The teaching goal of the courseware 1 of Understanding Mathematical Proportion, the first volume of the sixth grade;
1, so that students can understand the meaning of ratio in specific situations, master the reading and writing methods of ratio, know the names of each part of ratio and find the ratio.
2. Make students experience the process of exploring the relationship between ratio, fraction and division, understand the relationship between ratio and fraction and division, and rewrite the ratio into the form of the number of parts.
3. Make students cultivate the ability of analysis, synthesis, abstraction and generalization in activities, and experience the connection between mathematics and life and the fun of mathematics learning in the process of solving practical problems.
Teaching process:
Think about it, how do we get the speed of two people?
(2) Understand the meaning of the ratio 1. We drew a lot of comparisons just now. Look carefully at the ratios in Example 2: 900 15, 900/20, 2/3, 3/2 in Example 1, and so on. Do you think the ratio can represent the relationship between two numbers? 2. The teacher guides students according to their answers: the ratio in example 1 represents the multiple relationship between two numbers, and the ratio in example 2 represents the distance ÷ time. Whether it is the example 1, the example 2 or the actual ratio, it represents the division of two numbers. So what does the ratio of two numbers mean? (blackboard writing: a division relationship)
(3) Understand "ratio" and the difference between "ratio":
1, the meaning of the ratio is very clear, let's calculate together, what is the quotient of the previous term divided by the later term of the above ratio?
We call the quotient obtained by dividing the former term of the ratio by the latter term as the ratio.
2. What do these ratios mean?
3. Discussion: What do students think is the difference between ratio and ratio?
(The ratio refers to the division of two numbers, which consists of the former item, the comparison symbol and the latter item. This ratio represents the quotient obtained by dividing the former term by the latter term. The ratio is a number, which can be a fraction, decimal or integer. )
(4) "Give it a try"
1, complete the "try it": (students finish it independently, board name) 2. Teacher: According to the relationship between fraction and division, the ratio of two numbers can also be written as a fraction. For example, in addition to this form, 2: 3 can also be written as a fraction ratio: 3/2. (Blackboard: 3/2) Note that it should be regarded as a ratio, not a fraction, so write the first paragraph of the ratio first, then write a horizontal line to indicate the ratio, and finally write the last item, or should it be read as 3 to 2. )
(5) Relationship among ratio, division and score 1. Ask students to draw the relationship between ratio, fraction and division through observation, comparison and communication: are the symbols and ratios of the previous term, the latter term and the ratio equivalent to the division formula or fraction respectively? Can the last term of the ratio be 0? (Fill in the form according to the student report) The correlation difference is less than the proportional division score of the previous item 1, and complete the "exercise" 1, 2,3.
3. Complete question 4 of exercise 13.
4. Sweetness of sugar water (1) (show two cups of sugar water and mark the mass ratio of sugar water, the first cup is 1: 20 and the second cup is 1: 25). Do you know which glass of water is sweeter Why?
(2) (Show the third cup of sugar water, marked with 4g sugar and water 100g. Do you know that this sugar water is as sweet as that one just now? Think first, and then communicate with your deskmate. How do you compare?
(3) According to the mass ratio of the first cup of sugar and water 1∶20, can you tell the mass ratio of the first cup of sugar and syrup?
5, knowledge introduction:
Students, in fact, metaphor is widely used in our lives. Have you ever heard of the famous "golden ratio"? The courseware introduces the "golden ratio".
Verb (abbreviation of verb) summary:
What did we learn today? Did you get anything? Is there a problem?
(2) First, provide examples and feel the significance of comparison.
Situation 1: Which photos are similar?
Teacher: (Projection shows naughty photos a) This is our familiar friend-naughty. Grandpa Wisdom took some photos for him. (Show B, C, D, E) Look at the picture carefully. Which ones are more like Figure A?
Student observation chart. Think and answer.
It may be answered like this: Figure C is not like Figure E, one is getting fatter and the other is getting thinner.
Figure b and d, one is big and the other is small.
If this happens, the teacher will guide again: can you speak in the language of likeness, dissimilarity and deformity? Student: … Teacher: Pictures B, C, D and E are all rectangles. Why BD is as deformed as CE? Can you guess the reason? Student: …… Teacher: Let's study together. What is the relationship between the length and width of these rectangles?
Please take out the grid diagram, and we will draw it on the grid paper according to the shape of five diagrams. Please observe each rectangle carefully, fill in and compare, and talk about your findings in the group. Group activities, teachers patrol. Organize communication.
