Teaching objectives

Knowledge and skills

1. Understand the concept of line ratio.

2. Grasp the proportional line segment and its properties, and apply it to solve practical problems.

Mathematical thinking and problem solving

Through observation, operation, exploration, comparison and other learning processes, improve the ability to solve practical problems.

Emotion and attitude

Through the application of scale in map making, the practical application value of mathematics is realized.

Important and difficult

Emphasis: the properties of proportional line segment and its popularization and application.

Difficulties: the application of scale in maps.

Teaching design

-Situation introduction

In our life, we can often see figures with the same shape. Exploring the characteristics of this kind of graphics will help us better understand the graphic world. Starting today, we will enter the world of similar graphics.

Second, cooperate and exchange, and explore new knowledge.

Look at the two maps on page 40 of the textbook.

The scales of these two pictures are 1: 800000, 1: 1600000 respectively.

(1) Measure the distances from Nanjing to Xuzhou and Nanjing to Lianyungang on two maps respectively.

(2) What is the distance ratio between Nanjing and Xuzhou in these two maps? What is the distance ratio between Nanjing and the south of Lianyungang on the map? What is the quantitative relationship between these two ratios?

The two maps have the same shape, but different proportions. Therefore, to study isomorphism, we must first study proportional line segments.

Do it.

(1) Thinking and Exploration on Page 40 of Textbook 1.

(2) Thinking and exploration on page 4 1 of textbook 2.

For Yu (2), the teacher should remind students to use Pythagorean theorem to find the length of these four line segments, and then make a judgment.

Note: Using this set of questions, the definition of proportional line segments is consolidated, which further shows that the proportion of line segments is orderly, and the order of four line segments cannot be reversed at will.

Basic properties of proportion

Imitate the proportional nature in primary school mathematics, from A: B = C: D, what can you get?