Additional Mathematic Project Q2-Healthy Diet

7/31/2019 Additional Mathematic Project Q2-Healthy Diet

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NAME : OOI SUE CHENG

CLASS : 5ST

TEACHER : PN. WAN SAUDA BT. MOHD. ZAIN


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The aims of carrying out this project work are:

1. To apply and adapt a variety of problem-solving strategies to solve problems.

2. To improve thinking skills.

3. To promote effective mathematical communication.

4. To develop mathematical knowledge through problem solving in a way that increase

student interest and confidence.

5. To use the language of mathematics to express mathematical ideas precisely.

6. To provide learning environment that stimulates and enhances effective learning.

7. To develop positive attitude towards mathematics.


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First and foremost, I would like to thank God that finally, I have succeeded in finishing thisproject work. I would like to thank my beloved Additional Mathematics teacher, Pn. Wan Sauda

bt. Mohd. Zain for all the guidance she had provided me during the process in finishing this project

work. I also appreciate her patience in guiding me completing this project work.

I would like to give a thousand thanks to my father and mother for giving me their full

support in this project work, financially and mentally. They gave me moral support when I needed

it.

I would also like to thank my fellow friends who had helped me in finding the information

that Im clusless of, and the time we spent together discussing this project work.

Last but not least, I would like to express my highest gratitude to all those who gave me the

possibility to complete this coursework. I really appreciate all the help.

Again, thank you very much.


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NO CONTENT PAGE

1 OBJECTIVES 1

2 ACKNOWLEDGEMENT 2

3 INTRODUCTION 4 - 7

4 PART 1 8

Part 1 (i) 8

Part 1 (ii) 9 - 10

5 PART 2 11

Part 2 (a) 12

Part 2 (b) (i) 15

Part 2 (b) (ii) 15 - 16

6 PART 3 17

Part 3 (a) 17

Part 3 (b) 20

Part 3 (c) 17

Part 3 (d) 17 - 18

Part 3 (e) 18

Part 3 (f) 19

7 FURTHER EXPLORATION 21 - 25

8 CONCLUSION 26

9 REFLECTION 27


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A healthy diet is one that helps maintain or improve general health. It is important forlowering many chronic health risks, such as obesity, diabetes, hypertension and cancer. A healthy

diet involves consuming appropriate amounts of all essential nutrients and an adequate amount

ofwater. Nutrients can be obtained from many different foods, so there are numerous diets that

may be considered healthy. A healthy diet needs to have a balance of macro nutrients (fats,

proteins, and carbohydrates), calories to support energy needs, and micro nutrients to meet the

needs forhuman nutrition without inducing toxicity or excessive weight gain from consuming

excessive amounts.

A healthy diet is one that is arrived at with the intent of improving or maintaining

optimal health. This usually involves consumingnutrients by eating the appropriate amounts fromall of the food groups, including an adequate amount ofwater. Since human nutrition is complex, a

healthy diet may vary widely, and is subject to an individual's genetic makeup, environment,

and health. For around 20% of the human population, lack of access to food and malnutrition are

the main impediments to healthy eating. Conversely, people in developed countries have the

opposite problem; concern is often not about volume of food but appropriate choices.

Diet table
http://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Cancerhttp://en.wikipedia.org/wiki/Essential_nutrienthttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Human_nutritionhttp://en.wikipedia.org/wiki/Healthy_diethttp://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Nutrientshttp://en.wikipedia.org/wiki/Nutrientshttp://en.wikipedia.org/wiki/Food_groupshttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Humanhttp://en.wikipedia.org/wiki/Nutritionhttp://en.wikipedia.org/wiki/Genotypehttp://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Malnutritionhttp://en.wikipedia.org/wiki/Developed_countrieshttp://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Obesityhttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Cancerhttp://en.wikipedia.org/wiki/Essential_nutrienthttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Human_nutritionhttp://en.wikipedia.org/wiki/Healthy_diethttp://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Nutrientshttp://en.wikipedia.org/wiki/Food_groupshttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Humanhttp://en.wikipedia.org/wiki/Nutritionhttp://en.wikipedia.org/wiki/Genotypehttp://en.wikipedia.org/wiki/Healthhttp://en.wikipedia.org/wiki/Malnutritionhttp://en.wikipedia.org/wiki/Developed_countries


