Teaching content of the sixth grade math lesson plan (1);
Hebei Education Edition, Grade Six, Volume I, Page xx
Teaching objectives:
1. Make students understand the meaning of number and discount, and the relationship between number and fraction and percentage; Can solve the application problem about fractions.
2. Improve students' ability to analyze and solve application problems, and develop students' thinking flexibility.
Teaching emphases and difficulties:
Understand the meaning of multiples and discounts; Understand the meaning of fractions, fractions and percentages.
Teaching process design
Review preparation
1. Lizhuang planted 50 hectares of wheat last year and 60 hectares this year. Compared with last year, what percentage of wheat is planted this year?
Xiaohua's family contracted a vegetable field the year before last, and collected 4 1.6 tons of cabbage, 25% more than the previous year. How many tons of cabbage were harvested last year?
The teacher said: agricultural harvest is sometimes expressed by scores. Today, we are going to learn the application of fractions.
Blackboard writing: percentage application problem.
Learn a new course
1. Example of computer demonstration: the purchase price of each TV set in the mall is 1800 yuan, and the selling price is 20%. What's the price of each TV set?
2. The meaning of numbers.
Teacher: What are numbers? In the fifth grade, we learned that "a few percent" is a few tenths. For example, "10%" is one tenth, which is equivalent to 10%.
(1) Answer:
"Thirty percent" is ten (), rewritten as a percentage ().
"Thirty-five percent" is ten o'clock (), which is rewritten as a percentage ().
(2) What percentage is 725%?
What do you mean by adding 20% to the selling price? What should be the price first?
What else can I do? The students exchanged views on solving problems.
4. Give an example 2.
Example 2: The annual output of cotton in Cao Zhuang township last year was 374,000 kilograms. This year, due to insect pests, the output decreased by 15%. How many thousands kilograms of cotton will be produced this year?
(1) Students read the questions and understand the mathematical information in the questions.
(2) What does it mean to reduce production by 15%?
(3) Students answer independently and name students to talk about problem-solving ideas.
The teacher said: in column calculation, we can directly convert "into a number" into a percentage, and use the percentage to calculate the determinant.
Blackboard writing:
37.4×( 1- 15%)
=37.4×0.85
=3 1.79 (ton)
A: This year's cotton output is 365,438+790,000 kilograms.
3. practice.
Xiaolijia contracted a piece of land the year before last and harvested 8,000 Jin of wheat, an increase of 15% over the previous year. How many kilograms of wheat were harvested last year?
6. Class summary.
What did we learn today?
Teacher: Today, we learned the knowledge about "Cheng Shu", the meaning of "Cheng Shu" and the relationship between "Cheng Shu" and scores and percentages, and learned some practical and simple application problems about "Cheng Shu".
(3) Integrated feedback
1. Fill in the blanks:
(1) The cotton output of a county this year has increased by 30% compared with last year. This sentence means that () is 30% of ().
(2) The yield of a wheat field increased by 45% after a new variety was changed. This sentence means that the yield is ()% of () after changing new varieties.
2. Rewrite the following percentages as "Percent".
75% 60% 42% 100% 95%
The sixth grade mathematics teaching plan Volume II: People's Education Edition and Reflection (2) Teaching objectives;
1. Understand the necessity of introducing percentage, understand the meaning of percentage, and read percentage correctly. In specific situations, explain the meaning of percentage and realize the close relationship between percentage and daily life.
2. Experience the process of extracting percentage from practical problems and cultivate students' ability of inquiry and induction.
3. Let students experience the happiness of success in the process of operation and exploration.
Teaching emphases and difficulties:
Understand the meaning of percentage.
Teaching process:
First, with practice, to stimulate the introduction of interest
Teacher: Students, do you like traveling?
Health: I like it!
Teacher: Teachers also like to travel and have been to many places. Show me the photos of the teacher's trip and introduce them.
Design intention: Take yourself as an example, show tourist photos, grab students' attention and stimulate students' interest in learning Teacher: Who said that? What places of interest have you been to? Teacher: Today, the teacher will show you around the scenic spots in Shandong, ok? (Display information window 1)
2. Teacher: Who knows which cities and scenic spots in Shandong these pictures belong to?
Health: ...
Teacher: Read the following sentences and statistics. What questions can you ask if it's weird?
Design intention: By introducing the statistics of relevant data of tourist attractions into the new curriculum, we can find the application of percentage in life and cultivate students' awareness of finding and asking questions in life.
Second, experience cooperation and explore independently.
(A) Percent reading teaching method
Teacher: How do you pronounce 16%, 9% and 9.3%?
Student: 16% reading: 16.9% reading: 9.3% reading: 9.3% (reading by the whole class, another example)
Design intention: Students have a certain understanding of the percentage reading method. On the basis of guiding the reading percentage, ask students to give a few percentages for students to read at will, and deepen their impression of the percentage reading method.
