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Recommended answer 2011-4-4 20: 33 unit1graphic transformation
first kind
Subject: Axisymmetry
Teaching content: Example 1 and Example 2 on pages 3-4 of the textbook.
Teaching objectives:
1. Through a series of activities such as drawing, cutting, observing, imagining, classifying and finding the axis of symmetry, students can correctly understand the significance and characteristics of axisymmetric graphics;
2. If you master the symmetry of the plane figure you have learned, you can correctly find out its symmetry axis.
3. Cultivate and develop students' experimental operation ability, discover beauty and create beauty.
Emphasis and difficulty: I can draw symmetrical figures with the knowledge of axial symmetry.
Teaching preparation:
Teaching process:
First, review the introduction:
(1) Enjoy the following graphs and find the symmetry axis of each graph.
(2) students communicate with each other.
What other axisymmetric figures have you seen?
(3) The concept of axisymmetric figure:
If a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is an axisymmetric graph.
(4) Explore the properties of axisymmetric graphics through examples:
Example 1:
Students use a ruler to measure and calculate the distance between the opposite points on the left and right sides of each axisymmetric figure in the problem and the axis of symmetry. What patterns can you find?
Student exchange
Teacher: "In an axisymmetric figure, the distance between the opposite points on both sides of the axis of symmetry is equal." We can use this property to judge whether a graph is symmetrical or not. Or make a symmetrical figure.
Second, practice in class.
Judge whether the following figures are symmetrical, and if so, please point out their symmetrical axes.
Third, teach to draw symmetrical figures.
Example 2:
(1) Guide students to think:
First, how to draw? What to draw first? Draw what again?
B.how long should each line segment be drawn?
(2) On the basis of research, let students try to draw with pencils.
(3) Demonstrate the whole process of painting through courseware to help students correct their shortcomings.
Fourth, practice:
1, class exercises 1- questions 1 and 2.
2. Homework:
Blackboard design:
axial symmetry
If a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is an axisymmetric graph.
Teaching reflection:
Second lesson
Theme: Rotation
Teaching content: Example 3 and Example 4 on 5-5 pages of the textbook.
Teaching objectives:
1, through life cases, let students understand the translation transformation and rotation transformation of graphics. And can correctly judge these two transformations of graphics. Combined with the actual life of students, the phenomenon of translation and rotation is initially perceived.
2. Through hands-on operation, students can draw simple figures with horizontal and vertical translation on grid paper.
3. Mathematical thinking method of initial infiltration transformation.
Key points and difficulties: we can correctly distinguish translation and rotation phenomena, and draw simple figures of horizontal and vertical translation on grid paper.
Teaching preparation: slides and courseware.
Teaching process:
First, import
There are playground scenes in the courseware: ferris wheel, shuttle bus and carousel; Slide, trolley, train, speed skating.
Are all kinds of amusement events in the amusement park the same?
Can you classify them according to their different movements?
In amusement parks, slides, baby carriages, through trains, speed skating and other objects all move along a straight line, which is called translation (blackboard writing: translation).
Ferris wheel, shuttle bus and merry-go-round all move around a point or an axis, which is called rotation.
Today we will learn "rotation" together. Write on the blackboard.
Second, learn new lessons.
1, translation in life.
Translation and rotation are changes in the position of objects or figures. Translation means that an object moves in a straight line.
What translation phenomena have you seen in your life? Tell it to the children in your group first! Ask the students to answer it again.
That's great. You see, the elevators we have seen all move along a straight line, that is, translate.
Do you want to experience the translation yourself?
Everybody stand up. Let's move two steps to the left and two to the right. There are many translation phenomena in our life. Can you translate what is on your desk?
2. Rotation in life:
You are really smart children. You not only know the phenomenon of translation, but also learn the methods of translation. We just saw another phenomenon. What is this? (rotating)
Rotation is the movement of an object around a point or axis.
"What spinning phenomena have you seen?" Talk to your deskmate before reporting.
Just like the hands and compasses on the clock face, they all move around a point. These are all rotating phenomena.
Students' thinking is really open. Let's experience the phenomenon of rotation! Stand up. Let's turn left twice and turn right twice. Spinning is really interesting. Can you feel the rotation of the objects around you? Now let's relax and watch the translation and rotation in life!
3. Learning Example 3:
(1) Complete one of the questions with students * * *, and the rest will be done by students independently.
(2) For students with mistakes, make comments in the whole class.
4. Learning Example 4:
(1) When instructing students to count, they should find a point of an object, then see where the point goes after rotation, and then count how many squares it has passed.
(2) Let the students talk about the steps of drawing before drawing.
