1 .10 times 10:
Formula: head joint, tail to tail, tail to tail.
For example: 12× 14=?
Solution: 1× 1= 1.
2+4=6
2×4=8
12× 14= 168
Note: Numbers are multiplied. If two digits are not enough, use 0 to occupy the space.
2. The heads are the same and the tails are complementary (the sum of the tails is equal to 10):
Formula: After a head is added with 1, the head is multiplied by the head and the tail is multiplied by the tail.
For example: 23×27=?
Solution: 2+ 1 = 3
2×3=6
3×7=2 1
23×27=62 1
Note: Numbers are multiplied. If two digits are not enough, use 0 to occupy the space.
3. The first multiplier is complementary and the other multiplier has the same number:
Formula: After a head is added with 1, the head is multiplied by the head and the tail is multiplied by the tail.
For example: 37×44=?
Solution: 3+ 1=4
4×4= 16
7×4=28
37×44= 1628
Note: Numbers are multiplied. If two digits are not enough, use 0 to occupy the space.
4. Eleven times eleven:
Formula: head joint, head joint, tail to tail.
For example: 2 1×4 1=?
Answer: 2×4=8
2+4=6
1× 1= 1
2 1×4 1=86 1
5. 1 1 times any number:
Formula: head and tail do not move down, middle and pull down.
For example: 1 1×23 125=?
Answer: 2+3=5
3+ 1=4
1+2=3
2+5=7
2 and 5 are at the beginning and end respectively.
1 1×23 125=254375
Note: If you add up to ten, you will get one.
6. Multiply a dozen by any number:
Formula: The first digit of the second multiplier does not drop, the single digit of the first factor multiplies each digit after the second factor, and then drops.
For example: 13×326=?
Solution: 13 bit is 3.
3×3+2= 1 1
3×2+6= 12
3×6= 18
13×326=4238
Note: If you add up to ten, you will get one.
Recently, I started the final review of simple calculation. I made a pre-test before class, and less than half of the students in the class answered all the questions correctly. The problem is more serious. I carefully analyzed the reasons and summarized the following reasons and solutions.
First, understanding the laws and properties of operations is the premise of learning simple operations.
Many simple operations are the result of fully and reasonably applying the algorithms and properties. If students don't really understand the law and nature of operation, they can only draw a gourd ladle. In the process of solving problems, students' thinking is not clear, and they often make mistakes of one kind or another. Therefore, teachers should pay attention to guide students to discover the characteristics of various operation laws and properties, help students build corresponding knowledge systems, enable students to firmly grasp the operation laws and properties, and provide theoretical support for simple operations.
Error example1:378-146-104
=378-( 146- 104)
=378-42
=336
error analysis
The nature of subtraction is an important theoretical basis for simple operations in primary mathematics. This classmate's original intention is to use the nature of subtraction to make the calculation simple. Because of the incomplete understanding of the essence of subtraction, the calculation is wrong.
Solution strategy
Understanding the laws and properties of operations is the premise of learning simple operations. If students don't really understand the essence and laws of operation, they will only imitate examples to solve problems. Once there are no examples to refer to or imitate, students' thinking of solving problems is unclear and easy to make mistakes. Therefore, the teacher must first explain to the students these operational laws and operational properties.
Second, the flexibility of thinking is the soul of simple operation.
Simple operation breaks through the original operation order of the formula to some extent, and reorganizes the operation order according to the operation law and nature. Therefore, it is particularly important to cultivate the flexibility of students' thinking. It is necessary to cultivate students' keen observation and be good at discovering the characteristics of numbers and their previous connections. In teaching, we should strengthen targeted oral arithmetic exercises, such as multiplying the product of 125 and 25 by even numbers respectively, and adding two numbers that can be rounded up to improve students' ability to find simple calculation conditions. Second, make students develop forward thinking and backward thinking synchronously, and apply the algorithm forward and backward. Such as multiplication and distribution.
Error Example 2: 25× 97+75
=(25+75)×97
= 100×97
=9700
error analysis
The above phenomenon is more common in simple calculation, especially for those students who have difficulties in learning, because in their view, after learning simple calculation, all operations can be simple, and when they encounter an operation problem that cannot be simple, they will have a vague impression in their minds and do it at will. This phenomenon is the most common in mathematics learning, which is caused by the fixed role of thinking or the negative transfer of knowledge. This is closely related to our usual teaching. For example, after learning the double-digit additive commutative law, all the exercises are like this. For example, after learning the nature of subtraction, all the exercises are also the nature of subtraction. This practice can help students to consolidate their knowledge in time, which is conducive to the formation and proficiency of students' computing skills, but the disadvantage is that it is easy to form a stereotype, that is, to do whatever you learn without thinking.
Solution strategy
Because of its outstanding and simple characteristics, simple calculation is easy for us to focus on it, thinking that students can complete the teaching task by using the algorithm to do simple calculation. This view is not comprehensive. Simple calculation is part of the four calculations. Therefore, the teaching of simple calculation should be based on the real background of calculation teaching, and it cannot and should not be discussed without calculation teaching. Otherwise, students can only "see the trees but not the forest". When a variety of operation problems are mixed together, some students will "simply calculate" some problems that cannot be easily solved by using algorithms. Therefore, in the teaching of simple calculation, it is best to present exercises that can be simple and can't be simple at the same time, so that students can know that some exercises can make the calculation simple by using the algorithm, while others can't, and even make the calculation complicated by using the algorithm.
Of course, in addition, students' careful calculation and serious attitude are also necessary prerequisites. I believe that after these conditions are met, the accuracy of students' simple calculations will definitely improve.