04 Mathematics - West Indies Cricket Board

Te a c h i n g C a r d s
M AT H E M AT I C S
TARGETED OUTCOME
The aim is to develop, improve and apply the skills of mental
arithmetic, averages, probability, measurement, scales,
co-ordinates, angles and data handling.
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Te a c h i n g C a r d s
M AT H E M AT I C S
MENTAL MATH EXERCISES
Numeracy hour warm-up.
•
Practise and develop oral and mental skillsmental strategies and the four operations
•
Use all four operations in real life world
problems.
Pupils should also be encouraged to think of
their own problems.
1. A batter scored a six and two fours off
three balls before he was out. What was
his total score?
14
2. A batter has scored 82 runs. How many
more must she score to reach 100?
18
3. In three matches a bowler took 2 , 4, and
6 wickets. What was the average number
of wickets taken?
4
4. What is the total number of runs scored by a
batter in four matches – 23, 17, 15, and 30.
85
5. Afternoon play restarted at 2 p.m. The
players had 40 minutes for lunch. What
time did they stop play for lunch?
1.20 pm
6. How many balls are bowled in an innings
of 40 overs of six balls with an extra 12 no
balls bowled?
252
7. 60% of the runs were score in twos. If you
scored 80 runs, how many were scored in
twos?
48
8. Assuming a batter can score a maximum
of 6 runs from every ball, in an over of 6
balls what is the maximum number of runs
he can score?
36
9. The team scored 400 runs. One of the
batters scored 100 (a century). What percent
age of the team’s run did she score?
25%
10. Carl Hooper ‘s average score per game was
42. He played six games. What was his
total number of runs for the series?
252
11. The distance between the wickets is 20.12
metres. If the batter hits a ball and takes
three runs, how far does each batter run?
How many metres does each run altogether?
Convert this distance into centimetres.
60.36m/6036cm
12. If a bowler has bowled 38 balls, including
two no balls, how many overs has he
bowled?
6
13. The height of each stump is 71 cm. How
far would they stretch if all three were
placed end to end?
213cm
14. The opposition scored 185 runs. Your team
has a total of 144. How many more runs are
required to win? If there are 6 overs left to
play, what is the average number of runs
required per over if your team is to win?
42/7
PROBLEM-SOLVING
1. Sabina Park has a seating capacity of
15,000. If 85% of the seats are occupied,
how many seats are empty?
2,250
2. Excluding zero, the most common score
from a single ball are 1, 2, 3, 4 and 6.
Using these numbers, find ways in which a
player can score 10.
3. Challenge yourself by finding a score
which can be achieved in at least 20
different ways.
4. In Barbados, a bat costs $60, a ball $10, a
helmet and pads together cost $250 and a
set of whites costs $135. A cricket club
buys nine sets of whites, six balls, two
bats, and two sets of pads and helmets.
How much is spent?
$1,895
5. If a ticket to a Test Match costs $36 and
the ground has a capacity of 2000.
(a) How much money would the ticket office
receive if the game were a sell-out?
$72,000
(b) How much would it receive if only 60%
of tickets were sold?
$43,200
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Te a c h i n g C a r d s
M AT H E M AT I C S
6. The top six West Indian batter scored a
total of 247. The highest scorer scored
103, the lowest 15.
(a) Suggest possible scores for the other
four batters.
(b) Suggest another six scores that also
add up to 247.
PROBABILITY
• What is the mean, median and mode age
of the team?
• Create graphs to show the mean, median
and mode scores.
• What is the range of scores for the whole
batting team?
• Select one of the scores and show how the
score might have been reached through
scoring 1,2,3,4 or 6 runs from each ball.
•
Use the words ‘certain’, ‘likely’ or ‘not likely’
to complete these sentences that relate to
cricketing situations:
•
The batter has scored 0 in every innings
so far. It is…he will score 100 today
•
The batter is on 99 and is facing the worst
bowler in the opposing team. It is…he
will score 100
•
The ball has crossed the boundary. It is…
there will be a score of 4 or more
MEASUREMENT
•
If a batter has an equal chance of scoring
a 1,2,3, 4 or 6 from a ball, what is the
probability that he or she will score a 2?
The size of the wicket
•
Consider probability in a game of cricket,
i.e. what is the probability that:
• What was the average number of runs per
ball faced by each batter?
• Repeat the exercise using
other examples of scorecards
found on the Internet.
A list of useful websites can be found in ICT
section page 23.
Centimetres
c.1702
2 stumps
30.48 x 60.9
c.1775
3 stumps
55.88 x 15.24
(b) Everyone will score 4?
c.1787
3 stumps
60.96 x 17.7
(c) Someone will be caught?
c.1817
3 stumps
68.58 x 20.32
(a) Someone will score 1?
