Unit 6 "The size of the possibility"

Use scores to indicate the size of the possibility; Be able to design relevant schemes according to the specified possibility, and experience the pleasure of obtaining the success of the design scheme in the activity.

Unit 6 The size of the possibility

First, the context of unit learning content

Second, the class arrangement suggestions

Suggested class hours of teaching content

Touch the ball game: indicate the possibility with a score of 3.

Design activity plan: according to the specified possibility.

Small design scheme

Third, the characteristics of unit writing and teaching suggestions

1, the necessity of understanding the possibility with scores.

In order to improve students' understanding of the necessity of expressing learning possibility with scores, the textbook makes students "think" about the way of data representation in the form of questions, and through students' discussion and communication, students gradually realize the simplicity of data representation and the objectivity of description. Similarly, in the "discussion" column on page 87, it is also combined with life examples to make students realize the necessity of learning this part of knowledge.

2. Design the activity plan independently according to the specified possibility.

In order to make students realize that the knowledge they have learned is useful, the textbook specially compiles the content of "designing activity plan", which consolidates the knowledge of expressing possibility with scores and provides materials for students to solve practical problems. When designing an activity plan that meets the requirements, students should not only consider the practical significance of the score indicating the possibility, but also meet various requirements. In teaching, students can design two or three specific plans in groups, instead of listing all the situations in general.

In order to expand the scope of students' application of knowledge, the textbook has arranged "practical activities" (page 90). Students' rational design will involve the synthesis of all aspects of knowledge. Firstly, the relevant conditions are converted into component numbers, from which we can know that the profit-making part of the promotion activities accounts for a few cents of the total. Secondly, the attraction of promotion should be considered, and the design form should take into account all aspects of the needs of the shopping crowd. The last thing to consider is that the total amount should meet the given conditions. In addition, because each design is open, each student can design according to his own ability, thus providing conditions for each student to participate in learning activities.

3. Learn about possibilities in interesting activities.

Because of the abstraction of probability itself, it is difficult for students to understand this part of knowledge. In order to make it easier for students to learn and master the knowledge of this unit, students' favorite activities are arranged as much as possible in the compilation of teaching materials, aiming at enabling students to unconsciously master the knowledge of expressing possibilities by fractions through interesting activities and apply these knowledge to real life.

For example, the understanding of expressing the possibility with scores is based on the activities of students touching the ball, which is an activity that students are familiar with and has certain experience. In this way, when the method of data representation is put forward, students can build a new learning structure more smoothly. Another example is the 89-page "discussion" exercise and the 90-page "design activity plan", which not only improves students' interest in learning, but also consolidates what they have learned and improves students' ability to use what they have learned flexibly to solve problems.

Comprehensive application

First, the curriculum proposal

Suggested class hours of teaching content

Mathematics and transportation 4

Try to guess 2

Mathematics and life 4

Shangyi

1, Mathematics and Transportation-Yes.

The textbook creates a situation of "sending materials", presents information such as speed and distance through a simple road map, and requires students to solve three problems according to these information. The first question is to ask students to estimate the speed of two cars. Because the speed of the car is fast, the distance between the cars must be more than half, and the meeting place is closer to the ruins park. It is estimated that the meeting place is near Yancun Town. The second problem is mainly to solve the problem of finding the meeting time in the meeting problem with equations, and the key is to find out the equal relationship between quantities. Because the basic quantitative relationship of the trip problem is: speed × time = distance, and it takes reverse thinking to find the time, it is easier to guide students to understand how to solve problems with equations. The key to the third question is to make students understand "how far is the meeting place from the ruins park", which is actually to ask the distance of the van.

When teaching, present information first, guide to find out relevant mathematical information, and solve the first problem, and pay attention to let students talk about their own thinking methods. Then, solve the problem of "when will we meet after departure and how far is the meeting place from the ruins park". In order to help students understand the problem, you can draw a line diagram to help them understand. Let the students talk about "what is the total distance when two car shops meet, and which car shops are they", so as to analyze the quantitative relationship of "the distance traveled by van+the distance traveled by car = 50km", and then list the equations to solve the problem.

2. Mathematics and transportation-travel expenses

The special activity of "travel expenses" has designed two problems, which are actually the strategic choices to solve the problems. The first is the strategy of buying tickets, and the second is the strategy of renting cars.

