First, make full use of the five laws.

Teachers should teach the five major algorithms in the current textbooks (additive commutative law, law of addition and association, law of multiplication and exchange, law of multiplication and association, and law of multiplication and distribution), so as to guide students to find out the ins and outs, so as not to let a student fall behind, and to cultivate each student to consciously use simple methods and flexibly choose simple methods to calculate correctly and quickly according to different types of questions.

Second, skillfully use the top ten and the bottom ten.

Use the combination of the former and the latter to train. The first and last combination method is two digits. Their ten digits are the same, and the sum of digits is 10. Multiply the first ten digits and the last ten digits with two digits, and the two digits on the right side of the product are exactly the product of single digits, and the number on the left side of the product is exactly the product of the number on the tenth digit multiplied by 1 larger than it, and the combination is their product. For example, 54x56 = 30241x89 = 7209.

Third, pay attention to the combination of left and right numbers.

The fast algorithm of multiplying any two digits by 99 or multiplying any three digits by 999 is called left and right two-digit array method.

1. The ingenious calculation method of multiplying any two digits by 99 is to subtract 1 from these two digits as the two digits on the left side of the product, and then subtract 100 from these two digits as the two digits on the right side of the product, and the combination is their product. For example, 62x99=6 138, 48x99=4752.

2. The ingenious calculation method of multiplying any three digits by 999 is to subtract 1 from any three digits as the three digits on the left side of the product, and then subtract 1000 from the difference of any three digits as the three digits on the right side of the product, and the combination is their product. For example, 781x 999 = 780265438+396x999 = 395604.

Fourth, skillfully use the relationship between fraction and division to calculate.

In a problem with only two levels of operation, sequential calculation needs multi-step calculation, and it will be very simple to calculate by using multiplication and division relationship. For example, 24/18X36/12 = (24/18) x (36/12) = 24/18X36/12 = 4.

Fifthly, simple calculation is made by using the law of thermal expansion and contraction.

Some division problems are complicated to calculate directly and easy to make mistakes. A simple solution can be found by using the law of thermal expansion and contraction to make reasonable deformation. For example, 7/25 = (7x4)/(25x4) = 28/100 = 0.28,24/125 = (24x8)/(125x8) =199.

Clever calculation of subtraction of inverted two-digit or three-digit numbers.

Numbers such as 73 and 37, 185, 58 1 are called double or triple digits with numbers reversed. The ingenious calculation method is as follows.

1, using the inverse number to do two-digit subtraction, you can subtract the decimal from the large number in the two-digit number and multiply it by 9, and the product is their difference. Such as 73-37=(7-3)x9=36, 82-28=(8-2)x9=54.

2. For the three-digit subtraction with reciprocal, you can subtract the minimum number from the maximum number of three digits, multiply it by 9, multiply the two sides of the integral, and fill in 9 in the middle, which is their difference. For example, 581-158 = (8-1) x9 = 63, so 85 1- 158=693.