(d) Someone will score more than 20?
AVERAGES
INFO
Below is a Team Score Card (A copy
of this scorecard is also provided on
Information Sheet 8.)
Players
1
2
3
4
5
6
7
8
9
10
11
Age
24
27
29
27
25
22
25
27
30
27
21
Runs
72
44
22
16
15
10
10
21
8
7
5
8
Balls Faced
108
132
44
8
31
52
27
24
24
14
5
• Draw diagrams to scale and compare how
the size and constitution of the wicket has
changed over the years.
• Diagram 1 shows the dimension of a full-size
pitch. Measure your cricket playing area, for
example, the distance between wickets and
the distance to the boundary.
• Draw a diagram to scale of your cricketplaying area showing the distance you
have measured.
• Measure your stride, and estimate how
many strides are required to measure the
15 metres between wicket. This is the
recommended distance when playing
cricket with a soft ball. Mark out the playing
area using strides, then measure for accuracy.
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Te a c h i n g C a r d s
M AT H E M AT I C S
How To Choose The Correct Bat
The vertical height from the player’s wrist
(when their arms are hanging by their sides)
to the ground should coincide with the height
of the bat.
Diagram 1:
The dimension of a full-size cricket pitch.
• Convert the bat measurements from inches
to centimetres (1 inch = 2.54cm)
• Consider how a batter might choose the
correct bat – find an easy way to measure
against the body and compare answers
amongst the class
• Plot the height of pupils in your class and
the size of bat required on a graph
• Analyse the results (averages, patterns of
data).
Diagram 2:
Choosing the right bat.
SCALES
INFO
Using a scaled map of the
Caribbean similar to Information
Sheet 27 (found in the Social Studies
section), estimate and then measure
as accurately as possible the distance (in km)
between these grounds:
27
• Sabina Park and Antigua Recreation Ground
• Queen’s Park Oval and Bourda
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Te a c h i n g C a r d s
M AT H E M AT I C S
• Shaw Park and Tortola
ANGLES
• Kensington and Queens Park (Grenada)
Diagram 4 shows a right-handed batter scoring
strokes from the pavilion end of the pitch. A
total of 56 runs was scored.
• Mindoo Phillip Park and Arnos Vale
• Botanical Gardens and Jarette Park.
Pupils will first need to identify the location of
the cricket grounds on the map.
• Convert the distances into kilometres (1 mile
equals 1.61 kilometres)
• Re-draw the scale using kilometres.
CO-ORDINATES
The possible fielding positions in
cricket are mapped on a grid on
Information Sheet 9.
INFO
9
A poster featuring the field positions on a
co-ordinates grid is included at the back of
the folder.
• Using the diagrams, identify the co-ordinates
of various fielding positions for a righthanded batter
• Consider how these might change for a lefthanded batter. For example find the new
co-ordinates for ‘Deep mid-wicket’, ‘Longoff’ and ‘Long-on’ if a left-handed batter
was in
• What percentage of fielders is on the leg
side of the field? What percentage is behind
the batter? Approximate to the nearest
whole number.
Diagram 3:
Fielding Positions.
• Consider the fielding positions in relation to
the diagram
• What is the angle of the shot most
frequently hit?
• List the angle of shots in order of frequency
• Using the diagram, if a batter hits 50 balls,
how many would be to his or her right?
• Record the scoring strokes of a batter hitting
10 strokes in the playground. Draw a
diagram to represent his or her shots.
HANDLING DATA
Study the scorecard on Information Sheet 10.
• How many 1’s were scored?
• How many 4’s were scored?
• What was the average number of
scoring strokes hit by the batsmen?
INFO
10
• How many balls bowled by Rohan Gavaskar
resulted in no runs? (A ball that results in no
runs is recorded on the score sheet as a dot.)
• What was the average number of runs
scored per ball bowled?
• Explore various graphical techniques to
interpret the data. Which type of graph
presents the data in the clearest way?
Diagram 4
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Te a c h i n g C a r d s
Using the information provided
on Information Sheet 11 and 12,
or from information found on the
Internet, present the batting score
or bowling figures of a batter or
bowler in graph form.
M AT H E M AT I C S
INFO
11
INFO
12
INFO
Practise scoring a game of cricket
using the scoring template on
Information Sheet 13 and 14.
Build your own spreadsheet to
record the batting and bowling
figures of the players in your team.
13
INFO
14
A pre-recorded game of cricket could be used
for this activity.
21
Information Sheet 8
M AT H E M AT I C S
TEAM SCORE CARD
What to do.
•
•
What is the mean, median and mode age
of the team?
What is the range of scores for the whole
team?
