General Studies and Communication Skills

1. Identify activities carried out daily that require the application of Mathematics.

2. From which mathematical topics are the activities identified in question (1) derived?

There are several examples of areas where Mathematics is used in daily life. Examples include the following:

Peoples’ daily life is increasingly dictated by modern science and technology. In science, Mathematics is intensively used. Creative innovations carried out daily by people in the fields of science and technology increasingly apply the knowledge of Mathematics. Without the use and application of Mathematics, there is no modern science and technology. Mathematics, therefore, contributes significantly to the advancement of science and technology in the world today.

1. Explain ways in which Mathematics contributes to science and technology.

2. People who work as doctors, biologists, detectives/police and nutritionists require knowledge in Mathematics. Examine some of the situations they face in their day-to-day work in which they are required to use mathematical concepts.

3. Identify ways in which other professionals use mathematical concepts in their work.

Arithmetic is used and applied during addition, subtraction, multiplication, measurement and proportions. There is conversion from one metric system to another in the weighing and measuring of food ingredients. Mathematics is also used to determine the required amount of ingredients to achieve a certain taste and flavour in food. Th en there is use of probability and statistics in estimating food quantity requirements for a specified number of people. Consumers of food products and food processors use arithmetic to calculate the amount of calories in food cooked or produced. During food preparation, chefs mix a number of food ingredients to develop a recipe. They use various concepts of Mathematics, Chemistry, Economics and Biology in their daily work.

Discuss these questions.

1. Imagine that you are the accounting manager of a top hotel in Kigali City. Calculate the prices for the three most popular meals in Rwanda. Identify items to be costed such as food items, cooking gas, payment to staff , transport and other miscellaneous items that the hotel may use when preparing such meals. Determine the approximate cost of the three popular meals that can be on the hotel menu.

2. Explain how people use Mathematics in their daily lives when cooking.

These human activities use and apply Mathematics. Musicians use and apply mathematical knowledge in their body movements which are rhythmically in harmony with the wavelength of the musical sound produced. Dancers also follow rhythmic pace movements of arithmetic nature (subtraction and addition) or mechanical-geometrical nature (forward and backward movements, and circular movements). Sculptors estimate the length and thickness of wood required to produce a piece of art. This involves measurement of wood and the production of a piece of art following geometrical patterns.

Identify activities where musicians, artists and dancers use mathematical concepts.

People involved in the building and construction industry use and apply Mathematics in their daily life. The area to be covered and materials needed are calculated and measured. The external designs of structures such as houses, dams and bridges use and apply calculus, geometry, arithmetic, algebra, graph theory and statistics when designing and building them.

             

As part of the Umuganda activities in your Umudugudu, you are required to help in the construction of a motorable bridge. How are you going to proceed using knowledge acquired in Mathematics?

Travelers, motorists and cyclists consciously and unconsciously use Mathematics in their daily life. Pilots and motorists usually estimate the distance and the quantity of fuel required to cover the distance to travel. Similarly, travellers need to know their travelling schedules. When travelling between areas with a time difference, a traveller is expected to calculate the difference in time in order to plan.

Explain other examples of how mathematical concepts are used during travelling.

The business world uses a wide range of Commercial Mathematics due to a significant rise in commercial activities. The common branches of Commercial Mathematics used and applied are arithmetic, algebra and geometry.

Explain how Mathematics is used to conduct activities in business and economics.

Health professionals use and apply Mathematics on a daily basis when prescribing or administering drugs. They use arithmetic, geometry, algebra, statistics and graph theory when determining the cause, spread and effects of a disease in a specific area in times of an epidemic. Doctors' prescriptions are based on quantity of dosage per day depending on the weight of a patient and the length of time the medicine stays in the body of a patient.

Medics carry out additions, subtractions, multiplications, measurement, fractions, ratios, proportions, and algebraic expressions as they administer medi-cation to their patients on a daily basis. They weigh and measure the height of their patients and their body temperature. They also draw blood samples from patients to establish the cause of ailments. The conclusions are presented in the form of a graph or arithmetic. The results are then interpreted to administer proper medication.

Identify activities carried out by medical personnel, that use mathematical concepts.

Agriculturalists use and apply Mathematics to meet economic efficiency, food sustainability and food security. Economies of scale come into play in any agricultural activity. Activities such as estimating the number of people required to work on a farm during planting, weeding and harvesting, feeds needed for the animals, fertilisers and manure to be applied and vaccinations and medications administered to the animals require the use of mathematical concepts. These activities involve the use and application of arithmetic, algebra, geometry, mechanics and statistics. Geometry is applied in spraying crops on a piece of land or on cattle.

                                          

Identify agricultural activities that use mathematical concepts.

Most human activities today are performed using information technology. Computer software and applications solve problems such as predicting the occurrence of natural calamities, sea navigation, aircraft control, delivery of health care services and disease diagnosis, urban farming innovation, genetic engineering and selective breeding for better yields, innovations that propel the education sector and use of artificial intelligence.

People regularly give commands to computers to do a variety of functions reliably and correctly. Mathematics is the mother of Computer Science. Computer programming applies algorithmic designs and processes which are patterned on a set of logical rules to create software. Knowledge in algorithm has contributed to advancements in technology and innovations in the 21st Century. Computer software gives life to computers to perform a variety of functions when given specified commands.

