Introduction: Several typical wrong questions in primary school mathematics are sorted out by this year's graduate training network. Thank you for reading.
First, the concept is not clear.
(1) calculation problem
500? 25? 4 34- 16+ 14
=500? (25? 4) =34? 30
=500? 100 =4
=5
Error rate: 46.43%; 35.7 1%;
Cause analysis of wrong questions:
I have learned the rules of simple operations, but I still don't quite understand them. Students misuse the rules. When they see the problem and are disturbed by numbers, they only think about rounding, ignoring whether the simple method is feasible in these two problems. For example, students with 1 questions count 25 first? 4 equals100; The second problem is that 16+ 14 is equal to 30; Therefore, the operation order is changed and the calculation result is wrong.
Countermeasures to solve wrong problems:
(1) makes it clear that in the mixed operation of multiplication, division or addition and subtraction, if there is no simple operation factor, it should be calculated from left to right.
(2) Emphasize the calculation steps of mixed operation: a, carefully observe the topic; B clear calculation method: it can be calculated simply and conveniently, but not simply and correctly. And can tell the operation sequence. (3) On the basis of understanding the operation rules and four operation sequences, strengthen practice to achieve the goal.
Corresponding exercises:
14.4-4.4? 0.5; 7.5? 1.25? 8; 36.4-7.2+2.8;
(2) True or False
1, 3/ 100 ton =3% ton (? )
Error rate: 7 1.43%
Cause analysis of wrong questions:
What is the percentage? A number that represents the percentage of one number to another. ? It can only represent the multiple relationship between two numbers, not a specific quantity. It is precisely because students lack a correct understanding of the meaning of percentage that they make a wrong judgment on this issue.
Countermeasures to solve wrong problems:
(1) Make clear the difference between percentage and score; Understand the meaning of percentage.
(2) Find out where you have seen it in your life, so as to further understand the meaning of percentage.
2. Two rays can form an angle. ? ( ? )
Error rate: 64.29%
Cause analysis of wrong questions:
An angle consists of a vertex and two straight sides. Students don't understand the concept of diagonal correctly. Another reason is that the questions are not carefully examined and there is no in-depth thinking. When you see two rays, you think you can form an angle, regardless of the vertex!
Wrong problem solving strategy:
(1) Give a counterexample according to the meaning of the question to let students know that there is another necessary condition for forming an angle, that is, there is a vertex.
(2) The concept of recall angle. Emphasize two necessary conditions for forming an angle: a vertex and two rays.
(3) Educate students to carefully examine questions before doing them, whether they are simple questions or difficult questions, and never take them lightly.
(3) Fill in the blanks
1, the side length ratio of the two cubes is 1: 3, and the surface area ratio of the two cubes is (1:3); The volume ratio is (1: 5 or 1: 9).
Error rate: 42.86%; 35.7 1%
Cause analysis of wrong questions:
This topic is a part of comparative application. The purpose is to test students' ability to calculate the ratio of surface area to volume according to the side length ratio of a cube. Therefore, the calculation formula of cube surface area and volume is the key. Some students forget the calculation method of the surface area and volume of a cube, and some don't understand the significance of comparison, thinking that the surface area ratio and the side length ratio are the same, which leads to mistakes.
Wrong problem solving strategy:
(1) Consolidate the meaning of understanding ratio and the method of finding ratio.
(2) Define the calculation method of cube surface area and volume.
(3) Practice with similar questions to further consolidate the application of contrast.
Corresponding exercises:
The radius ratio of big circle to small circle is 3: 2, and the diameter ratio of big circle to small circle is (3:2). The ratio of the circumference of the big circle to the small circle is (3 ∶ 2); The area ratio of the big circle to the small circle is 9:4.
2. The height of a cylinder is constant, and the radius of its bottom is proportional to its volume.
Error rate: 78.57%
Cause analysis of wrong questions:
This topic is the content of direct proportion and inverse proportion. The main reason why students make mistakes is that they don't have a good understanding and grasp of the meaning of positive proportion and negative proportion, so they can't judge. There are also some' because they mistake the two variables of bottom radius and volume for bottom area and volume, which leads to the mistake of the problem.
