Lesson video

Hi everyone, my name is Miss Ku, and I'm really happy to be learning with you today.

Today's lesson will consist of some keywords that you may or may not have come across before, but I will be here to help.

You might find it tricky or easy in parts, but we'll learn together.

Really excited to be learning with you.

So let's make a start.

Hi everyone, under the unit of Arithmetic Procedures with Fractions, we'll be looking at problem solving with arithmetic procedures involving fractions.

And by the end of the lesson, you'll be able to use your knowledge of arithmetic procedures involving fractions to solve problems. So let's have a look at some keywords that we'll be using in our lesson today.

A proper fraction.

Now, a proper fraction is a fraction where the numerator is less than the denominator.

For example, 2/3.

An improper fraction is a fraction where the numerator is greater or equal to that denominator.

For example, 7/5.

And a mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

For example, three and 1/2.

Today's lesson will be broken into two parts.

First, we'll be solving problems involving fractions, and second we'll be using a calculator.

So let's have a look at the first part.

We'll be solving problems involving fractions.

Now, we use fractions in many different ways in real life.

And when approaching problem solving questions, have an idea of the strategy or approach needed, and then apply those fraction skills.

Identifying the strategy first and then completing the calculation breaks the problem solving question into chunks.

However, understanding the wording is firstly important before identifying a strategy.

So in real life, we sometimes do not use the word subtract, add, divide or multiply in context questions.

So I want you to have a look at these words, and which operation do you think is associated with these following words? Well, hopefully you've spotted lots of refers to multiplication.

Difference refers to subtraction, total refers to addition, shared refers to division, sum refers to addition and split between also refers to division.

So we can sometimes use these words in problem solving questions, and it identifies to us what operation that we need to use.

So without working out the answer, I want you to match the statement with the correct answer.

Aisha has 2/3 of a litre of water.

Lucas has 4/5 of a litre of water.

And Sam has 1/2 a litre of water.

I want you to match the statement on the left with the calculation on the right.

Which calculation do you think shows the total water of all three students? Which calculation do you think shows the difference in water between Lucas and Aisha? Which calculation do you think shows Aisha shares her water between two other friends? And which calculation do you think shows two lots of Aisha's water bottle? So you can give it a go and press pause if you need more time.

Well, hopefully you can spot the total water of all three students is 2/3 add 4/5 add 1/2.

Total refers to addition, summing.

The difference in water between Lucas and Aisha, well, difference refers to subtraction.

So it would be 4/5 subtract 2/3.

Aisha shares her water between her two friends.

Well, Aisha has 2/3 and she's sharing between her two friends, so it's a division of two.

Two lots of Aisha's water bottle.

So that would be what Aisha has, which is 2/3 multiply by two because there are two lots.

This is a nice little way to really focus on what the language in the question is asking you to do.

Sometimes, mathematical words are used to identify when to add, subtract, multiply or divide, and when calculating area of shapes, which operation do you think we tend to use? Well, we tend to use multiplication.

For example, the area of a rectangle is length multiplied by width.

The area of a triangle is 1/2 multiplied by the base times the perpendicular height.

So you can see how these formulas use multiplication when referring to area.

What about perimeter? Now, when calculating the perimeter of shapes, which operation do we tend to use? Well, we tend to use addition because perimeter is the total distance around a two dimensional shape.

So let's have a little look at an example.

Which statement do you think matches which calculation? To work out the parameter of rectangle A, which calculation do you think it would be? To work out the area of rectangle A, which calculation do you think it would be? To work out the area of rectangle B, which calculation do you think it would be? And to work out the difference in area between A and B, which calculation do you think it would be? So you can give it a go and press pause if you need more time.

Well done.

Well, hopefully you spotted the perimeter of rectangle A is summing up all those things, 1/2 add 3/4 add 1/2 add 3/4.

I also quickly want to show you how you could write the perimeter of rectangle A as two lots of 1/2 and 3/4.

It's exactly the same as summing up 1/2 add 3/4 add 1/2 add 3/4.

The area of rectangle A is a multiplication.

