Measures of distance. An satellite view of the 12 mile track (19km) which will be used for the world record attempt of BLOODHOUND SSC.

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1 Measures of distance This document aims to give KS3 students an understanding of imperial and metric measures of distance and speed. By the end of this worksheet students should be able to convert distances and speed between a variety of different units. An satellite view of the 12 mile track (19km) which will be used for the world record attempt of BLOODHOUND SSC.

2 Teachers Information To achieve a recognised world land speed the speed must be measured as an average over a fixed distance, either 1 mile or 1 kilometre. BLOODHOUND SSC will measure its land speed record attempt over 1 mile and will aim to average 1000mph. Historically, both metric and imperial measurements have been used in land speed record attempts depending on the nationality of the team attempting it. Aside from land speed record attempts, it is important that students understand and convert between metric and imperial units of measurement as both are still in use and being able to convert between the two is an important life skill. Learning Objectives To understand why different units of distance are used and to have a good idea of the actual distance that each unit represents. To be able to convert measures of distance between imperial and metric units. To be able to accurately convert measures of speed between various units. Possible Differentiation All students should understand that there are metric and imperial units of distance and should have a rough idea how of far each unit is. All students should also be able to convert between different units of distance. Most students should be able to independently convert between units of distance, both roughly and, if necessary, accurately. Some students should be confident in converting between various units of speed. Key Vocabulary Mile Foot Inch Kilometre Meter Centimetre Unit

3 Measures of length Length (or distance) measurements are everywhere. Why are there 2 different ways of measuring length? Before travel and communication between different countries was easy every county had their own way of measuring things. In the UK and USA this system was called the imperial system. This system had units such as miles, feet and inches but, because it was a system that was sort of invented as it went along, it was very difficult to work with. Miles Feet Inches 1 = 5280 = = 1 = = 0.08 = 1 In 1668, English bishop John Wilkins, invented a system which was much easier to understand, called the metric system. Kilometres Meters Centimetres 1 = 1,000 = 100, = 1 = = 0.01 = 1 Nowadays the metric system is officially used in 192 of the 196 countries and used worldwide in lots of important areas such as medicine and science. Although most the world now uses the metric system the imperial system is still used, at least partially, in the UK and the USA. Because both systems are still in use it is important that you can use both, and can convert numbers between each system.

4 It is very important that you know which units you are measuring in! In 1999 NASA lost a spaceship on a trip to Mars because the English scientists involved in the mission were using imperial units and the NASA team thought the units were metric. They completely lost the spaceship (it is suspected to have crashed) and the project had cost $125 million in total! Starter Converting Distances Find an object in the room (e.g. pencil case, desk, poster etc) and measure its size in both centimetres and inches. Record this data in a table such as the one below. Note: Your table will need space to record data for 11 objects. Size Object Cm Inches Desk (length) Desk (width) Pen Now find 5 different objects around the room and measure their size in centimetres only. Without performing any more measurements, find the size of each of the objects in inches. Hint: Use information from the object which was measured in both cm and inches to perform this conversion. Complete the sentence below to describe how you did each conversion. Size in inches = size in cm... Now find 5 more objects and measure their size in inches. Again, record this data in the table. Next convert the sizes measured in inches into centimetres and complete the sentence below to describe how you did the conversion. Size in centimetres = size in inches... 1 meter is equal to 3.3 feet. Using this information, complete the sentences below to describe the calculation necessary when converting between meters and feet. Size in feet = size in meters... multiplied by 3.3 Size in meters = size in feet... divided by 3.3 To convert a distance from units of kilometres to miles, the number must be divided by Fill in the correct units to the equation below. 1 mile = 1.61 kilometres

5 Distance conversions Check your understanding Work in pairs to put the following lengths in order from shortest to longest. Colour the ones which are metric units in red and the ones which are imperial units in blue. It may be easiest for students to do this activity if the table below is printed and cut out so that they can physically move the measurements into the correct order. The activity could also be performed on an interactive whiteboard. 1m 10cm 2km 6ft 20in 1mi 1cm 1in 1ft 50mi 150cm 1km 1cm, 1in, 10cm, 1ft, 20in, 1m, 150cm, 6ft, 1km, 1mi, 2km, 50mi Calculating and converting speed By now you should have had some practice at converting distances between metric and imperial units, but can we do the same with speed? Speed can also be measured in either imperial units (miles per hour for example) or metric units (meters per second is a very common example). So how can we convert between these units? Converting between units with the same time factor is exactly the same principle as converting distances e.g. a mph to kmph conversion would be a multiplication of 1.61, just the same as a miles to kilometres conversion. Using this information complete the following calculations: 1. 70kmph in mph 43.5mph 2. 10ft/s in meters/s 3.03meters/s