Wrong problem solving strategy:
(1) Define the meaning and judgment method of proportion. Two related quantities, one of which changes with the other, and in the process of change, the ratio of these two quantities is certain, so these two quantities are called proportional quantities; If the product of two quantities is constant, these two quantities are called inverse proportional quantities.
(2) Ask students to list the formula for calculating the volume of a cylinder, and find out the relationship between the radius of the bottom surface and the volume at a certain height according to the meaning of the question, so as to clarify the proportional relationship between them.
(3) Strengthen exercises with similar topics to achieve the goal.
Corresponding exercises:
The circumference of a circle is proportional to its radius.
3. Put 10g salt into 10g water, and the salt content of the brine is (10)%.
Error rate: 7 1.43%
Cause analysis of wrong questions:
Some students are right? Salt content? I don't understand this concept, so I don't know how to calculate it, which leads to mistakes. Some students are careless. The numbers of 10g of salt and100g of water in the topic can easily make those careless students get the wrong answer of 10% at once.
Wrong problem solving strategy:
(1) Understand the meaning of salt content. Combine the concepts of qualified rate and survival rate to further understand.
(2) Combined with sugar content, qualified rate, attendance rate and other issues, strengthen practice to achieve the goal. (3) Educate students to form the habit of carefully examining and thinking before doing the questions.
Corresponding exercises:
On the day of Value Tree Festival, a total of 104 trees were planted in the fifth grade, of which 8 trees did not survive. The survival rate of these trees is 92.3 1%.
4. The number of class A is 2/5 more than that of class B, and the number of class B is less than that of class A (2/5 or 3/5).
Error rate: 60.71%;
Cause analysis of wrong questions:
The student confuse 25, which represents a specific quantity, with 25, which represent multiples. Think that the number of people in class A is 2/5 more than that in class B, that is, the number of people in class B is 2/5 less than that in class A. You can't tell the number from the multiple. And take the number of class a as a unit in the future? 1? In the future, take the number of class B as the unit? 1? The concept is unclear.
Wrong problem solving strategy:
(1) Distinguish between quantity and multiple.
(2) Draw a line graph and build an intuitive and vivid model to help you understand.
(3) clearly take the number of Class B as a unit? 1? So the number of students in Class A is: (1+2/5)=7/5. So the number of people in class B is 2/5 less than that in class A? 7/5=2/7。
(4) Strengthen exercises with similar topics to achieve the goal.
Corresponding exercises:
The number of A is less than that of B 1/4, and the number of B is more than A 1/3. ..
Judgment: pile A is heavier than pile B 1/3 tons, and coal B is lighter than pile A 1/3 tons ... ( ? )
5. Divide a 5/6m rope into five sections on average, with each section accounting for (1/6) of the total length and each section being (1/6) long.
Error rate: 52%; 50%;
Cause analysis of wrong questions:
The relationship between each segment and the total length is between 1 and 5, that is, each segment accounts for1/5,5/6 of the total length? 5 = 1/6m, and the length of each segment is 1/6m. This question examines the understanding of the meaning of fractions and the application of fractional division, but students do not understand and master it. So I confused the two answers, because I couldn't tell the meaning of the two questions. Generally, this kind of topic will write the unit after the last bracket. However, in order to check the students' carefulness, the unit did not write, so some people who could have done it were wrong because of carelessness.
Wrong problem solving strategy:
(1) Understand the meaning of the score; Make clear the respective meanings of the two questions.
(2) Educate students to form the habit of carefully examining and thinking before doing the questions.
(3) On the basis of understanding the meaning of the score, strengthen the practice to achieve the goal.
