Teaching plan for mutual transformation of mathematics scores and decimals in fifth grade
Teaching objectives
(1) Knowledge objective: Make students understand the decimal method of component number, and convert fractions into decimals according to the relationship between fractions and division.
(2) Ability goal: to cultivate students' ability to observe, summarize and solve problems in the process of exploring new knowledge. (3) Emotional goal: to cultivate students' scientific attitude and exploration spirit towards knowledge in the process of summing up laws.
Teaching emphases and difficulties
(1) teaching focus: master the basic methods of fractional decimals and fractional components.
(2) Teaching difficulties: flexible use of decimals and fractions to solve practical problems.
teaching process
First, create situations and introduce new lessons.
Recently, Ming Ming and Huan Huan, who are in the same school year as us, have encountered some math problems about fractions and decimals. Would you like to help solve it? The students are very helpful. It is not easy to help them solve their problems. You must have a certain knowledge base. The teacher will test you first. Dare you accept the challenge?
Review old knowledge and bring out new knowledge.
1. Tell the meaning of the following score. (display light)
Step 2 fill in the blanks
(1) According to the relationship between fraction and division, 3? 5=
(2) 0.9 means () points (). 0.07 means () in ().
0.0 13 means () in (). 4.27 means () and () points ()
(Design intention: Consolidate the old knowledge and pave the way for the new curriculum. Stimulate students' thirst for knowledge, thus stimulating students' interest in learning new knowledge. )
Second, independent exploration, pregnancy shows vitality
Explore and discover, understand the meaning of the problem
1. Students have a good understanding of fractions and decimals. Let's take a look at Mingming and Huanhuan. What problems have they encountered?
(Xiudeng) In the school handicraft class, students are taught to weave Chinese knots. Huanhuan's Chinese knot uses 0.6 m red rope, and Ming's Chinese knot uses 3/5 m red rope. Who uses more red ropes? Why? (Read the title by name)
Teacher: If you want to know who uses more red ropes, what exactly do you want to do? Student: Compare fractions with decimals.
How to compare fractions with decimals? In this lesson, we will discuss the reciprocity of fractions and decimals.
Written on the blackboard)
[Design Intention: Combining with concrete examples in life, let students realize that mathematics is around us, and at the same time, start with problems to stimulate students' curiosity and active inquiry attitude in learning mathematics. ]
Teacher: The teacher believes that students will solve problems with wisdom. Do you have confidence? Let's look at the cooperation requirements together.
Query requirements:
How do these two figures compare? First think independently, record methods, and then communicate in groups.
Students try to do it and report it by name.
(3) Because 3/5=3? 5=0.6, so Huanhuan uses as many red ropes as Mingming.
Teacher: Students, it is clever of you to solve the same problem in three ways.
Let's ask the first student to report.
(1) According to the meaning of decimal, find 0.6 on the line segment diagram, which must be 6/ 10.
Teacher: He solved the problem by drawing according to the meaning of fractions and decimals. It was really great.
(2) Let's ask the second student to report.
Health: Because 0.6= 6/ 10= 3/5, there are as many red ropes as Mingming. Can you explain why? Sheng 1: use the decimal meaning, because there are six tenths in 0.6, which means six tenths, that is, 6/ 10, and 3/5 after the decimal.
Teacher: He divides decimals into numbers according to their meanings, and then compares them with scores. This method is very good, not only solves the problem, but also grasps the decimal method.
3. Cooperation and communication, showing vitality
Teacher: The teacher gave us a few extra decimal places, 1, 2, 3. Can you use decimal fractions?
Cooperation requirements: 1, divide 0.3, 0. 15, 0.543 into components, what do you find?
Please summarize the method of decimal in one sentence.
Health 1: one decimal place-a few tenths, two decimal places-a few percent, and three decimal places-a few thousandths.
Health 2: Write decimals as fractions. There are several decimals, so write a few zeros after 1 as the denominator and remove the decimal point of the original decimal as the numerator.
