Category 2 (9 categories in total)

I. teaching material analysis

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Textbook 12, page 94, Arrangement and Reflection, and page 95-96, Exercise and Practice, 5- 10.

Key points of knowledge

1. The difference and connection between direct ratio and inverse ratio;

similarities and differences

characteristic relation

The ratio (that is, quotient) of the ratio of two corresponding numbers in two related quantities must be = k (certain).

The product of two corresponding numbers of two quantities in inverse proportion must be x × y = k (certain)

Compared with the old textbook, the new textbook further strengthens the concept teaching of positive-negative ratio, highlights the visualization and simple application of positive-negative ratio, attaches importance to the connection between positive-negative ratio and real life, downplays the judgment of proportional relationship divorced from realistic background, and does not arrange the application of positive-negative ratio to solve practical problems.

2. The ratio of the distance on the picture to the actual distance is called the scale of this picture.

Distance on the map: actual distance = scale or = scale.

Teaching objectives

1. Make students further understand the quantities that are directly proportional and inversely proportional, and master the thinking method of whether these two quantities are directly proportional and what proportion.

2. Make students master the method of judging whether two related quantities are directly proportional or inversely proportional, and improve their analytical judgment ability.

3. Make students further understand the application value of ratio and proportion knowledge, and feel the close relationship between mathematics contents in different fields. It is another effective mathematical model to describe the quantitative relationship and its changing law to know the quantity of direct proportion and inverse proportion and let students feel the direct proportion and inverse proportion.

Second, teaching suggestions

Review the positive and negative proportions, focusing on their meanings. The textbook requires students to recall the method of judging whether two quantities are directly proportional or inversely proportional. Reviewing the direct proportional relationship is characterized by keeping the quotient of two related variables unchanged, and the inverse proportional relationship is characterized by keeping the product of two related variables unchanged. Through the judgment of questions 7 and 8, the concepts of positive proportion and inverse proportion are further consolidated. Question 9: Review the proportional images, in which whether the distance traveled by the car is proportional to the fuel consumption, we should use the images to find out several groups of corresponding numbers, make up the proportion and find out the proportion, and judge according to the meaning of proportional.

Review the knowledge of scales and arrange only one question. Use the scale of the plan and the measured distance on the plan to calculate the corresponding actual distance. The teaching topic 10 is to talk about the scale and specific significance of this scheme, get the numerical scale from the linear scale, and recall the significance and algorithm of the scale. It is necessary to sum up the methods and precautions for finding the actual distance by solving problems, and also talk about how to find the distance on the map.

Third, knowledge link.

1. Positive proportion and inverse proportion (textbook 6 P62 cases 1, case 2, case 63, case 3)

2. Scale (textbook 6, P48 case 6, P49 case 7)

Fourth, the teaching process

(A) the significance of positive proportion and inverse proportion.

1. Teacher's question: According to the meaning of direct ratio and inverse ratio, how to judge whether the two quantities are direct ratio or inverse ratio? (After discussion in groups, communicate)

2. Summary: First, are these two quantities related? Does one quantity change with another? Second, whether the ratio (or product) of the corresponding numbers of these two quantities in each group is determined.

3. Give some examples of direct ratio or inverse ratio in life and communicate in groups.

For example, the unit price of cucumber is fixed, and the quantity is directly proportional to the total price. Because, first, quantity and total price are interrelated, and the total price of one quantity changes with the change of another quantity. Second, the ratio of the corresponding figures of each group of these two quantities is the unit price. The unit price is fixed, so these two quantities are in direct proportion.

(2) practice.

1. Are the two quantities in the table proportional? Why?

Appendix 12 2.5 14 24

Addendum 18

Gross tonnage 42 26 100 24.4

Remaining tonnage 4 1 25 99 23.4

Factor 3 5 3 20

Factor 15 9 10 1.5.

The students said, in each table, first, are these two quantities related? Does one quantity change with another? Second, whether the ratio (or product) of the corresponding numbers of these two quantities in each group is determined. Then make a corresponding judgment.

2. Complete 95 pages of the textbook "Practice and Practice"

Question 7: Let the students do it independently before commenting. Pay attention to helping students solve difficulties when commenting.

Question 8: Guide the students to list several groups of corresponding values, then analyze the relationship between the two numbers in each group and make a judgment.

Question 9: Question 1 requires students to calculate the ratio of fuel consumption to driving distance according to the position of the points marked in the picture, and then make a judgment. Driving 75 kilometers consumes 6 liters of fuel. Question 2: Let the students draw points and lines on the grid provided by the textbook, and then guide the students to judge that the driving distance is not proportional to the fuel consumption when the car is driving in the urban area. Experience the value of the combination of numbers and shapes in solving problems.

(3) Audit Scale

1. The teacher asked: What is a scale? How many kinds of scales are there? Give an example to illustrate its meaning? (The emphasis is on the proportion of line segments)

2. For example, how to find the distance on the map? How to find the actual distance?

3. Complete the textbook Exercise and Practice, page 95, question 10.

(4) Evaluation summary:

What do you know about what you have learned after learning this lesson? Is there a problem?