(B) the significance of teaching percentage
1, Teacher: What do they mean?
(Taking 16% as an example, the group discussion indicated that the explanation was 9% and 9.3%.)
Draw a conclusion: the number that indicates that one number is a percentage of another number is called percentage.
Teacher: Percentage is also called percentage or percentage.
(blackboard writing: percentage)
Teacher: Percentages are usually expressed by adding% after the original molecule instead of fractions.
2. Think about it. Where have you seen percentages in your life?
Design concept: Look for percentage information from students' life around them to improve students' interest in learning percentage. Universality of practical application of permeability percentage. Let students perceive that there is mathematics everywhere in life.
(C) practice consolidation, knowledge extension
Practice independently.
1, so that students can understand the relationship and difference among decimals, fractions and percentages. Pay special attention to the difference between fraction and percentage: fraction can represent a specific number or the relationship between two numbers; Percentages can only represent the relationship between two numbers.
2. Practice the second question after class, read the relevant materials carefully and talk about the meaning of each percentage.
Design intention: in the process of language narration, deepen students' understanding of the meaning of percentage and consolidate their knowledge better.
3. Exercise questions 3 and 4 after class, paying special attention to understanding the meaning of 100%.
Design intention: integrate design into life practice, extend after class, study the mathematics around you, infiltrate "there is mathematics everywhere in life" while carrying out calculation consolidation exercises, cultivate students' problem consciousness and solve mathematical problems in life independently.
4. In the fifth question after class, considering the significance of the scores learned, the ethnic population is "1"(100%), with the Han population accounting for 92% of the total and the ethnic minority population accounting for 1-92%=8%.
Blackboard design:
Percentage of holiday tourism in Shandong
Sixth-grade math lesson plan teacher's edition and reflection (3) teaching objectives;
1. Make students understand the meaning of number and discount, and the relationship between number and fraction and percentage; Can solve the application problem about fractions.
2. Improve students' ability to analyze and solve application problems, and develop students' thinking flexibility.
Key points and difficulties:
Understand the meaning of multiples and discounts; Understand the meaning of fractions, fractions and percentages.
Teaching process:
First, review preparation
1. Convert the following numbers into percentages.
Li Zhuang planted 50 hectares of wheat last year and 60 hectares this year. Compared with last year, what percentage of wheat is planted this year?
Xiaohuajia contracted a vegetable field the year before last, and collected 4 1.6 tons of cabbage, 25% more than the year before. How many tons of cabbage were harvested last year?
The teacher said: agricultural harvest is sometimes expressed by scores. Today, we are going to learn the application of fractions.
Blackboard writing: percentage application problem
Second, learn new lessons.
1. Example of computer demonstration: the purchase price of each TV set in the mall is 1800 yuan, and the selling price is 20%. What's the price of each TV set?
2. The meaning of numbers.
Teacher: What are numbers? In the fifth grade, we learned that "a few percent" is a few tenths. For example, "10%" is one tenth, which is equivalent to 10%.
(1) oral answer
"Thirty percent" is ten (), rewritten as a percentage ().
"Thirty-five percent" is ten o'clock (), which is rewritten as a percentage ().
(2) What percentage is 725%?
What do you mean by adding 20% to the selling price? What should be the price first?
What else can I do? The students exchanged views on solving problems.
4. Give an example 2.
Cao Zhuang Township produced 374,000 kilograms of cotton last year. This year, due to insect pests, the output decreased by 15%. How many thousands kilograms of cotton will be produced this year?
(1) Students read the questions and understand the mathematical information in the questions.
(2) What does it mean to reduce production by 15%?
(3) Students answer independently and name students to talk about problem-solving ideas.
The teacher said: in column calculation, we can directly convert "into a number" into a percentage, and use the percentage to calculate the determinant.
Blackboard design:
37.4×( 1- 15%)
=37.4×0.85 =3 1.79 (ton)
A: This year's cotton output is 365,438+790,000 kilograms.
Sixth-grade math lesson plan teacher's edition and reflection (4) teaching objectives;
1, understand the meaning of proportion, know the names of each part of proportion, and get the basic properties of the score through observation, guess and verification.
2. According to the meaning and basic nature of proportion, we can correctly judge whether two proportions can form a proportion.
3. Cultivate students' ability to guess, verify, observe and summarize.
4. Let students experience the happiness of success in the process of inquiry and gain interest and confidence in mathematics learning.
Teaching emphasis: Understanding the meaning and basic nature of proportion can correctly judge whether two proportions can form a proportion.
Independently explore the basic nature of proportion.
