People's education printing plate sixth grade elementary school mathematics knowledge point book one
Unit 1: Fractional Multiplication
Importance of (1) fractional multiplication:
1, the fractional multiplication of integers has the same meaning as integer multiplication, and it is a simple operation to find the sum of several identical addends.
"Fraction multiplied by integer" means that the second factor must be an integer, not a fraction.
2. Multiplying a number by a fraction means finding the fraction of a number.
"A number multiplied by a fraction" means that the second factor must be a fraction, not an integer. The first factor is anything. )
(2) Calculation rules of fractional multiplication:
1, the arithmetic of decimal times integer is: numerator times integer, denominator remains unchanged.
(1) In order to make the calculation simple, it can be reduced first and then calculated. (integer denominator reduction) (2) reduction is to reduce the common factor with the following integer and denominator. (Integer cannot be multiplied by denominator, and the calculation result must be the simplest fraction).
2. The arithmetic of fractional multiplication is: use the product of molecular multiplication as numerator and the product of denominator multiplication as denominator. (numerator times numerator, denominator times denominator)
(1) If the fractional multiplication formula contains a band fraction, the band fraction should be converted into a false fraction before calculation.
(2) The method of fractional simplification is that the numerator and denominator are divided by their common factors at the same time.
(3) In the process of multiplication, the divisor is to cross out two divisible numbers in the numerator and denominator, and then write the divisor above and below respectively. (After reduction, the numerator and denominator can no longer contain common factors, so the calculated result is the simplest score).
(4) The basic nature of the fraction: the numerator and denominator are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.
(3) the relationship between products and elements:
A number (except 0) is multiplied by a number greater than 1, and the product is greater than this number. A×b=c, when b >; In 1, c> answer.
A number (except 0) is multiplied by a number less than 1, and the product is less than this number. A×b=c, when b < 1
A number (except 0) is multiplied by a number equal to 1, and the product is equal to this number. A×b=c, and when b = 1, c = a.
When comparing the sizes of factors and products, we should pay attention to the special situation when the factor is 0.
(d) mixed operation of fractional multiplication
1, the mixed operation order of fractional multiplication is the same as that of integers. Multiply first, then divide, and then add and subtract. If there are parentheses, count them first and then count them outside.
2. The law of integer multiplication is also applicable to fractional multiplication; Algorithms can make some calculations simple.
Multiplicative commutative law: a×b=b×a multiplicative associative law: (a×b)×c=a×(b×c)
Multiplicative distribution law: a× (b c) = a× b a× c
(V) Meaning of reciprocal: Two numbers whose product is 1 are reciprocal.
1 and reciprocal are two numbers, which are interdependent and cannot exist alone. A number cannot be called reciprocal. (It must be clear who is the reciprocal of who)
2. The criterion for judging whether two numbers are reciprocal is whether the product of the multiplication of two numbers is "1". For example: a×b= 1, then a and b are reciprocal.
3. Reciprocal method:
① Find the reciprocal of the fraction: exchange the positions of numerator and denominator.
② Find the reciprocal of an integer: 1 of an integer.
③ Find the reciprocal of the score: first turn it into a false score, and then find the reciprocal.
(4) Find the reciprocal of the decimal: first find the number of components, and then find the reciprocal.
4. The reciprocal of1is itself because 1× 1= 1.
0 has no reciprocal, because the product of any number multiplied by 0 is 0, and 0 cannot be used as the denominator.
5. The reciprocal of the true score is a false score, and the reciprocal of the true score is greater than 1 and itself.
The reciprocal of the error score is less than or equal to 1. The reciprocal of the score is less than 1.
(6) Fractional multiplication is applied to solve problems.
1, what is the score of a number? (by multiplication)
Given the unit "1", find the fraction of the unit "1" and multiply the fraction by the unit "1".
2. Find the quantity of the unit "1" skillfully: in a sentence with a score, the quantity before the score is the corresponding quantity of the unit "1", or the quantity after the words "Zhan", "Yes" and "Bi" is the unit "1".
3. What is speed?
Speed is the distance traveled per unit time.
Speed = distance/time/time = distance/speed/distance = speed × time
Unit time refers to 1 hour, 1 minute, 1 second and other time units with the size of 1, such as minutes, hours and seconds.
4. How much is A more (less) than B?
More: (A-B) less: (B-A) B
The sixth grade mathematics knowledge point book 1
1. According to the direction and distance, the position of the object on the plane can be determined.
2. The method of marking the position of the object on the plan:
First use a protractor to determine the direction, then use a ruler to determine the distance on the map according to the selected unit length, and finally find out the specific position of the object and mark it with the name.
3. When describing the road map, we should first determine each reference point according to the walking route, and then use each reference point to establish a direction marker to describe the direction and distance of the next target, that is, each step should be clear about where to go and how far to go.
4. Method of drawing road map:
(1) Determine the direction mark and unit length.
(2) Determine the position of the starting point.
(3) According to the description, start from the starting point, find the direction and distance and draw them one by one. Except for the first paragraph (with the starting point as the reference point), the end points of the previous paragraph should be the reference points of each other.
(4) Draw a "ten" direction mark with who as the reference point and who as the center, and then judge the direction and distance of the next position.
Math learning methods in the sixth grade of primary school
1, use mathematics in life to stimulate children's intrinsic learning motivation.
Mathematics runs through daily life. Parents can observe their children's preferences in daily life, integrate mathematical thinking, and guide their children to learn actively. And consciously think, guess, discuss, use your hands and brains, etc. Use the elements that children are interested in as the carrier of mathematical thinking, stimulate children's intrinsic learning motivation, make children feel the importance and interest of learning from each other, and make children more active in mathematics learning.
2. Grasp the sensitive period of mathematics and develop mathematical thinking step by step.
Studies have proved that children will have a "mathematical sensitive period" around the age of 4. They will suddenly have great interest in the concept of numbers, such as numbers, numbers, quantitative relations, arrangement order, number operation, physical characteristics and so on. And have a strong thirst for knowledge about their own changes, which shows that the child's mathematics sensitive period has arrived. After missing this "sensitive period of mathematics", some people are afraid of mathematics all their lives and have a headache when it comes to mathematics.
Faced with the purely abstract concept of "mathematics", the only way to make children feel relaxed is to start with concrete and simple objects. From sensory training, from the actual experience of "quantity" to the abstract understanding of "number" from less to more, into the calculation of addition, subtraction, multiplication and division, gradually cultivate children's mathematical mind and analyze integrated logical concepts. Let children know how many and how many objects, how big and how small, naturally associate with the relationship between concrete and abstract.
3. Discuss cooperation and use divergent mathematical thinking.
Every child has his unique imagination and thinking ability. In school study, we can make use of this difference in thinking, let children participate in teamwork, * * * build blocks or play origami games together, * * * discuss knowledge exchange and cooperation, use spatial thinking and colorful concrete combinations, and construct their own experience and knowledge while using hands and brains and divergent thinking in mutual communication, which is helpful to participate in teamwork.
When children are young, they mainly think in images and like to visualize all abstract problems, but this is not conducive to the cultivation of abstract thinking, so it is very important to cultivate children's good thinking habits. Specifically, mathematical thinking is to train children to summarize, analyze and solve problems in time, think step by step, consciously and gradually cultivate their abstract thinking ability and thinking quality, and strengthen training.
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