Mathematics teaching design case 1 teaching objectives:
1. Knowledge objective: To make students understand the definition of exponential function and master the image and properties of exponential function.
2. Ability goal: Through the introduction of definition, observation and discovery of image characteristics, students can understand the dialectical relationship between theory and practice, infiltrate the mathematical thought of classified discussion in time, and cultivate students' ability to explore, discover, analyze and solve problems.
3. Emotional goal: Through students' participation process, cultivate their good study habits of using their hands and brains, thinking more and practicing more, as well as their exploration spirit and perseverance.
Teaching emphases and difficulties:
1. Emphasis: the image and properties of exponential function.
2. Difficulties: The change of cardinal number A affects the properties of the function. The key to breaking through difficulties is to use multimedia.
Dynamic display, through the difference of color, deepen their perceptual knowledge.
Teaching methods: guided discovery teaching method, comparison method and discussion method.
Teaching process:
I. Case introduction
Last class, we learned the operational properties of exponents. Today, we are going to learn the function related to exponent. What is a function?
Student:-
T: It mainly reflects the relationship between two variables. Let's consider an example related to medicine: everyone is right? Sars? It should be familiar. Like other infectious diseases, there is a certain incubation period During this period, pathogens continue to multiply in the body. There are many ways to reproduce pathogens, and division is one of them. Let's look at the division process of a cocci:
C: Animated demonstration (when a cocci divides, it splits from 1 to 2, and then from 2 to 4,-. After such a cocci divide _ times, the functional relationship between the number of cocci y and _ is: y = 2 _).
S, T: (Discussion) This is the function of cocci number y about division number _, and what is the form of this function (exponential form).
From the analysis of function characteristics, radix 2 is a positive number that is not equal to 1, is a constant, and exponent _ is a variable. We call this kind of function an exponential function problem.
Second, the definition of exponential function
C: definition: function y = a _(a>；; 0 and a? 1) is called exponential function, _? r .
Question 1:a > 0 Why do you want to talk to A? 1?
Student: (Discussion)
C: (1) when
Meaningless;
(2) When a=0, a _ is sometimes meaningless, such as _=-2,
(3) When a = 1, the function value y is always equal to 1, so there is no need to study it.
Consolidation exercise 1:
Which of the following functions is an exponential function ()
a、y=_ 2 B、y=2_ 2 C、y= 2 _ D、y= -2 _
The teaching goal of case 2 of mathematics teaching design;
(1) Understand the concepts of sets and elements, and know the three characteristics of elements in sets;
(2) Understand the relationship between "attribution" and "non-attribution" between elements and sets;
(3) Master the commonly used number sets and their representations;
Teaching emphasis: master the basic concept of set;
Teaching difficulties: the relationship between elements and sets;
Teaching process:
First, introduce the topic.
Before military training, the school informed: At 8: 00 on August 15, the first year of high school will gather in the gymnasium for military training mobilization; Is this notice addressed to all senior one students or to individual students?
Here, set is a common word, and we are interested in the whole of some specific objects in the problem (not individual objects). To this end, we will learn a new concept-set (announcement theme), which is the sum of some research objects.
Read the contents of P2-P3 textbooks.
Second, the new curriculum teaching
(A) the related concepts of set
1. Cantor, the founder of set theory, called a set the sum of some different things. People can recognize these things and judge whether a given thing belongs to this whole.
2. Generally speaking, we call the research object an element, and the whole composed of some elements is called a set.
3. Thinking 1: judge whether all the following elements constitute a set and explain the reasons:
(1) is an even number greater than 3 and less than 1 1;
(2) Small rivers in China;
(3) Non-negative odd numbers;
(4) the solution of the equation;
(5) freshmen of 2007 in a school;
(6) patients with hypertension;
(7) mathematicians;
(8) All points in the third quadrant in the plane rectangular coordinate system.
(9) Students with good grades in the whole class.
Discuss and comment on the students' answers, and then explain the following questions.
4. On the characteristics of set elements
(1) Determinism: If A is a given set and _ is a specific object, it is either an element of A or not, and one and only one of the two cases must be true.
(2) Reciprocity: The elements in a given set refer to different individuals (objects) belonging to this set, so the same element should not appear repeatedly in the same set.