The length of the three rectangles 1 and ABD are all 1.5 times the width, and the width is two thirds of the length. And CE is not. 2. the length and width of d are twice that of a, and the length and width of a are twice that of b. Teacher: (Summary) There is a certain multiple relationship between the length and width of ABD's three rectangles. Can you classify these figures according to what we have just found?
Situation 2: Who is faster?
In life, we will also encounter such a problem: projection display: Teacher: What mathematical information do you get from the picture? Can you solve this problem? Please open page 49 of the book, fill in the form and answer the results orally. Organize communication.
Situation 3: Which booth is the cheapest to sell apples?
Teacher: Let's look at another problem: show the situation and talk about the obtained mathematical information and the solution to the problem. Fill in Form (2). Students complete and communicate independently.
Contact Scenario 2 and Scenario 3.
Teacher: Do you know the speed and unit price in your own words?
[Speed = Distance/Time Unit Price = Total Price/Quantity]
Second, recognize the teacher: As mentioned above, the division of two numbers (blackboard writing) is also called the ratio of two numbers.
For example, 6/4, write 6: 4 and read 6 to 4. 6 is the first term of this ratio, 4 is the last term, and 1.5 is the ratio of this ratio.
Read it. Write it. (Exercise 5 1 Page 1. Third, practice. (Exercise 5 1 Page 2. ) 4. Say and summarize the class.
We met Debbie today. Tell us what you have learned.
What other examples are there in life? What's the new problem?
(3) Teaching objectives:
1, understand the meaning of ratio, learn the reading and writing methods of ratio, master the names of each part of ratio and the methods of finding ratio.
2. Understand the relationship between ratio, division and fraction. The latter term of the ratio cannot be 0, and understand that things are interrelated.
3. Further cultivate students' abilities of analysis, comparison, induction and generalization, and autonomous learning.
Teaching emphasis: understand the meaning of ratio and the relationship between ratio and fraction and division.
Teaching difficulty: the meaning of understanding rate;
Meaning of ratio:
Q: Who will tell the teacher the number of people in our class?
How many boys are there? How many girls are there? (Blackboard) If we compare the number of boys and girls in our class together, what conclusion can we draw?
Are there fewer boys than girls?
Can it be expressed in a formula?
Blackboard: Use subtraction. What conclusion can be drawn from this formula?
There are more girls than boys. Q: Can you think of any other comparison methods besides subtraction?
What can be calculated?
Blackboard: What is the number of boys compared with the number of girls? How many times are there girls than boys?
Can you write formulas?
19/2727/ 19 Description: When two quantities are compared by division like this, there is a new representation: ratio. Q: How many girls are there than boys? Which quantity is compared with which quantity?
The number of boys like this is a fraction of the number of girls. It can be said that the ratio of male to female is 19 to 27. Who can say, how can I say that the number of boys is a fraction of that of girls? (student repeats) Please have a look again. How many times are there girls than boys? Which quantity is compared with which quantity?
Think about it according to the above example. How can we say that the number of girls is several times that of boys?
27 to 19 From the above example, we know that who is several times or a fraction of who, which can be said to be the ratio of who to whom.
2. Comparison of different categories: In daily life, there are many examples of comparing two quantities. Such as a car driving on the road.
Demonstration: A car travels 90 kilometers in 2 hours.
What can you work out?
That is, the speed. Formula: 90/2 = 45 (km) Look, students, which two quantities are actually used to compare vehicle speeds?
Then who can compare the speed with who?
Instructor: The speed of the car can also be said to be the ratio of distance to time is 90 to 2. In the common quantitative relationship, because the unit price = total price/quantity, the unit price can be said to be the ratio of who to whom.
Work efficiency can be said to be the ratio of who to whom.
3. Reveal the meaning of ratio:
What are the similarities between these examples in presentation?
Are all calculated by division. What is the ratio of who to whom?
So, what is the relationship between these two numbers?
When comparing two numbers with division relationship, they can all be said to be the ratio of the two numbers.
5/8 can be said to be the ratio of who to whom. 15/26?
4. Feedback exercise:
Show me a national flag. The length is 5 decimeters and the width is 3 decimeters.
Based on the above information, what comparison can you make?
Second, self-study other knowledge of comparison Through the above study, students have understood the significance of comparison. On pages 52-53 of the textbook, some other knowledge about comparison is also involved. Can you solve it yourself?
Students teach themselves for 3 minutes. Who will report it? What do you know about competition through reading and self-study?
Students can report from the following aspects: (out of order) What do you want to remind everyone when writing the names of each part?