Problem 1, the key to solve this problem is to understand the meaning of each preferential scheme and then solve it by calculating the total amount. The first picture, 4 adults, 1 child. After calculation, it is known that Plan A needs 680 yuan, Plan B only needs 500 yuan, and Plan B needs to save money. In the second picture, there are four children and two adults After calculation, we can know that Scheme A only needs 480 yuan, and Scheme A needs to save money. Through the calculation and comparison of two different situations, let students understand that they should choose different strategies to solve the problem according to the specific situation. Question 2: Mainly study the strategy of renting a car. Let the students talk about what information they have learned and their understanding of this information, such as what "limited to 40 people" means, and then let the students talk about the initial idea of solving the problem. Because the situation is complicated, students can be guided to find solutions to the problems by enumerating, as shown in the following table:

Bus (vehicle) 3 2 1 0

Passenger car (vehicle) 0 2 3 5

Passenger (person)120130115125

Rent (RMB) 3000 3300 2950 3250

As can be seen from the table, renting 1 bus and 3 minibuses is the most economical. The list is complicated and can be calculated in the form of group cooperation. Through communication, we can find out the most suitable scheme. If students have difficulty making their own lists, teachers can provide forms.

3. Mathematics and transportation-look at the pictures to find the relationship.

The content of this special activity is "Look at the pictures to find the relationship", mainly to let students know some charts representing the relationship between quantity, analyze the relationship between quantity and quantity according to the relevant information in the pictures, and answer questions as required. The focus of teaching is to know charts and get information from them. The first picture in the textbook shows the relationship between time and speed. Teachers can organize students to look at the picture before communicating, let students talk about what information they have learned from this picture, and let students understand the process of the change of broken lines and the meaning of each number (for example, drawing lines means that the speed has increased; 200 means the speed is 200 m/min; 3 means it's been 3 minutes, and so on. On this basis, let the students look at the pictures and answer the questions. In addition to communicating the results, the key is to let students talk about their ideas.

Second, try to guess.

The purpose of the comprehensive practice of this topic is to find some special laws by observing and thinking about the phenomena in daily life. In the activity of "chickens and rabbits in the same cage", this paper tries to solve the problem of the number of chickens and rabbits through the list and in the process of continuous adjustment. In the activity of "Rules in Lattice", we can infer the number of points in the subsequent graphs by observing the changing rules of the midpoint of the graphs before and after, understand the relationship between numbers and shapes, and initially develop the ability of observation, induction and generalization.

1, chickens and rabbits in the same cage

There are four ways to solve the problems raised in textbooks. The first three methods are to find the result of the problem through hypothetical examples and lists. The first table is a conventional example-by-example method. According to the situation of 20 chickens and rabbits, assuming that there are only 1 chicken, there are 19 rabbits and 78 legs ... In this one-by-one example, the sought answer is found; The second table first estimates the possible range of the number of chickens and rabbits to reduce the number of examples; The third table adopts intermediate enumeration method. Because there are 20 chickens and rabbits, so each chicken takes 10, and then the direction of the example is determined according to the actual data, which can greatly narrow the scope of the example.

2, the laws in the lattice

This activity is a good theme to help students build mathematical models, that is, to find some laws from intuitive operation and help students establish the relationship between numbers and shapes. Therefore, in organizing teaching, we should pay attention to the discovery and generalization of guiding laws and cultivate students' ability of induction and generalization.

Third, mathematics and life.

The comprehensive practice of this topic consists of three aspects: the identification of scores, the calculation of possibility and area. The purpose of this activity is to enable students to integrate what they have learned and solve some practical problems.

1, Mathematics and Life-Welcome the New Year

Before the activity, you can organize students to review the knowledge of fractions and addition and subtraction appropriately, and then organize students to carry out activities in order. After showing the data sheet, students can ask their own math questions and answer them themselves according to the information provided. Then, organize students to carry out field survey activities to understand students' ideas of welcoming the New Year (if there are a large number of students, survey activities can also be arranged in groups). "Long-distance running relay" activities should organize students to discuss for many times, and discuss the positions of five relay points for the first time. The determination of each position should be reasonable and well-founded, and there should be no blindness. When discussing the rationality of site selection design for the second time, let the students fully explain why it is unreasonable. The third discussion on redesign. Before the discussion, students can think independently and then discuss the new design. "Bonus Game" is an open activity. When students answer the first question, they don't necessarily decide to participate in the game according to the possibility of winning the prize. It also includes how much they like this award. Therefore, when organizing students' discussion, first express the possibility of winning each game, then talk about the projects that each student is willing to participate in and give reasons. The design of the second question is also open, and each student can design according to his own experience. Of course, in order to improve the efficiency of classroom teaching, it can also be arranged before class (or designed in the form of group cooperation), so that the discussion can be carried out directly during teaching.

2, mathematics and life-laying floor tiles

It provides students with mathematical problems with realistic background, and teachers should organize students to discuss ways to solve problems, so that students can realize the close relationship between mathematics and life.