Tisch
Teaching content: The theme map on page 9 1 and the example 2 on page 92 of the fifth grade mathematics textbook "Do it" and "Do you know" published by People's Education Press.
Teaching objectives:
1, knowledge and skills: explore and master the area formula of triangle, correctly calculate the area of triangle, and apply the formula to solve simple practical problems.
2. Process and method: Students experience mathematical activities such as operation, observation, discussion and induction, further understand the value of transformation methods, and develop students' spatial concept and preliminary reasoning ability.
3. Emotional attitude and values: Let students get positive emotional experience in exploration activities, and further cultivate students' interest in learning.
Teaching focus:
Understand and master the calculation formula of triangle area
Teaching difficulties:
Understand the derivation process of triangle area calculation formula
Test center analysis:
Can apply triangle area formula to solve practical problems according to specific conditions.
Teaching methods:
Creating situations-imparting new knowledge-consolidating summary-improving practice.
Teaching tools:
Multimedia courseware, triangle learning tool
Teaching process:
First, create a situation
Teacher: There are a group of children in our school who want to join the Young Pioneers. The school made them a batch of red scarves, so let's help calculate how much cloth to use. Are students confident to help the school solve this problem? (The red scarf is displayed on the screen)
Teacher: Students, what shape is the red scarf?
Health: triangle
Teacher: Can you calculate the area of a triangle? We will study and discuss this problem together in this class.
Blackboard writing: the area of a triangle
Second, explore new knowledge.
1, the courseware displays a parallelogram.
Teacher: How to calculate the area of parallelogram?
Health: area of parallelogram = base × height (blackboard writing: area of parallelogram = base × height)
Teacher: How did you get the area formula of parallelogram?
The derivation process of fertility theory
Teacher: When studying the area of parallelogram in our school, we transformed the parallelogram into a learned rectangle to study. How are you going to study the area of a triangle?
Health 1: I want to turn it into a graph I have learned.
Health 2: I want to see if triangles can become rectangles or parallelograms and quadrilaterals.
Step 2 do the experiment
Teacher: Please take out the prepared learning tools: two identical acute triangles, right triangles and obtuse triangles; A rectangle and a parallelogram can be used for operational research to see which group can find the formula for calculating the triangle area in many ways.
Students cooperate in groups, and teachers patrol and guide.
3. Show the results and deduce the formula.
Teacher: After guessing and verifying, the students deduced the formula for calculating the triangle area. Please show it to everyone.
Student demonstration
Report 1: a parallelogram composed of two identical acute triangles.
Report 2: A parallelogram composed of two identical obtuse triangles.
Report 3: A parallelogram composed of two identical right triangles.
In addition, two identical right-angled triangles can also be combined into triangles.
Area of triangle = area of rectangle (parallelogram) ÷2
= length × width ÷2
= bottom × height ÷2
4. Examples
Red scarf bottom 100cm, height 33 cm. How many square centimeters is its area?
Third, consolidate and upgrade.
1. One side of the part is a triangle. The base of the triangle is 5.6 cm long and 4 cm high. How many square centimeters is the area of this triangle? (Unit: cm)
2. Point out the bottom and height of the triangle below and calculate their areas with your mouth. (Unit: cm)
3. The picture above is a parallelogram. Fill in the blanks.
The area of parallelogram is 12 cm2, and the area of triangle ABC is () cm2.
4. Thinking about the problem, can you draw a triangle with the same area as the colored triangle in the picture?
Fourth, summarize and end this lesson.
1, student summary
What did you learn in this class? What did you get? (Intra-group theory-intra-group summary-inter-group communication)
2. Teacher's summary
Today, we discussed the calculation formula of triangle area together, which can be applied to solve practical problems.
Blackboard design:
Area of triangle
Area of parallelogram = base × height
Area of triangle = area of rectangle ÷2
= length × width ÷2
= area of parallelogram ÷2
= bottom × height ÷2
extreme
Teaching objectives:
1. In the actual situation, understand the necessity of calculating the trapezoidal area. 2. In the independent exploration activities, the process of deducing the trapezoid area formula has been experienced. 3. We can use the formula of trapezoidal area to solve the corresponding practical problems.
