Application of percentage

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Application of positive-negative ratio

This textbook mainly includes the following contents: position, fractional multiplication, fractional division, circle, percentage, statistics, mathematical wide angle and mathematical practice activities.

Fraction multiplication and division, circle and percentage are the key teaching contents of this textbook.

The directory is like this:::::: ; ：

I. Location (2 class hours)

Second, the decimal multiplication (12 class hours)

1. Fractional multiplication takes about 5 class hours.

2.4 Solve problems around class hours.

3. The understanding of reciprocal is probably 1 class hour.

Organize review for about 2 class hours.

Three. Fractional division (13 class hours)

1. Fractional division takes about 5 class hours.

2. Solve the problem for about 3 class hours.

3. The application of ratio and ratio is about 3 class hours.

Organize and review 2 class hours.

Four. Circle (8 class hours)

The understanding of 1. circle is about 3 class hours.

2. The circumference is about 2 hours.

The area of the circle is about 2 class hours.

Review 1 class hour

Determine the starting line of 1 lesson.

Verb (abbreviation for verb) percentage (15 class hours)

The meaning and writing of 1. percentage is about 2 class hours.

2. Percentages, fractions and decimals are exchanged for about 2 class hours.

3. Solve the problem in percentage for about 9 class hours.

Organize and review 2 class hours.

Statistics of intransitive verbs (2 class hours)

Reasonable deposit 1 class hour

Seven, mathematics wide angle (2 class hours)

Eight. Comprehensive review (4 class hours)

First, the teaching content and teaching objectives

This textbook includes the following contents: position, fractional multiplication, fractional division, circle, percentage, statistics, mathematical wide angle and mathematical practice activities.

Fraction multiplication and division, circle and percentage are the key teaching contents of this textbook.

In number and algebra, this textbook arranges three units: fractional multiplication, fractional division and percentage. The teaching of fractional multiplication and division is to cultivate students' ability to calculate four fractions and solve practical problems about fractions on the basis of learning integer and decimal calculation. The calculation ability of four fractions is an important basic skill for students to further study mathematics, which students should master. Percentage is widely used in real life. Understanding the meaning of percentage and mastering the calculation method of percentage will solve simple practical problems about percentage, and it is also the basic mathematical ability that primary school students should have.

In terms of space and graphics, this textbook arranges two units: position and circle. On the basis of existing knowledge and experience, the teaching of position allows students to go through a preliminary mathematical process through rich mathematical practice activities, understand and learn to express position with number pairs; Through the exploration and study of the characteristics and related knowledge of curve figure-circle, the basic method of learning curve figure is preliminarily understood, which promotes the further development of students' spatial concept.

In statistics, this textbook is arranged in the form of a fan-shaped statistical chart. On the basis of studying bar charts and line charts, learn to understand fan charts, know their characteristics, further understand the role of statistics in life and the methods to solve problems, and develop statistical concepts.

On the one hand, the textbook combines the knowledge of fractional multiplication and division, percentage, circle and statistics. And use what you have learned to solve simple problems in life; On the other hand, the teaching content of "Mathematics Wide Angle" is arranged to guide students to experience the diversity of problem-solving strategies and the effectiveness of using hypothetical methods to solve problems through activities such as observation, guessing, experiment and reasoning, to further understand the superiority of algebraic methods to solve problems, to feel the charm of mathematics and to develop students' problem-solving ability.

According to students' mathematical knowledge and life experience, this textbook arranges two practical activities of comprehensive application of mathematics, so that students can use what they have learned to solve problems, experience the fun of exploration and the practical application of mathematics, and cultivate students' awareness and practical ability of mathematical application through group cooperative exploration activities or activities with realistic background.

The teaching goal of this textbook is to enable students to:

1. Understand the significance of fractional multiplication and division, master the calculation method of fractional multiplication and division, skillfully calculate simple fractional multiplication and division, and perform simple fractional elementary arithmetic.

2. Understand the meaning of reciprocal and master the method of finding reciprocal.

3. Understanding the meaning and nature of ratio, seeking ratio and transforming ratio can solve simple practical problems about ratio.

4. Master the characteristics of the circle and draw the circle with compasses; Exploring and mastering the formula of the circumference and area of a circle can correctly calculate the circumference and area of a circle.