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Food Type Carnivore Omnivore Pescetarian Vegetarian Vegan Islamic Hindu Paleolithic diet
http://en.wikipedia.org/wiki/Carnivorehttp://en.wikipedia.org/wiki/Omnivorehttp://en.wikipedia.org/wiki/Pescetarianhttp://en.wikipedia.org/wiki/Vegetarianhttp://en.wikipedia.org/wiki/Veganhttp://en.wikipedia.org/wiki/Halalhttp://en.wikipedia.org/wiki/Diet_in_Hinduismhttp://en.wikipedia.org/wiki/Paleolithic_diethttp://en.wikipedia.org/wiki/Carnivorehttp://en.wikipedia.org/wiki/Omnivorehttp://en.wikipedia.org/wiki/Pescetarianhttp://en.wikipedia.org/wiki/Vegetarianhttp://en.wikipedia.org/wiki/Veganhttp://en.wikipedia.org/wiki/Halalhttp://en.wikipedia.org/wiki/Diet_in_Hinduismhttp://en.wikipedia.org/wiki/Paleolithic_diet


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Fruits andberries No Yes Yes Yes Yes Yes Yes Yes

Greens No Yes Yes Yes Yes Yes Yes Yes

Vegetables No Yes Yes Yes Yes Yes Yes Yes

Starchy vegetables No Yes Yes Yes Yes Yes Yes No

Grains No Yes Yes Yes Yes Yes Yes No

Poultry Yes Yes No No No Yes No Yes

Fish (scaled) Yes Yes Yes No No Yes No Yes

Seafood (non-fish) Yes Yes Yes No No Yes No Yes

Beef Yes Yes No No No Yes No Yes

Pork Yes Yes No No No No No Yes

Eggs Yes Yes Yes Yes No Yes No Yes

Dairy No Yes Yes Yes No Yes Yes No

Nuts No Yes Yes Yes Yes Yes Yes Yes

Women

Height Healthy Weight Range Kilograms
http://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/wiki/Berryhttp://en.wikipedia.org/wiki/Berryhttp://en.wikipedia.org/wiki/Leaf_vegetablehttp://en.wikipedia.org/wiki/Vegetableshttp://en.wikipedia.org/wiki/Cerealhttp://en.wikipedia.org/wiki/Poultryhttp://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Seafoodhttp://en.wikipedia.org/wiki/Beefhttp://en.wikipedia.org/wiki/Porkhttp://en.wikipedia.org/wiki/Egg_(food)http://en.wikipedia.org/wiki/Dairyhttp://en.wikipedia.org/wiki/Nut_(fruit)http://www.webindia123.com/health/diet/calorie/weight.htmhttp://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/wiki/Berryhttp://en.wikipedia.org/wiki/Leaf_vegetablehttp://en.wikipedia.org/wiki/Vegetableshttp://en.wikipedia.org/wiki/Cerealhttp://en.wikipedia.org/wiki/Poultryhttp://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Seafoodhttp://en.wikipedia.org/wiki/Beefhttp://en.wikipedia.org/wiki/Porkhttp://en.wikipedia.org/wiki/Egg_(food)http://en.wikipedia.org/wiki/Dairyhttp://en.wikipedia.org/wiki/Nut_(fruit)http://www.webindia123.com/health/diet/calorie/weight.htm


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(Pounds)

