The Purpose of the SBA Project
It is the view of CXC and Mathematics Teachers across the region that
students are not transitioning fluently enough from "School Math" to real
world applications. This has caused many governments to invest and train
members of the education systems in the delivery of STEM and STEAM
approaches in an attempt to bridge that gap between the real world and the
classroom.
The Mathematics SBA is an attempt by CXC to bridge that same divide and
forever link real world, everyday mathematics to the theoretical concepts
discussed in the classroom. In CXC's own words, the project may require the
candidate to collect data or demonstrate the application of Mathematics in
everyday situations.
The Project Title
It should be clear and concise and related to a real world problem. The title
may be in the form of a question or a precise and clear statement of intent,
call it a hypothesis if you wish, but its intention is to show what you will be
trying to accomplish.
Introduction
The introduction for the project should be well thought out and should be a
comprehensive description of the project itself. It should set the
background for what you intend to do. The objectives [whatever you plan to
accomplish] should be stated in the introduction and those objectives should
be very clear and precise.
Method of Data Collection
The method that you use to collect your data needs to be stated clearly
here. If you plan to use a survey, a questionnaire, an experiment, an
investigation... You must ensure that your Method is free from flaws as a
flawed method will lead to unreliable data and if your data is unreliable
then whatever conclusions you come up with will be flawed. Take some
time to talk with your teacher/advisor/facilitator to make sure that your
data collection method is sound. The instrument that you intend to use to
gather the data should be stated here, blank tables with headings, survey
questions, diagrams and general calculations about things you plan to
discuss.
Presentation of Data
The Presentation of your data needs to be accurate and well organized. You
may have used a survey or a table to collect your initial information, this
table needs to be properly laid out with appropriate column headers that
describe exactly what you are doing. In addition to the table you will need
to have at least one graph that shows your data. You may use any type of
appropriate statistical graph, bar char, pie chart, linear graph, histogram
etc. Your graphs need to be well labelled in terms of axes. You should also
introduce the graph don't just place it on the page. For example
The following graph shows ........ then add the graph.
if you are modelling data and looking for relationships or correlations I am
recommending that you use the software program GRAPH. It is excellent at
plotting scatters and can easily draw a best fit line or spline [You can talk to
your teacher about that.] that can help you with your analysis.
​
You also need to be accurate in your use of Mathematical concepts while
you present your data so make sure that everything is accurately worked out.
It is recommended that you use Microsoft Office or other spreadsheet
program to generate your graphs. CXC does want you to use the technology
that is available.
Analysis of Data
As stated immediately above, this is a Mathematics SBA so you need to use
the language of Mathematics as well as use mathematics concepts in your
Analysis. You must write in a coherent way. You do not need to be wordy
you only need to make sense of the data and write that understanding in a
way so that th e reader can understand what you mean. You should be
detailed and you should be coherent. Try to answer the following questions
as you write;
What is you data saying to you?
What patterns do you see, what trends?
Look at averages and compare quantities using percentages.
Its kind of like writing a statistical report. CXC doesn't have these in the
English A syllabus anymore but your English teacher knows how and can help
you so ask for help if you don't know how.
Discussion of Findings
So you have done your analysis, what exactly have you found out?
It may be what you thought you would find, it may be different but your
work has shown something. What is that something. State it clearly and
precisely. Please understand that your discussion of findings MUST follow
from your data and your analysis of that data. So don't try to impress anyone
by making claims that are not supported by the data that you have or by the
analysis you have done.
The conclusion
Ahh, relief, finally you have reached the end. Now all you need to do is
make a conclusion and you are good at this. After all your language teacher
did teach you how to do it.
Regardless, just make a summary of what you have done in the analysis of
data and in the discussion of findings. That will be good enough.
And finally
You do get marked for grammar and the use of English so make sure to at
least spell check your work. Yes it should be typed.
