Lesson video

Hello there.

My name is Mr. Goldie, and welcome to today's maths lesson.

And here is our learning outcome.

"I can use knowledge of non-unit fractions "to solve problems." And here are the keywords for today's lesson.

Bit tricky, these keywords, but have a go repeating the key word after I say it.

So the first keyword is denominator, and the next keyword is numerator.

Let's take a look at what those words mean.

"A denominator is the bottom number written in a fraction.

"It shows how many parts a whole has been divided into.

"A numerator is the top number written in a fraction.

"It shows how many parts we have." And here's our lesson outline.

So the first part of the lesson is called "Working out the Fraction", and the second part of the lesson is "Solving Problems".

Let's get started.

In this lesson, you will meet Sofia and Jacob.

Now lots of people find fractions a bit tricky.

Sofia and Jacob are here to help you.

Jacob and Sofia are looking at different fraction representations.

"First we're going to work out the fraction of the shape "that is shaded," says Jacob.

"There are seven equal parts," says Sofia.

"The denominator is seven." So the denominator, it's the bottom number in the fraction, and that tells us how many parts there are in total.

Three parts are shaded, the numerator is three.

So the numerator is the top number in a fraction.

And that shows how many parts that we have or how many parts we're talking about.

So Jacob said, "How many parts are shaded?" 3/7 of the shape are shaded.

"I'm going to shade 3/7 "of the next shape," says Jacob.

So the next shape is also divided into seven equal parts and Jacob shades three of them.

Remember, it doesn't matter which three he shades, he can shade any three and he will be shading 3/7 of the shape.

Next I'm going to find 3/7 of the oranges.

So Jacob circles three of the oranges.

Three out of the seven oranges, 3/7 of the oranges.

Jacob and Sofia are looking at different fraction representations.

"First we're going to work out the fraction of the shape "that is shaded," says Jacob.

"There are 11 equal parts.

"The denominator is 11," says Sofia.

The bottom number, our total number of parts is 11.

"Six parts are shaded.

The numerator is six." So the fraction of that shade that is shaded is 6/11.

"I'm going to shade 6/11 "of the next shape," says Jacob.

So the next shape is divided into 11 equal parts, Jacob shades six of them, so he has shaded 6/11 of that shape.

I'm going to find 6/11 of the apples.

There are 11 apples altogether, six of the apples would represent 6/11 of the total number of apples.

"What representation is the odd one out? "There are three representations there, "which is the odd one out?" "Write the denominator "and numerator for each representation." "Which one shows a different fraction?" So the first representation there are nine parts and five of them are shaded.

So that fraction there represented is 5/9.

The second shape, there are nine parts, six of them are shaded.

So that shape represents 6/9.

Last representation, there are nine bananas altogether, five of them have been grouped together.

So 5/9 of the bananas are in that group.

So that represents 5/9.

Which is the odd one out? That middle one, 'cause that shape actually represents 6/9, whereas the other two represent 5/9.

"6/9 is the odd one out." Thank you Jacob.

Now it's your turn to have a think about which is the odd one out.

"Which representation is the odd one out?" "Write the denominator and numerator "for each representation.

"Which one shows a different fraction?" Pause the video and see if you can work out which is the odd one out.

And welcome back.

Let's take a look, see if you got the right odd one out.

So that first representation is 5/10.

There are ten equal parts, five of them are shaded, so that represents 5/10 of the whole shape.

The second representation is also 5/10.

There are 10 equal parts, five of them are shaded.

That also represents 5/10.

And the last representation is 4/10.

There are 10 apples altogether, four of them have been put into a separate group.

So 4/10 of the apples are in that group.

So well done if you found the odd one out.

4/10 is the odd one out.

"Jacob and Sofia work out the fraction of pizza "that has been eaten." "The pizza has been cut up into five equal parts.

"The denominator is five." So our denominator is five.

That's the total number of parts.

"Three parts have been eaten," says Sofia.

"The numerator is three." So 3/5 of the pizza has been eaten.

So again, Jacob and Sofia work out the fraction of pizza that has been eaten.

Here's the pizza this time.

What fractions been eaten? "The pizza has been cut up into 12 equal parts.

"The denominator is 12." Now it's always easiest to find the denominator first, total number of parts, that's the easiest way of approaching fractions.

So there are 12 parts altogether.

That's the parts that have been eaten and the parts that haven't been eaten, 12 parts altogether.

So our denominator is 12.

"Seven parts have been eaten.

"The numerator is seven." So always find the denominator first, then find the numerator afterwards.

So our numerator is seven.

"So 7/12 of the pizza has been eaten." "Work out the fraction of pizza that has been eaten." So think carefully about how you are going to work out the fraction of pizza that has been eaten already and that has disappeared.

Think about the denominator, the total number of parts.

Think about the numerator, the parts that have been eaten.

Pause the video and see if you can work out what fraction of the pizza has already been eaten.

Welcome back.

Did you manage to find the answer? Did you manage to work out how much of the pizza has already been eaten? Let's see if you were right.

Jacob says, "The pizza has been cut up "into eight equal parts.

"The denominator is eight." Always find the denominator first, it's the easiest way of finding a fraction.

