The sixth grade mathematics courseware 1 the first volume of teaching content;
Page 50 ~ 5 1 and related exercises in the sixth grade mathematics textbook of the People's Education Press.
Teaching objectives:
1. Understand and master the basic properties of the ratio, and apply the basic properties of the ratio to simplify the ratio, and initially master the method of simplifying the ratio.
2. In the process of independent exploration, communicate the relationship between ratio, division and score, and cultivate mathematical abilities such as observation, comparison, reasoning, generalization, cooperation and communication.
3. Infiltrate and transform the mathematical thought initially, so that students can know that there is an internal connection between knowledge.
Teaching focus:
Basic properties of understanding rate
Teaching difficulties:
Correctly apply the basic properties of ratio to simplify ratio.
Teaching preparation:
Courseware, answer sheet, physical projection.
Teaching process:
First, review the introduction.
1. Teacher: Students, let's recall first. How much do you know by comparison?
Presupposition: the meaning of ratio, the name of ratio part, the relationship between ratio and fraction, division, etc.
2. Can you directly tell the quotient of 700÷25?
(1) What do you think?
(2) What is the basis?
Do you remember the basic nature of music score? Give examples.
An important factor that affects students' learning is what they already know, so this link is intended to let students communicate the relationship between ratio, division and score, reproduce the invariable nature of quotient and the basic nature of score, and lay the foundation for the basic nature of analogy and deduction ratio. At the same time, there is also a mechanism that permeates the transformed mathematical thought, which makes students feel that there is a close internal connection between knowledge.
Second, explore new knowledge.
(A) the basic nature of the conjecture ratio
1. Teacher: We know that ratio is closely related to division and fraction, while division is quotient invariant and fraction has the basic properties of fraction. Think about these two properties: what kind of laws or properties will proportion have?
Default: Basic attribute of ratio.
The students have guessed the basic nature of the ratio.
Default: The first and last items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
3. According to the students' guess, the teacher wrote on the blackboard that the first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
Design intention is more suitable for cultivating students' analogical reasoning ability than basic nature learning. On the basis of mastering the basic properties of quotient invariance and score, students can naturally associate with the basic properties of ratio, which not only stimulates students' interest in learning, but also cultivates students' language expression ability.
(B) the basic nature of the verification ratio
Teacher: As everyone thinks, ratio, like division and fraction, has its own regularity. Is it the same as everyone's guess that "the front and rear items of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged"? This needs us to prove through research. Next, please study in groups of four to verify whether the previous guess is correct.
1. The teacher explained the cooperation requirements.
(1) Complete independently: Write a ratio and verify it in your favorite way.
(2) Group discussion and study.
① Each student presents his own research results to the students in the group and communicates in turn (other students indicate whether they agree with the student's conclusion).
(2) If there are different opinions, give examples, and then the students in the group will discuss and study.
③ Choose a classmate to speak on behalf of the group.
2. Collective communication (ask the group spokesperson to explain with specific examples on the booth).
Preset: verify according to the relationship of ratio, division and score; Verify according to the proportion.
The teaching goal of the second unit of the first volume of the sixth grade mathematics courseware in primary school;
1. In specific cases, explore the method of determining the position, and several pairs can be used to represent the position of the object.
2. Be able to use several pairs on a square paper to determine the position.
course content
Location (1) New Teaching and New Teaching
Teaching objectives
1. In specific cases, explore the method of determining the position, and several pairs can be used to represent the position of the object.
2. Ask the students to determine the position on the square paper in pairs.
Teaching focus
The position of an object can be represented by several pairs.
Teaching difficulties
The position of an object can be represented by several pairs, which can correctly distinguish the order of columns and rows.
training/teaching aid
teaching process
First, import
1. There are 53 students in our class, but most students and teachers don't know each other. If I want to invite one of you to speak, can you help me think about how to express it simply and accurately?
2. Students express their opinions and discuss how to use the method of "which column and which row".
Second, new funding.
1, teaching example 1
(1) If the teacher uses the second column and the third row to indicate the position of XX, can he also indicate the position of other students in this way?
(2) Students practice showing other students' positions in this way. (pay attention to the column first and then the emphasis of the lines)
(3) Teaching writing: the position of XX is in the second column and the third line, which we can express as: (2, 3). Can you write down your position according to this method? (Students write down their positions in their exercise books and name their answers)
2. Summary example 1:
(1) How much data did you use to locate a classmate? (2)
(2) We are used to saying columns before rows, so the first data represents columns and the second data represents rows. If the order of these two data is different, then the position of the representation is different.
Step 3 practice:
(1) The teacher reads the name of a classmate in the class, and the students write his exact position in the exercise book.
(2) When do you need to locate yourself in your life? Talk about the way they determine their position.
4. Teaching Example 2
(1) We just learned how to express the position of our classmates. Now let's see how to show the location of the venue on such a schematic diagram.
(2) According to the method of example 1, the whole class discussed how to display the gate position. (3,0)
(3) Discuss and tell the location of other venues at the same table, and answer by name.
(4) Students mark the positions of "Bird House", "Orangutan House" and "Lion Tiger Mountain" on the map according to the data given in the book. (Projection Review)
Third, practice.
1, Exercise 1, Question 4
(1) Students independently find out where the letters in the picture are and tell the answers.
(2) Students mark the positions of letters according to the given data, and connect them into figures in turn, and check them at the same table.
2. Exercise 1, Question 3: Guide the students to know how to read the page numbers first and find the corresponding positions according to the data.
3. Exercise 1, question 6
(1) Write the position of each vertex on the graph independently.
