This textbook includes the following contents:
Fractional multiplication, position and square
Fractional division, ratio, circle, percentage, pie chart, mathematical wide angle and total complex number.
Xi et al.
Second, the changes in teaching materials:
Fractional multiplication: two forms of emphasizing the significance of fractional multiplication, adding examples.
2, as a teaching "what is the score of a number, calculate by multiplication".
The foreshadowing. Solve the practical problem of "what is the score of a number"
Arrange separately, but combine the meaning and calculation of fractional multiplication for teaching. raise
Multiplication of fractions and decimals. Increase the practical problem of finding the score of a number continuously.
Title. The practical problem of finding more (or less) scores than a number includes two examples.
Reduce it to one. The understanding of reciprocal has moved from the unit of fractional multiplication to the unit of fractional multiplication.
Digital division "unit.
Position and direction: Play the first volume of the sixth grade of the experimental textbook "Determining the position by using number pairs"
Move "to the first volume of the fifth grade, and put" the direction of use "in the second volume of the fourth grade experimental textbook.
Distance to determine the location "book moved to.
Fractional division: "Understanding reciprocal" has been moved from the unit of "fractional multiplication" to the book.
Unit. Set a cell for the content list of "Bi". Add two new problem solving types:
Sum time and difference time; The problem that the unit "1" can solve.
Contrast: The main difference from the experimental textbook is that it was originally in the decimal division unit, and this book is studied separately as the fourth unit. The teaching content remains basically unchanged.
Circle: The main difference from the experimental textbook is that the circle is drawn with compasses.
The names of each part, and then study the properties of the circle. Reduce the symmetrical length of the circle.
Added the content of "designing patterns with circles". Add circumscribed squares and circles to find circles.
"Solving problems" of inscribed circle and inscribed circle area. "Fan" is selected from within the school.
Make it a formal teaching content.
Percentage (1): The main difference from the experimental textbook is "percentage".
The "application" is divided into two parts. This book only teaches the general application of percentage, but it is very special.
Interest rate, discount, percentage and other applications were moved to the second volume of grade six. Divide the score by the percentage
The reciprocity of numbers and decimals, the calculation of percentages, and the calculation of percentages of numbers are a knot.
Together, pay attention to naturally guide students to score percentages and points in the application process.
Numbers and decimals are mutually transformed. Practical problems solved by adding the unit "1".
Department statistics chart: The main difference from the experimental teaching material is the addition of combination selection.
Applicable to the contents of statistical charts.
Mathematics Wide-angle Number-to-Number and Shape: Main Differences from Experimental Textbooks and Experiments
The question of "chickens and rabbits are in the same cage" in the first volume of the sixth grade textbook was moved to the second volume of the fourth grade, which was newly compiled.
The content of "the combination of numbers and shapes".
Three. Teaching material analysis and Suggestions
Principles of Psychology and Students
The structure of this textbook strives to conform to pedagogy,
Age characteristics continue to reflect the style and characteristics of experimental teaching materials. It still does.
Rich in content, paying attention to students' experiences and experiences, reflecting the formation process of knowledge,
Encourage the diversification of algorithms and problem-solving strategies, change students' learning methods and reflect open teaching methods.
1. Improve the arrangement of fractional multiplication and division ratio to reflect the reform of mathematics teaching.
New ideas, deepen students' understanding of mathematics knowledge and cultivate students' application consciousness.
On the basis of existing knowledge, help students build new knowledge independently. strengthen
Intuitive teaching, combined with practical operation and intuitive graphics, helps students understand arithmetic,
Master the method. Strengthen the communication and connection of fractional multiplication and division to promote the positive transfer of knowledge.
Dynamic, improve the ability to solve practical problems.
(1) does not teach the meaning of fractional multiplication and fractional division separately, but lets
Students understand luck by solving practical problems and combining specific situations and calculation processes.
Calculate the meaning.
(2) Through practical problems, the problems that need to be calculated by fractional multiplication and division are deduced.
Let students experience and understand the algorithm and calculation of fractional multiplication and division in real situations.
Science, organically combining problem-solving teaching with calculation teaching, is learning
At the same time, cultivate students' awareness of applying mathematics and their ability to solve problems.