3. Teacher: Who will summarize the methods and precautions of grading? (display light)
Student: Decimal score. Divide decimals into fractions with letters 10, 100 and 1000. What can be reduced is reduced.
Teacher: I believe that if you use this rule, you will make decimals faster. Ask the students to do the following questions quickly in this way.
(3) (Show the lamp) Practice: Play? 0.07, 0.24, 0.123,1.05. Try to do it with your exercise book.
Teacher: Just now we learned the decimal method of fractions, so how should fractions be decimal?
Let the third student report.
(4) Because 3/5=3? 5=0.6, so Huanhuan uses as many red ropes as Mingming.
Teacher: He uses fractional decimals (blackboard writing) to solve problems. Students, do you understand? Who can talk about the method of fractional decimal? (numerator divided by denominator), what should I do if I encounter infinite division:
4. Explore the method of fractional decimal by using the algorithm of fractional decimal.
The numerator (1) can be divided by the denominator to show the fractional part of the lamp. Except infinite, you can keep several decimal places according to the rounding method as needed.
(2) Teacher: Let the students do the following set of questions with the fractional method just now to see who can do it right and fast (light up). Exercise: Extract 3/4, 1/2, 4/7. report
[Design intention: Combining the meaning of decimals, gradually introduce students into the nearest knowledge development zone, so that students can find their own solutions to problems through observation, discussion and communication, and realize cooperative learning. ]
4. Break through difficulties and show vitality
Teacher: Just now we summarized the general methods of fractional decimals and fractional decimals, but some fractions have special denominators. What clever ways are there to convert fractions into decimals?
Discussion: Please observe the characteristics of the denominator of the following fractions. Can you find a more ingenious way to convert them into decimals? Think about it and communicate in groups.
Decimal 9/ 10, 43/ 100 and 7/25.
Birth 1: I like 9/10,43/100, so the denominator is10,100, 1000, which can be directly converted into decimals.
Health 2: Like 7/25, if the denominator is a factor of 65,438+00, 65,438+000, 65,438+0000, we can differentiate the fraction whose parent component is 65,438+00,65,438+0000, and then directly convert it into a decimal.
Teacher: Just now, the students summarized two special methods of fractional decimals, plus the general methods of fractional decimals that we summarized before. There are three methods for fractional decimals. Who will talk about three methods of fractional decimals?
Display lights: methods (read together)
I hope that in the process of doing the practical problems of fractions and decimals, we can flexibly choose the appropriate methods according to the characteristics of the problems, so as to improve the speed and accuracy of doing the problems.
[Design Intention: Because students have mastered the methods of decimals with denominators of 10, 100 and 1000, the scores with denominators other than 1000 are decimals, so they are generated. }
Verb (abbreviation of verb) expands and enriches vitality.
Teacher: The students are really amazing. They not only helped children solve problems, but also learned a lot of math knowledge. Next, the teacher will test everyone to see if they can use this knowledge to solve practical problems.
1. Basic problems
(1) Math Book 99 1 Question
Students observe the pictures, think about the meaning of fractions and decimals, and do it independently. After finishing, ask the students to talk about the meaning of fractions and decimals in each picture.
(2) There are three questions on page 99 of the math book.
Students connect independently first, and then communicate methods collectively. Decimal can be divided into numbers and then compared with the following scores; You can also convert the fraction into a decimal and compare it with the decimal above.
2. Ask questions flexibly,
There are three students in a mountaineering competition. From the foot of the mountain to the top of the mountain, it takes 3/4 hours for A, 0.8 hours for B and 3/25 hours for C. Can you compare which student climbs fast? Try to do it first, then report it.
Teacher: Students seem to compare sizes by fractional decimal method when doing this problem. Why not use the decimal method?
Student: The decimal method of decimals is very troublesome. Different denominators must be decomposed into fractions with the same denominator before they can be compared.
Summary: When both fractions and decimals are relatively large, it is generally convenient to convert fractions into decimals to compare sizes.