Make sure you create a content page
You definitely need a cover page with your personal and center information
You will most likely use electronic submission so save your document, back
it up somewhere, email yourself a copy , etc, just make sure that when your
teacher needs it you have it
And if you used a survey or questionnaire etc you can include those in an
appendix at the end of the back of the project
Make sure your work is well organized
AND Remember you have a 1000 word limit so avoid being wordy and write
clearly and to the point
CSEC Mathematics SBA ideas and Topics
Choose a topic that is suitable to you or modify an existing one. Please feel
free to suggest other topics
1. How much money do students spend on a daily basis? [survey]
2. What is the preferred type of vehicle used for public transportation in my
community? [Survey]
3. An investigation into the growth of "X type of seedlings" over a "X time
period"
4. Do students of form X spend more time on social media than on studying?
[survey]
5. Are school children/Students consuming too much sugar? ​ Modifications of
this question could include
 How many sugary drinks do students consume on a daily basis?
 A comparison of the sugar per serving of a selected number of [fruit,
soda, energy, flavored water] drinks ​ ​
 Do form X students drink more sodas than fruit based drinks?
6. What is the optimum angle to throw a ___________ to achieve the maximum
distance?
​
javelin
Shot-put
Discuss
7. What effect does the run up speed have on the distance covered in a
______________?
Long jump
Tripple jump
8. Does the location of a store affect the prices that are charged?
8. How does the amount of weight carried by an athlete affect their speed
over a 50m distance?
9. What is the cost incurred if a faucet/pipe is left dripping for a year?
10.What is the optimum range for scoring goals on a_______________​
Netball court
Football field
Basketball court
11. Does the height of the shooter affect the percentage of goals scored in a
netball match?
12.Is the penalty spot the best place to shoot a penalty from on the football
field?
13.Does the size of the ball used affect the number of goals scored in a netball
match? [hint: try using a netball, football or
volleyball to shoot goals
and compare the results]
14.Do drink companies give as much as they say they are? Here do a survey of
different brands of juice, measure the volume in each box
and compare with the
number printed on the carton; a variant of this question could include measuring mass of various
products
15.How are the winnings in a game affected if you use a biased die compared
to a fair die? [die is same as dice here]
16.Using the same cyclist is a BMX faster than a mountain bike over 100m
17.Is typing faster than writing?
18.What is the effect of the run-up speed on the bowling of a cricket ball?
19.How does the type of ball used affect the distance traveled when a cricket
ball is hit?
20.What is the safest angle to mount a ladder against a wall?
21.Does running a curve take longer than running the same distance on a
straight?
22.What effect does speed have on the distance gained in a vertical jump/high
jump?
23.How long on average does it take a student to travel to school. This could be
done in the form of a survey and can generate rich data and statistical analysis.
24.How well do students in my class measure up against each other? here you
could investigate the heights of students in your class or their mass etc
25.How long on average does it take to be served in the Tuck shop/Canteen
line at your school? This can be done in the form of a survey as well.
26.What type of lunches should be sold at school X's canteen in order to
maximize student patronage? [Survey]
CSEC Mathematics Sample SBA
SBA Title
Does it take longer to run 50m on the curved part of a track than it takes to run the same
distance on the straight?
Introduction
One of the most exciting events in the field of athletics is the 4x100 meters relay. This event is
a team event and much care and strategy goes into choosing the right persons for the right legs.
Athletes are chosen based on their ability to run the curve, the straight or their ability to hand
off or receive a baton. Some athletes prefer to run the curves while others prefer to run on the
straights. This SBA will attempt to discover if it takes longer to run the same distance on the
curve or the straight part of the track.
Method of collecting data
The student researcher will ask 20 classmates during PE time to run 50m on the curved part of
the track. They will all be using the same lane. Each person’s time will be measured using a
stopwatch, rounded to the nearest tenth of a second and the time will be recorded. Those same
persons on a separate PE class time will be asked to run 50m on the straight part of the track.
The results will be measured in the same way as the distance on the curve and recorded. The
two sets of times will then be compared and analyzed.
Presentation of data
The table below shows the data collected for the times taken to complete the 50m on the curve
and on the straight. The students here have been labeled using letters and not their unique
names.
