Relatively speaking, there are many people who make a fuss about the fourth item, but not many people who make a fuss about the fifth item. Of course, the fifth question is outside the syllabus and should be taught in the second lesson. However, this topic is very good, that is, to prevent children from simply using subtraction when they see the word "less", and to understand the purpose and meaning of solving problems as a whole. Then, how to prevent children from deciding addition and subtraction only by "more" or "less", and how to understand the purpose and meaning of solving problems as a whole? In the book "Primary School Mathematics Teaching and Innovation Ability Training", there is a special study on this kind of topic, which is recorded as follows:

1. Before doing this kind of problem, children must understand the mathematical concept of "as much".

(1) Through infiltration, I realized "as much". There are the specific weight of panda-squirrel, the specific height of brother and sister, the specific length of two pencils, and the specific weight of two groups of ducklings. The purpose of arrangement is to guide students to transform life language into mathematical language, and learn to describe comparative relations in mathematical language while realizing "as much as possible". For example, if the elder brother and sister are taller than each other, they should not be confined to the life language of "the elder brother is taller than the younger sister", but should incorporate the concept of "as much" into the narrative of mathematical language. Comparing the height of brother and sister, taking the height of sister as the standard, brother is not only as tall as sister, but also higher than sister, so brother is taller than sister, and sister is shorter than brother.

(2) Understanding "as much" by establishing corresponding relations.

Yellow leaves ☆ ☆?

green leaves

Show two yellow leaves and two green leaves, and then connect 1 green leaves and 1 yellow leaves with dotted lines. Teachers use gestures to teach students to express themselves in words: compare two yellow leaves, 1 green leaf facing 1 yellow leaf, 1 green leaf facing 1 yellow leaf.

Then show pictures of three lemons and three apples. The teacher guided the children to observe. We know that there are as many lemons as apples. (The teacher covers three lemons) There are three apples. We know that there are as many lemons as apples. Can you know the number of lemons? Student reason: There are as many lemons as apples. We know there must be three lemon oak trees in the apples. (The teacher covers three apples) There are three lemons. We know there are as many apples as lemons. Can you know the number of apples? Student reason: There are as many apples as lemons. We know that if there are three lemons, there must be three apples.

Through the previous reasoning, students have a more thorough understanding of "as much". "There are as many lemons as apples" means that there are several lemons, there must be several apples, there must be several apples and there must be several lemons.

(3) Through comparison, deepen "as much".

Teacher: What did you find through observation?

Health: There are not so many bees as butterflies.

Teacher: There are as many bees as there are butterflies.

Health: Hands-on connection, 1 bee face 1 butterfly, and there are as many as 4 bees and butterflies. Teacher: There are two butterflies with no bees facing them. Suppose there are two more butterflies than bees, and bees are two less than butterflies.

Teacher: There are not so many butterflies as bees. Is there any way to make butterflies as many as bees?

Health 1: 2 here comes the bee;

Health 2: fly away 2 butterflies;

Health 3: 1 The bees come, 1 The butterflies fly away.

2. Understand "large numbers" and "decimals" with the concept of "as many" as the core.

Which part of basketball is as much as football? What do you mean "this part of basketball is as much as football"? (There are several football, and there must be several basketball; There are several basketball parts, and there must be several football parts)-communicate the internal relationship between large numbers and decimals through "as much".

This part of basketball is as important as football. What about the basketball part? This is basketball, not just a part of football.

How many parts does the number of basketball consist of? The number of basketball is a combination of two parts, one is as much as football, the other is more than football, and the number of football is only a part of the number of basketball.

Teacher: There are not only as many basketballs as football, but also more than football. Let's just call the number of basketball "a large number", and the number of football is only this number? When it is part of the basketball number, we call the football number "decimal".

3. Master the concept of "as much" and understand the relationship between big and small numbers.

Knowing that there are 65,438+00 footballs is equivalent to knowing that there are 65,438+00 basketballs with the same number. If you remove 65,438+00 football from 65,438+05 basketball, there are five more basketball than football.

15- 10=5 (pieces)

Knowing that there are 65,438+00 footballs is equivalent to knowing that there are 65,438+00 basketballs and footballs. Combine these two parts with 65,438+00 basketballs and soccer balls and 5 soccer balls, and you will get 65,438+05 basketballs. ?

10+5= 15 (piece)

Judging from 15 basketball, if you subtract 5 more than football, it is the same number as football. There is 10 basketball in this part, and there must be 10 football.

15-5= 10 (piece)

After such training, students have a deep understanding of the relationship between size and number, which creates a solid knowledge base and thinking for solving the application problem of phase difference relationship.

4. Apply the concept of "as much" and correctly analyze the relationship between quantities.

The formation of correct problem-solving ideas depends on the correct analysis of quantitative relations, which comes from the correct application of related concepts. It can be seen that the process of deepening the application of the original concept is the process in which students gradually form their logical thinking ability.

"There are more poplars than willows", which means whose tree is bigger and whose tree is smaller? Since the number of poplars is a large number, which two parts does it include? There are as many parts as willows, and there are more parts than willows. What does it mean that the number of willows is a decimal? Willow is only a part of poplar. )

① If you know that there are 28 poplars and 15 willows, can you know how many poplars are more than willows? Knowing that there is 15 willow is equivalent to knowing what? (There are 15 trees in the part where there are as many poplars as willows.) What do you think of demanding more poplars than willows?

② If we know that there are 35 willows and 12 poplars are more than willows, can we know the number of poplars?

If you know that there are 72 poplars, 40 more than willows, can you know the number of willows? Ask for a willow, and what do you find? (the same part of poplar and willow)

You can also change "the number of poplars is more than that of willows" to "the number of willows?" "For training less than poplar.

After such thorough analysis and systematic training, children can understand the meaning of solving problems as a whole and distinguish who is a large number and who is a decimal. You probably won't show up, okay? The phenomenon of "more" has increased, while the phenomenon of "less" has decreased.