Corresponding exercises:
Judgment: There are 4/5 tons of coal to be burned for 4 days, with an average of 1/5 per day. ? ( ? )。
Second, the negative transfer of knowledge
(1) calculation problem
0.9+0. 1-0.9+0. 1 = 1? 1 =0
Error rate: 28.57%
Cause analysis of wrong questions:
As soon as students see examples, they will think of A? b-c？ The topic in the form of D confuses the law and only thinks about rounding, but ignores the simple feasibility. Thus, the operation rules are changed and the calculation results are wrong.
Wrong problem solving strategy:
(1) makes it clear that if there is no simple operation factor, it should be calculated from left to right.
(2) Emphasize the calculation steps of mixed operation: a, carefully observe the topic; B clear calculation method: it can be calculated simply and conveniently, but not simply and correctly. And can tell the operation sequence.
(3) On the basis of understanding the operation rules and four operation sequences, strengthen practice to achieve the goal. Corresponding exercises:
1/4? 4? 1/4? 4; 527? 50? 527? 50;
(2) Multiple choice questions
400? 18=224. If both the dividend and divisor are enlarged by 100 times, the result is (a) the quotient of 22+4b, the quotient of 22+400, and the quotient of 2200+400.
Error rate: 64.28%
Cause analysis of wrong questions:
This topic examines the knowledge related to the invariance of quotient. After the dividend and divisor are expanded by 100 times, the quotient remains unchanged, but the remainder is also expanded by 100 times. To get the original remainder, you need to reduce 100 times. Students mistakenly think that the quotient remains unchanged and choose the wrong A. The correct answer should be B.
Wrong problem solving strategy:
(1) checking calculation. Ask the students to use the quotient multiplier of answer A plus the remainder to check whether it is equal to the dividend, and find that choosing A is wrong.
(2) Clarify the essence of quotient invariance. But when the dividend and divisor are enlarged by 100 times, the quotient remains unchanged, but the remainder is also enlarged by 100 times. To get the original remainder, you need to reduce 100 times.
(3) On the basis of understanding the knowledge about business invariance, strengthen practice to achieve the goal.
Corresponding exercises:
Multiple choice questions: 2.5 divided by 1.5, the quotient is 1, and the remainder is (d).
a . 10 b . 0.0 1 c . 0. 1d . 1
(3) Fill in the blanks
Add 8 to the numerator of 4/ 1 1 and add (8) to the denominator to keep the size of the fraction unchanged.
Error rate: 2 1.4%
Cause analysis of wrong questions:
Because students misunderstand the basic nature of fractions, the method of multiplying the same number and adding the same number at the same time confuses the numerator and denominator, and mistakenly thinks that the numerator should also add 8.
Wrong problem solving strategy:
(1) Ask the students to match 4/ 1 1 with the answer 12/ 19.
Comparing the size, I found that the size of the score has changed, which caused me to think.
(2) Understand the basic nature of the score. The numerator and denominator of a fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
(3) Strengthen exercises with similar topics to achieve the goal.
Corresponding exercises:
Add 12 to the denominator of 2/3, and add (8) to the numerator to keep the size of the fraction unchanged.
Third, carelessness.
1, calculation problem
7? 7/9-7/9? 7 = 1- 1 =0
Error rate: 39.28%
Cause analysis of wrong questions:
This question is four operations to examine students' grades. There are two numbers in the two division formulas, 7 and 7/9. Because of carelessness, they will be considered equal in quotient. So wait until? 1- 1=0? Wrong answer.
Wrong problem solving strategy:
Educate students to carefully examine the questions before doing them, think more about simple questions and difficult questions, and never take them lightly.
Step 2 fill in the blanks
The hour hand of the clock is 3 cm long, and its tip went away in one day and night (18.84 cm).
Error rate: 67.85%
Cause analysis of wrong questions:
This problem is the content of "circle". Students know that this problem should be solved with the knowledge of finding the circle. But right? A day and a night? I didn't understand this word, and I didn't check it carefully. I only calculated the circumference of an hour hand, which eventually led to the wrong result.
Wrong problem solving strategy:
Please read the question carefully and explain? A day and a night? Meaning of.
(2) Make a request: carefully examine the topic and understand the topic before doing it.
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