Intro Quiz: Decimals and measures: Solving problems including the conversion of standard units of measure

Video: Decimals and measures: Solving problems including the conversion of standard units of measure

﻿Hi year six, welcome to our ninth lesson in the Decimals and Measures topic. Today we'll be solving problems involving the conversion of units of measure. All you'll need is a pencil and a piece of paper. So pause the video and get your equipment together if you haven't done so already. Here's our agenda for today's learning. We'll be solving problems involving the conversion of units of measure. So we'll start with a quiz to test your knowledge from our previous lesson. Then we'll start off by looking at how to convert money and then we'll approach multi-step problems, and finally some independent learning. So let's start with our knowledge quiz, pause the video now and complete the quiz and click restart once you're finished. Now, we'll start the lesson by sorting some statements into the appropriate category. So read the statement and decide whether it should go in the length, mass, volume, or capacity category. Pause the video now while we sort the statements. This is where your statements should have ended up. So in length, we have the width of a boat, the distance travelled by a snail and the circumference of a little finger. Remember the circumference is the distance around a circle. And then the height of Mount Everest, all measured in length, all measure length, sorry, and they can be measured in millimetres, centimetres, metres, or kilometres. Then in the mass, we have the weight of a mobile phone. In volume, we have the amount of medicine needed to be taken, the amount of squash shoes to make one drink and the amount of juice consumed by a child at lunchtime, and volume would be measured in millilitres or litres. And then we have capacity, the total water a swimming pool can hold, or the amount of water bottle can hold. Again, measured in millilitres or litres. So, in order to be able to access our multi-step problems, I just need to make sure that we're able to convert between pounds and pence. So let's think about how many pennies are equal to one pound? So one pound is equivalent to 100 pence. So thinking back to how we drawn our conversions using arrows across our numbers in previous lessons, how will we convert between pounds and pence? So to convert from pounds to pence, we multiply by 100. One pound multiplied by 100, gives us 100 pence, and remember when we're multiplying by 100, we're moving our digits two places to the left. So then if we multiply by 100 to get from pounds to pence, to get from pance to pounds, we must divide by 100. And dividing by 100, we're moving our digits two places to the right. So let's look at an example. We've got one pound 56, and we want to convert it to pence. Converting from pounds to pence we multiply by 100, so we need to move the digits two places to the left. So the one from the ones column moves into the 100s column, and then the five and six move across into the tens and ones column. So one pound 56 is equivalent to 156 pence. Now I'd like you to pause the video and practise the conversion between pounds and pence. So let's go through this solutions. First one to convert 2 pound 35 into pence, we multiply by 100, which gives us 235 pence. 45p converted to pounds. We divide by 100, which gives us 0.45 pounds. When we're going back into pence from pounds, so we're multiplying by 100, which gives us 1056 pence. 0.67 pounds multiplied by 100 gives it 67 pence. And 567 pences divided by 100 gives us 5 pound 67. Now we're going to use those skills to solve some multi-step problems involving the conversion of units of measure. So here's our first problem that we'll work on together. James is making a costume for a party and he buys the following lengths of material. So he buys this amount of plain fabric, and this amount of patterned fabric. And we can see the plain fabric costs 95 pence per square metre, and we can see the pattern fabric costs 1 pound 35 per square metre. So my first job is to find out how many square metres of each fabric James bought, and then I'll need to calculate the cost for each piece of fabric. So if I'm trying to calculate square metres, that means that I'm looking to calculate the area of the fabric. So we'll start off with the plain fabric, and we're calculating the area. So we're doing length times width. So for the plain fabric, I'll be doing four multiplied by 1.75. Remember when we're multiplying decimals, we want to make them into intengers fast, to make the multiplication easier, and then we'll convert back. So four times 1.75 is the same as four times 175 divided by 100. Because 175 is 100 times greater than 1.75, so we have to convert back. And that gives us seven metres squared. So he bought seven square metres of plain fabric, which costs 95p per metre square. So here, we therefore multiply the 95P by the seven metres, which means that he spent 665 pence on this fabric. And we can divide it by 100 so that we're working in pounds. So he spent 6 pound 65 on the plain fabric. Now, you may be feeling confident to pause the video and calculate the cost of the pattern fabric, if not keep watching and we'll go through it together. So we're looking at the pattern fabric now, and we're going to