Teaching preparation: slides, exercise paper
Teaching plan design:
learning plan
First, ask questions by yourself
Importance of [exploration task 1] ratio
Show several groups of ratios by projection, and ask students to write the ratios of each group.
Second, the basic nature of proportion
Teaching plan.
First, review old knowledge and new knowledge.
1, Dialogue: Students, we have learned a lot about Bi. How much do you know about Bi?
Answer: meaning, names of parts, basic nature, etc. )
Remember how to find the ratio? Can you quickly calculate the ratio of two proportions in the following groups?
2, the teacher blackboard title:
( 1)4:5 20:25 (2)0.6:0.3 1.8:0.9
(3) 1/4: 5/8 3:7.5 (4)3:8 9:27
[Comment: Cut to the chase, start with the students' existing knowledge and experience, which is convenient and quick, step by step, and prepare for the new lesson. Because these topics are still needed, I don't hesitate to write them on the blackboard-an effective way to present them.
Second, the significance of deepening the proportion
(A) the meaning of understanding
1, say the ratio of two ratios in each group, and write the ratio below the ratio.
The teacher asked: Did you find anything? (Three groups of ratios are equal and one group is unequal)
2. Yes, this phenomenon has long attracted people's attention and research. People connect the two ratios with an equal sign and write a new formula, for example, 4: 5 = 20: 25.
Teacher: Can the last group be connected by an equal sign? Why?
Mathematics stipulates that some formulas like this are called proportions. Today we are going to learn proportion (blackboard writing: proportion).
[Comment: Through oral calculation of the proportion, students inadvertently found that there are three sets of formulas with equal proportion and one set of formulas with different proportions, resulting in the proportion being like running water. Effective classroom teaching needs a perfect connection between old and new knowledge like this. ]
3. What proportion do students want to learn?
Student: If we want to study the meaning of proportion, what's the use of learning proportion? What are the characteristics of proportion ...)
Ok, let's study the meaning of proportion first. What is proportion? Look at these formulas on the blackboard. Can you tell me what the ratio is?
According to the students' answers, the teacher grasps the key point on the blackboard: the two ratios are equal.
What the students mean by proportion is correct, but it can be more concise in mathematics.
Disc play: two formulas with equal proportions are called proportions.
Students discuss and make it clear that if there are two ratios and the ratios are equal, a ratio can be formed; On the other hand, if it is a ratio, there must be two ratios and the ratios are equal.
5. Q: There are three ratios, and their ratios are equal. Can they form proportions?
[Comment: The meaning of proportion is actually a regulation. Students only need to find out what it is, not why. This session allows students to observe first, and then use their own words to say what the proportion is. Students can tell the key to the meaning of proportion-two proportions are equal, teachers can simplify sentences, draw concepts and pay attention to the cultivation of students' language generalization ability. After summing up the concept, the teacher did not come to an abrupt end, but continued to guide students to discuss, further understand the proportion from both positive and negative aspects, and deepen students' understanding of the connotation of proportion. Let students really experience the whole process of knowledge exploration and formation like mathematicians, and enjoy the happiness of success all the time! ]
(2) Practice
1, project an example of 1. According to the table below, first write the ratio of the amount of money bought twice to the amount of exercise books, and then judge whether these two ratios can form a proportion. (1) Students do it independently.
(2) Collective communication, clear: According to the meaning of proportion, judge whether two proportions can form a proportion.
2. Complete the questions in the exercise paper 1.
A car travels 200 kilometers in 4 hours in the morning and 3 hours in the afternoon 150 kilometers.
(1) Write down the ratio of driving distance and time in the morning and afternoon respectively. Can these two proportions form a proportion? Why?
(2) Write down the proportion of driving distance in the morning and afternoon and the proportion of time respectively. Can these two proportions form a proportion? Why?
[Comment: These two exercises not only help students to consolidate the meaning of proportion, but also learn to judge whether two proportions can form a proportion according to the meaning of proportion; It also allows students to further experience the application of proportion in life. In this link, a student designed a positive and negative proportional knowledge about "why", and the teacher also lost no time in evaluating it, which not only made the student enthusiastic, but also attracted the envious eyes of other students. Wonderful! ]
Just now, we wrote the proportion first, then the proportion. Do you think Debbie is the same as Debbie? What is the difference?
(Guide students to infer that the ratio consists of two ratios, with four numbers; A ratio is a ratio, there are two numbers)
4, know the name of the proportion of each part.
(1) blackboard writing: 4: 5
The former and the latter.
(2) blackboard writing: 4: 5 = 20: 25
Internal projects and external projects
(3) If the proportion is written as a fraction, can you point out its internal and external terms?