(3) Let students learn to choose a few points and fix their positions before drawing.
(4) Courseware demonstrates the drawing process to help students correct it.
5. Classroom exercises:
2. Page 6, question 2.
3. Page 9, 4 questions,
Homework after class:
Blackboard design: rotation
Translation and rotation are changes in the position of objects or figures.
Translation means that an object moves in a straight line.
Rotation is the movement of an object around a point or axis.
Teaching reflection:
The third category
Theme: Reward Design.
Teaching content: textbook page 7 ~ 1 1.
Teaching objectives:
1. By appreciating and designing patterns, students are more familiar with the symmetry, translation and rotation they have learned.
2. Appreciate the beautiful symmetrical figures and design your own patterns.
3. Let students feel the beauty of graphics, and then cultivate students' spatial imagination and aesthetic consciousness.
Key points and difficulties:
1. can draw beautiful patterns through symmetry, translation and rotation.
2. Feel the inherent beauty of graphics and cultivate students' aesthetic taste.
Teaching preparation: slides and courseware.
teaching process
First, situational introduction
Show four beautiful patterns on page 7 of the textbook with courseware, and let students enjoy them with music.
Second, learn new lessons.
(a) mode appreciation:
1. With beautiful music, we enjoyed these four beautiful patterns. what do you think?
2. Let students express their feelings freely.
(2) say:
1. Which character translated or rotated the pattern of each picture above?
2. Which picture above is symmetrical? Let the students observe and discuss before communicating.
Third, consolidate the practice.
(1) feedback exercise:
Complete question 3 on page 8.
1. How should I draw this pattern?
2. Observe carefully which patterns are obtained by what transformation?
(2) Expanding exercises:
1. Create patterns by symmetry, translation and rotation, respectively.
2. Communication and appreciation. Tell me what's good.
Fourth, the class summary
The knowledge of symmetry, translation and rotation is widely used in plane and three-dimensional architectural art and geometric images, and also involves other fields. I hope students will pay attention to observation and become excellent designers.
Verb (short for verb) Task:
Question 5 on page 9 of the textbook.
Blackboard design:
Appreciation and design
Mode 1 mode 2
Mode 3 Mode 4
The knowledge of symmetry, translation and rotation is widely used.
Teaching reflection:
the fourth lesson
Subject: Appreciation and Design Practice Course
Teaching content: textbook page 8 ~ 1 1.
Teaching objectives
1. By collecting patterns and communicating in groups, we can feel the beauty of patterns and provide reference for creating patterns in the future.
2. Cultivate students' aesthetic consciousness and spatial concept by appreciating patterns.
3. Experience the whole process of creative practice, feel creative fun, and further cultivate students' aesthetic taste.
Key points and difficulties:
1. Further use symmetry, translation, rotation and other methods to draw beautiful patterns.
2. Deepen the feeling of the inherent beauty of graphics and cultivate students' aesthetic taste.
Teaching preparation:
Courseware, square paper, square whiteboard paper, three handmade papers, scissors.
Teaching process:
I. Introduction to the Exhibition
Ask the students to collect patterns and communicate in groups before class.
Thinking: How are these patterns designed and what are their characteristics?
Introduce the most beautiful pattern in this group by name, and talk about its characteristics with thinking.
Second, learn new lessons.
(1) Try to create:
Ask the students to do questions 1 and 2 on page 8.
1. Encourage students to design patterns with the graphics they have learned and put forward different requirements for different students.
2. During the communication, the teacher praised and encouraged the students who were creative and beautifully painted.
(2) Design mode:
Do "practical activities" on page 10.
1, three steps are proposed:
(1) Select a favorite graphic first;
(2) Determine the symmetry, translation and rotation method you choose;
(3) Start drawing patterns.
2. Create a pattern by symmetry, translation and rotation, and then communicate with the whole class.
Third, consolidate the practice.
(1) feedback exercise:
1, making "snowflake":
Take a square piece of paper, fold it in half and cut it out as in the book. You can practice many times until you can cut out beautiful "snowflakes".
2. Exhibition of works.
3. Observe independently and try to do the fifth question on page 9.
Fourth, the class summary
The whole class exchanged works, selected good works to evaluate each other and exhibited them in the class.
Blackboard design:
Appreciation and design practice course
Picture 1 picture 2
Teaching reflection:
Factors and multiples of the second unit
first kind
Subject: factors and multiples
Teaching objectives:
1, students master the method of finding the factor and multiple of a number;
2. Students can understand that the factor of a number is limited and the multiple is infinite;
3. Be able to skillfully find out the factors and multiples of a number;
4. Cultivate students' observation ability.
Teaching emphasis: master the method of finding the factor and multiple of a number.
