People's education edition sixth grade mathematics knowledge point arrangement

Genius is diligence. Someone once said. If this statement is not completely correct, it is at least largely correct. Learning, even a genius, requires constant practice and memory. The following are some knowledge points of sixth grade mathematics that I have compiled for you, hoping to help you.

Knowledge points of sixth grade mathematics in People's Education Edition

Cylinders and cones

1. Know cylinders and cones and master their basic characteristics. Know the bottom, side and height of the cylinder. Know the bottom and height of the cone.

2. Explore and master the calculation methods of the lateral area and surface area of cylinder, and the calculation formulas of the volume of cylinder and cone, and use the formulas to calculate the volume to solve simple practical problems.

3. By observing, designing and making cylinder and cone models, understand the relationship between plane graphics and three-dimensional graphics, and develop students' concept of space.

4. The two circular surfaces of a cylinder are called bottom surfaces, and the surrounding surfaces are called side surfaces. The bottom surface is flat and the side surface is curved.

5. The side of the cylinder is rectangular after being unfolded along the height, the length of the rectangle is equal to the circumference of the bottom of the cylinder, and the width of the rectangle is equal to the height of the cylinder. When the perimeter and height of the bottom are equal, the side faces are square after being expanded along the height.

6. Surface area of cylinder = transverse area of cylinder+bottom area ×2, that is, S table =S side +S bottom ×2 or 2πr×h+2×π.

7. The transverse area of the cylinder = the perimeter of the bottom × the height, that is, the S side =Ch or 2πr×.

8. The volume of the cylinder = the bottom area of the cylinder × the height, that is, V=sh or πr2×.

Step-by-step method: In practice, more materials are used than the calculated results. Therefore, when you want to keep this number, the omitted number is 4 or less, and you must move forward 1. This approximate method is called step-by-step method.

9. A cone has only one bottom surface, and the bottom surface is a circle. The side of a cone is a curved surface.

10. The distance from the apex of the cone to the center of the bottom is the height of the cone. The cone has only one height. (Measuring the height of the cone: First, lay the bottom of the cone flat, place a flat plate horizontally above the apex of the cone, and measure the distance between the flat plate and the bottom vertically. )

1 1. Enlarge the side of the cone to obtain a sector.

12. The volume of a cone is equal to one third of the volume of a cylinder with the same height as its bottom surface, that is, V-cone = 1/3Sh or π r2× h..

13. Common cylindrical cones solve problems:

(1) Road surface area (transverse area) of the roller;

(2) The length of the road surface pressed by the roller (find the perimeter of the bottom surface);

(3) Tin bucket (side area and bottom area);

(4) Chef's hat (side area and bottom area); Ventilation pipe (side area).

Important and difficult knowledge points of mathematics in the sixth grade graduation examination of primary school

Ratio and proportion

Than:

Division of two numbers is also called the ratio of two numbers. The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison.

Ratio:

The quotient of the former term divided by the latter term is called the ratio.

The nature of the ratio:

The first and second terms of the ratio are multiplied or divided by the same number at the same time (except zero), and the ratio remains unchanged.

Proportion:

Two expressions with equal ratios are called proportions. A: b = c: d or

Nature of proportion:

The product of two external terms is equal to the product of two internal terms (cross multiplication), and ad=bc.

Positive proportion:

If A expands or shrinks several times and B also expands or shrinks several times (when the quotient of AB is constant), A is directly proportional to B. ..

Inverse ratio:

If A expands or shrinks several times and B also shrinks or expands several times (when the product of AB is constant), A and B are inversely proportional.

Proportion:

The ratio of the distance on the map to the actual distance is called the scale.

Proportional distribution:

Divide several numbers into several parts according to a certain proportion, which is called proportional distribution.

The sixth grade primary school graduation exam mathematics difficult knowledge point 4: geometric area

Basic idea:

In the calculation of some areas, if the formula cannot be used directly, it is generally necessary to cut, translate, rotate, fold, decompose, deform and overlap the graphics to make the irregular graphics into regular ones for calculation; In addition, we need to master and remember some conventional regional rules.

Common methods:

1. Connection auxiliary line method

2. Use two triangles with equal bases and heights to obtain equal areas.

3. Bold assumptions (some points are set at any point in the topic, and you can set any point in a special position when solving problems).

4. Use special laws

(1) isosceles right triangle, it is known that any side can find the area. (The square of hypotenuse divided by 4 equals the area of isosceles right triangle)

(2) After the trapezoid diagonal connection, the areas of the two waists are equal.

③ The area of the circle accounts for 78.5% of the circumscribed circle.

Knowledge points of sixth grade mathematics in People's Education Press: cylinders and cones

1. Know cylinders and cones and master their basic characteristics. Know the bottom, side and height of the cylinder. Know the bottom and height of the cone.

2. Explore and master the calculation methods of the lateral area and surface area of cylinder, and the calculation formulas of the volume of cylinder and cone, and use the formulas to calculate the volume to solve simple practical problems.

3. By observing, designing and making cylinder and cone models, understand the relationship between plane graphics and three-dimensional graphics, and develop students' concept of space.

