2. Understanding the meaning of positive proportion and inverse proportion can help us find examples of positive proportion and inverse proportion in our life, and we can use the knowledge of proportion to solve simple practical problems.

3. Knowing the image with positive proportional relationship, you can draw an image on grid paper with coordinate system according to the given data with positive proportional relationship, and you can calculate or estimate the value of the other quantity in the image according to one of them.

If you know the scale, you will find the scale of the plan and the distance or actual distance on the map according to the scale.

5, understand the phenomenon of zoom in and out, can use the form of grid paper to zoom in or out simple graphics according to a certain proportion, and realize the similarity of graphics.

6. Infiltrate the thought of function, and let students be inspired by dialectical materialism.

7. Meaning of proportion: Two expressions with equal proportion are called proportion. For example: 2: 1 = 6: 3

8. The four numbers that make up a proportion are called proportional items. The two items at both ends are called external items, and the two items in the middle are called internal items.

9. Nature of proportion: In proportion, the product of two external terms is equal to the product of two internal terms. This is the basic nature of the so-called proportion. For example, from 3: 2 = 6: 4, you can know 3? 4=2? 6; Or by x? 1.5=y？ 1.2 Description X: Y = 1.2: 1.5.

10, solution ratio: According to the basic properties of the ratio, if any three terms in the ratio are known, another unknown term in this numerical ratio can be found. Finding the unknown term in the proportion is called the solution ratio.

For example: 3: x = 4: 8, internal term multiplied by internal term, external term multiplied by external term, then: 4x=3? 8，x=6。

1 1, proportional and inverse ratio:

(1), proportional quantity: two related quantities, one changes and the other changes. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. Y/x=k (certain) is expressed in letters.

For example: ① the speed is constant, and the distance is proportional to the time; Because: distance? Time = speed (certain).

② The circumference of a circle is directly proportional to its diameter, because: The circumference of a circle? Diameter = pi (certain).

The area and radius of a circle are out of proportion, because: the area of a circle? Radius = product of pi and radius (not necessarily).

④ y=5x, and y and x are in direct proportion, because: y? X=5 (certain).

The number of pages read every day is fixed, and the total number of pages is directly proportional to the number of days, because: total number of pages? Days = number of pages per day (certain).

(2) Inverse proportional quantity: two related quantities, one changes and the other changes. 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. X in the letter? Y=k (ok)

For example, the distance is constant, and the speed is inversely proportional to the time, because: speed? Time = distance (certain).

2. The total price is fixed, and the unit price is inversely proportional to the quantity, because: unit price? Quantity = total price (certain).

3. The area of a rectangle is constant, and its length and width are inversely proportional, because: length? Width = area of rectangle (certain).

④、40? X=y, x and y are inversely proportional, because: x? Y=40 (certain).

⑤ The total amount of coal burned is certain, and the amount of coal burned every day is inversely proportional to the number of days burned, because: the amount of coal burned every day? Days = total coal quantity (certain).

12. Distance on the map: actual distance = scale;

For example, the distance on the map is 2cm, the actual distance is 4km, the scale is 2 cm: 4 km, and the final scale is 1: 200000.

13, actual distance = distance on the map? Scale;

For example, given a distance of 2cm and the scale on the map, the actual distance is: 2? 1/200000 =400000 cm = 4 km.

14, distance on the map = actual distance? Scale;

For example, given the actual distance of 4km and the scale of 1: 200000, the distance on the map is 400000? 1/200000=2 (cm)