Unit point analysis:
Teaching content:
This unit is based on students' understanding of fractions and fractional addition and subtraction operations, as well as the understanding and mastery of the meaning of integer multiplication, and further study of fractional multiplication. The main contents include the significance, calculation rules and simple application of fractional multiplication.
Three-dimensional target:
1. Knowledge and skills:
(1) Make students understand the meaning of fractional multiplication, master the calculation rules of fractional multiplication, and be able to calculate correctly and skillfully.
(2) According to the significance of fractional multiplication, we can solve some simple mathematical problems.
2. Process and method
(1) has experienced the process of asking questions from a mathematical point of view, understanding problems and solving problems by fractional multiplication.
(2) Through observing, guessing, proving and other mathematical activities, I can explain my point of view in an orderly way.
3. Emotions, attitudes and values
(1) Experience the exploration and challenge of mathematical problems through observation, conjecture, experiment and other mathematical activities.
(2) Further experiencing mathematics is closely related to daily life.
Teaching emphasis: explore and understand the significance and calculation rules of fractional multiplication.
Teaching difficulty: the meaning of multiplying a number by a fraction.
The key to teaching: understand that "a number multiplied by a fraction" is to find a fraction of this number.
Division of class hours:
1. Fractional multiplication (1)-2 class hours.
2. Fractional multiplication (2)-2 class hours.
3. Fractional multiplication (3)-2 class hours.
4. Practice 1-2 class hours.
5. Unit review-1 class hour.
Instructional design;
1. Fractional multiplication (1) 1
Teaching objectives:
Ability goal: according to the need of solving problems, explore relevant mathematical information and develop the preliminary ability of fractional multiplication.
Knowledge goal: learn the calculation method of integral multiple fraction, let students explore the calculation principle of integral multiple fraction, and students can calculate integral multiple fraction skillfully and accurately.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphasis and difficulty: students can skillfully calculate integral multiple scores.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional addition and subtraction problems.
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (divide first, then add and subtract molecules; The denominator remains the same ...) And pay attention to correcting students' mistakes and praise students who answer questions.
Second, teach new lessons.
Students, let's learn a new operation: fractional multiplication. Let the students think about what fractional multiplication is.
Discuss among the students at the same table, and the teacher asks the students to answer the questions.
The teacher writes examples on the blackboard to make students think about how to calculate.
Students list the formula 3× =. Students at the same table discuss with each other. How to calculate the integer multiplied by the fraction?
The teacher asked the students how they worked it out.
(student1:3× = =; Student 2: 3× = = ...)
Teachers and students summarize the calculation method of integer multiplied by fraction, integer multiplied by fraction, only integer multiplied by numerator, denominator unchanged. )
Third, consolidate the exercises:
Make two pages of textbooks and color them. Calculate, what is the sum of the two?
Let students skillfully calculate, and teachers correct students' wrong calculation methods in time.
Try 1.2 in the textbook.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication
3× = = 3× = = = =
Fraction multiplied by integer: integer multiplied by fraction, only integer multiplied by numerator, denominator unchanged. )
Fractional multiplication (1) 2
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal: learn the calculation method of integral multiple fraction, let students explore the calculation principle of integral multiple fraction, and students can calculate integral multiple fraction skillfully and accurately.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphasis and difficulty: students can skillfully calculate integral multiple scores.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional addition and subtraction problems.
4×
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (divide first, then add and subtract molecules; The denominator remains the same. ) and pay attention to correct students' mistakes and praise students who answer questions.
Second, teach new lessons.
Students, let's learn a new operation: fractional multiplication. Let the students think about what fractional multiplication is.
Discuss among the students at the same table, and the teacher asks the students to answer the questions.
The teacher writes examples on the blackboard to make students think about how to calculate.
Students list the formula 3× =. Students at the same table discuss with each other. How to calculate the integer multiplied by the fraction?
The teacher asked the students how they worked it out.
(student1:3× = =; Student 2: 3× = = ...)
Teachers and students summarize the calculation method of integer multiplied by fraction, integer multiplied by fraction, only integer multiplied by numerator, denominator unchanged. )
Third, consolidate the exercises:
Make two pages of textbooks and color them. Calculate, what is the sum of the two?
Let students skillfully calculate, and teachers correct students' wrong calculation methods in time.
Try 1.2 in the textbook.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication
3× = = 3× = = = =
Fraction multiplied by integer: integer multiplied by fraction, only integer multiplied by numerator, denominator unchanged. )
2. Fractional multiplication (2) 3
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal: continue to learn the calculation method of multiplying an integer by a fraction, so that students can calculate what the fraction of an integer is, and students can skillfully and accurately calculate the results of multiplying an integer by different fractions.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the results of multiplying integers by different fractions.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
Second, the audit import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional multiplication problems.
= = 2 1× =
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (Integer multiplied by fraction, integer multiplied by numerator, denominator unchanged. Pay attention to two restoration methods. )
Second, teach new lessons.