(3) with the help of operations and charts, guide students to explore and understand fractional multiplication,
Division algorithm and arithmetic. Exploration and understanding of fractional multiplication and division operation method,
It has always been a difficult point in teaching. According to the characteristics of students' thinking, the teaching materials are designed in color.
Origami, line drawing and other activities. Take the strategy of combining hands and brains and combining numbers and shapes.
To break through.
2. Arrange the unit of "ratio" separately, and the significance and nature of teaching ratio.
And applications. Putting "ratio" in the teaching after fractional division is mainly due to two considerations:
First of all, the ratio is closely related to the score. When two integers are divided (the divisor is not equal to 0), their quotient can be expressed as a fraction, or the ratio of two numbers is two.
The ratio of numbers can also be expressed in fractional form. Strengthen the connection between proportion and score,
Can deepen students' understanding and comparative understanding of the meaning of fractions,
You can also mention
The ability of high school students to use knowledge flexibly to solve simple practical problems. Second, advance.
The concept of teaching ratio can be used for the following teaching pi, percentage and statistics.
Good foundation. For example, with the concept of ratio, students can easily understand why it is percentage.
It can also be called percentage. Only the application of proportion is taught here.
For the problem of distribution, scale is taught in the application of proportion.
2. There are many teaching contents about percentage, and the teaching materials are set separately.
Meta-percentage teaching. The calculation of percentage is usually the number of components.
And decimals; The idea and method of solving practical problems by percentage lies in solving problems.
It's basically the same as solving the score problem. So the textbook only requires percentages.
Give appropriate examples to teach problems, and then strengthen the teaching of practical application of percentage.
study Closely combine life examples to guide students to understand the meaning and benefits of percentage.
Solve practical problems with percentages.
3. Provide rich space and graphic teaching content, and pay attention to hands-on practice and
Independent exploration promotes the development of students' spatial concept.
"Orientation and direction" should pay attention to connecting students' life experience with existing knowledge.
Guide students to explore new knowledge independently and develop the concept of space. Take the problem as the carrier, drum
Encourage students to overcome the difficulties in teaching through independent inquiry and cooperation and exchange, and initially establish the concept of coordinates.
In the teaching of "circle" unit, guide students to operate and explore the circle independently.
Features. Pay attention to guiding students to use and experience mathematical thinking methods such as transformation and limit.
Closely combine living materials to cultivate students' awareness of applying mathematics in daily life.
And ability.
4. Strengthen the teaching of statistical knowledge, cultivate students' statistical concepts and gradually form them.
Become a habit of thinking from a mathematical perspective.
In the specific arrangement of teaching materials, first, pay attention to the statistical knowledge learned before.
Knowledge to help students understand the characteristics and functions of fan-shaped statistical charts. The second is attention.
It is intended to excavate the mathematical materials in life and highlight the practical value of statistics. Teaching time knot
Let students fully feel the realistic cost of statistics by combining statistical examples in life.
Value. Make students know the applicability and limitations of various statistical charts through comparison.
5. Infiltrate mathematical thinking methods step by step to cultivate students' mathematical thinking ability.
And the ability to solve problems.
Cultivating students' good mathematical thinking ability is the most important thing in mathematics teaching.
One of the goals. Mathematics wide-angle unit allows students to experience discovery mode and application mode.
The type of query process. Make full use of correspondence and comparison between numbers and shapes to cultivate students' interest
Consciousness and ability to solve digital problems with graphics,
Let students feel the charm of mathematics
And beauty.
6. The cultivation of emotion, attitude and values permeates mathematics teaching.
The charm of learning, the harvest of learning, stimulate students' interest in learning and internal motivation.
This experimental textbook has arranged many reading materials and figures reflecting mathematical culture.
Learn historical facts, etc. , make students' mathematics learning activities colorful and full of charm. this
All these help students to understand the close relationship between mathematics and human life.
Understand; Understanding
The value of mathematics stimulates students' desire to learn mathematics.
(1) Provide rich materials to cultivate students' interest in learning mathematics.
Considering the growth of students' age and the expansion of their horizons, the textbooks pay attention to
Choose textbooks with profound knowledge and richer connotations for students to learn.
