LESSON ONE: WHAT’S YOUR DECISION?
| LESSON ONE: WHAT’S YOUR DECISION? | |
GOALS OF LESSON
To gain a ‘working’ knowledge of the game of cricket, including an understanding of how a batsman can be given out ‘RUN OUT.’
To gain an understanding of how mathematics can be used to assist with making a correct ‘run-out’ decision by examining a number of relevant variables.
FEATURES OF THE LESSON
Pupils will work in groups to brainstorm prior knowledge about the game of cricket, and to discuss the impact of modern technologies on the role of the umpire in decision-making.
Pupils will investigate run-outs from a series of film clips, still photos and hands-on simulation and discuss the factors which are critical if the umpire’s decision is to be correct.
Pupils will investigate how mathematics can be used to determine whether a batsman should be judged in or out from a still photograph.
SUMMARY
Pupils brainstorm prior knowledge about cricket and discuss the different ways a batsman can be ‘dismissed’ (be given ‘out’ by an umpire), with particular reference to ‘run out’ (5 minutes). |
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Pupils experience a 'run out' either indoors with props or outside, then they make decisions on three ‘run out’ situations from video clips from a test series in the 1960s. They then discuss how technology has influenced the adjudication of decisions by umpires in modern cricket (20 minutes). |
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Pupils examine a still photograph of a run-out situation and attempt to judge whether the batsman was ‘in’ or ‘out’. They attempt to justify their decision (10-15 minutes). |
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Pupils distil from a list of variables influencing a ‘run out’ those variables they consider important in developing a mathematical model to assist them to make a decision about the batsman in the photograph (15-20 minutes). |
PREREQUISITES
Basic knowledge of the game of cricket
PREPARATION
Photograph of run-out
Stumps, bails and cricket bat for demonstration purposes
Video clips of run outs, together with laptop computer and data projector
Each student should have a LOG BOOK (small exercise book) in which to record all observations, answers, calculations and reflections throughout the unit
Photocopies of Worksheet 1 (optional)
Prior Learning for Lesson One
Pupils should be familiar with the following concepts:
The difference between a CONSTANT, a quantity whose value is FIXED such as the length of a cricket pitch, and a VARIABLE, a quantity whose value can CHANGE, such as the speed of a batsman.
PLAN
1.1 WHOLE-CLASS DISCUSSION – ACCESSING PRIOR KNOWLEDGE
To introduce the lesson ask pupils:
Whether they play or have played cricket and why
Whether they watch it
What they like about the game
What they know about the game
What does it mean to be IN or OUT in a game of cricket?
The last question will lead to a discussion of how a batsman may be given ‘out’. List these on the whiteboard. The list will include bowled, caught, stumped, hit wicket, run out and others, a complete list is not important. Make it clear to the pupils that the RUN OUT rule in cricket is the focus of this investigation. (Advice for Teachers #1.1) At this point, the rule for a run out must be clearly stated and explained. (Advice for Teachers #1.2) It is important for students to make meaning of a 'run out' so teachers should conduct a simulation of what constitutes 'in' and 'out'. Some teachers may like to use real props for this part of the lesson. (Advice for Teachers #1.3) For an explanation of relevant cricket terms see Glossary.
Advice to Teachers
In some trial schools many students especially boys enjoyed this introduction and teachers found it time well spent to focus on the game and how it is played, as it gave usually disengaged students an opportunity to demonstrate their knowledge.
Teaching and Learning Issue 1: The need for Hands on Experience.
1.2 ACTIVITY: WHAT’S YOUR DECISION?
In order to pique pupils’ interest and ensure they understand how and when a batsman is ‘run out’ in cricket, show these photos and several of the video-clips of actual ‘run out’ situations. Instructions for showing video clips are supplied. In each case, ask pupils to give their decision after looking at the clip at normal speed. Play each clip again in slow motion and ask pupils to judge whether their decision was correct or not. The intention is for pupils to gain an appreciation of how little time umpires have to make decisions, and how important it is for umpires to be in the correct position on the field when doing so.
Pose the question
Estimate how much time an umpire has to make a decision in a close run-out situation. One second? Half a second? One tenth of a second?
Ask pupils to record this estimate in their books. It will be referred to later in the investigation.
1.3 WHOLE CLASS DISCUSSION - CAN YOU MAKE A DECISION FROM A PHOTOGRAPH ALONE?
Pose the questions
How has the technology, particularly the ‘third umpire’, influenced the umpiring of cricket in recent years? (Note: The issue of ‘third umpire technology’ can elicit strong feelings and this is likely to help pupils engage with the task. For the purposes of this Case Study, pupils should recognise that for ‘run outs’ the technology has made an important contribution).
What if ‘third umpire’ technology was not available? How might you decide if an umpire made the correct decision on a run out? (Perhaps we might have a single photograph only of the action, taken just at the critical time when the decision needs to be made.)
After this discussion, give each pupil a copy of the stimulus photograph(s) and read the following scenario:
In an Ashes test match between Australia and England over forty years ago a batsman ran to make his crease. As he ran the wicketkeeper whipped off the bails. The umpire judged the batsman to be "IN", but at the time the decision was very controversial!
In this Case Study you will use mathematics and a photograph of a cricket run-out to help you investigate and then make a decision: "Was the batsman out?"
Ask
Just by looking at the photograph, make a decision whether you think the batsman is IN or OUT. Give a reason for your choice.
Do you think this photograph is clear: in other words, can you easily tell from the photograph whether the batsman is in or out?
Reiterate that the aim of this Case Study is to investigate whether the batsman should have been judged in or out due to a run out.
1.4 ACTIVITY – CONSIDER ALL FACTORS
In this part of the lesson, a discussion will clarify the variables that pupils can potentially investigate in order to make a reasoned judgement about the batsman’s fate. Understanding what variables are and how they can be investigated is the essence of mathematical modelling, and this is an important objective of this Case Study. Hold a discussion to draw out and clarify these concepts, using the following questions as a prompt:
Pose the question
What EXTRA INFORMATION do we need to know to be able to decide whether the batsman was IN or OUT?
Consider your list of extra information. Which of these factors represent quantities that can change or vary?
Quantities that can change or vary are called "variables". Which of the variables in the list can be measured?
Using a thinking tool such as the de Bono “Consider All Factors”, ask for and list pupils’ suggestions. (Advice for Teachers #1.4)
Use the standard measurements for the lengths of a pitch and crease lines to draw a scale diagram of all the crease-lines on a standard batting pitch using the Standard Cricket Measures provided.
What is a "variable"?
Write a list of variables that relate to people going on train journeys.
In class you compiled a list of variables to do with deciding whether a batsman is IN or OUT in a run out situation. Choose the ones you think will be of most assistance with making a decision. Explain your choices.