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, sides and height of a cylinder. Know the bottom and height of the cone.
2. Explore and master the calculation method of lateral area and surface area of cylinder, as well as the calculation formula of cylinder and cone volume, and use the formula to calculate the volume to solve simple practical problems.
3. By observing, designing and making cylinder and cone models, we can understand the relationship between plane graphics and three-dimensional graphics and develop students' spatial concept.
4. The two circular surfaces of a cylinder are called the bottom surface, the surrounding surfaces are called the side surfaces, the bottom surface is a plane, and the side surfaces are curved surfaces.
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 edge height is square after expansion.
6. The surface area of a cylinder = lateral area of the cylinder+bottom area ×2, that is, S table =S side +S bottom ×2 or 2πr×h+2×π.
7. lateral area of cylinder = perimeter of bottom × height, that is, 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: More materials are actually used than the calculated results. Therefore, when you want to keep numbers, the omitted digits are 4 or less, and you must go 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: firstly, 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. Expand the side of the cone to get 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 πR2×h \
13. Common cylindrical cone solving 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 term and the second term 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:
Math learning methods in the sixth grade of primary school
Primary school mathematics learning must attach importance 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, putting forward targeted and valuable mathematical questions and asking difficult questions is an important aspect 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, like 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 the learning process, induction of laws and regulations, emphasis and difficulty of teaching content, formation of concepts, analysis of problem-solving ideas and hands-on practice. Students should also learn to ask questions from another angle.
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 thinking in images 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, brain-use and verbal communication, so that students can acquire new knowledge through seeing, 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 operated, observed and discussed by operating the self-made activity angle, so as to draw a correct conclusion. Carrying out similar teaching activities can help students 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 flexible thinking. Through "can you think of different ways?" "What else can you think of?" "Do you have a unique opinion?" Can you look at the 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.
The product of two outer terms is equal to the product of two inner terms (cross multiplication), and ad=bc.
Positive proportion:
If A expands or contracts several times and B also expands or contracts several times (when the quotient of AB is constant), A is directly proportional to B. ..
Inverse ratio:
If A expands or contracts several times and B also contracts 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:
Dividing several numbers into several parts according to a certain proportion is called proportional distribution.
Summary of sixth grade mathematics knowledge points;
★ Summary of the knowledge points reviewed at the end of the sixth grade mathematics.
★ Summary of Mathematics Knowledge Points in the Sixth Grade of Primary School
★ Summary of knowledge points in the first volume of sixth grade mathematics
★ Summary of knowledge points in sixth grade mathematics circle
★ Summarize the knowledge points of sixth grade mathematics.
★ Summary of important and difficult knowledge in sixth grade mathematics
★ Summary of Mathematics Knowledge Points in Grade Six
★ Sort out and summarize the knowledge points of the first volume of mathematics in the sixth grade.
★ Summary of mathematical knowledge points in the first volume of the sixth grade
★ Combing the knowledge points of sixth grade mathematics.