The teacher showed the textbook example: Xiaohong has six apples, and the naughty apple is Xiaohong; The smiling apple is red. How many apples are naughty and smiling?
The teacher asked the students to think about this example and ask questions.
Students fill in the boxes on the textbook examples themselves.
The teacher asked the students how they worked it out.
(student1:6× =; Student 2: 6× = ...)
Teachers and students compare the differences and connections between these two topics. Students initially understand the mathematical meaning of integer multiplied by fraction.
Third, consolidate the exercises:
Try to make a five-page textbook. What is the sum of 36?
Pay attention to let students experience the mathematical significance of finding integer fractions.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication (2)
6× = 6× =
The Mathematical Meaning of Integer Multiplying Fraction: What is the Fraction of Integer?
Fractional Multiplication (2) 4
Teaching objectives:
Knowledge goal: continue to learn the calculation method of multiplying an integer by a fraction, so that students can calculate what the fraction of an integer is, and students can skillfully and accurately calculate the results of multiplying an integer by different fractions.
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Emotional goals:
Let students feel the close connection between fractional multiplication and life, and cultivate their good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the results of multiplying integers by different fractions.
Teaching methods: Teachers and students alike induce and reason.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional addition and subtraction problems.
4× 12× =
Teacher: Check the students' questions back and forth and ask them to talk about the meaning of each formula.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer questions, paid attention to correcting the students' mistakes and praised the students who answered questions.
Second, classroom exercises
Students do the problem 1, and the teacher pays attention to let the students compare the height of the door and Xiaoming, and pay attention to the conversion of length units.
Students do the second question, and the teacher pays attention to reminding students to divide them into the simplest scores in time. Talk to each other at the same table about the mathematical meaning of each formula.
The students do the third question, and the teacher examines the students' problem-solving situation and helps the students in trouble in time.
When the students do question 4, the teacher pays attention to let the students distinguish the minimum and maximum range, and asks the students to tell their own answers.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication (2)
480× 180 (kg) 180× = 150 (kg)
3. Fractional multiplication (3) 5
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal: learn the calculation method of multiplying scores by scores, and students can skillfully and accurately calculate the result of multiplying one score by another.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the result of multiplying scores by scores.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional multiplication problems.
= = 2 1× =
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (Integer multiplied by fraction, integer multiplied by numerator, denominator unchanged. Pay attention to two restoration methods. )
Second, teach new lessons.
The teacher showed an example from a textbook: a rectangular piece of paper was cut the first time, and the rest was cut the second time. At this point, what is the rest of this paper money? If you cut off the rest for the third time, how much of this note will be left?
The teacher asked the students to think about this example and ask questions.
? Analyze the first cut it, the second cut the rest, that is. namely
Let the students see yes from the picture, think from =, and discuss at the same table.
The teacher asked the students to talk about the arithmetic of multiplying fractions by fractions. And encourage students' opinions.
The teacher and the whole class summed up the arithmetic of multiplying fractions by fractions: fractions multiplied by fractions, numerator multiplied by numerator, denominator multiplied by denominator as denominator.
Verification rule: let students origami to verify? Ask the students to analyze the reasons.
Class discussion: Let the students say, according to the illustration on page 7 of the textbook, what is the ratio of the red part to the diagonal part? How many parts are there in the whole paper? Let students further understand the relationship between the whole and the part; What is the initial understanding of the score?
Third, consolidate the exercises:
Try to do page 8 of the textbook.
Students are required to calculate by multiplying scores by scores. Pay attention to the first reduction point that can be reduced, such as the middle 7, 14 first reduction point.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication (3)
= = =
Arithmetic of fractional multiplication: numerator multiplication, denominator multiplication, divisible divisor.
Fractional Multiplication (3) 6
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal: learn the calculation method of multiplying scores by scores, and students can skillfully and accurately calculate the result of multiplying one score by another.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the result of multiplying scores by scores.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional multiplication problems.
× =
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate.
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (Fraction multiplied by fraction, numerator multiplied by numerator, denominator multiplied, can be divided into preferential points. )
Second, classroom exercises:
Students do the first question with some discounts and some erasures. Ask the students to verify the arithmetic of multiplying the score by the score again by origami, and pay attention to let the students know what the score is.
Students do the second question, pay attention to let students experience the relationship between the product of score multiplication and each multiplier.
Do the third question, and let the students understand the relationship between the score of the score and the total "1".
Students do the fourth question and let them know the size of the comparison sum "1".
When the students do the fifth question, what is the score that the teacher pays attention to?
Students do the sixth question and ask them to pay attention to the scores of different standards. A small part of the whole.
Students do the seventh question, and the teacher pays attention to let students solve practical problems in life by fractional multiplication.
Question 8: According to the knowledge of fractional multiplication, students can tell whether it is fair for Tang Priest to divide watermelons.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Fractional multiplication (3)
=
It belongs to the whole playground "1" and belongs to the whole playground "1".