At the same time, mathematics is influenced by emotions, attitudes and values. For example, in "than"
In the "Application" unit, pass "Do you know?" The introduction of "golden ratio"
Knowledge and works of art and architecture designed with the "golden ratio"; Mathematical wide-angle "number"
The idea of combining shape, number and shape can make some abstract mathematical problems intuitive.
Vividness can transform abstract thinking into image thinking, which is helpful to grasp mathematical problems.
The essence of; In addition, because of the combination of numbers and shapes, many problems are encountered.
The solution is simple and clear.
(2) Pay attention to reflecting the close relationship between mathematics and human life and mathematics.
Cultural value.
This textbook still pays great attention to the form of reading materials.
Combined with teaching content
Sort out some related historical materials of mathematics to enrich students' overall understanding of the development of mathematics.
Knowledge, cultivate students' interest and desire to explore and learn mathematics. If it is arranged.
Multiple "Do you know?" "Mathematics in Life" and "Reading Materials".
(3) Through independent exploration activities, students can gain successful learning experience and enhance their confidence in learning mathematics well.
The textbook designs many activities that require students to explore independently, such as inquiry.
When measuring the circumference of a circle, let the students measure the circumference by circling and rolling.
On this basis, guide students to explore the relationship between circumference and diameter.
Formula for calculating the circumference. Similarly, the derivation of the formula for calculating the area of a circle,
Let the students work in groups and cut and paste by hand, so as to "turn the circle into a square"
The calculation method of circular area is obtained. Another example is the teaching of "number and shape", and the safety of teaching materials comes first.
Sort out the problems with simple data, and let the students explore and solve such problems and find the problems themselves.
To understand the law, we should use the idea and law of combining numbers and shapes to solve complex problems. Let students
Have more opportunities to practice independent exploration,
And obtained through these activities.
Have a good experience such as success and ability improvement, so as to gradually enhance the ability to learn mathematics and study.
Self-confidence in mathematics.
Fourth, the teaching objectives:
1. Understand the significance of fractional multiplication and division, and master the calculation of fractional multiplication and division.
Method, more skilled calculation of simple fractional multiplication and division, will be simple.
Fractional elementary arithmetic.
2. Understand the meaning of reciprocal and master the method of finding reciprocal.
3. Understand the meaning and nature of the ratio, find the ratio and simplify it, and solve the existing problems.
Simple practical problems of closing the wall.
4. Master the characteristics of the circle and draw the circle with compasses; Explore and master the circumference
And can correctly calculate the circumference and area of the circle.
5. Know that the circle is an axisymmetric figure, and further understand the axisymmetric figure; Nengyun
Design simple patterns with translation, axial symmetry and rotation.
6. Be able to express the position with several pairs on the grid paper, and have a preliminary concept of coordinates.
Yes
7. Understand the meaning of percentage and calculate percentage skillfully.
Calculation can solve simple practical problems about percentage.
8. Know the fan-shaped statistical chart, and choose the appropriate statistical chart as needed.
Data.
9. Experience in finding, asking and solving problems in real life.
Process, experience the role of mathematics in daily life, and initially form a comprehensive application number.
Learn knowledge and solve problems.
10. Experience the diversity of problem-solving strategies, and use mathematics combining numbers and shapes.
The effectiveness of thinking method in solving problems, feeling the charm of mathematics and forming discoveries.
The life consciousness of mathematics has initially formed the ability of observation, analysis and reasoning.
1 1. Experience the fun of learning mathematics, improve the interest in learning mathematics, and establish
Confidence in learning math well.
12. Develop the good habit of working hard and writing neatly.
Five, the teaching focus
1. Fractional multiplication and division, ratio, circle, percentage, etc. Is the focus of this textbook.
Point out the teaching content.
2. Promote the development of students' spatial concept,
Preliminary Cultivation of Mathematical Thinking and Its Solutions
The method of the problem.
Sixth, teaching difficulties.
1. Understand the meaning of fractional multiplication and be skilled in calculating simple fractions.
Multiplication and division can perform simple fractional elementary arithmetic;
2. Make students understand the application of the number and percentage of fractional multiplication and division.
Relationship, will solve problems flexibly.
3. Analyze and think through the combination of numbers and shapes, so as to realize the combination of numbers and shapes.
The concept of harmony, the concept of experience limit.