Mathematics Courseware for the Sixth Grade of Primary School Part I: Basic Properties of Ratio
First, create situations and introduce new lessons.
1, ask questions
Teacher: What is the relationship between division, fraction and ratio?
2. Do the review questions. Teacher: What is the basis of your first question? What is its content? What about the second question?
3. Import theme:
We have studied the invariance of quotient and the basic properties of fractions before, and today we learn new knowledge on the basis of these old knowledge. Next, let's learn together. (blackboard title: the basic nature of ratio)
Second, learn new lessons.
1. The basic nature of teaching example 3.
(1) students fill in the form (2) problem: the invariable nature of the connection quotient and the basic nature of the score. Think about these two properties: what are the rules to follow when comparing?
(3) The basic nature of the teacher-student ratio * * * 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.
(4) Teacher: Which word do you think is more important? Except 0. How to understand it?
2. Teaching Example 4 Simplifies the basic nature of application ratio.
We have learned the simplest fractions before. Think about it: what is the simplest score? The simplest integer ratio is that both the former term and the latter term are prime numbers. For example, 9: 8 is the simplest integer ratio.
Show: Turn the following ratio into the simplest integer ratio.
( 1) 12: 18(2)(3) 1.8:0.09
(1) Let the students try to do the problem (1).
Teacher: How did you do it? What is the relationship between 6 and 12 and 18?
Guide students to summarize the method of simplifying integer ratio: divide the front and rear terms of the ratio by their common divisor, so that the front and rear terms of the ratio are prime numbers.
(2) Simplification (2)
Teacher: What are the terms before and after this ratio? (Fraction) We have simplified the integer ratio, so can we use the basic properties of ratio to convert the fractional ratio into the integer ratio first?
(3) Guide the students to summarize the method of simplifying the fraction ratio: (Show the demonstration courseware) Multiply the front and back items of the ratio by the least common multiple of its denominator at the same time, and then convert the fraction ratio into an integer ratio, and then simplify it into the simplest integer ratio.
(4) Simplify (3) 1.8:0.09
Teacher: Think about how to simplify the decimal ratio.
Ask the students to simplify the book independently and say its name.
Teacher: Then, what is the method to change integer ratio, fractional ratio and fractional ratio into the simplest integer ratio by applying the basic properties of ratio?
Third, consolidate the practice.
1. Practice filling in the blanks.
2. Do exercises 13, questions 5-8.
3. Supplementary exercises
choose
1. 1 km: 20km = ()
( 1) 1∶20、(2) 1000∶20、(3)5∶ 1
2. To make the same part, Party A will make 7 parts in 2 hours and Party B will make 10 parts in 3 hours. The work efficiency ratio of Party A and Party B is ().
( 1)20∶2 1、(2)2 1∶20、(3)7∶ 10
Fourth, class summary.
Teacher: What knowledge have you learned through today's study? What is the basic nature of ratio? How to apply the basic properties of ratio to turn integer ratio, fractional ratio and decimal ratio into the simplest integer ratio?
Mathematics Courseware for the Sixth Grade of Primary School Part II: The Basic Nature of Ratio
Teaching content:
Do the contents on pages 50 and 5 1 of the textbook, and practice questions 4-6 of the eleventh question.
Teaching objectives:
1, master the basic properties of the ratio, and simplify the ratio according to the basic properties of the ratio.
2. The invariable nature of the connection quotient and the basic nature of the fraction are transferred to the basic nature of the ratio.
Teaching focus:
Basic properties of comprehension rate.
Teaching difficulties:
The basic properties of ratio can be applied to simplify the ratio.
Teaching process:
First, exciting calibration.
1、20÷5=(20× 10)÷(×)=()
2. We studied the invariable law of quotient, the basic properties of fraction, and the relationship between connection ratio and division and fraction. Think about it: what kind of laws are there in the proportion? We will study this problem in this class.
Second, self-study interaction, timely inspiration
Basic properties of activity ratio
Learning style: group cooperation, report and exchange.
learning tasks
1, inspired and induced, found the problem: 6: 8 and 12: 16 are different, but their ratio is the same. What is the law? .
6:8=6÷8=6/8=3/4、 12: 16= 12÷ 16= 12/ 16=3/4
2. Observe and compare, and find the law.
(1) Use the relationship between ratio and division to study the law of ratio. (Law of Constant Quotient)
(2) Using the relationship between ratio and score to study the law of ratio.
3. Summarize the law of induction.
(1) Summary: The first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is called the basic property of the ratio.
(2) Question: Why should the "same number" here emphasize the exception of 0?
Activity-based simplified ratio
Learning style: try to train, report and communicate.
learning tasks
1, know the simplest integer ratio.
(1) Question: Who knows what kind of ratio can be called the simplest integer ratio?
(2) Induction: The simplest integer ratio must meet two conditions. One is that the front and rear terms of the ratio are integers, and the other is that the common factor of the front and rear terms of the ratio is only 1.
(3) Point out several simplest integer ratios.
2. Use nature and master the method of simplification.
(1) Write down the aspect ratio of two United Nations flags.
(2) Thinking: Are these two ratios the simplest integer ratio? Why? (There are other common factors besides 1 before and after the term. )
(3) try to simplify.
(4) Reporting communication: Just divide the front and back terms of the ratio by their common factors.
(5) think about it: these two are the same after simplification. What does this mean? The two flags are different in size and the same in shape.
(6) Show examples and organize exchanges.
① Least common multiple of denominator:1/6: 2/9 = (1/6×18): (2/9×18) = 3: 4.
(2) First, the front and back terms are converted into integers, and then simplified as: 0.75: 2 = (0.75×100): (2×100) = 75: 200 = 3: 8.
③ Calculated by fractional division:1/6÷ 2/9 =1/6× 2/9 = 3/4.
(7) Abstract: If both the front and rear terms of a ratio are fractions, then multiply the front and rear terms by the least common multiple of the denominator at the same time; If the front and back terms of a ratio are decimals, praise them first, and then simplify them.
Third, the standard evaluation
1. Complete the "doing" on page 5 1 of the textbook and make collective revision.
2. Complete questions 2, 4, 5 and 6 of exercise 1 1 on page 52 of the textbook.
Fourth, class summary.
What did we learn in this class? What did you get?