"Elementary School Mathematics Syllabus" clearly points out: "Practice is an important means for students to master knowledge, form skills and develop intelligence". It is true that our students actively carry out thinking activities under the stimulation of various exercises arranged by us, and then complete their learning tasks, which plays a key role in whether students can really understand the classroom content. The purpose of practice is to acquire knowledge. Designing exercises well has become the focus of mathematics teaching. In order to make classroom exercises really work, teachers need to design unique and effective exercises for the students in this class. Moderately efficient, let students master knowledge and develop their abilities. Only in this way can our students practice more effectively and save time. In the usual teaching, many teachers have misunderstandings about students' knowledge acquisition. First of all, they think that input is directly proportional to output. If a student writes a wrong word, he will be fined ten times. Listening to an open class, a teacher assigned homework (1), 4 hours and 8 kilometers, 1 how many kilometers per hour? (2)6 hours and 3 kilometers, 1 how many kilometers per hour? The first question students quickly made the correct answer of 8 ÷ 4 = 2; The second question is the same as the first one. I didn't think much, so I said it was the wrong answer of 6 ÷ 3 = 2. The second is to form skills, the more the better. From a psychological point of view, people form skills, not the more the better, it has a downward point. For example, in the sixth grade review exam, he took more exams, so he didn't invest. On the contrary, he became worse and worse. Let's imagine: after a new lesson, give students the same type of exercises of 10. If students can do it, doing so much is just mechanical repetition. Why do they have to do so much? If he can't even do one question, what's the point of asking him to do more? Mathematics class should focus on "quality" rather than "quantity"! Why do some students don't need to do a lot of exercises after class, but some students wander in the sea of questions every day, but there is no improvement? The reason is the difference between "quality" and "quantity". Therefore, it is very important to arrange students' exercises scientifically and reasonably. I will talk about some superficial understanding based on my own teaching practice. First, practice should be recalculated. For example, when teaching a two-digit number divided by a one-digit number 42÷3, the teacher can explain the reasoning to the students with a small stick. One bundle for each person (10), and then unpack the bundle before distributing. After understanding natural arithmetic, students can easily accept vertical division. Second, practice should highlight the key points. Mathematics teaching is carried out in units, each unit can be divided into several "knowledge blocks", and several teaching hours of the same "knowledge block" have different emphases or knowledge points. Classroom exercises are designed around the teaching focus of each class. For example, the first two classes teach "two-digit division and written calculation", and the key and difficult point is to try quotient. The exercises before the new course should pave the way for learning the trial commercial law, which can be designed as follows: 1, and the maximum number of words in brackets: 24× () < 89; 2. Estimation: 79× 8 =□, 490× 3 =□. The practice in teaching should help to understand the trial business law. Third, practice should be graded. The exercise design of each class should be designed according to the structural characteristics of knowledge and the cognitive rules of students, so as to make it from shallow to deep, with levels and slopes, one set after another, interlocking. For example, in the teaching of percentage cognition, the following exercises can be designed.
Basic exercise: 7 3 = ()%, 80%= () Fill in decimal places.
Comprehensive exercises: 43%, 0.745% and 7.5% innovative exercises from small to large;
(5 4 -45%)×(40%-4%)
Through the above-mentioned exercises, students can understand and master knowledge in the process of simple application, comprehensive application and innovation, and at the same time take care of the learning level of students at different levels in the class, so that they can all benefit. Fourth, practice should be innovative. It is necessary to train students' thinking and develop their intelligence in multiple ways and angles, which is also an important basis for classroom practice design. To achieve this goal, teachers are required to create innovative situations. 1. Design associative questions to train the agility of students' thinking. Teachers can design exercises by guiding students to make horizontal, vertical and reverse associations. If you see "A is 5/6 of B", let the students think: (1) The ratio of A and B is 5: 6 (horizontally); (2) The ratio of B to A is 6∶5 (reverse); (3)b is 1 1/5 times that of A (horizontally and reversely); (4)a is smaller than B 1/6 (vertical); (5)b is more than A 1/5 (vertical and reverse); (6)a increases its 1/5 to be equal to B (vertical); (7)b reduces its 1/6 to be equal to A (vertical). 2. Design more problems to train students' thinking flexibility. For example, after learning the fractional application problem, the teacher can show the application problem: "Cut a 64-meter-long iron wire by 5/8 of its total length and make 20 square frames with the same circumference. How many boxes can the rest be made? " Ask students to use different methods to solve problems: (1) Use fractions to solve problems: ① 20 ÷ 5/8-20 =12; ②64×( 1-5/8)÷(64×5/8÷20)= 12; ③64 ÷(64×5/8÷20)-20= 12; ④20÷〔5/8÷( 1-5/8)〕= 12; ⑤20÷(5/8÷ 1)-20= 12; ⑥20×〔 ( 1-5/8)÷5/8〕= 12; ⑦20×( 1÷5/8)-20= 12。 (2) Proportional method: assuming that X square frames can be made, 5/8 ∶ 20 = (1-5/8) ∶ x is obtained. (3) Solving by engineering problems: ① (1-5/8) ÷ (5/8 ÷ 20) =12; ② 1÷(5/8÷20)-20= 12。 3. Design changeable questions (or multiple questions) to train students to think in multiple directions. "Ask more questions in one question" and "change more questions in one question" can guide students to observe and analyze problems from multiple angles and levels, communicate the internal relations of knowledge and cultivate creative thinking ability. For example, (1), the cock has 120.
However, the number of hens is 3 1 of that of roosters. How many hens are there? ② The cock has 120.
However, it is 3 1 of the number of hens. How many hens are there? (3) The cock has 120.
However, hens are 3 1 more than cocks. How many hens are there? (4) The cock has 120.
Only 3 1 more than hens. How many hens are there? (5) The cock has 120.
However, hens are 3 1 less than cocks. How many hens are there? (6) The cock has 120.
Only 3 1 less than hens. How many hens are there? (7) The cock has 120.
However, hens are 3 1 more than cocks, and cocks are a few points less than hens. (8) The cock has 120.
However, the cock is 3 1 less than the hen, and how much is the hen more than the cock?
4. Design open exercises to cultivate students' broad thinking. If you fill in the appropriate number () in the following formula, you need to carry it continuously: 235× (). Through observation and trial, students finally get that if they can carry the number 2, they can carry it continuously.