Teaching emphasis: Understand and master the formula for calculating trapezoidal area.
Teaching difficulty: understanding the derivation process of trapezoidal area calculation formula. Preparation of teaching AIDS: ladder, scissors and courseware.
Teaching process:
First of all, reveal the topic and clarify the theme.
1. We will find many plane graphics in our life. Is there one in this classroom?
Please look at this set of pictures and see who you have found. Call out its name as soon as you find it! What happens most often? (trapezoidal) blackboard writing II. Trapezoid, we have known it since the fourth grade. Who will introduce it?
Today, let's learn more about this friend and study the area of the trapezoid. (blackboard writing)
Second, recall old knowledge and establish contacts.
1. area, what figures have we calculated now? Do you remember their calculation method? (courseware)
2. Looking back, how did we deduce the area calculation method of parallelogram and triangle? Do you remember?
Students, when we study the calculation of their area, we all use a very important mathematical idea-transformation. (blackboard writing) Convert the graphics you want to learn into the graphics you have already learned, find out the relationship between them, and then deduce the formula for calculating the area. This idea is also used in this course.
Third, transform the trapezoid and derive the formula.
(a) The need of application leads to the guess 1. What sports do students like? Do you like basketball? (Courseware shows basketball court) Do you know what area this place is? This is a 3-second restricted area, and the opposing team members are limited to stay in this area for more than 3 seconds.
2. But we haven't learned the calculation method of trapezoid area. What do you think the trapezoidal area may be related to? How do you want to deduce the calculation method of trapezoidal area?
The students are very thoughtful. Is it like the students think? Let's verify it. Before starting the operation, the teacher made three suggestions: (1) Think about how you can transform the trapezoid into a learned figure.
(2) According to the relationship between the transformed graph and trapezoid, the calculation method of trapezoid area is deduced.
(3) Fill in the report form and compare which group moves faster. Do you understand? Let's start!
(2) Group activities for ten minutes.
(3) Report
1. Just now, the students transformed the trapezoid into various figures! Now let's ask the students in these groups to talk about their ideas. Listen up, everyone. Do you agree? Do you have anything to add? Report: parallelogram: How do two trapezoids combine into a parallelogram? Some students spell a rectangle. Let's see how they spell it. Square is a special rectangle, so the result of your deduction should be the same. Is it?
Teacher: Students, look at these figures. Are they rectangles or squares? Look again. (Moving the chart) What did you find? Transition: It seems that as long as two identical trapezoids can be combined into one ... (blackboard writing) The area of the parallelogram we have learned: ... (blackboard writing) Then we can deduce the area of the trapezoid according to the relationship between the two figures. Somebody help the teacher clean up. The base of a parallelogram is a trapezoid. .........................................................................................................................................................................
3. I just showed the assembling method, and some students completed the task with only one trapezoid. They used the method of division. Do you all understand? Please tell the students in this group briefly how you deduced it. Your group's method is really unique! Different methods. What's your conclusion?
4. Summary: The students really used their brains and came up with so many different methods. But these methods all have something in common. Who wants to talk?
5. Is that right? Then let's read the trapezoidal area formula we deduced by the method of "transformation"! (Courseware) If you use letters, will you?
6. What should we pay attention to in this formula? Don't forget when calculating. Fourth, deepen understanding and consolidate new knowledge.
1. Summary: All right, students, just now, we used what we have learned to transform the trapezoid into the learned figures by splicing, dividing, rotating and translating, and according to the relationship between the figures, we deduced the calculation method of the trapezoid area.
Have you remembered this method? That teacher is going to test you! (true or false)
3. Through the research and analysis just now, I believe everyone must have a deep understanding of the calculation method of trapezoidal area! How big is this three-second restricted area? Will you beg? What are the requirements? (Show the courseware) Try to write.
4. The calculation method of trapezoidal area is often used in life. Do you want to solve some problems in life with new knowledge?