Courseware presentation: 4/5=20/25
[Comment: Write the ratio first, then write the ratio in the exercise, which naturally leads to the difference between the ratio and the ratio, and then from the name of each part of the ratio to the name of each part of the ratio, which is interlocking and natural and smooth. ]
5, summary, transition:
Just now we learned the meaning of proportion and the names of its parts. We know that proportion has many applications in life. Next, let's study whether the proportion has any regularity or nature. Are you interested?
Third, explore the basic nature of proportion.
1, projection display:
Can you form several equations with the numbers 3,5,10,6? (There are two numbers on each side of the equal sign)
2. Think independently and write it in the exercise book.
The student's equation may be: 10÷5=6÷3.
Or10: 5 = 6: 3; 3÷5=6÷ 10 or 3: 5 = 6:10; 3:6=5: 10; 5×6=3× 10……
According to the students' answers, the teacher's camera guides the consolidation of books: 3× 10 = 5× 63: 5 = 6: 10.
3:6=5: 10
5:3= 10:6
6: 3= 10:5……
3, guide to discover the law
(1) Are there any different multiplication formulas? (No, the position of the exchange factor is still the same)
I can only write one multiplication formula, but I have written so many proportions. Are these proportions the same? (No, because the ratio is different)
(2) So, are there any similar characteristics or laws between these proportional formulas? Careful observation, can you find the nature or law of proportion?
(3) Students think independently first, and then communicate in groups to explore the law.
(blackboard writing: the product of two external terms is equal to the product of two internal terms. )
[Comment: "With these four numbers, several equations can be formed." Different students write different formulas, and there are many differences. Here, give full play to the role of communication and make every student's thinking a useful teaching resource. Considering that it is difficult for students to directly explore the basic nature of proportion, the teacher gives appropriate guidance, and through the horizontal connection between multiplication formula and proportion formula, students can find invariance in change, so as to explore the nature. ]
4. Verify the conjecture:
Teacher: This is your guess. If you have a guess, you must verify it.
(1) Look at the blackboard. Are the products of internal and external terms equal? Students verify that the inner product is equal to the outer product. )
(2) Students write a ratio at will to verify. Division patrol guidance.
Teacher: A classmate also wrote a comparison. He thinks that the inner product and the outer product of this ratio are not equal. Let's see why.
Blackboard: 1/2: 1/8 = 2: 8
All beings pondered for a moment and found that the equation was not established.
Health: 1/2: 1/8 = 4, while 2: 8 = 1/4, these two ratios cannot form a proportion.
Teacher: Before the newly discovered law, it seems that a condition-proportionality (blackboard writing) must be added. This law is called the basic nature of proportionality.
[Comment: Provide students with a large number of examples, let them verify in many aspects, from individual to general, and let students learn to study problems scientifically and realistically. ]
5. Think that 4/5=20/25 means that the products of those numbers are equal. Courseware display: cross multiplication.
6. Summary: How did we discover the basic nature of proportion just now? Write some proportional formulas, observe and compare them, find the rules, and then verify them.
Timely summary and evaluation can not only help students to sort out the context of knowledge, but also make them feel the joy of creation and build up their confidence in learning. Especially the teacher's evaluation: this is how scientists study problems! It also gives students great glory! ]
Fourth, feedback improvement.
Complete exercises 2, 3 and 4.
Attached exercise paper: 2. Can two proportions in the following groups constitute a proportion? Write down the proportion of the composition and explain the reasons for the judgment.
14: 2 1 and 6: 9 1.4: 2 and 5: 10.
Let the students know clearly that we can judge whether two ratios can form a ratio by the meaning and basic properties of the ratio.
3. Determine which of the following specific energies and the composition ratio of 1/5: 4.
①5:4 ②20: 1
③ 1:20 ④5: 1/4
4. Fill in the appropriate number in ().
① 1.5:3=( ):4
12:( )=( ):5
[Comment: The arrangement of exercises aims to further consolidate and apply the meaning and basic nature of proportion. The second question of the fourth question is an open question, and the answer is no, which is intended to further let students experience and understand the beauty and unity of "change" and "invariance" in mathematics. ]
Five, leave blank after class
At the same time, at the same place, the person 1.5m high and the shadow 2m long. The tree is 3 meters high and the shadow is 4 meters long.
(1) The ratio of height to shadow length is ()
The ratio of tree height to shadow length is ()
(2) The ratio of person height to tree height is ()
The ratio of figure length to shadow length is ()
What did you find?
Why can the height of two different objects in the same place at the same time be directly proportional to their shadow length? Please refer to the relevant materials after class.
[Design Intention: Mathematics serves life and can better test the quality of mathematics learning in life! "Leaving the classroom with questions" is the concept of the new curriculum. Without a perfect classroom, regret is a kind of beauty! ]
Sixth, the class summary: What did you gain in this class?
The last chance was given to the students, who summed it up clearly.