The purpose of this unit is to engage the student in applying their knowledge and skills of measurement and algebra within the science learning area; to investigate a physical system.
Students develop their skills and knowledge on the mathematics learning progressions measurement sense and using symbols and expressions to think mathematically, in the context of time and motion in sports.
Students will apply their understanding measurement and algebraic skills, solving problems involving time and motion in the context of sporting trivia.
This cross-curricular, context based unit has been built within a framework that has been developed with input from teachers across the curriculum to deliver the mathematics learning area, while meeting the demands of differentiated student-centred learning. The unit has been designed around a six session focus on an aspect of mathematics that is relevant to the integrating curriculum area concerned. For successful delivery of mathematics across the curriculum, the context should be meaningful for the students. With student interest engaged, the mathematical challenges often seem more approachable than when presented in isolation.
The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.
The following five sessions are each based around a model of student-centred differentiated learning.
(This activity is intended to motivate students towards the context/integrated learning area and to inform teachers of each student’s location on the learning progressions, multiplicative thinking and measurement sense):
An international tennis champion has an average serving speed of 200 kmph. The typical distance the ball travels diagonally from his racquet to just inside the opposite service line is approximately 20 m. Estimate how much time elapses from the moment of the serve to when the ball bounces (and thus the time the opponent has to prepare to return the service)?
In this activity, the teacher(s) will be able to locate their students on the measurement sense learning progression by observing their management of the quantities involved in the problem. This activity integrates mathematical skills and knowledge with the science learning area, the physical world. In this unit of learning activities, the SI units of measurement have been used to ensure validity of the physical relationships used in calculations. Students may be more comfortable measuring with derived units such as minutes or hours for time, but should be encouraged to convert these measurements into seconds the SI unit for time, ensuring clear and accurate mathematical communication.
Mathematical discussion that should follow this activity involve:
Focusing on problem solving involving the relationship between physical quantities; speed, distance and time.
Activity
A cricket pitch is just over 20 m long. The fastest of the fast bowlers can manage to bowl the ball at a speed of over 40 ms-1. If the reaction time of the batsman is 0.2 s, does he have time to react to such a fast bowl, determining how he should swing his bat?
Discussion arising from activity:
Building ideas
In the game of cricket there are many speeds that need to be taken into account when batsmen try for runs. Find the following speeds in ms-1.
Reinforcing ideas
In a game of cricket, a batsman can get the ball away at 28 ms-1. The ball is caught at the boundary, 64 m away and returned by the fielder at 20 ms-1.
Extending ideas
In a game of cricket, a batsman can get the ball away at 28 ms-1. The fielder takes 1.5 s for the fielder to catch and throw the ball, with a launching speed of 20 ms-1.
The batsmen take 3.0 s to sprint the length of the wicket and a further 1.0 s to turn and prepare to run again.
Focusing on problem solving involving the relationship between physical quantities; speed, distance and time, with the need to convert into consistent units.
Activity
An Olympic sprinter runs the 100 m in just under 10 s. A cheetah can run at a speed of 120 kmph. By how many seconds would the cheetah beat the Olympic sprinter if they were to race 100m?
Discussion arising from activity:
Building ideas
Compare the following world record times* for different track events.
Distance
|
100 m
|
400 m
|
4 x 100 m relay
|
Time
|
9.58 s
|
43.03 s
|
36.84 s
|
*The records are as at the time of writing this activity.
Reinforcing ideas
Compare the following world record times* for different track events. Times greater than 59.99 s are given in the format minutes:seconds or hours:minutes:seconds.
Distance
|
100 m
|
400 m
|
1500 m
|
3000 m
|
10 000 m
|
42 km
|
Time
|
9.58 s
|
43.03 s
|
3:26.00
|
7:20.67
|
26:17.53
|
2:02:57
|
*The records are as at the time of writing this activity.
Extending ideas
Compare the following world record times* for different track events. Times greater than 59.99 s are given in the format minutes:seconds or hours:minutes:seconds.
Distance
|
100 m
|
400 m
|
1500 m
|
3000 m
|
10 000 m
|
42 km
|
Time
|
9.58 s
|
43.03 s
|
3:26.00
|
7:20.67
|
26:17.53
|
2:02:57
|
*The records are as at the time of writing this activity.
Focusing on problem solving involving the relationship between physical quantities; speed, distance and time.
Activity
An Olympic sprinter takes just 37 steps to cover 100 m in 10 s. How does the the ‘cadence’ (step rate) of the sprinter compare with the wings of a hummingbird which have a flap rate of 80 times per second?
Discussion arising from activity:
Building ideas
A sprinter takes 120 steps to run 200m.
Reinforcing ideas
A 200 m sprinter takes 22 s to complete the race, with an average number of 2.5 strides per second.
Extending ideas
A 200 m sprinter with legs that are 1.0 m long takes 21.50 s to complete the race, with an average number of 2.4 strides per second.
Focusing on estimating using the relationship between physical quantities; speed, distance and time, with the need to convert into consistent units.
Activity
A famous cycle race covers 3540 km over a number of stages. The time for each stage is expected to be completed by a cyclist riding at an average speed of 42 kmph is just over 4 hours. Estimate how many stages are there in the race.
Discussion arising from activity:
Building ideas
The 200 competitors in a cycle race that covers 3540 km are expected to take a total 500 000 pedal strokes. How far, on average, does each pedal stroke carry a competitor?
Reinforcing ideas
The 200 competitors in a cycle race that covers 3540 km are expected to require a total of 800 tyre changes.
Extending ideas
The 200 competitors in a cycle race that covers 3540 km are expected to require the equivalent energy of 50 000 hamburgers (at 2000 kJ of energy per burger).
Focusing on finding and comparing travel distances, speeds and times using everyday measurements.
Activity
Which was the fastest method of transport in these endurance feats?
Discussion arising from activity:
Building ideas
In 2015, Kevin Carr completed his record breaking around the world run. He took 621 days to run 26 200 km.
Reinforcing ideas
In 2017, Mark Beaumont followed the 11, 320 km route described in the ballooning book ‘Around the World in Eighty Days’. The two differences were that Mark was on a bicycle and that he did in in 78 ½ days. How much faster was Mark on his bicycle than the fictitious balloonists?
Extending ideas
In 2016, Thomas Coville completed his solo sail around the world. He took 49 days, 3 hours sailing at an average speed of 41.5 kmph.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/improbable-sports at 8:54pm on the 26th February 2024