3. Knowledge development, 100 page, do you know?
Teacher: Students, in fact, some fractions can be converted into finite decimals, and some fractions cannot be converted into finite decimals. What's the mystery? Do you want to know? Will you please learn the textbook on page 100 by yourself? Do you know that?/You know what? Do you know that?/You know what? , and answer the following two questions:
Thinking (light film):
What did you learn from reading?
(2)7/8, 7/25, 7/40, 7/9.7/30, 7/44, which of these fractions can be converted into finite decimals? What can't be converted into finite decimals? Why?
Health: a simplest fraction, if the denominator contains no other prime factors except 2 and 5, this fraction can be reduced to a finite decimal; If the denominator contains prime factors other than 2 and 5, this fraction cannot be reduced to a finite decimal. (light)
Teacher: Students, you are great. Scores contain many mysteries. As long as you study hard, you will gain more.
Design intention: On the basis of highlighting key points, breaking through difficulties and following students' cognitive rules, the exercises are designed to be interesting, basic, hierarchical, flexible and vivid. This class not only pays attention to all students, but also takes care of students who have spare capacity. Let students reasonably use the method of mutual transformation to flexibly solve practical problems in life, experience the joy of success in the process of acquiring knowledge and solving problems with knowledge, fully let students perceive the close relationship between mathematics and life, and further strengthen the consolidation and extension of knowledge)
6. Summarize and sublimate, and create vitality
Today, we learned the reciprocity of fractions and decimals. Through the study of this lesson, we deeply realize that mathematics comes from life and is applied to life. I hope students can use what they have learned today to solve more practical problems in life.
(Design intention: The design of this link makes students feel that knowledge comes from life and returns to life. It is closely related to our life. We don't study mathematics for the sake of learning mathematics, but let mathematical knowledge serve our lives better.
Mutualization of Fractions and Decimals
Decimal fraction
( 1) 0.6= 6/ 10= 3/5,
Because 3/5=3/5
So Huanhuan uses as many red ropes as Mingming.
Fractional decimal
(2)3/5=3? 5=0.6,
Because 0.6=0.6
So Huanhuan uses as many red ropes as Mingming.
Teaching reflection:
The exploration law of whether the fractions whose denominator is not integer 10, integer 100 and integer 1000 can be converted into finite decimals does not appear in the teaching materials. In order to broaden students' thinking and let them explore deeply, I asked students to practice converting fractions with decimals other than integer 10, integer 100 and integer 1000 into decimals, and then guided them to classify the fractions according to whether they can be converted into finite decimals and explore the law.
Primary school mathematics scoring method
1, don't buy counseling books indiscriminately.
About mathematics, I kept all the papers from the first to the last, three dozen thick. After you keep these papers, when you start reading from the first one, it will be the same as a tutorial. Because the review is based on chapters, the items are very clear. Of course, it is recommended to choose one or two materials that suit you and do fine work.
2. Every piece of paper is blank.
Don't leave wrong questions and questions you don't understand. Every question should be made clear. If not, ask someone else, ask the teacher. I was embarrassed to ask the teacher at first, because the foundation was too poor. Maybe the question I don't know is actually just a formula question, so I asked all my classmates around me. Fortunately, people around you are tired of asking. I want to thank them here.
3. Every knowledge point required by the outline, from theorems, derivation, examples, after-class exercises, and every step, needs to be done by yourself.
Don't be impatient, don't feel bored, you are a rookie, still thinking about Dapeng spreading its wings?
Be practical. Then, every time you study, you will find a different experience. What should you do next? Next, write down your experience. Then, find the exercises related to this unit, open them and brush them.
In the process of brushing the questions, you will find that I didn't understand this knowledge point as thoroughly as I thought, but only understood the surface. At this time, you will enter the state.