5. Know that the circle is an axisymmetric figure, and further understand the axisymmetric figure; Translation, axial symmetry and rotation can be used to design simple patterns.

6. Be able to express the position with several pairs on the grid paper, and get a preliminary understanding of the idea of coordinates.

7. Understanding the meaning of percentage and calculating skillfully can solve simple practical problems about percentage.

8. Understand the fan chart, and choose the appropriate chart to represent the data as needed.

9. Experience the process of finding, asking and solving problems in real life, understand the role of mathematics in daily life, and initially form the ability to solve problems by comprehensively applying mathematical knowledge.

10. Experience the diversity of problem-solving strategies and the effectiveness of using hypothetical mathematical thinking methods to solve problems, and feel the charm of mathematics. Form the consciousness of discovering mathematics in life, and initially form the ability of observation, analysis and reasoning.

1 1. Experience the fun of learning mathematics, improve the interest in learning mathematics, and build confidence in learning mathematics well.

12. Develop the good habit of working hard and writing neatly.

Second, the writing characteristics of teaching materials

The arrangement and treatment of teaching content in this textbook is guided by the ideas and principles of compiling a whole set of experimental textbooks, and strives to make the structure of the textbooks conform to the principles of pedagogy and psychology and the age characteristics of students, and continue to reflect the styles and characteristics of previous experimental textbooks. This textbook still has the characteristics of rich content, paying attention to students' experience and understanding, embodying the formation process of knowledge, encouraging diversification of algorithms and problem-solving strategies, changing students' learning methods, and embodying open teaching methods. At the same time, due to the different teaching contents, this textbook also has the following obvious characteristics.

1. Improve the arrangement of fractional multiplication and division, embody the new concept of mathematics teaching reform, deepen students' understanding of mathematics knowledge and cultivate students' application consciousness.

The knowledge and skills of quartering operation are the basic knowledge and skills that primary school students should master. The calculation method of four fractions is different from the calculation method of integers and decimals, and it is slightly more complicated than the calculation method of integers and decimals, so it is difficult for students to understand and master. The addition and subtraction of fractions is different from the addition and subtraction of integers and decimals in calculation method, but it is related to the addition and subtraction of integers and decimals in arithmetic. Only numbers with the same unit can be added or subtracted directly. In order to highlight this rule of * * *, and students have learned the simple addition and subtraction of fractions with the same denominator, in the second volume of the fifth grade, the experimental textbook arranged the addition and subtraction of fractions with the same unit for interspersed teaching. The multiplication and division of fractions are closely related, and the teaching of fractional division needs to be based on fractional multiplication; Moreover, there are many contents in the fractional multiplication and division method, so it is difficult for students to understand its arithmetic. Therefore, this experimental textbook still adopts the arrangement of fractional multiplication and fractional division in unit teaching. In the specific arrangement, the two units first teach the algorithm and theory of each calculation in combination with practical problems, and then arrange some problems with special quantitative relations to be taught separately in the "problem solving" section. By solving practical problems and understanding the quantitative relationship of such problems, we can master the ideas and methods of solving problems and further deepen students' understanding of fractional multiplication and division. This arrangement is focused and helps students to understand and master the arithmetic, algorithm and practical application of fractional multiplication and division.

Similar to the arrangement of the original compulsory education textbooks, the section of "ratio" is still arranged in the fractional division unit, and the significance, nature and application of teaching ratio are discussed. There are two main reasons for teaching the "ratio" in grades in advance: First, the ratio is closely related to grades. When two integers are divided (the divisor is not equal to 0), it can be expressed as a fraction or a ratio of two numbers, and the ratio of two numbers can also be expressed as a fraction. Strengthening the connection between ratio and score can deepen students' understanding and comparative understanding of the meaning of score, and also improve students' ability to use knowledge flexibly to solve simple practical problems. Second, the concept of pre-teaching ratio can lay a good foundation for post-teaching pi, percentage and statistics. For example, with the concept of ratio, students can easily understand why percentage can also be called percentage. The application of proportion here only teaches the problem of proportional distribution, and the application of proportion teaches the scale.

Like the calculation teaching of integers and decimals, the multiplication and division teaching of fractions should also reflect the idea of calculation teaching reform. Therefore, the arrangement of experimental textbooks has the following improvements compared with the original compulsory education textbooks.