Arithmetic of fractional multiplication: numerator multiplication, denominator multiplication, divisible divisor.
4. Exercise 1 7
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal:
Reviewing the calculation methods of multiplying a fraction by an integer and a fraction by a fraction, students can skillfully and accurately calculate the results of multiplying a fraction by an integer and multiplying a fraction by another fraction.
Emotional goals:
Let students feel the close connection between fractional multiplication and life, and cultivate their good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the results of multiplying scores by scores and multiplying scores by integers.
Teaching methods: Teachers and students alike induce and reason.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional multiplication problems.
5× × =
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate. What's the difference between these fractional multiplication operations?
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (Fraction multiplied by fraction, numerator multiplied by numerator, denominator multiplied, can be divided into preferential points. Fraction multiplied by integer, integer multiplied by numerator, denominator unchanged. )
Second, classroom exercises:
Students do the first question and ask them to multiply their scores by integers to find out the content of protein and fat in1000g beef.
Students do the second question, pay attention to let students multiply the score by the integer knowledge, and find out the number of days with good air quality in our city throughout the year. Cultivate students' environmental awareness of protecting the environment from childhood.
Students do the third question and ask them to calculate the formula of integer times score and score times.
Students do the fourth question, and let them learn to compare the scores of the whole "1".
When the students do the fifth question, the teacher pays attention to asking the students to get a score of the whole.
Students do the sixth question, let them use the knowledge of integral multiple fractions to solve the life problems about fractions in life, and cultivate students' humanitarian thought of "one party is in trouble and many parties support"
Students do the seventh question, and the teacher pays attention to let students solve practical problems in life by fractional multiplication.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Exercise 1
1000× 200 (g)
Arithmetic of integer multiplied by fraction: integer multiplied by numerator, denominator unchanged, can score about.
Exercise 1 8
Teaching objectives:
Ability goal:
According to the needs of solving problems, we can explore relevant mathematical information and develop the ability of fractional multiplication.
Knowledge goal: review the calculation methods of multiplying a score by an integer and a score by a score, so that students can skillfully and accurately calculate the results of multiplying a score by an integer and a score by another score.
Emotional goal: let students feel the close connection between fractional multiplication and life, and cultivate a good interest in learning mathematics.
Teaching emphases and difficulties:
Students can skillfully calculate the results of multiplying scores by scores and multiplying scores by integers.
Teaching methods: Both teachers and students like induction and reasoning.
Teaching preparation: teaching reference books and teaching materials.
Teaching process:
First, check the import:
The teacher shows the teaching blackboard and asks the students to calculate the following fractional multiplication problems.
12×
Teacher: Go back and forth to patrol the students' questions and ask them how to calculate. What's the difference between these fractional multiplication operations?
After the search, the students raised their hands to answer questions.
The teacher asked the students to answer the questions. (Fraction multiplied by fraction, numerator multiplied by numerator, denominator multiplied, can be divided into preferential points. Fraction multiplied by integer, integer multiplied by numerator, denominator unchanged. )
Second, classroom exercises:
Do the eighth question, let the students understand the meaning of discount in shopping malls, and find out what the scores of an integer are. Such as: =?
Students do the ninth question, pay attention to let students multiply the scores by integers, and find out how many pears, apples and bananas each account for the total number of fruits.
Students do the question 10, and ask them to calculate what fraction of the score is. Pay attention to remind students to make an appointment in time.
Students do the problem 1 1, let them calculate the number of fractional multiplication first, and then learn to compare fractions.
Students do the problem 12, and the teacher pays attention to let the students observe the statistical chart and find out how much more money was added in 2004 than in 2003.
Ask the students to do the problem 13, let them use the knowledge of integer times the score to solve the life problems about the score, and pay attention to remind the students to know the length unit.
Students do the problem 14, and the teacher pays attention to let students use fractional multiplication to solve practical problems in life.
Fourth, the class summary:
Students, what knowledge have you learned in this class? (Ask students to answer)
Blackboard design:
Exercise 1
15× 10 (m) 15- 10=5 (m)
5. Unit Review 9
Teaching objectives
1. Explore and understand the significance of fractional multiplication in operational activities in combination with specific conditions;
2. Explore and master the calculation method of fractional multiplication and calculate it correctly;
3. It can solve the practical problems of simple fractional multiplication and realize the close connection between mathematics and life.
Teaching emphasis and difficulty: be able to calculate fractional multiplication skillfully.
Training points:
Fill in the blanks.
1. Look at the chart.
Addition formula:
? Multiplication formula:
" 1"
2. Fill in the appropriate numbers in the brackets below.
M = () cm min = () sec
Ton = () kg = () g.
3. A crusher 1 hour can crush tons of feed and () tons of feed in one hour.
4.5 meters is 5 meters ().
5. The number A is, the number B is, and the number B is ().
6.× a, when a (), the product is less than, when a (), the product is greater than.
8. fill in the box >,