Seven parts have been eaten, the numerator is seven.

So 7/8 of the pizza has been eaten.

Very well done if you've got 7/8 as the answer.

I'm gonna move on to a slightly more tricky problem.

"Jacob and Sofia work out the fraction of pizza "that has been eaten." but this time we can't see the parts that have been eaten already.

Jacob says, "I can't see exactly how many pieces there were.

"We need to try and work it out." Sofia, very sensible approach to this, Sofia, well done.

Sofia says, "I think another part would be equal "to half of the pizza." So Sofia sketches out another part of the pizza and she says, "That's equal to half." Jacob says, "The other half of the pizza "would also be divided into three parts." So Jacob sketches out the other half of the pizza, which is also three parts, and now they can work out how many parts have been eaten.

We can now see how many parts have been eaten.

4/6 of the pizza has been eaten.

There are six parts altogether, four of them have been eaten.

"Work out the fraction of pizza that has been eaten." "Try and work out "how many parts the pizza was divided into." So pause the video and see if you can work out what fraction of that pizza has been eaten.

Think about how Sofia and Jacob approached this problem and how they worked it out.

Pause the video and see if you can find the answer.

And welcome back.

Did you get the answer? Do you think you got it right? Let's see whether you got the correct answer.

So Sofia says, "Another two parts would be equal "to half of the pizza." So we sketch out another two parts that is equal to half and then the other half of the pizza would also be divided into four parts.

So we can sketch out the other half of the pizza too.

Sofia says, "You can now see "how many parts have been eaten." So how many parts have been eaten? 6/8 of the pizza has been eaten.

There were eight parts altogether and six of them have been eaten.

Very well done if you solved that problem, 'cause that was quite a tricky one.

And let's move on to "Task A".

So in "Task A" you're going to write the fraction.

"Use all three representations to show the fraction." So in that first example, you've actually got the fraction already given to you: 4/7.

And then there are two shapes to shade in.

And then there are seven bananas.

Think about how many bananas you've got to select.

That second group of representations, the fraction is missing, but that first shape has already been shaded.

So can you show that fraction in the other two representations and work out what the fraction is? And then the bottom one, we've got three representations and a missing fraction.

But this time it's the middle fraction that has been given to you.

So can you work out what the fraction is? And can you complete the other representations and write the fraction as well.

So don't forget, always start with the denominator, the total number of parts, and then write the numerator, the number of parts you've got, the number of parts that are shaded.

Here's part two of "Task A".

So, "Work out the fraction of pizza that has been eaten." And again, think about the denominator first and then work out the numerator.

So that first shape there, how many parts are there altogether? That's your denominator.

But how many parts have been eaten? That's your numerator.

So that's part two of "Task A".

Part three of "Task A".

A bit of a challenge, needs a bit of thinking about this one.

So, "Work out the fraction of pizza that has been eaten.

"Estimate or draw the missing parts to help you." So think about how you're gonna work out what fraction of the pizza has been eaten.

Pause the video and have a go at "Task A".

And welcome back.

How did you get on? Did you manage to get to part three of "Task A"? Did you manage to answer part three? Very well done if you did.

Let's take a look at those answers.

So here are some possible answers for part one of "Task A".

Of course your answers may look slightly different as long as you have completed the representations correctly.

So first three representations should all show 4/7.

The next three representations should all show 7/11.

And then those last three representations should all show 5/12.

There are 12 equal parts, five of them are shaded, or five of those apples are put into a separate group.

Well done if you completed part one of "Task A".

And here are the answers for part two of "Task A".

So that first pizza 8/9 have been eaten.

That second pizza, 4/5 of the pizza have been eaten.

Next pizza, 11/12 have been eaten.

And that last pizza, 7/10 of the pizza have been eaten.

So very well done if you completed part two of "Task A".

And then here are the answers for part three of "Task A".

It's a bit of a challenge this one, wasn't it? So that first pizza, 2/3 of the pizza has been eaten.

The second pizza, 3/4 of the pizza has been eaten.

And that last one, 9/12 of the pizza have been eaten.

And again, for 3/4 and 9/12, you may have completed or sketched out a half of the pizza first of all, and then worked out how many parts were in a half before you could work out how many parts were in a whole.

So very well done if you've got onto to part three and got the right answers as well.

That's excellent work, very good thinking.

And let's move on to part two of the lesson.

So part two of the lesson is "Solving Problems".

We've done a little bit of problem solving already.

We're gonna meet some more problems now.

"Jacob is looking at his fruit bowl." "I wonder what fraction of apples "are in the bowl?" says Jacob.

So he's just looking at the apples to start off with.

Sofia is ready with the answer I think.

Sofia says, "There are four apples in total." So we're ignoring the bananas and the oranges 'cause that's not what Jacob is looking at at the moment.

So there are four apples in total.

The denominator is four.

"Three apples are in the bowl.

The numerator is three." So Jacob says, "3/4 of the apples are in the bowl." "Jacob studies the bananas next." Jacob seems very fascinated by his fruit bowl.

I wonder why? "I wonder what fraction of bananas "are in the bowl? says Jacob." "There are three bananas in total," says Sofia.