The Histogram below shows the times taken to complete the 50m run on the straight part of the
track. The majority of the athletes finished the race within 7 – 8 seconds.
This histogram below shows the times taken for students to finish the 50m on the curve. The
Histogram shows that the majority of students finished within 8 – 9 seconds.
The comparative bar chart below shows the times side by side for each athlete who completed
the two events.
The Line graph below shows the times in seconds it takes to complete both events. It gives a clearer
picture of the times taken to complete both events and gives a clearer basis for analysis of the
events.
Analysis of data
The 50m straight run had a range of 2.7 seconds. This means that it took 2.7 seconds for all the
athletes to cross the finish line once the first person had crossed. The 50m run on the curve had a
range of 3.3 which is 0.6 which is 3.3 seconds longer than on the straight. The average time taken to
run the 50m on the straight is given as 7.69 seconds. The average time taken to complete the 50 run
on the curve was calculated as 8.56 seconds. On average it took 0.87 longer to complete the 50m
run on the curve than it took to complete the run on the straight. The average speed taken
complete the 50m run on the straight was calculated using the formula S+D/T, this showed that the
speed on the straight was 6.5m/s compared with 5.8m/s on the curve. The average speed over the
50m straight was faster than on the curve by 0.7m/s.
The table below shows the difference in times taken to complete the two events for each student.
The table shows that all athletes had at least a marginal increase in the time taken to complete the
events.
Discussion of findings
While it was expected based on the observation of especially 4x100m relays where the curves
become very critical, that it would take longer to run the curve than on the straight it needs to be
pointed out that in an actual relay the person running the third leg will often run just as fast as the
person running the second or anchor leg since those persons do not use a cold start out of the blocks.
he data shows that if both starts are cold, that is if both start out of the blocks, then it takes a
longer time to run the 50m around the curve than on the bend. While in some cases there is a very
small difference the fact remains that there was a difference.
Conclusion
This SBA started with the assumption that it takes longer to run 50m on the curved part of a track
than on the straight assuming that in both cases a cold start is used. The data shows beyond doubt
that it does indeed take a longer time to run the curve.
Appendix of Diagrams and Mathematical Knowledge used
The standard 400m track, the redline shows the approximate 50m on the curve and the blue line
shows the approximate 50m straight.
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
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Bar Graph
Line Graph
Histogram
Grouped distribution
Average speed
Range
Mean
Mathematics SBA Sample 2 - Using a Survey
Title
How satisfied are students of Royal High School with the lunch
services offered by the school canteen?
Introduction
Royal High School has 750 students who mostly use the school canteen for lunch services. The
canteen has been serving the staff and students well for many years but students have been
becoming increasingly restless with the service that they are getting. Students complain of various
issues to do with the food and the time it takes to get served. Other students complain about the
attitudes of members of the canteen staff while they are being served.
In order to understand the students problems more clearly a team of student researchers decided to
undertake a survey to find out how satisfied the students were with the food and service offered
from the canteen.
1.
2.
3.
How satisfied are students with the food served at the canteen?
How long on average does it take to be served?
How satisfied are students with the customer service given?
The information that is gathered from the survey will be shared with the head of the canteen
staff so that decisions can be made about how to improve the services offered by the canteen.
Method of data collection
In order to gather information about the issues at hand the researchers decided to use a survey
instrument. A total of 100 students were selected, male and female. There are 5 grade levels
and 20 students were taken from each grade level. Each student answered a survey consisting of
11 questions. The results of the survey were than organized and presented.
Survey Questions
1.
2.
Do you buy or consume any form of cooked lunch from the canteen?
3.
4.
5.
6.
7.
How satisfied are you with the length of time it takes to be served?
Approximately how long does it take for you to be served your lunch, from your entry into the
canteen until you are served?
How satisfied are you with the cost of the lunch?
How satisfied are you with the amount of food you get when you compare against the cost
How satisfied are you with the presentation of the food?