Name the first and last item of each ratio below and find out the ratio.
14:2 15/9 0。 5:2。 52/9: 1/3 proportional decimal writing.
Rewrite the following ratios into component forms.
The relationship between the ratio of 25:10021:18 and division and fraction.
List the relationship between the three to guide students: Is there a limit to the latter term of the ratio? Why can't it be 0?
Why is there a 2:0 writing in the football match?
Just now we talked about the relationship between ratio, fraction and division. What's the difference between the three?
Let the students discuss.
Summary: ratio is the relationship between the division of two numbers; The score is a number; Division is an action.
Third, consolidate the exercises:
It seems that the effect of students' self-study is very good. There are still a few small problems that teachers need to help solve.
1, fill in the blanks:
Xiaohua has 12 chickens and 9 ducks.
The ratio of chickens to ducks is, and the ratio is.
The ratio of the number of ducks to chickens is.
I bought 3 Jin of apples and used 7.5 yuan.
The ratio of the total price to the quantity of apples is.
The understanding of mathematical ratio in the first volume of the sixth grade courseware 2 (1) The basic concept of ratio.
1. The division of two numbers is also called the ratio of two numbers. The quotient obtained by dividing the former term by the latter term is called the ratio.
2. Ratios are usually expressed by fractions, decimals and integers.
3. The last item of the ratio cannot be 0.
4. Compared with division, the former term of ratio is equivalent to dividend, the latter term is equivalent to divisor, and the ratio is equivalent to quotient;
5. According to the relationship between fraction and division, the former term of ratio is equivalent to numerator, the latter term is equivalent to denominator, and the ratio is equivalent to the value of fraction.
6. The basic nature of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
(2) Find the ratio
Find the ratio: divide the former term of the ratio by the latter term of the ratio.
(3) Simplify the ratio
Simplify the ratio: divide the former term of the ratio by the latter term of the ratio to find the ratio of the fraction, and then change the ratio of the fraction into the ratio.
(D) the application of the ratio
The first application of 1 Ratio: the sum of two or more quantities and the ratio of these two or more quantities are known. What are these two or these two quantities?
For example, there are 60 students in the sixth grade, and the ratio of male to female is 5: 7. How many boys and girls are there?
Topic analysis: 60 people are the sum of the number of boys and girls.
Think about solving problems:
The first step is to find each copy: 60÷(5+7)=5 people.
Step 2, find boys and girls: boys: 5×5=25, girls: 5×7=35.
2. The second application of the ratio: knowing the number of one, the ratio of two or more numbers, what are the other numbers?
For example, there are 25 boys in the sixth grade, and the ratio of boys to girls is 5: 7. How many girls are there? How many people are there in the class?
Topic analysis: 25 Boys is one of them.
Think about solving problems:
The first step, each request: 25÷5=5 people.
The second step is to find girls: girls: 5×7=35 people. Class: 25+35=60 people
3. The third application of ratio: knowing the difference between two quantities and the ratio of two or more numbers, what are these two or more quantities?
For example, in the sixth grade, there are 20 more boys than girls (or 20 fewer girls than boys), and the ratio of boys to girls is 7: 5. How many boys and girls are there? How many people are there in the class?
4. Demand quantity = known quantity × demand quantity/known quantity.
5. The application of ratio in geometry;
(1) Given the circumference of a rectangle, the length-width ratio is a: b, and the length, width and area are found.
Length = perimeter ÷2×a/(a+b)
Width = perimeter ÷2×b/(a+b)
Area = length × width
(2) Given the ratio of the side length to the length, width and height of a cuboid A: B: C, find the length, width, height and volume.
Length = perimeter ÷4×a/(a+b+c)
Width = perimeter ÷4×b/(a+b+c)
Height = perimeter ÷4×c/(a+b+c)
Volume = length× width× height
(3) Given the ratio of three angles of a triangle as A: B: C, find the degrees of three inner angles. These three angles are:
180×a/(a+b+c)
180×b/(a+b+c)
180×c/(a+b+c)
(4) Given the perimeter of a triangle, the length ratio of the three sides is A: B: C, and find the length of the three sides. These three aspects are:
Circumference ×a/(a+b+c)
Circumference ×b/(a+b+c)
Circumference ×c/(a+b+c)
Xiaoshengchu is an important turning point for children in primary school. The above is the understanding of the proportion of mathematics knowledge points in Xiaoshengchu. I hope these can provide some help to the students who are preparing for junior high school on 20 17. I wish them excellent results in the 20 17 junior high school entrance examination!