"The denominator is three." There's only three bananas.

So each of the bananas represents a third of the bananas.

Two bananas are in the bowl.

The numerator is two.

The two is the top number in our fraction.

"2/3 of the bananas are in the bowl," says Jacob.

"Jacob ponders the whole fruit bowl." "I wonder what fraction of fruit is in the bowl?" And again, Sofia is ready with the answer.

"There are 12 pieces of fruit in total." So this time we're talking about all the bits of fruit, the bananas, the apples, and the oranges because they are all types of fruit.

"So there are 12 pieces of fruit in total.

"The denominator is 12." "Nine pieces of fruit are in the bowl.

"The numerator is nine." "9/12 of the fruit is in the bowl," says Jacob.

Here's one for you to try on your own.

"Jacob thinks about the oranges." "What fraction of oranges are in the bowl?" he asks.

What do you think? How would you work out what fraction of oranges are in the bowl? Pause the video and see if you can work out the answer.

Think about the denominator, think about the numerator.

And welcome back.

Did you manage to work out the answer? Do you think you got it right? Let's take a look.

So Sofia says, "There are five oranges in total.

"The denominator is five." "Four oranges are in the bowl.

"The numerator is four." 4/5 of the oranges are in the bowl.

Very well done if you've got that as your answer.

And let's move on to "Task B".

"Sofia and Jacob ice some cakes for a cake sale." Sofia says, "My five cakes look like this." Jacob says, "My seven cakes look like this." And on the plate are the cakes left after the cake sale.

Now your first few questions will be based upon that problem.

Let's take a look at what the questions are.

"So what fraction of Jacob's cakes are left? "What fraction of Jacob's cakes were sold? "What fraction of Sofia's cakes were sold? "And what fraction of the cakes were sold altogether?" So that's part one of "Task B".

Think very carefully about what the denominator is going to be in each fraction, and think about what the numerator is going to be.

And here's part two of "Task B".

Jacob seems to moved on from studying fruit, he's now looking at pandas instead.

So Jacob is studying these pandas, a bit more exciting than fruit, I'm sure, Jacob.

"I have some questions about these pandas," says Jacob.

Jacob would like to know, "What fraction of the pandas are sat on boxes? "What fraction of the pandas are wearing hats? "What fraction of the pandas sat on boxes are wearing hats? "And what fraction of the pandas wearing hats "are sat on boxes?" So again, think very carefully about the whole in each fraction, what is the denominator? And think very carefully about the parts that we are talking about.

Think about what the numerator is going to be.

So pause the video and have a go at "Task B".

And welcome back.

How did you get on? Did you complete part one? Did you get onto part two? Did you complete part two? Well done if you did.

Let's take a look at the answers.

Here are the answers for part one of "Task B".

"So what fraction of Jacob's cakes were left?" He'd made seven cakes altogether and he had two left.

So 2/7 of his cakes were left.

"What fraction of Jacob's cakes were sold?" Well, he'd made seven cakes and he sold five of them.

So 5/7 of his cakes were sold.

"What fraction of Sofia's cakes were sold?" Well, Sofia made five cakes and sold four of them.

So she sold 4/5 of her cakes.

And then finally, "What fraction of the cakes were sold altogether?" Well, between them they'd made 12 cakes, so the denominator would be 12, and nine of them were sold.

So 9/12 of the cakes were sold.

So well done if you got those as the answers for part one of "Task B".

And let's look at the answers for part two of "Task B".

"So what fraction of the pandas are sat on boxes?" Well, there are 15 pandas altogether and nine of them are sat on boxes? So 9/15 are sat on boxes.

"What fraction of the pandas are wearing hats?" Well, there are 15 pans altogether, 11 of them are wearing hats.

So 11/15 of the pandas are wearing hats.

Gets a little bit more tricky now 'cause you've got to think very carefully about what the whole is going to be, what the denominator is going to be.

"What fraction of the pandas sat on boxes "are wearing hats?" Well, we know there are nine pandas sat on boxes.

So what fraction of those nine pandas are wearing hats? 5/9.

Five of the pandas sat on boxes are wearing hats.

So nine pandas are sat on boxes.

The whole has been divided into nine equal parts.

Five of the pandas are wearing hats.

And then finally, question d, "What fraction of the pandas wearing hats are sat on boxes?" Well, how many pandas are wearing hats? There are 11.

11 of them are wearing hats.

"So 11 pandas are wearing hats.

"The whole has been divided into 11 equal parts," each panda represents one equal part.

"Five of those pandas are sat on boxes." So five of the pandas wearing hats are sat on boxes.

Very well done if you managed to complete part two.

So you have some tricky questions there with a bit of reasoning going on.

And hopefully you're feeling a bit more confident about solving problems using fractions.

Very well done in today's lesson.

Excellent work.

And let's move on to the lesson summary.

"So a whole is divided into parts.

"The denominator is the bottom number in a fraction.

"It is the total number of parts "a whole has been divided into.

"The numerator is the top number in a fraction.

"It is the number of parts that have been selected.

And finally, "Fractions can be represented "in different ways.".