calculate the area first. So that will be two metres times 1.5 metres. Again, we'd rather multiply integers than decimals. So we know that two times 1.5 is the same as two times 15 and then divided by 10. So the area of this fabric is three metres squared. We know that the pattern fabric costs 1 pound 35 per square metre. So we're going to multiply 1 pound 35 by three square metres. And that gives us 4 pound five. And then the last thing is that we wanted to know how much he spent all together. So we need the total cost of both pieces of fabric. So we're adding the total cost of each, which gives us a total of 10 pound 70. So now I'd like you to have a go at this problem by yourself. Laura is also buying material for a costume. She spends 10 pound 15 altogether. She buys four metres squared of pattern fabric. So how much plain fabric did Laura buy? Pause the video now, and answer the question. So let's go through this one together. So we know that she spent a total of 10 pound 15, and she bought four metre squared of pattern fabric. So we need to work out how much she spent on pattern fabric. So we can look at four metre squared, multiplied by 1 pound 35 is 5 pound 40. So she spent 5 pound 40 on pattern fabric, which means if we subtract 5 pound 40 from 10 pound 15, she had 4 pound 75 left to spend on plain fabric. So if we know that it's 95P per square metre, and she spent 4 pound 75 on it, we need to think how many times does 95 go into 4 pound 75. So we're going to do a division. And that gives us five metres squared. So she bought four metre square patterned, and five metre squared of plain fabric. Let's have a look at another question together. So here we have two shops that sell apples at different prices. In shop one, it's 1 pound 22 per kilogramme. And in shop two, it's 11p per 100 grammes. Zak wants to buy 500 grammes of apples, and we want to know which shop should he go to to get the best deal. So first of all, we need to look at the first cost which is given per kilogramme. And we need to think about how many grammes is in one kilogramme. Think about that prefixed kilo. So one kilogramme is equivalent to 1000 grammes. So the first bag is 1 pound 22 per 100 grammes, how much would it cost for 500 grammes? We need to think about the relationship between 1000 grammes and 500 grammes. Well, we know that 500 is 1/2 of 1000. So we're going to have to divide the cost by two to find the price of 500 grammes. So 1 pound 22 divided by two is equal to 61P. So in shop one, Zak will spend 61p on apples. Now I'd like you to have a go at calculating how much it would cost for him to buy 500 grammes of apples from shop two. Remember that in shop two, you're given the price per 100 grammes. So think about what I've done here with the relationship between the two amounts. Pause the video now, and have a go at calculating how much he'd spend in shop two. So we know in shop two, it's 11p per 100 grammes. He wants to buy 500 grammes, so he wants to buy five times that amount. So you multiply 11 by five, which gives us 55P. So Zak should go to the second shop for the best deal. He'll spend six p less on apples in the second shop. I want you to have a go at a similar question independently. So again, we've got two shops. In shop one, the price for a kilogramme of apples is 1 pound 22. And in shop two, the price for 100 grammes is 11p. Zakia bought 2.5 kilogrammes of apple from shop one and Sope bought the same amount of apples from shop two. So who spent more? You may want to do some conversion so that you're working in whole and the same units. So you might want to think about converting this to grammes to help you work it out. Pause the video now and solve the problem. So, Zakia bought 2.5 kilogrammes of apples from shop one. So we know that 1 pound 22 is the price for one kilogramme, but she wants 2.5. So that's 2.5 times as many. So you had to do the same to the cost. So one pound 22 multiplied by 2.5, which is the same as 122 times 25, and then divided by 100. Which means that she spent three pound five. Let's see how much Sope spent. So in shop two, it's 11p per 100 grammes, Sope wants 2.5 kilogrammes, which if we convert to grammes is 2,500 grammes. So we need 25 times this amount. So 11p therefore needed to be multiplied by 25, which gives two pounds, sorry, 275 pence, and then divide that by 100 to convert it to pounds, which gives us two pounds 75, which means that Zakia spent more. So in shop one, 2.5 kilogrammes of apples is 20p more, not 20p, 30p more expensive than in shop two. And now it's time for you to apply everything you've learnt about converting units of measure, to answer some questions independently. So pause the video, complete the task, and then click restart once you're finished. So our first question, we're looking at arranging five p coins into different arrays and calculating the area and perimeter. A five p coin has a diameter of nine millimetres, the diameter being the measurement from boundary to boundary and through the centre of the coin. And Aleeyah has 20 of these coins and arranges them in a rectangular array. So I've sketched my first array. In this one, I did it, was just one coin by 20, okay. So, I know that the height of this is nine millimetres because that's the diameter. I need to know the length of it. So I've got 20 coins with a diameter of nine