So looking at those lengths and widths of rectangle A, it's 1/2 multiplied by 3/4.

The area of rectangle B is 2/5 multiplied by 2/3.

And the difference in area between A and B, well, to work out the area of A, you multiply the 3/4 by the 1/2.

To work out the area of B, it's 2/5 multiplied by 2/3.

And we are doing difference, so once we get those answers, we subtract.

Well done if you got this one right.

So now, without calculating, match the statements and explain how you knew which statement matched which calculation.

See if you can give it a go and press pause if you need more time.

Well, let's have a look at our question.

The land A consists of two and 3/5 metres in width and three and 2/3 metres in length.

And our first statement says each metre squared will cost £24.

Now, because it's referring to metres squared, that means we're looking at area, and remember area uses that multiplication.

So that means the multiplication of the lengths is the area, then they're multiplied by 24, indicating it's £24 per metre squared.

Now, the next statement says each metre will cost £24.

Well, metres refers to perimeter or length.

So we had to sum and then multiply by the 24.

So here, you can see it's the addition of the lengths is the perimeter, and then multiply by that 24 gives us £24 per metre.

This is a nice little check question as we're not calculating, we're just understanding how the calculation comes about.

So let's move on to a check question where we are going to calculate our answer.

A rectangular grass plot of land has lengths four and 2/5 metres by two and 1/10 metres, and the Oak teacher wants to plant wildflowers in the plot of land.

And it costs £10 per metre squared.

Now, without using a calculator, how much will it cost the teacher to fill the area with wildflowers? See if you can give it a go and press pause if you need more time.

Great work, everybody.

So let's see how you got on.

Well, given the question refers to metres squared, its area, so we're looking at multiplying.

Four and 2/5 multiplied by two and 1/10, converting these two improper fractions, it's 22/5 multiplied by 21/10.

Now, using your skills on multiplying fractions, we have 462/50, which works out to be 231/25 because we've simplified, giving us nine and 6/25 metres squared.

Now, remember it costs £10 per metre squared, so we have to round up.

So nine and 6/25 rounds up to give 10 metres squared.

Giving that it costs £10 per metre squared, 10 multiplied by 10 is £100.

So it's going to cost our Oak teacher £100.

Now let's have a look at the same grass plot, but the Oak teacher wants to put a fence all the way around the plot.

The fence costs £5.

45 per metre.

Without a calculator, how much will it cost to fence around the plot? See if you can give it a go and press pause if you need more time.

Well done, so hopefully you spotted because we're putting a fence all the way around, it's perimeter.

So we need to add these lengths together.

So adding up all our fractions, two and 1/10 add four and 2/5 add two and 1/10 add four and 2/5.

Summing up our integers first, we have 12.

And summing up our fractions using a common denominator, we have one.

So that means adding up our lengths and widths, we have a total length of 13 metres.

Given the fact that each metre costs £5.

45, we multiply £5.

45 by 13.

For me, I've chosen this method, but there's lots of different ways in which you can multiply £5.

45 by 13.

I've chosen to multiply £5.

45 by 10 add £5.

45 times two add £5.

45 times one.

Summing these together, I get £70.

85.

So the cost to fence around the plot is £70.

85.

This is a great question as we're using knowledge on summing mixed numbers, as well as multiplication of decimals.

Now it's time for your task.

For question one, don't use a calculator, ensure you show your working out.

We have a rectangular flower bed with lengths three and 2/3 metres and a width of two and 3/5 metres.

And Jacob wants to plant flowers inside the plot, but needs to buy compost.

The compost bags each cover one metre squared, and the cost of each bag is £5.

70.

How much will it cost Jacob? For B, Jacob also needs to put a metal edging around the plot, and the edging is sold in metres of £3.

42 per metre.

How much will it cost Jacob to put the edging around the flowerbed? See if you can give this a go and press pause if you need more time.

Well done, so let's move on to question two.

Question two states that you're not allowed to use a calculator, and you have to show your working out.

Now, on a school trip, each bottle contains 3/4 of a litre of water.

Three teachers have a different number of water bottles to give to the students in their groups.