(3) Disorder: A given set has nothing to do with the order of elements in the set.
(4) Set equality: the elements that make up the two sets are exactly the same.
5. The relationship between elements and sets;
(1) If A is an element of the set A, it is said that A belongs to (belongto)A, and it is recorded as: A? A
(2) If A is not an element of set A, it is said that A does not belong to (does not belong to) A, and it is recorded as aA.
For example, if we a represents the set of "1all prime numbers in ~ 20", then there are 3? A
4A, wait.
6. Letter representation of sets and elements: sets are usually represented by uppercase Latin letters A, B, C ... The elements of sets are represented by lowercase Latin letters A, B, C, ...
7. Commonly used number sets and symbols:
Non-negative integer set (or natural number set), recorded as n;
A set of positive integers, denoted as N_ or n+;
Integer set, denoted as z;
Set of rational numbers, recorded as q;
Set of real numbers, denoted as r;
(2) Give an example:
Example 1. Use "?" Or ""symbol to fill in the blanks:
( 1)8N； (2)0N；
(3)-3Z； (4)Q；
(5) Let A be a collection of all Asian countries, then China A, the United States A, Indian A and British A.
Example 2. It is known that the element of set p is, if 3? P and-1P, find the value of m.
(3) Classroom exercises:
Exercises in textbook P51;
Summarize:
This lesson begins with examples, naturally and aptly introduces the concepts of set and set, explains the concept of set with examples, and then introduces common sets and their notation.
Task:
1. Exercise 1. 1, question1-2;
2. Preview the representation of the collection.
In the third part, the mathematical teaching case design establishes a functional model to describe practical problems.
The content analytic function model itself comes from reality and is used to solve practical problems, so the content of this section is to analyze and explore the displayed examples, so that students have more opportunities to discover or establish mathematical models from practical problems and experience the application value of mathematics in practical problems. At the same time, this topic is an inquiry-based classroom teaching for students who have just entered senior high school on the basis of the images and properties of learning functions in junior high school. In the process of solving a specific problem, students change from understanding knowledge to skillfully using knowledge, so as to dialectically view the relationship between knowledge understanding and knowledge application, which is closely related to the functional knowledge they have learned and complements each other. ; On the other hand, the function model itself combines practical problems. Empty talk theory can only make students unable to really understand the application of function model and the process of establishing and solving problems in the application process, but the ideas and methods excavated and refined from simple, typical and familiar function model are more acceptable to students. At the same time, students should try their best to learn and feel the selection and establishment of function models in simple examples. Because it is impossible to build a function model without function images and data tables, there will be a certain amount of raw data processing, and computers, calculators and drawing tools may be used. Our teaching should pay more attention to selecting the appropriate function model and the construction process of the function model through the analysis process of practical problems. In this process, students should focus on the establishment of the model, at the same time understand the operability and effectiveness of the model, learn to establish the model to solve practical problems, cultivate and develop organizational thinking and expression ability, and improve logical thinking ability.
Teaching objectives
(1) embodies the basic process of establishing a function model to describe real problems.
(2) Understand the wide application of function model.
(3) Improve students' ability to find, analyze and solve practical problems through students' operation and inquiry.
(4) Improve students' interest in exploring and learning new knowledge, and cultivate students' scientific attitude of being brave in exploring.
Focus on understanding and establishing a functional model that describes the basic process of real problems, and understand the wide application of functional models.
It is difficult to establish a functional model to describe the data processing in practical problems.
Analysis of teaching objectives Through analyzing and processing the samples sampled by the whole class, students realize that the focus of this lesson is to describe the basic process of real problems by using functional modeling and improve their ability to solve practical problems. While guiding and highlighting the key points, students can break through the difficulties of this lesson through group cooperative inquiry, so as to realize the requirements of knowledge and ability in the process of group cooperative learning inquiry (goal 1, 2, 3) in the basic process of how to use function modeling to describe real questions, so as to let students experience the universality of function application, at the same time, improve students' interest in exploring and learning new knowledge, and cultivate students' active participation, independent learning and courage to explore science.
Anticipated problems in students' study and the presupposition of solutions.
① Normality of tracking points; ② Speed of actual operation; ③ Calculation speed of analytical formula ④ Not checked after calculation.