(1) Don't teach the meaning of fractional multiplication and fractional division separately, but let students understand the meaning of operation by solving practical problems and combining the specific situation and calculation process.

(2) Through practical problems, the problems that need to be calculated by fractional multiplication and division method are introduced, so that students can experience and understand fractional multiplication and division algorithm and arithmetic in real situations, organically combine problem-solving teaching with calculation teaching, and cultivate students' awareness of applying mathematics and problem-solving ability while learning to calculate.

(3) With the help of operations and charts, guide students to explore and understand the algorithm and arithmetic of fractional multiplication and division. The exploration and understanding of fractional multiplication and division is always a difficult point in teaching. According to the characteristics of students' thinking, the textbook designs activities such as coloring, origami and line drawing. , using the strategy of combining hands and brains and combining numbers and shapes to make a breakthrough.

(4) There is no written narrative calculation rule, which simplifies the description of mathematical deduction process and the hint of problem-solving ideas, and provides more space for students to explore and communicate through intuitive and operational means.

(5) Adjust the arrangement of application problems of score multiplication and division, and pay attention to cultivating students' ability to solve practical problems with mathematics.

Solving problems by fractional multiplication and division was once a difficult teaching content in primary school mathematics teaching. According to the requirements of the standard, the arrangement of this set of experimental teaching materials reduces the complexity of the quantitative relationship in the topic, thus reducing the difficulty of solving problems. On the other hand, the practical problems often encountered in daily life are analyzed to cultivate students' consciousness and ability to solve practical problems with mathematics.

2. Improve the arrangement of percentage, pay attention to the transfer of knowledge and connect with practice, and strengthen the cultivation of students' learning ability and application consciousness.

A percentage is a number, which is used to indicate that one number is a percentage of another number, and is usually also called percentage and percentage. Because the denominator of percentage is unified and easy to compare, it is widely used in industrial and agricultural production, scientific research and daily work. There are many teaching contents about percentage, such as its meaning and writing, its interaction with decimals and fractions, its application in practice and so on. Therefore, there is still a separate unit in the experimental textbook to teach percentages.

The calculation of percentage is usually divided into components and decimals; Solving practical problems by percentage is basically the same as solving fractional problems in solving ideas and methods. Therefore, there are not many examples in the textbook as new knowledge to teach, but only examples to teach the problem of percentage, especially the problem of increasing or decreasing percentage, and then strengthen the teaching of practical application of percentage. For example, combined with the percentage, the calculation of meeting the standard rate and budding rate (attendance rate, qualified rate and powder yield are also suggested); Introduce the knowledge of percentage calculation in discount, tax payment and interest.

Similarly, the arrangement of this part of teaching materials also pays attention to the new concept of current mathematics teaching reform. First, strengthen the connection between mathematical knowledge and real life. With the continuous prosperity of China's economic life and the wide application of mathematical knowledge, the practical application of percentage is becoming more and more extensive. Therefore, in the arrangement of this unit, the teaching materials are rich in content, close to students' lives and full of the flavor of the times. For example, in the teaching of percentage meaning, the textbook lists a large number of examples of percentage application in current real life in the form of theme maps; In the arrangement of "integral of percentage and score", interactive teaching is introduced by solving practical problems, so that students can experience the practical application of interactive knowledge. In the "percentage problem solving" section, the teaching of "discount" of goods that students are more likely to contact at present has been added, and so on. This arrangement enables students to know percentage, understand its meaning and feel its application in real life, which is conducive to forming students' correct understanding of the value of mathematics and improving students' ability to solve problems with mathematics. Secondly, it strengthens the exploration and openness of teaching. The textbook pays attention to setting up effective mathematical activities with appropriate opportunities, so that students can experience and understand the percentage of knowledge through independent exploration. For example, in the teaching of percentage meaning, on the basis of enumerating the application examples of percentage in life, we should ask the teaching materials to be wizard-like, so that students can try to talk about the specific meaning of these percentages themselves and experience and understand the meaning of percentage in independent exploration, discussion and communication. For another example, when teaching the practical problem of percentage, on the basis of exploring the meaning and solution of germination rate in question (2), the textbook designed a group cooperative inquiry activity of "doing one thing" to let students discuss how to get attendance, survival rate and hit rate. It not only expands the range of knowledge students have learned, but also deepens their understanding of percentage knowledge. It also cultivates good study habits of independent exploration and cooperation.