Take out your notes and start writing. Why are you wrong about this question? What are the corresponding knowledge points? Are there different solutions? Sometimes, a topic can make me spend 1 hours writing two pages of loose-leaf pages slowly, but it just deepens your understanding of this knowledge principle. Trust me, it's worth it.
Then every day, I will encounter the same type of questions and put them together. After a long time, you will gradually find that there are actually several knowledge points that are really wrong. After a thorough understanding, the score will come up.
4. sort out the wrong questions.
I made too many mistakes at first, especially in unit review. Sometimes there will be one or two papers, so I will keep the papers and write the answer steps in the blank or on post-it notes. I said that I left all the papers that the third-grade teacher reviewed from the first chapter, so leaving too many wrong papers is equivalent to mistakes. Turn over the wrong questions at the weekend (because I wrote the steps, it's easy to review. )
In fact, the wrong questions are out of order. I just put a wrong question on the wrong book when I thought it was valuable. Don't worry about the order when reviewing, just urge yourself not to make mistakes repeatedly. It would have been very helpful to turn over this wrong question before the exam!
5. Organize your notes.
I have two math notes, one is some methods and skills summarized by our teacher, the memory of some formulas and the concept of laws (this should be easy to remember! It is often used when doing problems! It's easy to do the problem without a formula? ..................................................................................................................................................................................
6. About newspapers.
Because the notes have to be deleted (who will copy the questions themselves these days? Go and stand in the corner! ) It's in my notes, so I always want two papers (the teacher asks who wants two), one for myself and one for cutting questions (sometimes both sides are annoying, so I sometimes take three).
ps:
I made my own paper, so I have to mark it after listening to the questions. I have a set of morning light markers, which are quite easy to use. Mark the questions I can't do with a color, but it will be a typical color. Be sure to write the process of doing the problem clearly on paper! Be sure to write the process of doing the problem clearly on paper! Be sure to write the process of doing the problem clearly on paper! Say the important things three times! Otherwise, if you look at the paper, you will forget to cry, and there is no place to cry.
7. train a set of test papers in a limited time every day.
Not for knowledge, but after doing more, you will clearly know how much time each question needs and how to do it best for you, which naturally speeds up the pace. Because when I was in the exam, I was most afraid of not knowing the bottom of the paper and did all the wrong questions in a hurry. I started doing that three months before the exam, which was particularly effective, but I always regret not starting earlier. If possible, start this mode as soon as possible!
Tips for children to learn math well
1, tutoring children in mathematics at home, the questions should be flexible and diverse, which can arouse their thinking.
Many parents help their children learn math, which is just a few boring math problems, so that children can easily get bored and feel uninterested in math. How much is 3+7? How about 7+3? How about 8+2? At this time, if you supplement the question in turn: Are those two numbers 10? How many such formulas are there? How to judge that you have finished writing? Is it regular? Let children find the rules: 0+ 10, 1+9, 2+8, 3+7, 10+0, and then put forward that the sum of those two numbers is equal to 1 1? How many such expressions are there? Then it is put forward that the sum of two numbers is equal to 100, and this formula can be supplemented by several lines. These questions can cultivate children's ability to explore mathematical laws. Sometimes, when you are busy doing housework, the child asks you to give him a problem to do. You can draw a geometric figure on paper and let the children talk about it. For example, draw a circle and let the children imagine. Some children say it looks like pie; Like a full moon; Like the buttons of mom's beautiful coat. As long as it is round, no matter what you say, the more you say, the better. This can cultivate children's imagination and observation.
2. The questions compiled for children in daily life can make children experience life and enrich their life knowledge.
Keeping goldfish is children's favorite thing. Do subtraction for children, can you make it up? There are five goldfish in the goldfish bowl, one is dead, and several children have had the experience of keeping goldfish. They may not simply answer four questions. Does he mean to ask if this dead goldfish has been fished out? So he has two answers: four or five. Thinking more about such problems can cultivate children's habit of thinking comprehensively. At the dinner table, if there is a rich dish, let the children divide it into two categories. It is up to the children to decide which method to divide it. Especially when there are many children, the enthusiasm will be higher. There are many ways of division: such as squeezing, plant division, seafood or non-seawater division, cooking and soup division; Cold dishes and hot dishes are classified. Parents should make appropriate tips to let their children learn a little classification thought and enrich their life knowledge.
