only got one near it, but I can work out this one, two tenths added to something is equal to five tenths.

This has to be three tenths.

And now I can work out this final one, Three tenths add it to something is equal to five tents.

So this one has to be two tenths.

I've completed the pyramid.

Now it's time for you to have a go.

Here is your fraction pyramid.

Can you fill in the missing bricks? Pause the video now to have a go at your task.

And when you're done, come back, we'll go over the answers and we'll look at a third task.


Let's have a look.

Let's have a look at which ones we can work out.

So here you should have had eight twelfths, Eight twelfths added to seven twelfths is equal to one and three twelfths.

There you should have had three twelfths to create eight twelfths above it.

Four twelfths, two twelfths.

Sure fraction period has been much fun.

If you've got any corrections, have a look at them now before going on to the next task.

Task three.

Mystery numbers.

I like the sound of this one.

Are you ready to be a detective? Let's have a look at an example together.

If Jake's number is 60 what's Mary's number.

How do you know? So we've got four people, and each of them are giving us a clue.

I've got Jake, Ben, Anna and Mary.

We know that Jake's number in this example is 60.

Let's write that next to Jake's speech bubble there to remind me.

Ben says, my number is three fifths of Jake's.

Let's see if we can work out Ben's number.

If we work out Ben's number, We should be able to work out Anna's number.

And then if we work out Anna's number, we should be able to work out Mary's number Which is what we need to find out.


So Ben's number, Three fifths of 60.

I know that one fifth of sixty would be 60 divided by five.

Sixty divided by five is 12.

Now 12 multiplied by three would get us 36.

Ben's number is 36.


My number is four sixths of Ben's.

Now Ben's was 36.

Anna's four sixths.

So one sixth of Ben's would be six.

So four sixths of Ben's, would be four times six, Anna's his number is 24.


My number is two thirds of Anna's number.


One third of Anna's number 24, would be 24 divided by three which would be eight.

Her number is two thirds.

So eight times by two.

Mary's number is 16.


Hopefully you followed that.

I might've used a little bit more working out as I went along.

If I wanted to take a little bit longer and check my answers.

So feel free to do so.

Here is your version of the problem.

Pause the video now to have a go.

When you're done, come back and we'll go over the problem answers to this final one.


Let's go over the answers.

So Jake's number this time was 72.

Ben says, my number is five eighths of Jake's.

One eighth of 72 would be nine.

So Ben's number is five lots of nine which is 45.

Anna says, my number is a third of Ben's.

A third of 45 is 15.

And Mary says, my number is two fifths of Anna's.

So one fifth of Anna's would be three.

So two fifths would be six.

Mary's number is six.

Maybe you could have a go at creating your own version of that reasoning problem for your friends to solve.

If you're all done, it's time to complete the quiz.

Thanks very much.

Take care.