In view of the above possible problems, what I deal with in pre-class is to prepare some drawing paper for students before class to improve the standardization of drawing points, and at the same time, in order to improve the corresponding calculation speed, let students use calculators to cooperate with many people through group discussion. After the analytical formula is obtained, students should be guided to draw only one good standard, not many standards, and to think of the screening results and lead to inspection.
Multimedia-assisted teaching with teaching tools (ppt, computer).
teaching process
Teaching preface:
Function model is one of the most widely used mathematical models. Once many practical problems are defined as functional relationships, we can grasp and solve problems by studying the properties of functions.
teaching process
Teaching preface:
Function model is one of the most widely used mathematical models. Once many practical problems are defined as functional relationships, we can grasp and solve problems by studying the properties of functions.
Teaching content, teacher-student activity design intention
Explore the introduction of new knowledge;
Teacher: Do people think I am fat?
Student answers
Teacher: When we meet a person in the street, we always judge whether he is fat or thin. We usually measure whether he is fat or thin by ourselves or others. Then we saw some formulas to calculate whether he is fat or not. At present, the world uses body mass index (BMI) to measure whether he is fat or not;
Weight/height? The body mass index (measured in meters) is within the normal range of 18.5-22.5, with a body mass index greater than 22.5 as overweight and a body mass index greater than 30 as obesity.
The teacher calculated his grades on the blackboard. Since it can be calculated by a formula, it shows that this problem can be solved by mathematical knowledge. Can a person's height and weight be used to determine the standard of this formula?
Student answers
Teacher: Of course, the more people you look for, the better. Then let's find fewer people to study in class first. Let's choose a classmate from each group to talk about your height and weight.
The student said that the teacher filled in the relevant data on a form displayed by PPT.
Teacher: OK, with these data, we can study. So what should we do with the data just collected?
Students answer (expectation: draw a scatter diagram to find the function)
Teacher: OK, let's draw a line by group first, and then discuss which function image your group thinks fits.
Students act and answer.
Teacher: OK, let's divide the work. Your group will calculate this resolution function and those groups will calculate that resolution function.
Students work in groups.
Teacher: (Write the formula calculated by the students on the blackboard) Why is the analytical formula calculated by everyone not exactly the same?
Student answers
Teacher: Can all our calculated resolution functions be used to describe this problem?
Student answers
Teacher: How can we test it?
Student answers (replace other points for verification)
Teacher: Then let's test which model is more in line with the data.
Students will be tested in groups.
Teacher: Well, we worked hard to get a formula by using the data just collected, which is a fat and thin standard that suits everyone's situation. It is standard in our class. Can it be used to measure students in other classes? Then let's figure out how the teacher's grades are.
Teacher: It can be seen that the evaluation of teachers' weight by the world obesity standard is basically consistent with the results calculated by the established mathematical model. It can be seen that the model is generally in line with the actual situation, and it seems that the teacher is really determined to lose weight.
Teachers ask questions from common phenomena in life and guide students to think.
Students cooperate to explore practice, with the help of the group, determine the feasible function model with the data table, and show their own results.
The teacher instructs the students to test the results.
Students use calculators and drawings to form the focus of this section by group cooperation, and break through the difficulties while completing the task.
Through examples in daily life, introduce the main contents of this section, improve students' interest in this class and improve the efficiency of group learning.
Students use group cooperation to complete the task, forming the key framework of this section: function describes the basic process of practical problems, thus achieving the teaching goal of 1, 3,4.
Course summary
Teacher: Let's recall the process of solving the problem just now (guiding students to answer collectively)
Summarize the basic process of describing real problems with function modeling (the teacher shows it with PPT)
Teacher:
Let's input the data ourselves and calculate your situation.
After class, we can use the time of research study to investigate the height and weight of the whole grade students, and further understand the basic process of functional modeling to describe real problems.
The teacher used PPT to show the basic process of functional modeling to describe the real problem.
The teacher left an extended homework for the students to finish after class.
Students consolidate the teaching objectives 1, 2, 3, 4 by exploring, forming the focus of this section.
Expand the problem and let students experience the basic process of functional modeling to describe real problems, thus consolidating the teaching objectives of this section.
Reflection after class
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