6 3. 5cm/min in inches/min 2.3inches/min meters/min in ft/min 330ft/min Converting between speeds with a different time factor requires a little more thought. Lets take the example of BLOODHOUND SSC travelling at 1000mph, how fast is that in meters/s? It is easiest to perform this calculation in stages. Firstly we can convert the distance from miles to kilometres: 1000 miles/hour = 1610 kilometres/hour Next we can convert kilometres into meters: 1610 kilometres/hour = 1,610,000 meters/hour. The final part of the calculation is to convert the time factor of the speed. Currently we are measuring how many meters is travelled in 1 hour, but we want to know how many meters are travelled in 1 second. In order to calculate this we need to know how many seconds there are in 1 hour. 1 hour = 60 minutes 1 minute = 60 seconds 60 x 60 = 3600 seconds in 1 hour. Currently we know that the car travels 1,610,000 meters in 1 hour so to find how many meters are travelled in 1 second that number must be divided by 3600 (i.e. the number of seconds in 1 hour). 1,610,000 / 3600 = 447 meters/s Hint: Whenever you perform conversion calculations, especially complicated ones like this, it is a good idea to perform a 'reality check' at each stage. For example does it sound sensible that 1,610,000 meters/hour is the same as 447 meters/s? Given that we are measuring over a much shorter time period (a second rather than an hour) this answer does sound plausible. Doing this sort of check can highlight any silly errors, such as multiplying instead of dividing, which are easy to make when doing this type of calculation.

7 Fill in the blanks This table is quite challenging. You will need a separate piece of paper to write down your working as you try to convert between each of the units (its always a good idea to show your working, even if you don't think you need to, just in case you make a mistake). Note: Mach 1 is the speed of sound, 340 meters/s. mph meters/s kmph Mach Snail x10-6 Walking pace Cheetah Car on a motorway Jet plane (Boeing 747) Bullet BLOODHOUND SSC Game - Quick-fire questions Very often when converting between imperial and metric units it is not important that you are completely accurate, you may just need a rough idea. For this activity you should work in groups of 3. 1 person will be the host whilst the other two are the competitors. The host asks a question from the selection below and the competitors try to answer as quickly as they can, the first to answer correctly wins the point. Once one competitor reaches 3 points that game is won and people should switch roles. The correct answer for each question is not an exact answer but is within a range. For example: Question: A mobile phone screen may be 3.5 inches diagonally, what size is that in cm? Answer: The correct answer for this activity is any number between 8 and 10cm (actual answer is 8.89cm).

8 If you can run 10 kilometres in an hour, how long will you take to run 10 miles? Any answer between 1 hour 30 mins and 1 hour 45 minutes inclusive (exact = 1 hour 37 mins). The speed limit in French villages is 50kmph, how fast is that in mph? 25-35mph (31mph) The average height of a woman in the UK is 5ft 3in, how tall is that in cm? m (1.6m) A large television may be 55in across, how big is it in cm? cm (140cm) The average length of a football pitch is 340ft, how long is that in meters? m (104m) You are flying from London to New York, a journey of about 3500 miles, how far is that in km? km (5633km) The current land speed record is 1228kmph, how fast is that in mph? mph (763mph) The drive from Southampton to Edinburgh takes roughly 7 hours when you average 60mph, how long would it take if you were travelling at 60kmph? hours (11.27 hours) The long jump world record is 8.95m, how far is that in feet? 28 31ft (29.4ft) BLOODHOUND SSC will cover a mile in 3.6 seconds, how long will it take to do 1 kilometre? seconds (2.24 seconds) The fastest swimmers in the world swim at a top speed of 2.2m/s, how fast is that in ft/s? ft/s (7.2ft/s) An A4 piece of paper is 21cm tall, how tall is it in inches? 6 10 inches (8.27 inches) Run out of questions? Think of your own to challenge your friends to answer! Remember you need to work out the correct answer before you can use the question.