Yes that’s right you would need to divide by 10 and then multiply by 16. What would you have to divide 10 by and then multiply your answer by to get 16?
There is still another way that we can calculate this conversion using the functional relationship between miles and kilometres. 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.Īs 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. This can be simplified to 28 over five or it could be written as a decimal 5.6. Yes, that’s right you need to divide by 10 and then multiply by 56.Īs a fraction this can be written as 56 over 10. 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. If you are feeling confident you can solve this problem in one step. In this case we multiplied 1.6 km by a multiplier of 56 to get our conversion.
You then use the multiplier to complete the conversion. In this case what one mile is when converted to kilometres. First you calculate how much a single unit is when converted. This process we have just looked at is a way of finding the multiplier for any conversion. We use the word equivalent as our initial assumption that 10 miles is the same as 16 km is an approximation. This tells us that 56 miles is approximately equivalent to 89.6. 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. What do you think we have to multiply the right-hand side by this time? We want to work out how many kilometres there are in 56 miles, so our next step is to multiply 1 x 56. 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. To do this on the left-hand side we need to divide by 10. The first step in this example would be to find out how many kilometres there are in one mile. We’re going to start by looking at how you solve this type of problem into steps.
We are going to demonstrate a simple way of setting out this type of problem that might help you. 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 explore a way of representing this problem that will help you solve any problems like this and lots of other problems as well. 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.Ī typical example you are likely to meet is converting miles to kilometres. The unit will develop pupil’s conceptual understanding by sharing alternative representations, which will provide students with a framework that will help them to apply their understanding of proportional reasoning to a range of contexts linked to conversions.
#IUNIT CONVERSIONS HOW TO#
Securing an understanding of how to tackle proportional reasoning questions can help learners to approach problems given in a variety of contexts, instead of regarding them as unconnected topics. This can mean that they are then unable to apply these rules independently and in more complex, less familiar situations.īecause of the way they are introduced, and if links are not made, learners often think of different types of conversion as completely different topics, and do not make the wider link to proportional reasoning. They will also calculate distance travelled as area under a speed–time graph.Ĭonversions can be a difficult topic to teach, because learners often learn rules without really understanding why these rules work. We are going to apply our understanding in practical situations including travel graphs and currency conversion graphs.Įxtended learners will apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.
We are also going to interpret and use graphs to inform our understanding of direct proportion linked to conversions. We are going to look at how to use current units of mass, length, area, volume and capacity in practical situations, and express quantities in terms of larger or smaller units.
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