Lesson video

Hi, welcome to our last lesson on fractions.

Today we'll be looking at problem solving with fractions.

Well done for all your really hard work this week, I know that your teachers would be so proud of the work that you've done.

Good job.

So get your pencil and piece of paper ready, and let's go through today's agenda.

We're doing problems with fractions in the context of shape.

Then we'll be looking at fractions in lengths and perimeter, we'll be finding missing lengths, then your independent task followed by a final quiz to test your knowledge from today's lesson.

Here's your Do Now.

Use the key vocabulary in purple to fill in the blanks.

Pause the video now to complete the task.

So we can use fraction notation to describe part of a whole.

The denominator represents the total number of equal parts and the numerator represents that number of parts that we are describing.

So in our example, if this spacebar is the whole, then the shaded section represents two out to three parts, So 2/3 or in written form two thirds of the whole.

The unshaded section here is 1/3 as a fraction or written in words like this one third of the whole.

Now we're looking at fractions in the context of perimeter.

So we're looking at the shape.

The shape is a square, so we know that all of the sides are the same length.

We can label each side a.

Because they're the same length, they can be assigned that same letter.

To calculate the perimeter, which is the distance around the shape, we can add all of the sides together, a + a + a + a equals the perimeter.

We also can use our knowledge of multiplication to write that as a x 4.

Now this one only works when it's a square because the sides are the same length.

Now let's look at a square with fractions.

So the fraction that represents the length of each side is 1 3/4.

The square has sides that measure 1 3/4 of a centimetre each.

I don't need to label it on all sides because I know they're the same length, but just to make it really clear, I'm going to show it on all of the sides.

If you're only given one measurement that usually will mean that the sides are equal and it's a square.

So we're going to use the repeated addition strategy because we haven't learned multiplication of fractions yet, that is coming.

So we will be doing 1 3/4 + 1 3/4 + 1 3/4 + 1 3/4 to give us the perimeter of the shape.

Now, we can either convert these into improper fractions, add and then convert back to mixed numbers, or we could keep them as mixed numbers and then do some converting after.

I think it's more efficient to use these as improper fractions so that's what I'm going to do.

So 1 3/4 as an improper fraction is 7/4.

So now I know that I'm doing 7/4 + 7/4 + 7/4 + 7/4, and that will give me my perimeter.

I know that 7 + 7 + 7 + 7 is 28.

So the perimeter is equal to 28/4.

And then I'm going to convert that back into a mixed number.

I know that there are seven lots of four quarters in 28 quarters, so this actually converts to 7.

So the perimeter of the shape is seven centimetres.

Let's do another one together.

This is a right-angled triangle.

I know that because one of the angles measures 90 degrees It's also a scalene triangle, which means that all of the sides are different lengths.

And here are the measurements for the sides.

So to find a parameter, I add the three sides together.

So that is 1 1/3 + 3 1/4 + 3 1/2.

Now I know that they all need to have the same denominator first to work with them, so I'll have to do some converting here.

And again, I want them to be as improper fractions so I can work with them easier.

So 1 1/3 = 4/3, 3 1/4 = 13/4, and 3 1/2 = 7/2.

My common denominator for 3 4 and 2 is 12.

So I'm going to convert them all to equivalent fractions with the denominator of 12.

So 4/3 x 4 to make 16/12, 13/4 x 3 to make 39/12 and 7/2 x 6 = 42/12.

Add the three numerators together, and that gives us 97/12.

Okay, I'm going to put it down here and then I'm going to think about converting this back to a mixed number.

I know that there are eight lots of 12/12 in 96.

So eight wholes with 1/12 remaining, so 8 1/12.

So the perimeter of the triangle is 8 1/12 centimetres.

Now it's time for you to practise by yourself.

Pause the video and calculate the perimeter of the shape.

So you will have noticed that you were only given two measurements here.

That's because this is a rectangle which has two lots of equal sides.

So I can put on this one is 1 1/5 centimetres, and this one is 2 1/2 centimetres.

So again, we convert first to improper fractions.

So this one, 2 1/2 converts to 5/2.

And again, down here.

And this 1 1/5 is 6/5.

So now we're working with 6/5 + 6/5 + 5/2 + 5/2.

You know that we need to have these with the same denominator, the common denominator is 10.

So we're converting them all to fractions with the denominator of 10.

And this will be 12/10 because we're multiplying it by 2.

And this will be 25/10 because we're multiplying by 5.

12 + 12 + 25 + 25 = 74/10.

Which converts to 7 4/10 and simplifies to 7 2/5.

So the perimeter of the rectangle is 7 2/5 centimetres.

Now we're going to look at finding missing lengths where we are given the perimeter.

This is an isosceles triangle, which means that it has two equal sides and two equal angles.

These angles are the same.

I know that because of these two lines marked on two of the sides, those lines means that the sides are equal.

So then if I know that this side and this side are equal, I can label this side 1 1/3 centimetres.

So this time I'm given the perimeter, the perimeter is 4 1/2 centimetres.

And I'm being asked to find the missing length, which I will call a.

So I know that if I think about part-whole models, I know that 1 1/3 + 1 1/3 + a is equal to the perimeter of 4 1/2.

because I knew that part + part + part = whole.

Now if I rearrange that to have the whole at the beginning to find the missing part, then I do whole 4 1/2 subtract part that I know 1 1/3 subtract other part that I know 1 1/3 is equal to a.

So I'm going to convert them first to improper fractions.

9/2 - 4/3 - 4/3 = a, then I need to convert them to improper fractions with the same denominators, the common denominator is 6.