Players
Age
Runs
Balls Faced
1
24
72
108
2
27
44
132
3
29
22
44
4
27
16
8
5
25
15
31
6
22
10
52
7
25
10
27
8
27
21
24
9
30
8
24
10
27
7
14
11
21
5
5
SCORING STROKES OF A RIGHT-HANDED BATSMAN
The diagram opposite shows how a batter
scored 56 runs.
What to do.
•
Measure the angle of each of the shots
he hit
•
At what angle did he hit the balls most
frequently?
22
Information Sheet 9
M AT H E M AT I C S
CO-ORDINATES
The grid below shows the possible fielding positions for a right-handed batter.
What to do.
Find the coordinates for each of the fielding positions.
Close Field
In Field
Out Field
In Field
1. Wicket-keeper
6. Point
15. Deep Extra Cover
20. Umpire 1
2. Slip
7. Cover Point
16. Long-Off
21. Umpire 2
3. Gully
8. Mid-Off
17. Long-On
4. Silly Mid-Off
9. Mid-On
18. Deep Mid Wicket
5. Backward
Short Leg
10. Mid-Wicket
19. Long Leg
11. Square Leg
12. Backward
Square Leg
13. Fine Leg
14. Bowler
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Information Sheet 10
M AT H E M AT I C S
DATA HANDLING – SCORE CARD
Study this score card.
•
How many boundaries were scored by West Indies?
•
How many wickets did Kamal and Sairaj take?
•
How many runs did Hinds score?
24
Information Sheet 11
M AT H E M AT I C S
DATA HANDLING
Batting Figures – First Class Cricket
Player
Matches No. of Runs Highest Score Average 100’s
50’s
C. Gayle
56
3,899
259*
43.80
10
16
D. Ganga
54
2,468
138
28.36
4
12
R. Sarwan
76
3,975
122
34.26
6
26
B. Lara
201
16,386
501*
49.95
45
69
C. Hooper
295
19,720
236*
46.29
55
95
S. Chanderpaul
124
8,020
303*
47.17
19
23
R. Jacobs
104
4,745
131
35.94
9
24
D. Ramnarine
59
638
43
8.98
0
0
M. Dillon
57
632
52
8.20
0
1
C. Cuffy
68
306
37
5.10
0
0
R. King
58
295
30
6.02
0
0
* indicates not out
Bowling Figures – First Class Cricket
Player
Matches
Wickets
Bowling Average
Best
C. Gayle
56
32
36.68
4-86
D. Ganga
54
1
82.00
1-7
R. Sarwan
76
14
31.92
6-62
B. Lara
201
4
102.75
1-1
C. Hooper
295
495
35.05
7-93
S. Chanderpaul
124
52
41.78
4-48
R. Jacobs
104
–
–
–
D. Ramnarine
59
221
24.75
6-54
M. Dillon
57
189
28.21
6-40
C. Cuffy
68
187
27.21
7-80
R. King
58
194
24.28
7-82
25
Information Sheet 12
M AT H E M AT I C S
Batting Figures – Test Cricket
Player
Matches No. of Runs Highest Score Average 100’s
50’s
C. Gayle
16
816
175
30.22
1
4
D. Ganga
15
563
89
20.85
0
2
R. Sarwan
17
1,059
91
37.82
0
9
B. Lara
83
7,221
375*
50.49
18
34
C. Hooper
92
5,020
178*
35.10
10
26
S. Chanderpaul
51
2,934
137*
38.60
2
23
R. Jacobs
37
1,476
113*
27.33
1
7
D. Ramnarine
12
106
35*
6.23
0
0
M. Dillon
21
280
36
7.36
0
0
C. Cuffy
7
45
15
5.00
0
0
R. King
14
50
12*
3.57
0
0
*indicates not out
Bowling Figures – Test Cricket
Player
Matches
Wickets
Bowling Average
Best
C. Gayle
16
7
24.85
3-25
D. Ganga
15
-
-
-
R. Sarwan
17
0
-
-
B. Lara
83
0
-
-
C. Hooper
92
103
50.13
5-26
S. Chanderpaull
51
6
116.16
1-2
-
-
-
-
D. Ramnarine
12
45
30.73
5-78
M. Dillon
21
76
31.81
5-111
C. Cuffy
7
18
42.38
4-82
R. King
14
44
27.77
5-51
R. Jacobs
26
Practice scoring your own game of cricket using this blank scorecard template together with the bowling analysis
template on Information Sheet 14.
What to do
Information Sheet 13
M AT H E M AT I C S
27
Practice scoring your own game of cricket using this blank scorecard template together with the bowling analysis
template on Information Sheet 13.
What to do
Information Sheet 14
M AT H E M AT I C S
28