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1

First unit circle

1. Let students know the characteristics of a circle: radius, diameter and center. Understand the relationship between radius and diameter in the same circle. You should know that a circle is an axisymmetric figure with countless symmetry axes, all of which pass through the center of the circle. Knowing that there is a circle in life makes our life better.

2. Know concentric circles and equal circles. You should know that the position of the circle is determined by the center of the circle, and the size of the circle is determined by the radius or diameter. Equal circles have the same radius and different positions; Concentric circles have different radii and the same position.

3. Make students know the meaning of circumference and pi, master the calculation formula of circumference and calculate circumference correctly. This paper introduces Zu Chongzhi's achievements in the study of pi, and permeates patriotic education. In practice, if the diameter or radius can be calculated according to the circumference of a circle, the circumference of a semi-circle can be calculated: the circumference of a circle × 1/2+ diameter. Find the perimeter of the combined figure.

4. Understand the meaning of the area of a circle, go through the derivation process of the formula for calculating the area of a circle, and master the formula for calculating the area of a circle.

5. Be able to correctly calculate the area of a circle by using the formula of the area of a circle, and solve some simple and practical problems by using the knowledge of the area of a circle. Can flexibly use the area formula of a circle. Given the circumference of a circle, the area of the circle will be calculated, and the area of the combined figure will be calculated. Can calculate the area of the ring, know that in the case of equal perimeter, square, rectangle and circle, the area of the circle is the largest.

6. In the activities of estimating and exploring the formula of circular area, I realized the idea of "turning a curve into a straight line" and initially felt the limit idea.

Application of the second unit percentage

This unit focuses on the application of percentage in life. Knowledge points are: 1. Know the meaning of percentage: the number that indicates that one number is the percentage of another number is called percentage. Percentages are also called percentages or percentages. Percentages are usually not written in the form of fractions, but expressed by percent sign "%"; Percent is sometimes defined as a fraction whose denominator is 100, but there is a difference between percentage and fraction: a fraction can represent a specific quantity or a multiple relationship between two quantities; However, percentage can only represent the multiple relationship between two quantities; So it is an unnamed number, that is, a number that cannot take units.

2. Understand the meaning of "increase by a few percent" or "decrease by a few percent" under specific circumstances, and deepen the understanding of the meaning of percentage.

3. Be able to solve the practical problem of "increasing by a few percent" or "decreasing by a few percent", improve the ability to solve practical problems by using mathematics, and realize the close connection between percentage and real life.

4. Knowing the significance of the percentages of attendance, flour yield and survival rate and their application in real life, we will calculate this percentage.

5. Know the meaning of discount. A number that indicates that one number is a few tenths or a few percent of another number is called a number. Discount refers to selling at dozens or one tenth of the original price. 15% discount means selling at 85% of the original price. Fractions and discounts cannot be expressed in decimals.

6. It can solve the practical problem of "how much a number increases" or "how much a number decreases".

7, further strengthen the understanding of the percentage meaning, and can solve practical problems according to the equation of percentage meaning, and can solve the equation containing percentage.

8. Be able to use percentage related knowledge to solve some practical savings.

5, can use the meaning of the ratio to solve the practical problem of distribution according to a certain proportion, and improve the ability to solve practical problems.

Expanding ability: the ratio can be simplified by calculating the ratio.

Unit 5 Statistics

1. Know the characteristics of composite bar chart and composite line chart, understand the similarities and differences between simple chart and composite chart, and use composite bar chart and composite line chart to represent the corresponding data on the chart of vertical axis and horizontal axis to realize the function of data.

2, can understand the composite bar chart, and can make simple analysis, judgment and prediction according to the relevant information in the composite bar chart.

3. Will collect and sort out information. And through data analysis, problems are found, so as to decide what statistical chart to use to describe the data.