4'10" 109-121 49-54

5'0" 113-126 51-57

5'1" 115-129 52-58

5'2" 118-132 53-59

5'3" 121-135 54-61

5'4" 124-138 56-62

5'5" 127-141 57-63

5'6" 130-144 58-65

5'7" 133-147 60-66

5'8" 136-150 61-68

5'9" 139-153 63-69

5'10" 142-156 64-70

5'11" 145-159 65-72

6'0" 148-162 67-73

Men

HeightHealthyWeight Range

(pounds)Kilograms

5'2" 131-141 59-63
http://www.webindia123.com/health/diet/calorie/weight.htmhttp://www.webindia123.com/health/diet/calorie/weight.htm


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5'3" 133-143 60-64

5'4" 135-145 61-65

5'5" 137-148 62-67

5'6" 139-151 63-68

5'7" 142-154 64-69

5'8" 145-157 65-71

5'9" 148-160 67-72

5'10" 151-163 68-73

5'11" 154-166 69-75

6'0" 157-170 71-77

6'1" 160-174 72-78

6'2" 164-178 74-80

6'3" 167-182 75-82

6'4" 171-187 77-84

PART I

If you look around your class, you will notice that your classmates are different in terms of height,

mass, shoe size etc. You probably would have expected most people to be around the average

mass. Based on these studies, the ministry has collected data and interpreted it into statistical data

for further action.


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Hence, briefly discuss

(i) History about statistic, and

(ii) Application of statistic in everyday life.

History About Statistic

The history of statistics can be said to start around 1749 although, over time, there have

been changes to the interpretation of what the word statistics means.

In early times, the meaning was restricted to information about states.

This was later extended to include all collections of information of all types, and later still

it was extended to include the analysis and interpretation of such data.

In modern terms, "statistics" means both sets of collected information, as in nationalaccounts and temperature records, and analytical work which requires statistical inference.

Statistical activities are often associated with models expressed usingprobabilities, and

requireprobability theory for them to be put on a firm theoretical basis.

A number of statistical concepts have had an important impact on a wide range of sciences.

These include the design of experiments and approaches to statistical inference such

as Bayesian inference, each of which can be considered to have their own sequence in the

development of the ideas underlying modern statistics.

Pierre-Simon, marquis de Laplace, one of the main early developers of Bayesian statistics.

Application Of Statistic in Everyday Life

Statistic is the collection of data and its representation or interpretation. Statistics use three means

of comparison through the data mean, median and mode.

Mean is used as one of the comparing properties of statistics. It is defined as the average of

all the clarification.
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Bayesian_inference


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(i) It helps teachers to see the average marks of the students.

(ii) It is used in factories, for the authorities to recognize whether the benefits of the

workers is continued or not.

(iii) It is also used to contrast the salaries of the workers.

(iv) To calculate the average speed of anything.

(v) It is also used by the government to find the income or expenses of any person.

(vi) Using this the family could balance their expanses with their average income.

Example to find the mean:

Find the mean of 4,7,2,9,3.

Solution:

Mean = (4+7+2+9+3)/5=5

Median is defined as the middle value of any observation. Its application in daily life are as

follow:

(i) It is used to measure the distribution of the earnings

(ii) Used to find the players height e.g. football player

(iii) To find the middle age from the class students.

(iv) Also used to find the poverty line.

Example to find the middle value:

From the series 7,2,4,9,1,6,8 the middle values is calculated by arranging the series into

ascending order that is 1,2,4,6,7,9. Here, the median value is 6.


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Mode contains the highest frequency in any data. Its application are as follows:

(i) It is used to influx of the public transport.

(ii) The number of games succeeded by any team of players.

(iii) The frequency of the need of infants.

(iv) Used to find the number of the mode is also seen in calculation of the wages, in the

patients going to the hospitals, the mode of travel etc.

Example to find mode:

1,2,3,3,3,4

Solution:

In this the mode is 3 because it recurs the most.

PART II

The Ministry of Health has done many studies on the effect of food sold in the school canteen on

children. To support the government effort, you are required to run the project. This project

required you to obtain the mass and height of 100 students in certain forms of your school.

Based on the raw data collected, tabulate your data into a frequency table.


