How fast is fast?

Purpose

This unit is designed to provide students with a measurement context in which to use number operations. In calculating speed from distance and time, they will apply number strategies as they convert between units.

Specific Learning Outcomes
• calculate speed from measured distance and time
• solve multiplication problems using doubling and halving strategies
• use known multiplication facts to solve multiplication problems
Description of Mathematics

This unit explores the concept of speed. Students will realise that speed is made up of two measurements, one of distance travelled, and one of time taken. These two measurements can be used to calculate speed, which can be converted to different units.

Required Resource Materials
bike

measuring tape

Key Vocabulary

speed, distance, time, kilometres, metres, seconds, minutes, hours, reasonable, accurate, approximate, prediction

Activity

Session 1

In this session we discuss speed. What does it mean? How fast is fast?

1. Ask students the key question:
How fast is fast?
2. Record some answers on the board. Expect responses to come in a range of forms, eg 100 km an hour, 100 miles an hour, a cheetah running, the speed of light, 100 ‘kay’, 10 metres per second, etc. You may wish to record the speed of light and sound under these if they are suggested, possibly after all other suggestions have been collected.  The speed of light is around 300,000,000 metres per second and the speed of sound is around 340 metres per second (in air).
3. Ask students to tell you how they would measure the speed of something.  Discuss their suggestions.
4. Refer back to the list of speeds that students said were fast.  Ask:
Which of these are actual speeds?
What do all the actual speeds have in common?
Support and guide the discussion to reach the conclusion that all have both a distance unit and a time unit involved in them.
5. Explain to students that speed is usually described by how far an object travels in a given amount of time. We usually use kilometres per hour or metres per second.
6. Pose the question:
How fast am I travelling if I travel 100 kilometres in 2 hours?
7. As the students give their answers encourage them to explain the strategy they used to find them:
I went half of 100 which is 50. So I was travelling 50 kilometres per hour.
I divided 100 by 2 to work out how far for each hour. 100 divided by 2 is 50.
8. Pose further questions of the same form:
How fast am I travelling if I travel 40 kilometres in half an hour?
How fast am I travelling if I travel 10 metres in 2 seconds?

Session 2

In this session students find their speed over a 1km run in kilometres per hour.

1. Ask students to estimate how fast they think they can run for 1 kilometre.  Record students’ predictions.
2. Ask students how far they think a kilometre is. Use a unit like ‘lengths of the field’, or ‘laps of the tennis court’.
3. Explain to students that you are going to find out how fast they can actually run, by running a kilometre and timing how long it takes.
4. Move outside and measure either the length of the field or the distance round the tennis court and agree on a course which is 1 kilometre long.
5. Time students running around the course. Give each student their time in minutes and seconds.
6. Back in the classroom challenge students to work out their speed in kilometres per hour. First give students a couple of minutes to try to work out their speed on their own, then return together as a class to discuss strategies used.
I took over 6 minutes, and there are 60 minutes in an hour. I know 6 x 10 is 60, so if I ran that speed for an hour I would go 10 kilometres.
I took 4 minutes and 52 seconds to run 1 kilometre, and I know that that is nearly 5 minutes. There are 60 minutes in an hour, which is 12 lots of 5, so I ran at about 12 kilometres per hour.
7. Help students work out some ‘markers’ like the ones above. 1km in 5 min = 12km per hour, 1km in 6 min = 10km per hour. This will make it easier for them to approximate their own speeds.
8. Discuss how students could work out their speeds if they are between the ‘markers'. Depending on the ability of your students you may want them to be more or less accurate. If students are using mental strategies the nearest half or quarter kilometre per hour is probably reasonable. If students are using calculators then you will need to discuss how many decimal places are appropriate.
How many minutes did you take?
How many minutes are there in an hour?
How many times will …go into…?
How many seconds did you take?
How many seconds are there in an hour?
How many times will …go into…?
9. Ensure that all students have found their speed in kilometres per hour, then compare with their predictions from the start of the lesson.
10. Ask students how fast they think the fastest runners in the world can run 1 kilometre.
11. The world records for the 1000m are:
Men:               2:11.96            Noah Ngeny (1999)
Women:           2:28.98            Svetlana Masterkova (1996)
12. Ask students to work out the approximate speeds of the world record holders in kilometres per hour.