Unit 6 Observing Objects

1, can correctly identify the shape of the five small cube combinations of three-dimensional graphics * * * * Observe the front, side and top of * * * from different directions, and can draw sketches. 2. We can restore the three-dimensional figure according to the plane figure observed from the front, side and above, and further realize that the shape of the three-dimensional figure can be determined from three aspects, and the number range of cubes needed to construct this three-dimensional figure can be determined according to the shape of the plane figure observed from two given directions.

Problems, improve the ability to solve practical problems. Know that interest is the extra money after the principal is deposited in the bank for a period of time; The principal is the money in the bank; Interest rate is the percentage of interest to principal in a certain period; Interest tax is a tax levied on interest income stipulated by the State Bank. Will calculate interest. Interest = principal × interest rate× time

9, combined with savings and other activities, learn to manage money reasonably, and gradually develop a good habit of not spending money indiscriminately.

Unit 3 Graphic Transformation

1. Through observation, operation and imagination, we can know how a simple figure translates or rotates into a complex figure, experience the transformation of the figure and develop the concept of space. With the help of calculation and analysis on grid paper, the transformation process of graphic translation or rotation is expressed in an orderly way.

2. You can use puzzles to transform various graphics on grid paper. Can use the transformation of graphics to design beautiful patterns on square paper, and further understand the role of translation, rotation and axial symmetry in pattern design.

3. Appreciate the patterns and feel the magic of the graphic world. Through the interesting and beautiful patterns in life, we can know the beauty of mathematics and experience the magic of the graphic world.

Understanding of the fourth unit ratio

1, can abstract the process of comparison from specific situations and understand the meaning of comparison.

2, can read and write the ratio correctly, can find the ratio, and understand the relationship between the ratio and division and fraction. 3. Be able to use the knowledge of ratio to explain some simple life problems and feel the widespread existence of ratio in life.

4. To understand the necessity of simplifying the ratio, we can use the invariance of quotient or the basic properties of fraction to simplify the ratio and solve some simple practical problems.

2

Cylinders and cones

First, the rotation of the surface

1. The relationship of "point, line, surface and body" is: the movement of points forms a line; The movement of the line forms the surface; The rotation of the surface forms a body.

2. Characteristics of cylinder:

* * *1* * The two bottom surfaces of the cylinder are two circles with the same radius. * * * 2 * * The distance between the two bottoms is called the height of the cylinder.

***3*** Cylinders have countless heights, all of which are of equal length.

3. The characteristics of the cone:

* * *1* * The bottom of the cone is a circle. The side of a * * 2 * * cone is a curved surface. * * * 3 * * The cone has only one height.

Second, the surface area of the cylinder

1. Cut along the height of the cylinder, and the side of the cylinder expands into a rectangle * * * or a square * * *.

* * * If it is not cut along the height, it may be a parallelogram * * *

2. lateral area of cylinder = perimeter of bottom × height, expressed in letters: S side =ch.

3. The application of the formula of cylinder side area;

* * *1* * Given the perimeter and height of the bottom surface, the formula can be used to calculate the lateral area:

S side = ch

* * * 2 * * Given the diameter and height of the bottom surface, the formula can be used to calculate the lateral area:

S plane =? DH；

* * * 3 * * Given the radius and height of the bottom surface, the formula can be used to calculate the lateral area:

S plane =2? right hand

4. Calculation method of surface area of cylinder: If the side surface area of cylinder is represented by S edge, the bottom of S represents the bottom surface area, D represents the bottom surface diameter, R represents the bottom surface radius and H represents the height, then the surface area of cylinder is:

S table =S side +2S bottom 2 or S table =dh+d/2=2 or S table =2rh+2r.

5. Special application of cylindrical surface area calculation method:

* * *1* * The surface area of a cylinder only includes the side area and the bottom area.

Such as a cylindrical object, such as a bucket without a lid.

* * * 2 * * The surface area of a cylinder only includes the side area, such as chimney and oil.

Cylindrical objects such as pipes.