3. Provide rich teaching content of space and graphics, pay attention to hands-on practice and independent exploration, and promote the development of students' space concept.

The main goal of space and graphics teaching in primary schools is to develop students' concept of space. Like the previous volumes, this textbook continues to focus on promoting the development of students' spatial concepts as the research focus of spatial and graphic content arrangement. In the teaching content, two units, "position" and "circle", are arranged.

The teaching content of "location" is the expansion and perfection of the corresponding teaching content in the first phase. Students have learned how to determine the position of objects according to rows and columns in the lower grades. Through the study of "position and direction" in the middle grades, they know that the position of objects can be determined according to two conditions in the plane. On the basis of the above study, this textbook teaches how to express the position of an object with number pairs and how to determine the position with number pairs on grid paper. Promote the further development of students' spatial concept through teaching, and lay a good foundation for junior middle school to learn Graphics and Coordinates. In the arrangement of teaching materials, first of all, pay attention to using students' existing knowledge and experience-using "which group is which group" to describe the position of objects in actual situations-to learn new knowledge, and upgrade students' existing experience in time, so that the specific situation can be quickly mathematized, abstracted as learning how to determine the position on the plane and helping students understand the method of determining the position with numbers. On the other hand, pay attention to presenting rich life situations and realistic materials to help students master the method of determining positions with number pairs. For example, provide a chessboard for students to practice determining the position of chess pieces; Show the map or road map and let the students know how to find a place on the map. Mathematics in Life also introduces the method of determining the position of chess pieces with 19 horizontal lines and 19 vertical lines on the chess board, and the practical application of the method of determining the position with the latitude and longitude on the earth, which broadens students' horizons. In practice, teaching materials focus on providing students with the opportunity to solve problems by comprehensive application of knowledge and developing students' spatial concept. For example, in exercise 1 question 6, let the students use the number pair to determine the position of the vertex after the graphic translation; Question 7: Contact the knowledge of orientation and ask students to describe the actual orientation and walking route of the building according to the data on the map. In the process of solving problems by comprehensively applying what they have learned, students can deepen their understanding of using numbers to determine the location content, experience the connection between mathematical knowledge and exercise their spatial imagination.

Circle is a kind of curve figure, which has different characteristics from straight line figure. Before this volume, the plane figures in all textbooks were straight lines. Therefore, the teaching of "circle" is the beginning for students to systematically understand the characteristics of curves and graphs. Although there have been circles in the teaching of lower grades, it is only an intuitive understanding. The teaching of this book should understand the characteristics, perimeter and area of a circle. From learning straight line graphics to learning curve graphics, both the content itself and the method of studying problems have changed. Through the study of circle, the textbook enables students to understand the basic methods of learning curve graphics, and also permeates the internal relationship between curve graphics and straight graphics. In this unit, the textbook also discusses the axisymmetric characteristics of a circle by using students' preliminary knowledge of axisymmetric graphics, and gives the concept of axisymmetric graphics, which makes students' knowledge about axisymmetric graphics systematic and develops the concept of space better. The arrangement of teaching materials strengthens inspiration and exploration, and pays attention to hands-on operation, so that students can explore the characteristics of the circle, the calculation method of the circumference and area of the circle through communication and thinking in their own exploration activities. For example, when teaching the area of a circle, the textbook inspires students to find their own ideas and methods to solve problems, and recalls the conversion methods used before, so as to convert the area of a circle into the area of a familiar straight line figure to calculate. The textbook also focuses on infiltrating mathematical culture and patriotism education by introducing the historical materials of pi.

4. Strengthen the teaching of statistical knowledge, cultivate students' statistical concepts, and gradually form the thinking habit of thinking from a mathematical perspective.

Through the previous five years of mathematics study, students have mastered some knowledge in statistics and probability, formed some abilities and accumulated some experience. This textbook is about the teaching of statistical knowledge, that is, the teaching knowledge of fan-shaped statistical charts. Make students understand the characteristics and functions of fan-shaped statistical charts through teaching; Valuable mathematical information can be obtained from the fan-shaped statistical chart. In teaching, students should also go through the simple process of data collection, sorting, description and analysis, and make simple judgments and predictions according to the results of statistical data analysis, so as to better understand the role of statistical knowledge in solving problems and form a good statistical concept.