millimetres. Nine times 20 is equal to 180 millimetres. So to calculate the area, I multiply 180 by nine, which gives me 1,620 millimetres squared. And then I have to divide this by 100 to turn into centimetre squared, which gives me 16.2 centimetre squared. The other way you may have done it was to convert in the first place to centimetre so you may have had 18 centimetres multiply by 0.9 centimetres. Then the perimeter we're adding all of the sides together, or you may have used your knowledge of to put things in brackets. So 180 plus nine plus 180 plus nine or 180 multiplied by two, plus nine multiplied by two gives us 378 millimetres, which is equivalent to 37.8 centimetres. So for my second one, I arranged them like this. So it's two coins high and 10 wide, which is 18 millimetres high and 19 millimetres wide. I calculated the area by multiplying those dimensions, which gave me 1,613 millimetres squared. And then I divided it by 100 to get my answer in square centimetres, which is 16.2. And what I realised was the area is going to be the same each time. It will be the perimeter that will change. So the perimeter of this one, I added the sides all together, which was 216 millimetres, and then divided it by 10 to give my answer in centimetres. You may also have drawn an array which was four coins by five coins. And again, it would have had an area of 16.2 centimetre squared, but this time a perimeter also of 16.2. On to question two, we've got a market stall that sells drinks at different prices. One sells them at 65 pence per 100 mililiters, and the other one charges three pound 50 for 500 mils. And Hassan buys 600 millilitres of drink, so we want to know how much would he pay at each stall? So I said, for the second one, you should work out the cost per 100 millilitres first. We'll come to what that looks like in a minute. So the first one, 65p for 100 mils, to calculate the cost for 600 millilitres, we just multiply it by six. 65 times six gives us 390 pence, which divided by 100 gives us three pound 90. For the second one, we've got three pound 50 is equal to 500 mils. So if we calculate, if we divide that by five, we can find a price for 100 millilitres. So three pound 50 divided by five is 70P. So in this stall is 70p per 100 millilitres. So now we can use that information to calculate 600 millilitres. And therefore we multiply it by six. So we'll do 70 times six, which gives us 420 pance, which is equivalent to four pound 20 . Question three, we're still on the drink stalls. We've got the same prices again. Beka spend 17 pound 50 on 2.5 litres of drink for her family. And we need to work out which stall did she buy it from? So what I've done is I've converted 2.5 litres into millilitres, so that I'm always working in the same units. That was my first job. So in the first stall, 65p for 100 millilitres. So we need to calculate the cost for 2,500, which is 25 times 100 millilitres. So 65 times 25 gives us 1,625 pence, which is 16 pound 25. So it looks like it's probably going to be the second stall, but it's important that we check our answer. So we'll go to the next one and have a look. So she spend on the second stall, it's three pound 50 for 500 millilitres. So for 2,500, we need to multiply that by five, three pound 50 multiplied by five gives us 17 pound 50. So she bought it from the second stall, and she spent a lot of money on 2.5 litres of drink. Now the third and final questions involve calculating the perimeter. So a farmer fences three rectangular fields. So the distance around the fields, we can see the dimensions of her fields and which materials she used to fence them and their different prices. So we'll start with field A, which is eight metres by five metres, which means that it has a perimeter of 26 metres adding all those sides together. She used wire for this fence, which is 50p per metre. So she needed 26 metres wire. So 26 multiplied by 50p gives us 1,300p and that converts to 13 pounds. So that was her first fence. In field B, which is 30 metres by 25 metres, the perimeter is 110 metres, so that's how much of the fence material she needs. And she use plastic for this one, which is 75p per metre. So 110 metres multiplied by 75p gives us 8,250P, which converts to 82 pound 50. And then for the final fence, she used wood and the perimeter was 23 plus 18 plus 23 plus 18, which is 82 metres. And we can see that it was one pound 20 per metre. I've converted that into pence, just to ease the calculation. 82 times 120 is equal to 9,840 pence. And that converts to 98 pound 40. And then, you have to add those three numbers together in order to calculate how much she spent altogether. So 13 pounds plus 82 pound 50 plus 98 pound 40 is equal to 193 pound 90. Great work today year six. In our next lesson, we will convert between units of time. I'll see you then.

Worksheet: Decimals and measures: Solving problems including the conversion of standard units of measure

Completed: Decimals and measures: Solving problems including the conversion of standard units of measure

In today’s lesson, we will convert between pounds and pence, and then work on multi-step problems involving calculation of measure.

Maths

Decimals and measures: Solving problems including the conversion of standard units of measure

Introductory Quiz

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