Third, the volume of the cylinder

1. Volume of cylinder: the size of the space occupied by the cylinder.

2. Volume of cylinder = bottom area × height. If V represents the volume of a cylinder, S represents the bottom area and H represents the height, then V=Sh.

3. The application of cylindrical volume formula:

* * *1* * When calculating the volume of a cylinder, if the bottom area and height are given in the question, you can use the formula: V=Sh.

* * * 2 * * Given the radius and height of the cylinder bottom, the volume can be calculated by the formula: V2 = RH；;

* * * 3 * * Given the diameter and height of the bottom of a cylinder, the volume can be calculated by the formula: V2=? * * * d/2 * * * h；

* * * 4 * * Given the circumference and height of the cylinder bottom, the volume can be calculated by the formula: V2=? ***C/2？ * * * h；

The volume of cylindrical container = bottom area × height, which is V=Sh in letters.

5. The application of cylindrical container formula is the same as that of cylindrical volume formula.

Fourth, the volume of the cone.

1. The cone has only one height.

2. The volume of the cone = 1/3× bottom area× height.

If V represents the volume of the cone, S represents the area of the bottom and H represents the height, the letter formula is: 1/3Sh 3. Application of cone volume formula;

* * *1* * When calculating the volume of a cone, if the bottom area and height are given in the question.

These two conditions can be directly applied to the formula "v= 1/3 Sh".

* * * 2 * * When calculating the volume of a cone, if the sum of the radii of the bottom surface is given in the question,

High these two conditions, you can use 1/3πr? h

* * * 3 * * When calculating the volume of the cone, if the sum of the diameters of the bottom surface is given in the question,

High these two conditions, you can use 1/3π***d/2***? h

* * * 4 * * When calculating the volume of a cone, if the sum of the perimeter of the bottom surface is given in the question,

High these two conditions, you can use 1/3π***c/2r***? h

Positive proportion and inverse proportion

First, the number of changes.

There are many interdependent variables in life. When one quantity changes, the other quantity changes.

Second, direct proportion.

1. The meaning of positive proportion: two related quantities, the change of one quantity,

The other quantity will also change. If the ratio of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and their relationship is called proportional relationship. If the letters X and Y are used to represent two related quantities, and the letter K is used to represent that their ratio * * * must be * * *, then the positive proportional relationship can be expressed as: y/x=k*** must be * * *.

2. Use the meaning of direct ratio to judge whether two quantities are direct ratio: Yes.

Although some related quantities change with the change of another quantity, the proportion of their corresponding numbers is not necessarily proportional, such as the sum and difference of the minuend, the area and side length of the square, etc.

Third, draw a picture.

The proportional image is a straight line. Fourth, the inverse ratio

1. The meaning of inverse proportion: two related quantities, one variable,

The other quantity will also change. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. If the letters X and Y are used to represent two related quantities and K is used to represent their products, the inverse relationship can be expressed as: X Y = K * * * must be * * *. 2. Judge whether the two quantities are inversely proportional: First, think that these two quantities are

Is not an associated quantity; Then, the quantitative relationship is used to judge whether the product of these two quantities is determined; Finally draw a conclusion.

Observation and exploration of verb (abbreviation of verb)

When the two variables are inversely proportional, the drawn image is a smooth curve.

Six, graphics scaling

When a picture is enlarged or reduced, the picture can only be similar if it is drawn in the same proportion.

Seven. scale

1. Scale: The ratio of the distance on the map to the actual distance is called this map.

The scale of. Distance on the map = actual distance × actual distance on the scale = distance on the map/scale 2. Scale classification: whether to reduce the scale according to the actual distance.

Expand, divided into scale reduction and scale expansion. According to different forms of expression, scale can also be divided into line scale and numerical scale.

3. The application of scale:

*** 1***, knowing the scale and the distance on the map, find the actual distance.

Scale = distance on map/actual distance on map = actual distance × actual distance on scale = distance on map/scale 2/2.