Session 3

In this session students find their speed over 100m, both in metres per second and in kilometres per hour.

1. Ask students to estimate how fast they think they can run for 100 metres. Record students’ predictions. Discuss whether they think they can run faster for 100 metres than they did for a kilometre. Why or why not?
2. Ask students to describe how far they think 100 metres is.  They should be able to use their experience from the previous session to make a reasonable estimate.
3. Explain to students that today you are going to find out how fast they can actually run, by running 100 metres and timing how long it takes.
4. Move outside and agree on a course which is 100 metres long.
5. Time students running around the course. Give each student their time in seconds.
6. Back in the classroom challenge students to work out their speed in metres per second. First give students a couple of minutes to try to work out their speed on their own, then return together as a class to discuss strategies used.
I took 20 seconds, and went 100 metres. I know that 20 goes into 100 5 times so I must have gone 5 metres each second.
I took 16 seconds to run 100 metres. 16 x 2 = 32 and 32 + 32 + 32 = 96 so there are six and a bit lots of 16 in 100. I must have been going over 6 metres per second.
7. Discuss how students could work out their speeds if the numbers don’t work out evenly. Depending on the ability of your students you may want them to be more or less accurate. If students are using mental strategies the nearest half or quarter metre per second is probably reasonable. If students are using calculators then you will need to discuss how many decimal places are appropriate.
How many seconds did you take?
How many metres would that be for each second?
If you share 100 metres among … seconds, how far did you go each second?
8. Ensure that all students have found their speed in metres per second, then challenge them to work it out in kilometres per hour. They may want to start again from their time for 100 metres, or work it out from their speed in metres per second. Discuss the different methods:
There are 60 seconds in a minute, so 6 metres per second is the same as 360 metres per minute, and there are 60 minutes per hour so 360 metres per minute is 60 x 360 metres per hour. 60 x 360 is the same as 30 x 720 (doubling and halving) and I can work that out by 3 x 72 x 100 = 21600. 21600 metres per hour is 21.6 kilometres per hour. I was running more than 6 metres per second, so that is more than 21.6 kilometres per hour.

16 seconds for 100 metres is the same as 160 seconds for 1 kilometre. That’s 2 minutes and 40 seconds. Two and a half minutes goes into an hour 24 times, so I was running less than 24 kilometres per hour.
9. Compare students’ speeds with their predictions from the start of the lesson.
10. Ask students how fast they think the fastest runners in the world can run 100 metres.
11. The world records for the 100m are:
Men:              9.58 seconds                Usain Bolt (2009)
Women:           10.49 seconds              Florence Griffith-Joyner (1998)
12. Ask students to work out the approximate speeds of the world record holders in kilometres per hour.

Session 4

In this session students will attempt to calculate the speed of student on a bike, both in metres per second and in kilometres per hour.

1. Ask students how fast they think a student on a bike can travel.
2. Provide them with a bike and allow them to carry out the experiment themselves using both of the two courses from the previous sessions.
3. Provide assistance as required with calculations as outlined in the previous session.
4. Encourage the students to share the strategies used in the calculations.
5. Discuss results as a class.
How much faster did you go on the bike?
Did you think it would be that much faster?
6. The world records for the 1 kilometre time trial are:
Men:                Arnaud Tournant          58.875 seconds
Women:           Anna Meares   68 seconds (no record for 1km – 500m record x 2)
7. Ask students to work out the approximate speeds of the world record holders in kilometres per hour.

Session 5

In this session students are challenged to work out the speeds travelled by athletes in their world record performances over various distances.

1. Ask students what distances they think people can run the fastest.
2. Discuss why we can run faster over shorter distances.
3. Work out the speed travelled by the fastest 200m runners
The world records for the 200m are:
Men:               19.19   seconds                        Usain Bolt (2009)
Women:           21.34   seconds                        Florence Griffith-Joyner (1998)
4. Are these speeds slower or faster than for the 100 metres? Why or why not?
5. Challenge students to find the times for other races (either running, riding, or driving) and calculate their speeds. The IAAF (International Association of Athletic Federations) website is a good source of records. http://www.iaaf.org/statistics/records/