Each student gets an equal share.

Teacher A has two bottles, teacher B has four bottles and teacher C has four bottles too.

For question A, how much water does each teacher have to share? For B, there are three students in teacher A's group, so how much water will each student get? In C, there are six students in teacher B's group, so how much water would each student get? And for D, there are five students in teacher C's group.

So how much would each student get? See if you can work it out and press pause if you need more time.

Well done, so let's go through these answers.

For question one, hopefully you spotted because we need to buy compost for each metre squared, that means we are multiplying.

So three and 2/3 multiply by two and 3/5 is nine and 8/15.

Now, remember, we have to round up, so that means he needs to buy 10 bags, each costing £5.

70 each, so it's going to cost Jacob £57.

For part B, we needed to work out the edging all the way around, so we had to sum those lengths and widths.

The method I've chosen here is summing up all those integers and then summing up all those fractions, thus giving me a total perimeter of 12 and 8/15.

But we have to round up because edging is sold per metre, so it's 13 times 3.

42.

For me, I've chosen to work it out as 10 multiplied by 3.

42 add two multiplied by 3.

42 add one multiplied by 3.

42, thus giving me an answer of £44.

46.

So to edge all the way around the flower bed is going to cost Jacob £44.

46.

For question three, we had to work out how much water does each teacher have? Well, remember a bottle is 3/4 of a litre.

So teacher A has two lots of 3/4 of a litre, which is 3/2 of a litre.

Teacher B and C both have three litres, four lots or 3/4 litres.

Well done if you got that one right.

For question B, we know that teacher A's group has three students.

So if teacher A has 3/2 litres, divide this by three, each student gets 1/2.

There are six students in teacher B's group.

Well, we know teacher B has three litres.

So three litres divided by six is 1/2 a litre each for each student.

And for D, we know teacher C's group has five students.

So if three divided by five is 3/5, so each student gets 3/5 of a litre each.

Great work, everybody.

So let's move on to the second part of our lesson, which is using a calculator.

Now, we'll be using the Casio fx-991 ClassWiz, and it can do so much including calculating with fractions, but it is important to know where all these buttons are associated with fractions.

Inputting proper or improper fractions is really easy and uses this fraction button.

So let's have a look at the example of 245/1,000.

Inputting this in, you simply press 245, the fraction button, 1,000, and then execute, and it should look like this.

The great thing is it simplifies it to give you the answer of 49/200.

The Casio 991 ClassWiz also allows you to change the format of a number.

For example, if you press five, fraction button, eight, and execute, 5/8 will display on your screen.

If you wanna convert this to a decimal, simply press format, scroll down to decimal, and then execute.

And it converts it into a decimal, which is 0.

625.

It's also important to remember where the mixed number button is.

You can access this by pressing shift and the fraction button, and you can see the proper format of a mixed number on the calculator screen.

From here, you can then insert the integer and the proper fraction.

So let's input five and 7/8 into our calculator.

You press shift and then fraction button and then insert the five and 7/8.

Once you press execute, it will automatically convert it into an improper fraction.

So now let's have a look at a quick check using our calculator.

I want you to work out the following.

Remember to use the fraction button for the proper or improper fraction, and press shift and that fraction button for inputting mixed numbers.

I want you want you to write the answers from your calculator display of the following.

So you can give it a go and press pause for more time.

Well done, let's see how you got on.

Well for A, you should have got 13/15.

For B, 211/35.

And for C, 1,134/115.

Well done if you got that right.

So remember the Casio ClassWiz allows you to change the format of a number.

If you were to input the improper fraction as eight, fraction button, five, and execute, you can see it displayed here.

But to convert it to a mixed fraction, press format, scroll down, and then you can see that option, mixed fraction.

Press execute, and then it will convert it into a mixed number for you.

So let's see if you can use those skills.

Using your calculator, work out the following, but I want the answer as a mixed number where possible.

Now, remember, use that format button to change the display of your answer.

See if you can give it a go and press pause if you need more time.

Great work.

Let's see how you got on.

Well for D, you should have had 157/125.