Teaching difficulty: be able to skillfully find out the factors and multiples of a number.
Teaching process:
First, introduce new courses.
1. Show the theme map and ask the students to do a multiplication formula.
2. Teacher: See if you can read the following formula.
Display: Because 2×6= 12.
So 2 is a factor of 12, and 6 is also a factor of 12;
12 is a multiple of 2 and 12 is also a multiple of 6.
3. Teacher: Can you talk about another formula in the same way?
(Name the students)
Teacher: Do you understand the relationship between factor and multiple?
Then can you find other factors of 12?
4. Can you write a formula to test your deskmate? Students write formulas.
Teacher: Who will work out a formula to test the class?
5. Teacher: Today we are going to learn factors and multiples. (Exhibition theme: factor multiple)
Pay attention to watch p 12 together.
Second, the new grant:
(a) looking for factors:
1, example 1: 18 What is the factor?
From the factor of 12, we can see that there is more than one factor of a number, so let's find the factor of 18 together.
Students try to finish: report
(The factors of 18 are: 1, 2, 3, 6, 9, 18).
Teacher: Tell me how you found it. (Student: By division,18 ÷1=18 ÷ 2 = 9, 18 ÷ 3 = 6, 18 ÷ 4 = by multiplication.
Teacher: What is the minimum factor of 18? What's the biggest? When we write, we usually arrange it from small to large.
2. In this case, please look for the factor of 36 again.
The factors of Report No.36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Teacher: How did you find it?
Give examples of errors (1, 2, 3, 4, 6, 6, 9, 12, 18, 36).
Teacher: Is this ok? Why? No, because you only need to write one repetition factor, you don't need to write two sixes. )
Look carefully, what is the smallest and largest factor of 36?
It seems that the smallest factor of any number must be () and the largest must be ().
3. Which factor are you looking for? (18, 5, 42 ...) Please choose one of them and write it in the exercise book, and then report it.
4. In fact, in addition to writing a number factor in this way, it can also be expressed by a set, such as
/kloc-factor of 0/8
Conclusion: We have found so many factors. How do you think to find them so as not to miss them easily?
Start with the smallest natural number 1, that is, start with the smallest factor and find all the way. In the process of searching, one by one, from small to uppercase.
(2) Find multiple:
1. We found the factor of 18 together. Can you find a multiple of 2?
Reports: 2, 4, 6, 8, 10, 16, …
Teacher: Why can't I find it?
How did you find these multiples? (Health: Just multiply 2 by 1, 2 by, 3 by, 4 by …)
So what is the minimum multiple of 2? Can you find the biggest one?
2. Ask the students to finish the questions 1 and 2: Find multiples of 3 and 5.
The multiples of Report 3 are: 3,6,9, 12.
Teacher: Is this ok? Why? How should I change it?
Rewritten as: multiples of 3 are: 3, 6, 9, 12, ...
How did you find it? (Multiply 1, 2, 3, ... by 3 respectively)
The multiple of 5 is: 5, 10,15,20, ...
Teacher: To express multiples of a number, besides this method of literal narration, it can also be expressed by sets.
Multiples of 2, multiples of 3 and multiples of 5.
Teacher: We know that the number of factors of a number is limited, so what is the multiple of a number?
The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple.
Third, the class summary:
Let's recall, what did we focus on in this class? What did you get?
Fourth, work independently:
Complete Exercise 2, Question 1 ~ 4.
Teaching reflection:
Second lesson
Title: Characteristics of multiples of 2 and 5
Teaching objectives:
1, master the characteristics of multiples of 2 and 5.
2. Understand and master the concepts of odd and even numbers.
3. These characteristics can be used to judge.
4. Cultivate students' generalization ability.
Teaching emphases and difficulties:
1 is a characteristic of numbers that are multiples of 2 and 5.
2. The concepts of odd and even numbers.
Teaching tools: slides.
Teaching process:
First, review preparation
1, ask questions.
Name all the factors of 20.
② Name five multiples of 8.
What is the minimum factor of ③ 26? What is the maximum factor? What is the minimum multiple?
2. Fill in the number in the assembly circle as required.
Second, learn new lessons:
Characteristics of multiples of (1)2.
Teacher: (Exercise 2) What is the relationship between the number in the right set circle and the number in the left set circle?
Teacher: Please look at the numbers in the circle on the right. What are the characteristics of their single digits?
(The units are 0, 2, 4, 6, 8. )
Teacher: Please name several multiples of 2 to see if the operator meets this feature.