4. The two circular surfaces of a cylinder are called bottom surfaces, and the surrounding surfaces are called side surfaces. The bottom surface is flat and the side surface is curved.

5. The side of the cylinder is rectangular after being unfolded along the height, the length of the rectangle is equal to the circumference of the bottom of the cylinder, and the width of the rectangle is equal to the height of the cylinder. When the perimeter and height of the bottom are equal, the side faces are square after being expanded along the height.

6. Surface area of cylinder = transverse area of cylinder+bottom area ×2, that is, S table =S side +S bottom ×2 or 2πr×h+2×π.

7. The transverse area of the cylinder = the perimeter of the bottom × the height, that is, the S side =Ch or 2πr×.

8. The volume of the cylinder = the bottom area of the cylinder × the height, that is, V=sh or πr2×.

Step-by-step method: In practice, more materials are used than the calculated results. Therefore, when you want to keep this number, the omitted number is 4 or less, and you must move forward 1. This approximate method is called step-by-step method.

9. A cone has only one bottom surface, and the bottom surface is a circle. The side of a cone is a curved surface.

10. The distance from the apex of the cone to the center of the bottom is the height of the cone. The cone has only one height. (Measuring the height of the cone: First, lay the bottom of the cone flat, place a flat plate horizontally above the apex of the cone, and measure the distance between the flat plate and the bottom vertically. )

1 1. Enlarge the side of the cone to obtain a sector.

12. The volume of a cone is equal to one third of the volume of a cylinder with the same height as its bottom surface, that is, V-cone = 1/3Sh or π r2× h..

13. Common cylindrical cones solve problems:

(1) Road surface area (transverse area) of the roller;

(2) The length of the road surface pressed by the roller (find the perimeter of the bottom surface);

(3) Tin bucket (side area and bottom area);

(4) Chef's hat (side area and bottom area); Ventilation pipe (side area).

Math learning methods in the sixth grade of primary school

Primary school mathematics learning must pay attention to the cultivation of children's innovative consciousness and the development of innovative ability. In a sense, forming the habit of creative learning is more important than how much knowledge you have gained. This needs to start from the following aspects:

1. Cultivate students' habit of asking questions.

Participating in and experiencing the discovery and formation of mathematical knowledge, being good at discovering and putting forward targeted and valuable mathematical questions, and questioning and asking difficult questions are important aspects of cultivating creative learning habits. In the process of mathematics learning, we should gradually cultivate students' study habits of independent inquiry, positive thinking and active questioning, so that they want to ask, dare to ask, love to ask and know how to ask.

The cultivation of questioning habits can also begin with imitation. Teachers should pay attention to the words and deeds of asking questions and teach students where to find doubts. Generally speaking, questioning can occur in the connection of old and new knowledge, confusion in learning process, conclusion of laws and regulations, key and difficult points in teaching content, formation of concepts, analysis of problem-solving ideas and hands-on practice. Students should also learn to change angles and ask questions.

2. Cultivate students' habit of combining hands and brains and paying attention to practice.

Psychological research tells us that the thinking of primary school students is in the transition stage from concrete image thinking to abstract thinking and logical thinking, especially for lower grade children. Their thinking still stays in the concrete thinking of images, and their abstract thinking can only be carried out with the support of perceptual materials. Therefore, primary school mathematics education must attach importance to cultivating students' good habits of hands-on, thinking and oral communication, so that students can acquire new knowledge through watching, touching, spelling, posing and speaking.

For example, when learning the "preliminary understanding of the angle", is there any connection between the size of the angle and the length of both sides? This problem can be discussed while operating, and the correct conclusion can be drawn by observing and discussing it from the perspective of self-made activities. Carrying out similar teaching activities will enable students to develop the study habit of using their hands and brains and being diligent in practice.

3. Cultivate students' good thinking habits.

Cultivate students' habit of thinking and solving problems from multiple angles, and cultivate students' multi-directional and flexible thinking. Through "can you think of different ways?" "What else can you think of?" "Do you have any unique ideas?" Can you look at this problem from another angle? "Words, such as inspiration and induction, encourage students to think, speak, be afraid of mistakes and express different opinions, and cultivate students' innovative thinking habits.

People's education publishing house sixth grade mathematics knowledge points finishing related articles;

★ Finishing the knowledge points of the sixth grade mathematics review (full version)

★ Combing the knowledge points of sixth grade mathematics.

★ Summary of the knowledge points reviewed at the end of the sixth grade mathematics.

★ Summary of the knowledge points reviewed at the end of the sixth grade mathematics.

★ Sort out and summarize the knowledge points of the first volume of mathematics in the sixth grade.

★ Essentials of Sixth Grade Mathematics of People's Education Edition Volume II

★ Knowledge points of mathematics in sixth grade of primary school

★ A Complete Collection of Mathematics Learning Methods and Skills in the Sixth Grade of Primary School

★ Summary of Mathematics Knowledge Points in the Sixth Grade of Primary School

★ Review the knowledge points in the first volume of sixth grade mathematics.

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