So 27/6 because I multiplied by 3 subtract 8/6 multiplying this fraction by 2, subtract 8/6.

Then 27 take away 8 take away 8 is 11/6.

And I can convert that back to a mixed number, which is 1 5/6 centimetres.

So the missing length here is 1 5/6 centimetre.

Let's do another one together.

This is an irregular quadrilateral.

It's a four sided shape when no sides are equal in length.

So I know the perimeter and I'm being asked to find the missing lengths.

So it's always helpful to write out the equation for what you're doing.

So I know the whole, 4/3 take away the parts, 2/3 which is this one.

Take away 1 1/2, which is this one.

Take away 1/2 which is this one is equal to a.

That gives me my missing length.

So improper fraction first.

4 1/3 equivalent to 13/3.

Subtract 2/3, that's fine as it is.

Subtract 3/2 subtract 1/2 equals a.

So now we have them all as improper fractions, we need to do the next step where they are improper fractions with the same denominator.

Again, it's 6 this time.

So I'm multiplying this by 2 to give me 26/6.

This is multiplied by 2 as well 4/6.

This is multiplied by 3, 9/6.

and this is multiply by 3, 3/6 equals a.

24 - 4 - 9 - 3 = 10/6, and I can do a final conversion, 10/6 = 1 4/6 which is equal to 1 2/3.

So our missing length was 1 2/3 of a metre this time.

Now it's your turn.

Pause the video and work out the missing length a.

So starting with your equation, you know, the whole, you know, the perimeter, 3 2/3.

And you're subtracting the known part.

So you subtract the 2/3 and 1 1/6 which will give you a.

Convert to improper fractions, 11/3.

Take away 2/3 take away 7/6 equals a.

Now we're looking for a common denominator, which is 6.

Multiply this by 2, 22/6.

Take away 4/6 take away 7/6.

And I know that 22 takeaway 4 is 18, take away 7 is 11/6 which is equivalent to 1 5/6 as a mixed number.

1 5/6 of a metre is my missing length.

Now it's time for your independent task.

Pause the video and complete the task.

Once you've finished, click resume video in the top right hand corner of your screen so that we can go through the answers together.

So for question 1 a, you're looking at a rectangle and calculating the perimeter.

I'm going to add in those other two measurements.

So we know here that we are doing 3/4 + 3/4 + 1/2 + 1/2.

We just need to convert them to have the same denominator, which is 4.

So 3/4 stays the same and 1/2 become 2/4.

Altogether this is equal to 10/4 and it converts to 2 2/4, which simplifies to 2 1/2 metres.

So that is the perimeter for your first shape.

Perimeter is equal to 2 1/2 metres.

The second shape you would have recognised as an isosceles triangle.

These two lines here showing us that the sides are the same length.

So I can label this 1 1/3 metres, and I'm going to do this up at the top.

So I know that + 1 1/3 + 1 1/3 + 5/6 is equal to my perimeter.

Whoa, sorry about that.

Let me write that again.

Perimeter.

It's very hard writing on this screen.

And then I convert to improper fractions.

So 4/3 + 4/3 + 5/6.

Then I need the same denominators, which is 6 so 8/6 + 8/6 + 5/6 = 21/6 which converts to 3 3/6, which simplifies to 3 1/2 metres, so our parameter here is 3 1/2 metres.

Onto the next question.

You're being asked to calculate the perimeter, first of the square.

We know that the sides that are equal or 1 1/2 centimetres.

So you are adding four lots of 1 1/2.

I'm just going to take one step out here, I know that 1 1/2 converts to 3/2.

So I'm doing 3/2 + 3/2 + 3/2 + 3/2 and that equals two 12/2.

And I know that there are six lots of 2/2 in 12/2 so this converts to 6 centimetres.

So my perimeter here is 6 centimetres.

This is an equilateral triangle, which means that all of the sides and all of the angles are equal.

Okay.

So here we're doing 5/7 + 5/7 + 5/7 + 5/7 which is equal to 15/7 which converts to 2 1/7.

So your perimeter is 2 1/7, looking at the units, metres.

Onto the last question.

Here you're given the perimeter and you're asked to find the missing length.

So this is an irregular quadrilateral for a.

So we know we were looking at 5 1/3 of a metre as our perimeter, subtract our known measurements 1 1/3, 1 1/2, 5/6.

Okay.

So then we convert to.

What do you call them? Improper fractions.

So this is 16/3 and this is 4/3.

I'll just put equals a on there, sorry.

And this is 3/2 and this is 5/6 equals a.

And then I need to have them as improper fractions with the same denominator, common denominator is 6.

So 32/6 takeaway 8/6 takeaway 9/6 takeaway 5/6 is equal to 10/6.

I need to just move up to here.

10/6 = 1 4/6 = 1 2/3, so that is your missing length there.

And then your final one, an isosceles triangle.

So you know this side is also 3/4 of a metre.

And a is your missing length.

So you're looking at perimeter 2 1/6 subtract the two known lengths which is equal to a.

Improper fractions first where necessary.

So 13/6 take away 3/4 take away 3/4 is equal to a.

Then we need a common denominator, which is 12.

26/12 take away 9/12 take away 9/12 is equal to 8/12 which simplifies to 2/3 of a metre.

Now it's time for your final knowledge quiz.

Pause the video and complete the quiz to see what you have remembered.

Great work today.

In our next lesson, we're going to move on to our new topic, which is missing angles and lengths.

I'll see you then.