Students just give an example.
Teacher: Who can talk about the characteristics of numbers that are multiples of 2?
After the students answered, the teacher wrote on the blackboard: the number of units is 0, 2, 4, 6, 8, all multiples of 2.
2. Oral answer exercise: (Slide) Please fill in the following numbers in the circle as required (it is a multiple of 2, not a multiple of 2).
1,3,4, 1 1, 14,20,23,24,28,3 1,40 1,826,740, 1000,643 1。
After the students answered, the teacher introduced the definitions of odd and even numbers.
Writing on the blackboard: Write "even number" and "odd number" on the upper two circles.
Teacher: Should ellipsis be placed in the upper two assembly circles? Why?
After the students discussed, the teacher explained:
Among the finite numbers listed in this question, odd and even numbers are finite, but natural numbers are infinite, and so are odd and even numbers, so write ellipsis in the set circle.
Teacher: Have you ever met odd and even numbers in our daily life? What are they customarily called? (singular, even. )
3. Exercise: (Group the novels first, and then the whole class will answer them in unison. )
Name five multiples of 2. (Requirements: two digits. )
② Name three digits that are not multiples of 2.
③ Name even numbers within 15 ~ 35.
④ How many even numbers are there within 50? How many odd numbers are there?
(2) Characteristics of multiples of 5.
1, the teacher first draws two groups of circles on the blackboard, and then asks: Can you find out the characteristics of multiples of 5 like studying the characteristics of multiples of 2?
Fill in the numbers, observe and discuss. Choose a classmate to fill in the blanks on the blackboard when the teacher is on patrol.
Teacher: What are the characteristics of multiples of 5?
Teacher: Please give some examples of multi-digit verification.
Teacher: Tell me again what kind of number is a multiple of 5.
Blackboard: Numbers with units of 0 or 5 are multiples of 5.
2. Practice:
(1) In descending order, say a multiple of 5 within 50.
(2) (Slide) Which of the following numbers is a multiple of 5?
240,345,43 1,490,545,543,709,725,8 15,922,986,990。
(3) (Slide) Pick out the numbers that are both multiples of 2 and multiples of 5 from the following numbers. What are the characteristics of these figures?
12,25,40,80,275,320,694,720,886,3 100,3 125,3004。
After the students answered, the teacher wrote on the blackboard: the unit number is 0.
The teacher casually said a number, please immediately say whether this number is a multiple of 2 or 5, or both, and explain the basis for judgment.
Third, consolidate the feedback:
1. There are () multiples of 2 and () multiples of 5 among the natural numbers from 1 to 100.
2. Odd numbers less than 75 and greater than 50 are ().
3. The number in () is a multiple of 2 and 5 at the same time.
4. Use five numbers of 0, 7, 4, 5 and 9 to form a multiple of 2; A multiple of 5; Numbers that are both multiples of 2 and 5.
Class summary: What did you learn in this class? What did you get?
Teaching reflection:
The third category
Title: Characteristics of multiples of 3
Teaching objectives:
1, after looking for multiples of 3 in the natural number table within 100, I realized the characteristics of multiples of 3 on the basis of activities and tried to summarize the characteristics in my own language.
2. Feel the mystery of mathematics in the exploration activities; The value of experiential mathematics in the law of application.
Teaching emphasis and difficulty: it is the characteristic that a number is a multiple of 3.
Teaching process:
First, put forward the topic and look for the characteristics of 3.
Teacher: Students, we already know the characteristics of multiples of 2 and 5, so what are the characteristics of multiples of 3? Who can guess?
Health 1: Numbers with 3, 6 and 9 are multiples of 3.
Health 2: No, the numbers with 3, 6 and 9 are not multiples of 3. For example, l 3, l 6, 19 are not multiples of 3.
Health 3: In addition, numbers like 60, 12, 24, 27 and 18 are not 3, 6 and 9, but they are all multiples of 3.
Teacher: It seems that we can't determine whether it is a multiple of 3 just by observing the unit, so what are the characteristics of a multiple of 3? Today we are going to study together. (revealing the topic)
Teacher: Please find a multiple of 3 in the table below and mark it. (The teacher shows the number table within 100, and the students have one. After the students' activities, the teacher organizes the students to communicate, and presents a form in which the students circle multiples of 3. ) (as shown below)
Second, independently explore and summarize the characteristics of 3:
Please find a multiple of 3 in the table below and mark it. (The teacher shows the table within 100, and the students use the table of p 18. After the students' activities, the teacher organizes the students to communicate, and presents a form in which the students circle multiples of 3. ) (as shown below)
Teacher: Please look at this table. What characteristics do you find in multiples of 3? Communicate your findings with your deskmate.