What specific aspects of the presentation of the food do you think needs improvement? Please
state
8. How satisfied are you with the taste of the food served?
9. What specific aspects of the taste of the food do you think needs improvement? Please state
10. How satisfied are you with the level of customer service that you receive?
What specific aspects of the customer service do you think needs improvement? Please state
Presentation of Data
he bar chart below shows the frequency with which students use the canteen's services
The table below shows the length of time it takes for the students to be
served
How satisfied are you with the length of time it takes to be served?
How satisfied are you with the cost of the lunch
How satisfied are you with the amount of food you get when you compare against the cost
Satisfied are you with the presentation of the food?
How satisfied are you with the taste of the food served?
How satisfied are you with the level of customer service that you receive?
Analysis of Data
The survey revealed that 39% of the persons always get their lunch from the canteen while 61% got
their lunch from the canteen sometimes. All the persons surveyed were impacted in some way by
the canteen. When responding to the time it takes to be served 32% of the persons were served in
10 minutes or less while 68% of the students waited over 10 minutes to be served. The modal
interval of time in which students were served was 15 – 20 minutes which had 39%. The mean
waiting time was 14 minutes. The data revealed that 72% of the students were either dissatisfied or
very dissatisfied with the time they had to wait to be served. Only 28% were satisfied with their
waiting time. A total of 97% of the students were satisfied with the price of the lunch. This
corresponded with 73% of the students saying they were satisfied with the amount of food they
received.
A total of 61% of the students were dissatisfied with the presentation of the food. Their reasons
included that the chicken was often over fried or cut too big to fit in the box. Sometimes too much
gravy was put on the food causing lunch boxes to leak and cause the rice to look soggy. A total of
56% of the students were dissatisfied with the taste of the food they got. Some of their reasons
included that the food was salty or too fresh, tasted burnt or spoiled.
When students were asked about the customer service 45% were dissatisfied and 55% were satisfied.
The students mentioned that some staff were kind to them and would accommodate their needs as
to what part of the meat they wanted and whether or not they wanted vegetables. Other staff
demonstrated a take it or leave it approach.
Students were dissatisfied in three main areas, the length of time it took to be served, the
presentation of the food and the taste of the food. The students were satisfied with the cost of the
food, the amount of food they got and generally with the customer service. The customer service
rating was close however.
Discussion of Findings
The researchers found that the average waiting time to be served was 14 minutes. Most students
were dissatisfied with that length of time. The researchers also found that the majority of students
were satisfied with both the cost of their lunch and the amount of food that they got. A total of 61%
were dissatisfied with the presentation of the food served and 56% were dissatisfied with the taste
of the food. Only 45% of the students were dissatisfied with the customer service they got. The
students were dissatisfied with three areas, time to be served, taste and presentation while being
satisfied with price, amount of food and customer service.
Conclusion
The research team can conclude that students are dissatisfied with the length of time they have to
wait to be served, the taste of the food and the presentation of the food. While they are satisfied
with the cost, the amount they got and the customer service. It is fair to conclude overall that
students generally are not satisfied with their lunches and the services offered by the canteen.
Mathematics SBA Sample 3 - Using an investigation/Experiment
Title
How does the amount of weight carried by an athlete affect their speed over a
50m run?
Introduction
The purpose of this research was to determine if and how the amount of weight
carried by an athlete would affect his/her speed over a 50m run. The student
researcher had observed that professional athletes always train by dragging
weights behind them.
Some attach small tyres by string and move up to heavier tyres in progressive
resistance training. Athletes do this to build stamina, speed and strength. The
student researcher wanted to investigate if there is a relationship between the
weight and speed. Information obtain from this SBA investigation could be used
by coaches to help train their athletes. This could probably lead to a
customizable weight program for each athlete or in general a more scientific
way of looking at weight training. The Researcher specifically wants to find out,
1. Is there a relationship between the weight and the time taken to run the
distance?