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Mass of Students (kg) Tally Frequency

21 - 40 14

41 - 60 50

61 - 80 24

81 - 100 8

101 - 120 4

Table 1

a) Draw a histogram from the Table 1 and find the mode mass.

b) Hence, draw another two histogram by changing to a smaller class intervals and increasing

of the classes.


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Mode mass is 52.0

i. Explain briefly, what do you observe as the class size decreases and the number of

classes increases?

As the class size decreases and the number of classes increases, the range of mass of

students decreases follow by the tally and frequency also decreases. Therefore, as the

value of frequency of number of students decreases, the accuracy of data increases.


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ii. Find mode for every histogram that you have drawn and interpret it.

The mode for the first and second histogram are 52.0 while the mode for the third

histogram is 51.5. As the size of class decrease, the value of the frequency alsodecrease and more accurate. The mode is measure according to the highest frequency.

Therefore, the most accurate mode is 51.5.

Class Size 10 Class Size 5


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Mass of students Frequency Mass of students Frequency

21 30 4 21 25 1

31 40 10 26 30 3

41 50 24 31 35 4

51 60 26 36 40 6

61 70 14 41 45 10

71 80 10 46 50 14

81 90 5 51 55 15

91 100 3 56 60 11

101 110 2 61 65 10

66 70 4

71 75 6

76 80 4

81 85 2

86 90 3

91 95 1

96 100 2

101 105 1

106 110 1

111 115 1

116 120 1

PART III


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a) Using the data from Table 1, complete Table 2 below.

Mass of Students (kg) Upper Boundary Frequency Cumulative Frequency

0 20 20.5 0 0

21 - 40 40.5 14 14

41 - 60 60.5 50 64

61 - 80 80.5 24 88

81 - 100 100.5 8 96

101 - 120 120.5 4 100

Table 2

b) Hence, draw an ogive based on the data.

c) From the ogive, find median, first quartile, third quartile and interquartile range.

Median = 55.5

First Quartile = 48.5

Third Quartile = 66.5

Interquartile range = Third Quartile First Quartile

= 66.5 48.5

= 18.0

d) Without drawing an ogive, find the median, first quartile, third quartile and interquartile

range.

Median = L + [ (N/2 F)/fm ] C

= 40.5 + [ (50-14)/50 ] x 20

= 54.9

First Quartile = L + [ (N/4 F)/fm ] C

= 40.5 + [ (25-14)/50 ] x 20


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= 44.9

Third Quartile = L + [ (3N/4 F)/fm ] C

= 60.5 + [ (75-64)/24 ] x 20

= 69.67


= 69.67 44.9

= 24.77

e) State the range and interquartile range. What is the different between the range and

interquartile range?

Range = largest midpoint smallest midpoint

= 110.5 30.5

= 80.0


= 69.67 44.9

= 24.77

Different between range and interquartile range = 80.0 24.77

= 55.23

f) Calculate the mean, variance and standard deviations. Explain briefly why mean, variance

and standard deviations are used in statistic to interpret data.

Mass of Midpoint,x Frequency,f fx fx


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Students (kg)

21 - 40 30.5 14 427 13023.5

41 - 60 50.5 50 2525 127512.5

61 - 80 70.5 24 1692 119286.0

81 - 100 90.5 8 724 65522.0

101 - 120 110.5 4 442 48841.0

100 5810 374185

Mean = 5810/100

= 58.1

Variance = (374185/100) (58.1)

= 366.24

Standard deviation = 366.24

= 19.137

Mean, variance and standard deviations are used in statistics to interpret data because:

Mean - It is widely known.

- It can be calculate easily and accurately.

- It can represent the data as a whole.

- In enables comparison between one data with the whole set of data.

Variance It takes into consideration all the values in the set of data.

Standard deviation It takes into consideration the deviation of each value in the set of

data from their mean.

The body mass index, BMI = mass (kg)/ [ height(m) x height (m)] gives an indication on the

physical state of a person as being underweight, normal, overweight or obese.