(2) Vertex A is translated 5 units to the right. Where is it? What data has changed? Point a is further shifted upward by 5 units. Where is it? What data has also changed?
(3) Translate point B and point C according to the method of point A, and get a complete triangle after translation.
(4) Observe the pictures before and after translation and tell me what you found. (The graph remains the same, the column, that is, the first data changes when moving to the right, and the row, that is, the second data changes when moving up).
Fourth, summary.
What did we learn today? What do you think of your present situation?
Verb (short for verb) homework
Exercise 1: Question 1, 2,5,7,8.
The teaching goal of the sixth grade mathematics courseware 3, the first volume.
(1) It is clear that the position of an object can be determined according to two conditions: direction and distance.
(2) Understand the application of location knowledge in life and feel the connection between mathematics and daily life.
(3) Cultivate students' ability to analyze problems from multiple angles.
Emphasis and difficulty in teaching
Teaching emphasis: the position of an object can be determined according to two conditions: direction and distance.
Teaching difficulty: skillfully express the direction of the object relative to the observation point.
teaching tool
courseware
teaching process
Activity 1 teaching process
(A review of old knowledge, the introduction of new lessons:
Teacher: What have we learned about location and direction?
Teacher: 1. Show the sign of the cross direction with courseware, and mark the east, south, west and north according to the student's report.
2. Show the northeast, southeast, northwest and southwest directions, and still mark the names according to the student report.
3. What are the angles between northeast, southeast, northwest, southwest and east, south, west and north? Mark the results according to the students' narration.
(Design intention: On the premise of letting students recall the relevant old knowledge in their minds, through the intuition of courseware, help students activate the relevant old knowledge and clear the way for learning new knowledge. )
Teacher: Who can introduce the layout of our campus to the guests (show the scene map)? Please describe the location of the building.
Teacher: The teacher asked, "How do you judge the directions of east, south, west and north in the picture?" ?
Lead the students to the conclusion that the sun is in the east in the morning, so this map is drawn in the direction of up north, down south, left west, right east.
(Design intention: By creating scenarios, students will naturally be brought into learning, which will help students to further understand how to collect useful information to judge the direction in life and the knowledge point that the direction is relative. )
(B) create a situation, independent inquiry:
Teacher: Please take the campus as the observation point and introduce the direction of the buildings around the school to the guests.
Teacher: Let's keep looking at the pictures. Who can tell us the direction of Shiqiang town health center and brick factory?
Then show the location of Yuezhuang community and ask the students to try to describe it.
Teacher: Let's judge who is more accurate.
Teacher: Who will tell us the specific location of Yuezhuang Community?
When the students are talking, the teacher uses gestures to sweep the corresponding corners from due east and writes on the blackboard: due east by south.
Teacher: Who wants to say it again?
Can you gesticulate with your hands when you are talking? (Strengthen students' perceptual knowledge)
Teacher: This angle is 30. How many degrees is this angle? (Sweep the included angle between the direction of Yuezhuang Community and due south by hand)
Teacher: Who can talk about the direction of Yuezhuang community in another way?
Health: Yuezhuang Community is 60 south to east of our school. (sweeping with gestures)
Teacher: (blackboard writing: south by east)
Summary: When we introduce the direction of an object, we usually describe it from a smaller angle. (Courseware hides another saying)
(Design intention: create problem situations through courseware, return the classroom to students, let students explore the description method of the direction in the discussion, and help students understand and deepen their perceptual knowledge with gestures. Through the exploration of different description methods, students are inspired to analyze problems from multiple angles and improve their thinking level.
Teacher: Now, please talk to each other in groups about the direction of Hushan vegetable garden in our school.
Show the answers with the students' narratives and ask what else to say.
After that, practice describing the location of China Mobile Business Hall and Tiantai Community in the same way, and write down the words of orientation on the blackboard while students describe them, such as north-west, north-west, south-west and south-west.
Summary: We learned eight new locative words (southeast, southeast, northeast, northeast, northwest, northwest, southwest, southwest) and gave students appropriate incentives.
(Design intention: Try to make students better apply what they have learned to real life by practicing the description method of consolidating the direction. )
The teacher guides the students to continue to look at the pictures and describe the direction of Tuoda shoe factory, which leads to conflicts.
Teacher: It's all 30 degrees east by north. Why are there two buildings? (Students point out different distances)
This leads to the accurate expression of building location, and adds a condition-distance on the basis of direction. Let the students practice speaking.
(Design intention: Ask questions through conflicts caused by courseware, stimulate students' thirst for knowledge and exploration, and feel the importance of distance when determining the position of objects. )
Several buildings just introduced reappear in the courseware, but the distance is increased at this time, and then the description method of each building position is shown with the narration of the students.
Arrange students to practice introducing other buildings around the school. The teacher clicks on the corresponding position with the students' narration. (and guide students to pay attention to the change of direction signs here)
(Design intention: consolidate new knowledge and help students further understand the connection and difference between old and new knowledge)
(3) Consolidate practice and improve application ability;
Give the students time to finish the exercise paper in their hands, then the teacher will mark the size of each corner with courseware and show the empty answers together with the students' reports. ) and pay attention to timely incentives.
(Design intention: consolidate the narrative method of object position and put it into words. Help students understand the importance of scale)
Teacher: (showing the second question) Who found the difference between the second question and the first question? (Design intention: To improve students' ability to look at pictures and improve their hands-on operation ability by identifying the direction in pictures lacking directional words)
Finally, the teacher leads to summarize, ask questions and inspire.
Teacher: Can you be more specific?
Teacher: Today, the students are very attentive in class. I hope you can keep such an excellent learning state in class tomorrow. Class is over.