In the specific arrangement of teaching materials, first, pay attention to the connection with previous statistical knowledge to help students understand the characteristics and functions of fan-shaped statistical charts. For example, pay attention to the connection with the histogram that students have already learned. By comparing the characteristics and functions of bar chart and fan chart, guide students to understand the characteristics and functions of fan chart. Second, pay attention to the excavation of mathematical materials in life and highlight the practical value of statistics. In terms of material selection, teaching materials focus on selecting from life and production, and try to dig out the relevant mathematical elements around students, which not only broadens the channels for students to collect data, but also highlights the close relationship between statistics and production and life, so that students can realize the practical value of statistics. For example, the materials selected in the textbook involve sports, nutrition, environmental protection, population, etc., which expands the scope of students' information processing and better understands the role of statistical knowledge and methods in real life, which is conducive to developing students' statistical concepts and forming a good habit of thinking from a mathematical perspective.

5. Infiltrate mathematical thinking methods step by step to cultivate students' mathematical thinking ability and problem-solving ability.

Mathematics learning can not only enable students to acquire the necessary knowledge and ability to participate in social life, but also effectively improve students' logical reasoning ability, thus laying the foundation for developing higher quality. Therefore, cultivating students' good mathematical thinking ability is one of the important goals of mathematics teaching. One of the general ideas of this experimental textbook is to systematically and step by step infiltrate mathematical thinking methods, and try to present important mathematical thinking methods with vivid and interesting examples in a simple form that students can understand. Through teaching, students are influenced by mathematical thinking methods, form their interest and desire to explore mathematical problems, and gradually develop their mathematical thinking ability. On this basis, in the "Mathematics Wide Angle" unit of this textbook, an interesting mathematics topic "Chicken and Rabbit in the Same Cage" which is widely circulated in China is arranged. Through teaching, on the one hand, students can understand the ingenious ideas of the ancients to solve such problems, feel the wisdom of their ancestors, and stimulate their interest in learning mathematics; On the other hand, through the exploration and comparison of various problem-solving methods, students can realize the diversity of problem-solving strategies and the superiority of solving problems by algebraic methods, promote the development of students' logical reasoning ability, feel the mathematical thinking method of simplifying the complex, cultivate students' ability of observation, analysis, reasoning and solving problems, and explore mathematical problems.

Cultivating the ability to solve problems with mathematics is one of the important goals of compulsory education mathematics curriculum, so problem-solving teaching plays an important role in mathematics teaching. It is not only a process of developing students' mathematical thinking, but also an important way to cultivate students' awareness of application and innovation. Like the previous textbooks, this textbook still pays attention to integrating problem-solving teaching into the teaching of all parts, and cultivates students' ability to solve problems with mathematics through the teaching of all parts. At the same time, in the "mathematical wide angle" unit and comprehensive application of mathematics, the teaching of comprehensive application knowledge to solve problems and diversified problem-solving strategies has been strengthened, so that students can gradually improve their mathematical thinking ability and problem-solving ability. This textbook has designed two comprehensive application activities of mathematics, namely "determining the starting line" and "reasonable deposit". Through group cooperation and inquiry activities, students can comprehensively apply the mathematical knowledge and methods they have learned (such as the practical application of pi, percentage, savings deposit, interest rate of national debt, etc.) to solve problems, realize the application value of mathematics in daily life, enhance students' awareness of applying mathematics, and continuously improve their practical ability and problem-solving ability.

6. The cultivation of emotion, attitude and values permeates mathematics teaching, and stimulates students' interest and inner motivation with the charm of mathematics and the harvest of learning.

This mathematics curriculum reform emphasizes the cultivation of students' emotions, attitudes and values, and comprehensively improves students' quality. Senior pupils have gained some knowledge and life experience, and have a certain desire to explore natural and social phenomena. At this time, educators need purposeful inspiration and guidance. In mathematics teaching, students should form rich emotions, positive attitudes and correct values through mathematics learning activities, which is also an important foundation for students' learning, survival and development. This experimental textbook not only covers all fields of mathematics teaching content, but also provides rich materials for students to explore the wonderful world of mathematics, and pays attention to arranging many reading materials and mathematical historical facts reflecting mathematics culture in combination with the teaching content, so as to make students' mathematics learning activities colorful and full of charm. All these help students understand the close relationship between mathematics and human life, understand the value of mathematics, and stimulate their desire to learn mathematics.