2. How is the speed impacted by the weight carried?
Method of Data Collection
To carry out this investigation the researcher will ask a classmate to run with
weights and while the activity is being done the researcher will take
measurements and record the Data in a table. The time will be recorded using
the stopwatch on the researcher’s phone. The Physical Education and Sports
Department have a variety of weights that they use in their gym. These weights
will be borrowed from the department to be used in the
experiment/investigation.
The researcher will mark out a 50m distance on the field along the 100m
stretch using a measuring tape. The student will run 50m distance without any
weights and his time will be recorded to the hundredth of a second. After
resting adequately, the student will run with the first weight. The runs will be
done over a two-day period. Each time will be recorded. The student will
attempt to run s fast as possible each time. The speed will be calculated using
the formula S = D/T. This information will also be placed in the table.
The data will be modelled using graphing software to look for any patterns or
relationship.
Presentation of Data
The table below shows Time taken to run a 50 m distance with
the speed calculations included
The graph below shows a linear model of the relationship
between the weight carried and the time it takes to run the
50m distance.
The graph below shows a linear model of the relationship
between the weight carried and the speed obtained in each run
the 50m distance.
Analysis of Data
The data that was recorded during the investigation showed some interesting
results. The student ran the 50-meter distance without any weight in a time of
9.15 seconds. This translated to a speed of 5.5m/s. On the second run the
athlete carried a 10 pound load and this increased the time slightly to 9.4
seconds with a corresponding decrease in speed at 5.3m/s. when the weight
was increased to 20 pounds the time increased to 9.8 seconds with a speed of
5.1m/s. That same pattern continued as the weight increased so di the time
and the corresponding fall in the speed achieved. At 30 pounds the athlete ran
at 4.8m/s in a time of 10.4 seconds. At 40 pounds his time was 11.97 seconds
and his speed was 4.1m/s. Re 45-pound weight carried resulted in a further
increase in time.
The student took 12.95 seconds to complete the journey and recorded a speed
of 3.9m/s. At 50 pounds the student ran the 50-meter distance in 14.05 seconds
with a speed of 3.6m/s.
The data for the weight carried and time taken was modeled using graphing
software to search for any patterns in the data. The results were surprising and
unexpected. A best fit line was drawn through the data points and revealed a
linear function of the form f(x)=0.098x+8.4. The gradient of this function tells
us that for every pound added there was an increase in time of approximately
0.1 seconds.
When the weight and the speed were modeled together using the same
software a similar linear pattern was observed. This has a best fit line of f(x) =
- 0.039x +5.67. This meant that for every pound added the rate of decrease in
speed was approximately -0.04 meter per second.
Discussion of Findings
The researcher discovered that there was a linear relationship between the
amount of load carried and the time it took to run the 50m distance. The time
increased proportionately as the weight increased. The data revealed a linear
function of the form f(x)=0.098x+8.4. The gradient of this function tells us that
for every pound added there was an increase in time of approximately 0.1
seconds.
There was also a linear relationship between the amount of weight carried and
the speed obtained in each run. As the weight increased the student ran the
distance progressively slower. The linear model from the graph gave a function
f(x) = - 0.039x +5.67. This meant that for every pound added the rate of
decrease in speed was approximately -0.04 meter per second.
Conclusion
he Researcher had set out to see if there a relationship between the weight and
the time taken to run the distance? The Researcher also wanted to find out how
the speed of the student is impacted by the weight carried?
The data shows clearly that in each case there is a linear relationship between
weight carried and time taken and between weight carried and speed obtained.
For every pound added there was an increase in time of approximately 0.1
seconds and for every pound added the rate of decrease in speed was
approximately -0.04 meter per second.
Choosing the right type of graph to represent your data
Before you decide on what type of graph you need you first need to understand a little
about the type of data that you have collected while doing your SBA. CXC does expect that
you will choose graphs that you have used throughout the curriculum especially while doing
the statistics unit.
Numerical Data can be broadly classified in one of two groups.


Discrete data
Continuous data.
Discrete data
can be described as data that can only take whole values, the kind
of data where a fraction value doesn't make much sense. Discrete data can be counted,
e.g. the number of people participating in a survey, the number of voters, number of
feet or fingers, number of vehicles passing a point within a given time etc.
