The first teaching goal

1. Let students understand the meaning of solution ratio.

2. Make students master the method of solving the ratio and understand the ratio.

Teaching focus

Make students master the method of solving ratio and learn to solve ratio.

Teaching difficulties

Guide the students to rewrite the proportion into the form that the product of two internal terms is equal to the product of two external terms according to the basic properties of proportion, that is, the equation with unknown numbers.

teaching process

First, review preparation

(1) Solve the following simple equation and dictate the process.

2=8×9

(2) What is proportion? What is the basic nature of proportion?

(3) Using the basic nature of proportion, which of the following groups can be judged as two proportions?

6∶ 10 and 9∶ 1520∶5 and 4∶ 15∶ 1 and 6∶2.

(4) According to the basic properties of proportion, rewrite the following proportion into other equations.

3∶8= 15∶40

Second, the new teaching

(1) reveals the significance of solution ratio.

1. Substitute into any of the above two questions (one can be changed at will), and discuss: If any three items are known, can you find another unknown item in this ratio? Explain why.

2. Student communication

According to the basic properties of proportion, if any three terms in the proportion are known, it can be rewritten as the form that the product of inner terms equals the product of outer terms. By solving the equation we have learned, we can find another unknown term in this ratio.

3. The teacher made it clear that according to the basic nature of the proportion, if any three items in the proportion are known, another unknown item in the proportion can be found. Finding the unknown term in the proportion is called the solution ratio.

(2) Teaching examples 2.

Example 2. The solution ratio is 3∶8 = 15∶ 1

1. Discussion: How to turn this proportional formula into a learned equation with unknowns and find the solution of the unknowns.

2. Organize students to communicate and make it clear.

(1) can be rewritten as: 3 = 8× 15 according to the basic properties of the ratio.

(2) When rewriting, write the product with unknown terms on the left side of the equal sign, and then solve it according to the method of solving simple equations learned before.

(3) Standardize the process of writing solution ratio on the blackboard.

Solution: 3 = 8× 15

=40

(3) Teaching Example 3

Example 3. Solution ratio

1. Organize students to answer independently.

2. Student report

3. Exercise: Understand the following proportions.

=∶=∶

Third, the class summarizes.

In this lesson, we learn proportion. Think about it. What is the key to solving the proportion? (according to the basic properties of proportion, the proportion formula is transformed into a simple equation that has been learned), and then the simple equation can be solved.

Chapter 2 1, teaching objectives

1. Understanding the meaning of solution ratio and mastering the method of solution ratio will help us to understand solution ratio correctly and solve practical problems according to the proportion of meaning.

2. Learn to apply the significance and basic nature of proportion to solve practical problems.

Second, the teaching focus: master the method of solving the ratio and learn to solve the ratio.

Third, teaching difficulties: applying the meaning and basic nature of proportion to solve practical problems in life.

Fourth, teaching presupposition:

(A), self-study feedback

1, what is the solution ratio?

The length-width ratio of our national flag is 3:2. If the length of our national flag is 240 cm, what is the width of our national flag?

(1) Can you answer me? After answering independently, talk to each other at the same table.

(2) Feedback communication

① 240 ÷ 3× 2 = 160 (cm)

② Solution: Let the width of our national flag be cm.

240:=3:2

3=240×2

=240×2÷3

= 160

The width of our national flag is 160 cm.

(3) What do you think?

(2) Key points.

1, using proportion to solve practical problems

(1) Do you understand the second scheme?

(2) The simplest integer ratio of the length and width of the national flag can form a ratio with the actual length ratio, so we can set the width of the national flag as cm, establish a ratio of 240: = 3: 2, and then calculate the value by solving the ratio.

(3) Summary: This method is called solving practical problems in proportion.

2. Dissolution ratio method

(1) How did you achieve the solution ratio of 240: = 3: 2?

(2) According to the meaning of proportion, first find the ratio of 3:2, then convert the ratio into an equation, and then find the numerical value.

(3) According to the basic property of proportion, "the product of two external terms is equal to the product of two internal terms", the proportion is transformed into an equation, and then the value is obtained.

(4) How can we be sure that this value is correct? (check)

(5) Which solution do you prefer? Why?

(3), consolidate the exercise

1, and solve the following ratio

: 10=:0.4:= 1.2:2=

2. Shrink the triangle on the left to get the triangle on the right, and find the unknown X.. (Unit: cm)

Students finish independently, report and communicate.

Xiaoli has prepared two cups of honey water. The first cup used 25 ml of honey and 200 ml of water. The second cup used 30 ml of honey and 250 ml of water.

(1) Write the volume ratio of honey to water in each cup of honey water to see if it is proportional.

(2) According to the ratio of honey to water in the first cup of honey water, how many milliliters of honey should be added to 300 milliliters of water?

Students answer the first question and write it on the blackboard. Then let the students observe whether it can be proportional.

Analysis: The first question should be said to be relatively simple, and the ratio is 25:200 and 30:250 respectively.

(4), share the harvest, talk about feelings

What did you get from this lesson? Random thoughts in class