3. Parents should not give answers to questions that can be operated by hand, so that children can operate, experience and comprehend.
In order to test children's intelligence, parents will ask their children: a rectangular piece of paper has four corners. How many corners are left after cutting one corner? Children will blurt out, three. At this time, parents should not tell their children the answer, but let them cut it themselves. When I cut it, I found five corners. Keep cutting and see if you can cut three. Children have seen retractable sliding doors or security window. These doors or windows are quadrangular in structure. Ask them why they don't make triangles but quadrilaterals. Let the children form a quadrilateral and triangle with bamboo sticks, and then press them to see if they will be deformed. Let the children understand? Stability of triangles? And then what? The instability of quadrilateral? . Do it yourself and think for yourself, and you can understand some conclusions and lay the foundation for invention.
In short, half of children's good learning quality comes from their parents' influence. When asking questions to children, we should also pay attention to methods, so that children can think positively and do it happily, which can stimulate interest, develop intelligence and achieve the purpose of cultivating ability.
Children's math games are really colorful, so how should parents choose? The following recommended games are of great help to your baby's math study.
Count backwards
Ask children to recite a series of numbers dictated by adults in reverse order, such as 32 1 when dictation 123. When reciting numbers, you are not allowed to look at the written numbers or write down the dictated numbers with your own hair pen. This requires children to pay great attention to listening, recite the numbers immediately, and think hard at the same time, that is, recite the order of the numbers backwards through reverse thinking. In the investigation of 1987, it is found that 8.5% of 4-year-old children and 72.5% of 5-year-old children can recite backwards. 7.4% of 5-year-old children, 74.5% of 70-month-old children and 98.5% of 76-month-old children can recite backwards. 1995 found that at the age of 4, 82% of people can recite two digits, 25% can recite three digits, 10.2% can recite five digits and 3.4% can recite six digits. Binet.Alfred's L-M Scale requires 3 digits for 7 years old, 4 digits for 9 years old and 5 digits for 12 years old. Only adults with high IQ can recite six figures. Webster's 1950 pointed out that repeating and reversing numbers is a way to measure intelligence. If adults can't repeat five digits and reverse three digits, there is a 90% chance that they will be diagnosed with mental retardation and memory defect, and they can't concentrate on any hard work.
Do you know how old you are
From 10 month, if adults ask? How old are you, the baby will stand up and answer, 15 months will speak for himself? 1 year? . Does the baby who talks late talk for 28 months? Two years old? . However, both Binet.Alfred Scale and gesell Scale believe that you should be 5 years old to correctly answer your age.
Draw a square
Children around 3 years old are required to draw at least one square with a right angle. Children in our country can learn to draw squares from 30 months, and then it is 44 months. Because many Chinese characters are square, children are used to reading square characters, and some parents let their babies learn to write Chinese characters at the age of two and a half, so it is easier for children in China to draw square characters. The age ratio of learning to draw a square is five years old, and that of gesell is four and a half years old. The DSST scale (Frankberg 1967) used for screening at ordinary times is 4-5 years old.
Know coins and change money
At 50 months, 74.6% of children will recognize three kinds of coins. At 53 months, 76.8% of children will use 1 and 2 to make 5 points, or 1 and 5 cents to make 1 yuan. 78.2% children aged 5-6 learn the game of trading with coins.
Binet.Alfred stipulated that he could recognize four kinds of coins when he was six years old. In America, there are four kinds of coins: 1, 5, 1 and 25. Binet.Alfred L-M Scale stipulates that you should learn to change money at the age of 9, that is, you should change money within 35 minutes. Coins in our country are based on 10, which may be relatively easy, but it is also considerable to advance 3-4 years.
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