Continuous data
on the other hand is data that has to be measured. This type of
data can take any type of value including fractional values. Examples of continuous
data are time, length, mass, volume etc
​
Types of graphs that you may use in your SBA to
represent discrete data
Line graph
Line graphs are used to track changes in data over a period of time. Line graphs can also
be used to compare changes over the same period of time for more than one group. Line
graphs are good for showing the periods of greatest or least change over other periods.
Examples could be used to show the number of tourists arriving at a destination over 5
years, the cost of an item over a period of time the changes in the price would be tracked,
the growth of a plant over a period of time or the changes in a budget over time
Bar Graph
Bar graphs are used to compare things between different groups or to track changes over
time. The same information that’s placed on a line graph can be placed on a bar graph.
However, when trying to measure change over time, bar graphs are best when the changes are
larger.
Pie Chart
Pie charts are best to use when you are trying to compare parts of a whole. They do not
show changes over time.
When graphing distributions containing continuous data such as on the table below the
options in Microsoft Excel which most people use become limited. You can put this
information in a bar graph as follows
However it is best to represent the information as a histogram. This kind of data can also
be used to draw a cumulative frequency curve or frequency polygon. A sample cumulative
frequency curve is shown below
If you are trying to find a relationship between two quantities such as in the table below
which shows the heights of students and the distance they can throw a cricket ball then a
scatter plot is useful
This information is better plotted in software such as
graph
[you can find
the graph software here <https://www.padowan.dk>]that can do the scatter and put a best
fit line through it thus giving a better interpretation of the relationship. This is seen
below
Writing your data analysis for your CSEC SBA
One of the major weakness, so far, to emerge out of the Mathematics SBA
project is the inability of students to communicate what their data is
saying. The ability to look for patterns in data, to communicate their
ideas and to communicate using Mathematical language is wanting.
he following snippets are meant to be samples that students can look at
and get ideas of how to write mathematically or how to write up a simple
data analysis. This will not just be useful for the Mathematics SBA but
for all areas where a discussion of data is required.
Between 2000 and 2006, 1.98 million tonnes of bauxite was produced with
2006 being the year with the highest production record of 350 thousand
tonnes. The production of bauxite has been steadily increasing over the
period except in 2005 where there was a decline. There was an average
production of 282.9 thousand tonnes per year over the seven year period
and a 75% increase in production between the years 2000 and 2006.
The number of tourists visiting has increased steadily over the years
2000 to 2006 starting with 150 thousand in 2000 and ending with 450
thousand in 2006. The pattern is somewhat similar but slightly different
when the number of stop over visitors is examined. The 2001 figures
decreased slightly over 2000 but recovered by 2002. The same pattern was
observed between 2003 and 2005, the number of stop over visitors has
increased steadily however from 2004 to 2006. When both stop over and
visitors are compared it is observed that the number of persons stopping
over is always 50% or less of those visiting.
When the savings patterns of Andy and Jane are compared it observed that
Jane’s savings increased steadily over the period January to July with
the highest rate of savings. Andy’s rate of saving increased from
January to April with the highest rate of increase observed between
January and February. Andy’s savings decreased between April and June
and rebounded in July. In both instances the mount of money saved in
July was higher than in January. Jane had a 100% increase while Andy had
a 175% increase.
The data shows that almost one third of the students 33% used WhatsApp
as their main social media tool while a quarter, 25% used Facebook.
Combined Facebook and WhatsApp accounted for 58% of total usage while
only 42% of students used other APPS. Instagram was the third most
popular with a 16% usage, Twitter had 12% and Snapchat had 10%. The
least popular social media type was Telegram which only had a 4% usage.
A cursory look at the data shows that of the 100 students measured the
majority was in the interval 171 – 180 centimeters. 91% of the
student’s height were between 141 and 180 centimeters. Significantly
owever most were concentrated in the 150 – 180 cm group, 83%. The mean
height observed was 163.1 centimeters.