This is an improper fraction, so that means we need to convert it into a mixed number to give us one and 32/125.

E, we have 124/15.

This is an improper fraction, so we can convert it to a mixed number to give us eight and 4/15.

Next we have F, which gives us simple answer of three.

That was a great question because remember to scroll out to leave that radical or square root.

Well done if you got that one right.

Now let's have a look at another check question, but we'll be using our calculator, and I want you to give your answer as a decimal.

The garden has a length of five and 4/5 metres by four and 2/3 metres.

It has a rectangular pond in the centre with lengths three and 1/4 by two and 1/2 metres.

The question wants you to work out the area of the grass and the garden.

And if bags of seeds cost £6.

45 and are sold in boxes covering three metres squared, how much do you think it would cost to reseed the grass? Think about your strategy first, and you are using a calculator.

See if we can give it a go and press pause if you need more time.

So let's have a look to see how you got on.

Now, this is the calculation that we should be using.

The whole area of the garden is four and 2/3 multiplied by five and 4/5, and we're subtracting the area of the pond, which is two and 1/2 multiplied by three and 1/4.

This would give us the area of the grass.

Now, remember your calculator will do everything here, so just ensure you press that mixed number function on your calculator.

As a decimal, we should have 18.

941, so on and so forth.

And as a mixed number, 18 and 113/120.

Part B states that each bag of seeds cost £6.

45, and they're sold in boxes of three metres squared.

So from here, we're going to divide our area by three.

This allows us to find out how many three metres squareds fit into our garden, which is 6.

313, et cetera, et cetera.

However, we can't go to the shop and ask for 6.

313 et cetera boxes.

So we have to round up.

Seven boxes are needed, so the cost would be seven multiplied by £6.

45, which is £45.

15.

This question really does focus on the strategy, as well as using your calculator effectively to work out those answers.

Massive well done if you got this one right.

So now let's have a look at your task.

Question one shows Aisha is restoring some old picture frames, and she wants to cover the frame in gold leaf.

We need to work out the area of the frame, and then we need to work out the cost.

Now, remember, gold leaf in this case costs £12.

84 per metre squared.

So how much is it gonna cost Aisha to gold leaf the entire picture frame? See if you can give it a go.

Press pause if you need, and remember how to access those functions on your calculator.

Well done, so let's move on.

Question two shows a square, and the square has a length of two and 2/5 units, and it's been plotted on an axis.

Now, the coordinate of A is one and 3/4 and two and 2/5.

The question wants you to write the coordinates of B and C and D, giving your answer as an improper fraction.

This is a great question.

See if you can give it a go.

Press pause if you need.

Well done, so let's see how you got on in question one.

Well, hopefully you spotted to work out the area of the picture frame only, you work out the area of the whole big rectangle and subtract the smaller rectangle in the middle.

This gives you three and 251/420.

Now we have to round up, so that means we need four metres squared worth of gold leaf.

So we multiply four by £12.

84, which gives us £51.

36.

Massive well done if you got that one right.

For question two, the square has a length of two and 2/5.

So from our coordinate A, we need to add two and 2/5 vertically and horizontally.

So let's work out B first.

Well, B is found by simply adding two and 2/5 to the x coordinate of A.

So that would give us four and 3/20 and two and 2/5.

Let's have a look at the coordinate C.

So we're adding vertically two and 2/5 to that y coordinate, giving us one and 3/4, still remains the same for the x coordinate.

And four and 4/5 is our y coordinate of C.

For D, you can work it out either way you want.

For me, I'm going to look at B, and for B I'm gonna add on that two and 2/5, thus giving me an answer of four and 3/20 and four and 4/5.

Massive well done if you got that one right.

So in summary, we use fractions in many different ways in real life.

When approaching problem solving questions, really do have an idea of the strategy or approach needed, and then apply those fractional skills or multiplying by decimal skills, ensuring to understand the key words which indicate which operation to use.

And knowing which buttons to press on a scientific calculator is so important.

Remember to use that fraction button for proper or improper fractions, and press shift on that fraction button for inputting mixed numbers.

Massive well done today, everybody.

It was great learning with you.