The design of exercises must be considered from two aspects: the content of teaching materials and the basis of students, and overcome subjectivism and formalism that are not based on objective reality, so as to be targeted. The degree and quantity of practice should also be determined according to the needs of different students. For example, if the teaching division is fractional division, its main task is to convert the divisor into an integer, and the dividend will move the position of the decimal point accordingly, and then calculate according to the calculation rule of fractional division in which the divisor is an integer. Its teaching focuses on "seeing" (seeing how many decimal places the divisor is) and "moving" (moving the decimal point of the divisor to make the divisor an integer, and then moving the decimal point position of the dividend accordingly). In view of this, I only designed vertical exercises without calculation: 0.28÷0.7, 2.8÷0.07, 28÷0. 14, 0.208÷ 1.04. After these problems are solved, future exercises will be easy. For example, in the teaching of practical problems, the focus is on the understanding of the quantitative relationship of practical problems. In practice, we can design some practical problems that only calculate formulas, and focus on analyzing the problem-solving ideas.

Second, there should be interesting design exercises.

Pupils' fascination with mathematics often begins with interest, from interest to exploration, from exploration to success, generating new interest in successful experience and promoting the continuous success of mathematics learning. However, the abstractness and rigor of mathematics often make them feel boring. In order to make students realize that mathematics is so vivid, interesting and charming in mathematics learning activities, it is very important to strengthen their interest in mathematics practice. Therefore, when designing exercises, properly compiling some interesting exercises can make teaching entertaining, reduce the psychological burden of students' exercises and improve the efficiency of exercises. For example, when learning the lesson of prime numbers and composite numbers in the fifth grade of primary school, this lesson is an abstract and boring concept teaching. In order to prevent students from being tired of learning, I carefully designed the following exercises: in 1-20, there are _ _ odd numbers, _ _ even numbers, _ _ composite numbers and _ _ prime numbers. This exercise allows students to complete it independently. But I didn't stop there, and then I said, "Did you find anything?" If you let the students finish it alone, you may not get any conclusion, so my design intention is to let the students discuss it in groups. Sure enough, after group discussion, many conclusions were drawn. For example, prime numbers are not all odd numbers; The number of combinations is not necessarily even, which not only changes the types of questions, but also reflects the characteristics of individual and group combinations.

Thirdly, there should be various design exercises.

The design of classroom exercises pursues the diversification of questions and practice methods, which can make students learn actively, actively, solidly, interestingly and flexibly. Turn the simple mechanical copying and problem-solving practice into the practice of participating in activities with your head, mouth, hands and other senses. Question types can include oral calculation exercises, pen calculation exercises, application exercises, selection exercises, judgment exercises, comprehensive exercises, operation exercises, competition exercises, game exercises and so on. Let students not only do it, but also use their mouths and brains. Moreover, students can practice in groups, independently or in groups. For example, in the classroom practice of teaching multiplication formula and using formula to find quotient, the following exercises can be designed to integrate knowledge into the game. In this way, the effect of unconscious memorization is often more labor-saving than rote memorization.

1.

Yes, the password. That is to say, write out the first parts of four or five multiplication formulas and label them. Divide the class into two lines facing each other. Draw a mark on each line. One says and the other answers.

2.

Turn the turntable. Make two concentric circles with cardboard, write the number 1-9 on the inner and outer circles respectively, make a circle to align the inner and outer numbers, say the product of every two numbers, and calculate the number of 9 per turn.

3.

Guess the card. Write a card before the activity. Such as 72, 45, 24, 56, 363, etc. After each student draws a card, he says that the number on the card is the product of several times.

4.

Catch the red flag. The teacher writes the formula first, then writes the product in groups. Finish the calculation first and then see which group wins the red flag.

The above game practice methods can greatly improve students' proficiency and interest in oral arithmetic, and liberate them from a large number of copying assignments.

Fourth, there should be hierarchical design exercises.

Students exist as concrete living individuals. When designing questions, we must clearly affirm the individual particularity of students' cognitive activities and face up to their differences in existing knowledge and learning motivation, so the design questions must be hierarchical. The so-called hierarchy means that there are all kinds of small problems in the problem, some of which are shallow, medium and difficult to meet the needs of students at all levels. This has formed a series of problem chains. Shallow memory problems can be used for simple mechanical imitation, deep problems can be used for mastering and consolidating new knowledge, and high-level problems can be used to guide students' knowledge transfer and application. Topic arrangement can be from easy to difficult, forming a gradient. Although the starting point is low, the final requirement is higher, which conforms to the cognitive law of students, so that students with average grades can correctly answer most exercises, and students with excellent grades can also do more difficult exploratory exercises, so that all students can be improved to varying degrees. Teachers should design different types and levels of exercises, from basic imitation exercises to improved variant exercises, and then to expanding thinking exercises, changing the slope of exercises, and at the same time not sticking to books, encouraging students with innovative ideas. Take care of students at different levels, so that students at different levels can experience the opportunity of success and maintain their enthusiasm for learning.

The design of exercises should follow the development order from easy to difficult, from simple to complex, from basic to variant, from low to advanced, so that students at different levels can have a successful, happy and enjoyable experience after studying hard, and make students learn more actively. For example, when teaching the commutative law and associative law of addition in the fourth grade of primary school mathematics, a set of exercises with strong hierarchy is designed: the first level (basic problems, similar examples) simply calculates the following questions: 15+264+25, 36+25+64+25. The second level (variant questions, slightly changed from the examples) and the third level (comprehensive questions, where new knowledge is properly combined with old knowledge) can be simply calculated as follows: (96+49)+ 15 1, (92+58)+(45+100.