(1) Provide rich materials to cultivate students' interest in learning mathematics.

Considering the growth of students' age, the expansion of their horizons and other factors, experimental textbooks pay attention to the selection of textbooks with deep knowledge and richer connotations, so that students can be influenced by emotions, attitudes and values while learning mathematics. For example, in the "Comparative Applications" section, "Do you know?" This paper introduces the knowledge of "golden ratio" and the works of art and architecture designed with "golden ratio"; The mathematical wide-angle "chicken and rabbit in the same cage" contains the mathematical thinking method of simplifying complexity; The mathematical comprehensive application of "reasonable storage" permeates the design idea of optimization scheme, and so on. Simple and ingenious problem-solving strategies embody wonderful mathematical methods. Strict logical reasoning, accurate calculation, and perfect principles and laws all subtly make students realize the unique beauty of the form, structure and method of mathematics, which is conducive to stimulating students' interest in learning mathematics and forming a stable interest in exploring mathematics.

(2) Pay attention to the close relationship between mathematics and human life and the cultural value of mathematics.

Like the previous experimental textbooks, this textbook still pays attention to the form of reading materials, and arranges some relevant mathematical historical materials in combination with the teaching content to enrich students' overall understanding of the development of mathematics and cultivate students' interest and desire in exploring and learning mathematics. For example, several "Do you know?" "Mathematics in Life" and "Reading Materials". This paper introduces the application of mathematical knowledge in real life, the stories of ancient mathematicians and so on. These contents can not only make students have a strong interest in mathematics itself, but also stimulate their desire to expand their knowledge and further explore and study, and also have the function of cultivating students' scientific sentiment and spirit.

(3) Through independent exploration activities, students can gain successful learning experience and enhance their confidence in learning mathematics well.

Combined with the age characteristics of students and the teaching content, this textbook has designed many activities that require students to explore independently. For example, when exploring the circumference of a circle, let students first measure the value of the circumference by rounding the circle, and then guide students to explore the relationship between the circumference and the diameter, and get the calculation formula of the circumference of a circle. Similarly, the introduction of the formula for calculating the area of a circle allows students to cooperate in groups, cut and collage by hand, so as to "turn the circle into a square" and get the calculation method of the area of a circle. Another example is the teaching of "chickens and rabbits in the same cage". The textbook first uses small data to arrange problems, so that students can explore ways to solve such problems themselves, and so on. Let students have more opportunities to apply mathematics knowledge and practice independent exploration, and gain good experiences such as their own success and ability improvement through these activities, so as to gradually enhance their confidence in learning and using mathematics.

Three, teaching AIDS and learning tools need to be prepared in teaching.

In the previous teaching books for teachers, many teaching AIDS and learning tools have been introduced, some of which can still be used, such as sticks, squares, protractors, triangles, rulers, calculators and so on. Combined with the teaching needs of this book, this paper introduces several teaching AIDS and learning tools with good use effect for reference.

1. Circular cardboard is used as a teaching aid to demonstrate score calculation and understanding circle. You can make several circles of the same size out of cardboard. Two circular cardboard pieces were made into teaching AIDS, as described in the textbook for fifth-grade teachers on page 14, to demonstrate different scores. The teaching aid used for teachers' demonstration is larger, and the learning tool used for students' operation can be smaller.

2. Compass is used to teach circle. Teachers should prepare compasses that can draw circles on the blackboard. Every student should also prepare a set of compasses for his own use.

3. The teaching aid used to explain the formula for calculating the circular area can be made of cardboard according to the pictures on page 68 of the textbook for teachers to demonstrate. In addition, the same picture is printed in the appendix of this textbook. Students can cut it out and stick it on cardboard as a learning tool for operation.

4. The grid is used to draw the learning position. There are some 10× 10 square papers printed in the appendix of this textbook, which students can cut and use.

5. Other teaching AIDS teachers can also prepare or design some teaching AIDS and learning tools according to the needs of each part of the teaching content. For example, in teaching, draw the upper case on the simple road map of the area as a teaching aid; When teaching percentages, we can collect some commodity labels containing percentages to indicate the content or performance as teaching AIDS or learning tools. Teachers can also make other suitable teaching AIDS according to their own needs.