After the students communicate at the same table, organize the whole class to communicate.
Health 1: I found that only numbers within 10 are multiples of 3.
Health 2: I found that multiples of 3 appear every two numbers, regardless of horizontal or vertical.
Student 3: I watched them all. That classmate's guess just now was wrong. 10 numbers from 0 to 9 may be multiples of 3.
Teacher: The number of digits is irregular, so is it regular?
Health: There are no rules. 1 ~ 9 These numbers have all appeared.
Teacher: Did the other students find anything else?
Health: I found that multiples of 3 are regularly arranged in a diagonal line.
Teacher: Your observation angle is different from that of other students, so are the numbers on each diagonal regular?
Health: From top to bottom, both serial numbers are ten digits increased by 1, while the single digits decreased by 1.
Teacher: What are the similarities between the number composed of ten digits plus 1 and single digits minus 1 and the original number?
Health: I found that the diagonal of "3" and the other two numbers, 12 and 2 1, add up to 3.
Teacher: This is an important discovery. What about the other diagonals?
1: I found that the sum of two numbers on the diagonal of "6" is equal to 6.
The number on the diagonal: "9", and the sum of the two numbers is equal to 9.
Health 3: I found several other columns, except that the sum of the numbers 30, 60 and 90 on the side is 3, 6 and 9, and the sum of other numbers is 12, 15, 18.
Teacher: Who can sum up the characteristics of multiples of 3 now?
Health: The sum of digits of a number is equal to 3, 6, 9, 12, 15, 18, etc. This number must be a multiple of 3.
Teacher: Actually, the numbers 3, 6, 9, 12, 15 and 18 are all multiples of 3, so how do you say this sentence?
Health: The sum of digits of a number is a multiple of 3, so this number must be a multiple of 3.
Teacher: Just now, we found the law from the numbers within 100, and obtained the characteristics of multiples of 3. If it is a number with more than three digits, are the characteristics of multiples of 3 the same? Please find a few more figures to verify.
Students write their own digital verification, then communicate in groups and come to the same conclusion.
The whole class read the conclusion in the book.
Third, consolidate the exercises:
Do it after p 19.
Fourth, the class summary:
What did you learn from this course?
Teaching reflection:
the fourth lesson
Theme: prime numbers and composite numbers
Teaching objectives:
1. Understand the concepts of prime number and composite number, judge whether a number is prime number or composite number, and classify natural numbers according to the number of divisors. 2. Cultivate students' ability of independent exploration, independent thinking and cooperative communication.
3. Cultivate students' spirit of daring to explore scientific mysteries and fully display the charm of mathematics itself.
Teaching focus:
1, understand and master the concepts of prime numbers and composite numbers.
2. Learn to judge whether a number is prime or composite.
Teaching difficulties: distinguish odd numbers, prime numbers, even numbers and composite numbers.
Teaching process:
First of all, explore and find, summarize the concept:
1, Teacher: (Show three identical small squares) The side length of each square is 1. How many different rectangles can you spell by using these three squares to make a rectangle?
Students think independently, and then the whole class communicates.
2. Teacher: How many different rectangles can these four small squares spell?
Students think independently, raise their hands and answer after imagination.
3. Teacher: Students, think again. If there are 12 such small squares, how many different rectangles can you spell?
Teacher: I think many students already know it without drawing. (Name it)
4. Teacher: Students, what do you think will happen to the number of different rectangles if more squares are given?
The students almost said with one voice: the more the better.
Teacher: Are you sure? Guide the students to discuss. )
5. Teacher: Students, when you spell a rectangle with small squares, sometimes you can only spell more than one rectangle. And give an example.
Let the students discuss in groups first, and then communicate with the whole class. The teacher writes on the blackboard according to the students' answers.
Teacher: Students, like the numbers above (3, 13, 7, 5, 1 1), we call them prime numbers in mathematics, and the numbers below (4, 6, 8, 9, 10,/kloc).
After students think independently, communicate in groups, and then communicate with the whole class.
Guide students to summarize the concepts of prime numbers and composite numbers, and write them on the blackboard with students' answers: (omitted)
6. Let the students illustrate which numbers are prime numbers and which numbers are composite numbers, and give the reasons.
7. Teacher: What do you think "1" is?
Let the students think independently and then discuss.
Second, hands-on operation, quality table.
1, the teacher shows: 73. Ask the students to think about whether it is a prime number.
Teacher: It is not easy to know what 73 is at once. It would be convenient if there is a quality table to check. (The students all say "Yes". )