1. Identify and explain how computer software and applications used in Rwanda have made life easy or solved problems for people in the country.

2. Discuss possible computer innovations that you think would solve problems that currently exist in Rwanda.

3. Explain any three topics in Mathematics used and applied in computers to produce high quality photos, video games, audios and videos.

Ancient Greeks developed and established various types of sports and games that became part of the Greek culture. The sporting culture led to the establishment of the Olympic Games. The rules and regulations of the games were established to ascertain fair competition among participants. Mathematics was used to draft rules and establish measurements of various sporting arenas and games. From then on wards, Mathematics has consistently played a significant role in sports. A number of topics in Mathematics such as mechanics, geometry, trigonometry, algebra and statistics are used and applied. Designing of all sporting facilities use and apply Mathematics.

       

1. Explain how mathematical concepts are used in sporting activities worldwide.

2. Discuss other human activities, not mentioned in this section, where Mathematics is used and applied in everyday life.

Reasoning means thinking about something in a logical way or making sense of something in order to come to a conclusion. The use and application of Mathematics in our daily life promotes reasoning. Imaginative powers trigger reasoning abilities which encompass creativity, innovation, invention and discovery. In this way, reasoning ability is developed through the use of Mathematics.

The quality of reasoning improves as one learns various topics in Mathematics. The higher the level of Mathematics studied, the better a person’s reasoning capacity is refined. People are able to advance their reasoning ability through a leap of logic, problem solving techniques and abstract ways of thinking. Inventions have characterised scientific revolution worldwide, having been aided by advanced powers of successive reasoning developed through Mathematics. In this way, new scientific ideas developed through logical reasoning, using Mathematics, have led to technological innovations, inventions and discoveries currently being witnessed in the world today.

1. Discuss five ways in which various groups of professionals promote reasoning in their daily activities.

2. Students who work together in groups are likely to enrich their reasoning abilities. Discuss.

3. Identify various technological innovations, inventions and discoveries being witnessed in the world today.

Counting is the process of assigning numerical values to objects. Counting is the first human activity of life-long learning. The application of Mathematics to real life situations develops interest and curiosity in learners. Throughout the education process, people perfect the art of counting in Mathematics. Counting, therefore, promotes problem solving skills as it is a core skill in life.

1. Discuss ways in which modern technology helps people develop counting skills.

2. Identify three topics in Mathematics which you think have contributed to the promotion of counting in people’s daily life.

People have perfected counting and calculations, with or without the use of calculating devices. Knowledge and skills of Mathematical concepts have promoted calculation skills in daily life. Calculating devices such as computers and calculators are developed from the Number Theory using algorithm. In people’s daily life, calculations play a significant role in carrying out various activities. If the right commands are used, these devices give the correct answer. The grasp of numbers and operations required to give commands to calculating devices helps people carry out efficient calculations in a wide range of problem solving situations.

Without an adequate grasp of arithmetic, a person using a calculating device is likely to make errors. Mathematics, therefore, helps one to carry out calculations correctly. Making wrong calculations may be costly in accounting or fatal in the wrong administration of pharmaceutical drugs to a human being or livestock.

With the help of your teacher, make a visit to the nearest market or shopping centre. Observe and discuss how traders use and apply Mathematics to make calculations in their daily activities.

Most activities that people carry out involve taking measurements, for example, weighing ingredients before cooking. It is vital to take measurements when carrying out various activities to avoid waste or making wrong judgments. Mathematics, therefore, enhances accuracy in carrying out measurements in people’s daily life.

1. Name and explain different devices used in taking measurements.

2. Describe the types of measurements that make up the International Metric System.

3. Explain the importance of taking measurements in the daily life of an ordinary person or a professional.

Time management is the process of organising tasks or activities in accordance with the estimated time to accomplish them. Human activities are time-scheduled to fulfill daily obligations. Utilisation of time, according to tasks that are to be accomplished, is important in the daily life of people.

Mathematics, therefore, is important in managing time. Arithmetic is useful in enhancing time management. Sequencing of events in our daily life depends entirely on how we measure and observe time. One needs to read the clock, consult a diary, refer to the calendar, count the passage of time, plan for time, schedule time, compute time and track time. Tracking time involves calculations. Th is is how Mathematics comes into use in the promotion of time management.

Discuss the usefulness of taking measurements in regards to time management.

1. Define the term Mathematics.

2. Identify branches of Mathematics used by the ancient Egyptians in the building of the pyramids.

3. Explain uses and applications of geometry in the daily life of farmers in Rwanda.

4. What is the meaning of the term symmetry? Explain the application of symmetry in building and construction work.

5. Discuss topics in Mathematics which are used and applied in football matches or any other sport.

6. In the contemporary world, a good knowledge of Mathematics is required if one is to succeed in life. Discuss this statement citing relevant examples.

7. To what extent do you believe that the knowledge of Mathematics is continuously evolving to solve the complex human problems of every generation of humanity?

8. Write an article pointing out to students the importance of Mathematics in people’s daily life.

With examples, analyse the uses and application of Mathematics using daily life scenarios in people’s life.