5. The calculation method of trapezoidal area is more widely used in life, from small to large.
Verb (abbreviation of verb) conclusion
Reduction is a very important and commonly used idea in mathematics. In the study of graphics, students used the strategy of transformation many times. In fact, we also used it in the study of calculation. Then the purpose of our transformation is to turn the unknown into the known. What do you think when you encounter unknown new problems in the future? Can any unknown problem be transformed? This question is left to the students to think about.
Tisso
First, create a situation and introduce the game.
1, game import. Test your eyesight and see who can find a triangle with exactly the same shape and size. The blackboard shows the following topics and triangles in advance. The same triangle found by the students is overlapped and pasted on the left side of the blackboard. )
(1) Find: Show several groups of identical triangles, and let the students find them after disrupting the order.
(2) Spelling: What figures can these two identical triangles spell?
Put a pair of identical triangles on the left, and ask the students to spell out several learned figures on the stage, such as a rectangle, a square, a parallelogram, a big triangle and a combination of two right triangles, and stick them on the left side of the blackboard respectively. )
3. Introduce a new lesson: Can you calculate the area of these mosaics?
Second, hands-on operation, explore communication.
1, to guide students to find ideas: Just now, our graphs are all composed of two identical triangles, so what is the connection between these triangles and the composed graphs? Is there a formula for calculating the area of a triangle? Can you calculate the area of the triangle from these spliced figures?
2. Group cooperation and exploration.
3. Show the students' exploration process and report the exchange.
Teacher: Which group would like to share your findings with you?
Two representatives of each report group came to the stage to report the experiment with the experimental report form, and posted the spelled numbers on the blackboard.
Two identical acute triangles are spliced into a parallelogram, the base of which is equivalent to the base of the triangle, and the height of which is equivalent to the height of the triangle; The area of each triangle is half that of the parallelogram.
Do you have different spellings?
4. Summarize and express the formula in letters.
(1) Guide students to summarize the calculation formula of triangle area.
Teacher: According to the sharing and communication just now, let's summarize the calculation formula of triangle area. Will the area of parallelogram be calculated? How to calculate the area of triangle?
Area of parallelogram = base × height.
one half
Area of triangle = base × height ÷ 2
(2) Use letters to express the formula.
Teacher: If the letter S represents the area of the triangle, A represents the bottom of the triangle and H represents the height of the triangle, how can the formula for calculating the area of the triangle be expressed in letters? (blackboard writing: S=ah÷2)
Third, practical application and innovation.
1, learn P85 example 1
Teacher: You are great! The calculation formula of triangle area is derived. Let's apply this formula to solve some practical problems. The symbol of the Young Pioneers is a red scarf. Do you know how big the red scarf you wear every day?
The bottom length of this red scarf is 1 m, and the teacher also measured the height of 33CM (the example of P85 shown in the courseware is 1). Can you work it out now?
Students' column calculation. The teacher patrolled the exercise book with different answers, showed the students the completion and asked them to comment.
S = a h S = a h ÷ 2
= 100×33 = 100×33÷2
=3300 (square centimeter) = 1650 (square meter)
(1) is wrong. He did this to find the area of parallelogram, not triangle.
How about finding the area of a triangle?
S = a h ÷2, don't forget to divide by 2. (Emphasize ÷2. )
2. Know the traffic warning signs and infiltrate safety education through calculation. (textbook page 86)
Teacher: Young Pioneers should abide by the traffic rules in an exemplary way. Traffic warning signs can help us better abide by the traffic rules. Do you know these warning signs? (Let the students know one by one)
……
* For everyone's safety, the Department is going to make two such warning signs. How many pieces of iron are needed? Can the students help us calculate? (Courseware shows topics and pictures)
3. Question 3 on page 86 of the textbook: Choose a triangle you like, measure relevant data and calculate the area.
4. use your head. Compare the sizes of the following two triangles (group discussion) Exercise 5.
Conclusion: The areas of two triangles with equal base and equal height are equal.
Fourth, evaluate the experience and summarize the promotion.
Can you talk about what you have learned from this course? Can you comment on each group or other students?