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BMI Categories BMI

Underweight < 18.5

Normal 18.5 24.9

Overweight 25 29.9

Obese > 30

i) Calculate BMI for every student from the survey and classify them into categories as

above. Hence calculate the percentage of each category.

ii) Display the result on your school notice board as a guide for pupils to take care of their

eating habits by practicing the moral values.

It is important to practice good eating habits. Good eating habits mean practicing moral

values by taking food in the correct quantity at the correct time.

Good eating habits include:


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a) Taking meals at the appropriate time. We have to eat breakfast, lunch and dinner at the

correct times.

b) Refraining from overeating or eating too little during a meal.

c) Eating a balanced diet

d) Eating sufficient amounts of fibre from fruits and vegetables.

e) Drinking at least 2 to 3 litres of water daily. This will help to flush out toxins from the

body.

f) Avoiding excessive fatty food and food rich in sugar or high in sodium .

iii) An obese person is more prone to develop diseases such as diabetes, stroke and heart

attack. Comment on this statement. Suggest ways and strategies that a person can adopt to

reduce or increase mass and live a healthier life.

- Obesity is defined as the condition where a persons body exceeds 20% the normal weight

(according to height) where the person exceeds 30 of BMI.


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- The person easy to get diabetes, stroke and heart attack.

- Factors which lead to obesity include eating excessive, eating too much carbohydrates and

fats as well as lack of exercise.

- Diabetes is cause by the person who consume high content of glucose in food.

- A diet rich in saturated fats result in heart attack because it block the blood flow in the

blood vessel, the narrow of lumen causes high blood pressure.

- High blood pressure causes the small arteries to burst and lead to strokes in brain.

- Ways to live a healthier life are:

Practicing balanced diet.

Avoid foods rich in fats and red meat

Avoid smoking.

Consume more fruits and vegetables

Exercise and lead a healthy lifestyle.

Avoid intake of high sugar content food

Choose wholemeal bread.

Take cereals for breakfast instead of fried food.

Cut down sugary foods and sweets.

Reduce intake of fried food.

Eat low fat, low sugar snacks without monosodium glutamate (MSG).

Finally, I managed to complete my Additional Mathematics Project Work. I learnt deeply

about the history of statistic and its application that helps us to collect, analyse and interpret data


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properly. We use to apply statistic in our daily life. By using statistic, I answered and presented my

project work systematically and clearly. I managed to obtain the mass and height of 100 students in

my school and interpret it by using frequency table and histogram. Therefore, I should be thankful

to the people who contribute in the idea of statistics.

Besides that, I also learnt to calculate the body mass index of every students in my survey.Fortunately, 68% of these students have a normal weight. I was clearly known that the important of

healthier life to prevent diseases such as diabetes, stroke and heart attack. We must practice good

eating habits and healthy diet.

In addition, I learn to solve more Additional Mathematics question. Every time I succeeded

solving the question, more and more challenging questions I will go through. This will attract my

attention because it is special, exciting and interesting.

Lastly, I felt so happy to complete this task. I would like to thank everyone who lend a

hand to me in conducting this project work. I did learnt a lot. Thanks again.

During conducting this project, I learnt that Additional Mathematics is a very interesting

subject. It is vital because it is closely related to our daily lives. Its existence help us a lot in our


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social life. Human being depend on Additional Mathematics to have a better life style. Statistic

helps human to calculate data and perform in an order manner. Next, I also learnt that the

necessary to practice a balance diet and healthy lifestyle.

Besides that, I had learnt to be punctual to and independent in completing this project in

time. I also learnt to discipline myself to finish the project. Then, I learnt to be patient whenanswering the questions one by one.

Moreover, I am glad to accept this project work. Through this project, i gained lots of

knowledge and experience. I felt happy when I succeeded in answering the question. The more

challenging question I solved, the more I increase the great interest towards Additional

Mathematics.

Lastly, I found that Additional Mathematics seemed easier to understand than before. I

managed to answer every single question without much problems. Additional Mathematics is truly

an interesting subject for all of us.

Additional Mathematic Project Q2-Healthy Diet

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