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Topic outline
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Video transcript
This unit of work is Unit conversions
Unit conversions can be a difficult topic to teach because students often learn rules without really understanding how they work and are then unable to apply these rules independently and in more complex, less familiar situations. Learners often think of different types of conversion as completely different topics and do not make the wider link to proportional reasoning.
We are going to look at how to use different units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.
We are also going to interpret and use graphs to inform our understanding of direct proportion linked to conversions, applying our understanding in practical situations
This unit of work is just one of several approaches that you could take when teaching this topic and you should aim to adapt the resources to match ability level of your learners as well as your school context.
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Lesson 3 video
Video transcript
A typical example you are likely to meet is converting miles to kilometres. We are going to explore a way of representing this problem that will help you solve any problems like this and lots of other problems as well. Remember there is not necessarily a right or a wrong way of solving this type of problem just valid and invalid ways of solving them. We are going to demonstrate a simple way of setting out this type of problem that might help you.
We’re going to start by looking at how you solve this type of problem into steps. The first step in this example would be to find out how many kilometres there are in one mile. To do this on the left-hand side we need to divide by 10.
If we are going to maintain the equavalence of the left-hand side to the right-hand side of our visual representation, then we must divide the right-hand side by 10 as well. This will give us 1.6.
We want to work out how many kilometres there are in 56 miles, so our next step is to multiply 1 x 56.
What do you think we have to multiply the right-hand side by this time?
Yes, that’s right we need to multiply the right-hand side by 56 as well and this gives us an answer of 89.6.
This tells us that 56 miles is approximately equivalent to 89.6.
We use the word equivalent as our initial assumption that 10 miles is the same as 16 km is an approximation.
This process we have just looked at is a way of finding the multiplier for any conversion. First you calculate how much a single unit is when converted. In this case what one mile is when converted to kilometres. This is why it’s called unitary method. You then use the multiplier to complete the conversion. In this case we multiplied 1.6 km by a multiplier of 56 to get our conversion.
If you are feeling confident you can solve this problem in one step.
Look at the image what would you have to divide and then multiply 10 by in order to get to 56? Remember what you did in the starter for this lesson.
Yes, that’s right you need to divide by 10 and then multiply by 56.
As a fraction this can be written as 56 over 10. This can be simplified to 28 over five or it could be written as a decimal 5.6. However, at the moment it will be better to leave it in its original form as this will help us to see more clearly what is happening.
As you can see we now need to multiply the right-hand side by the same fraction and as you can see we arrive at the same answer that we got when completing the calculation into steps. Which is of course what we would expect.
There is still another way that we can calculate this conversion using the functional relationship between miles and kilometres.
What would you have to divide 10 by and then multiply your answer by to get 16?
Yes that’s right you would need to divide by 10 and then multiply by 16. Once again you could simplify this fraction or even turn into a decimal but is more useful to keep it as it is as it helps you to see clearly what is happening when you do this calculation.
As you can see if you then divide 56 by 10 and multiply it by 16 you get 89.6 which is the same answer we got using the two previous methods.
As well as using this method as an alternative you can also use it to doublecheck what you’ve already done as both methods, using a multiplier or a functional relationship, will arrive at the same answer and if they don’t you know you’ve done something wrong.
You can use this framework to solve any proportional reasoning problem including conversion problems.
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