Formulas commonly used in primary school mathematics. Formulas are very common in our study. In fact, most of the solutions in our school can be solved by formulas, and there are many kinds of formulas. The following is a list of commonly used formulas in primary school mathematics.
Table 1 1, additive commutative law: Two numbers are added and exchanged, and the same position is added.
2, the law of addition and association: three numbers are added, the first two numbers are added first, or the last two numbers are added first.
Add these numbers together and add them to the third number, and the sum remains the same.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplication and association law: multiply three numbers, first multiply the first two numbers, or multiply the last two numbers.
Multiply this number and then multiply it with the third number, and their product remains the same.
5. Multiplication and distribution law: when the sum of two numbers is multiplied by the same number, two addends can be added.
Multiply this number separately, and then add the two products, and the result remains the same. Such as: (2+3) × 5 = 2× 5+3× 5.
6. Nature of division: In division, the dividend and divisor expand (or shrink) simultaneously.
Same multiple, same quotient. Divide 0 by any number other than 0 to get 0.
7. Equation: An equation with equal left and right sides is called an equation. Basic properties of the equation:
Both sides of the equation are multiplied by the same number, or divided by the same number that is not 0, and the left and right sides are still equal.
8. Equations: Equations with unknowns are called equations.
9. One-dimensional linear equation: An equation with an unknown number of one degree is called one-dimensional linear equation.
10, fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
1 1, addition and subtraction of fractions: addition and subtraction of fractions with denominator, only numerator addition and subtraction, denominator unchanged.
Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12. Comparison of scores: Compared with the score of denominator, the score with large numerator is large, and the score with small numerator is small.
Compare the scores of different denominators, divide first and then compare; If the numerator is the same, the score with higher denominator is smaller.
13. Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is a numerator, and the denominator remains unchanged.
What can be reduced is reduced first, and then calculated.
14, the fraction is multiplied by the fraction, the product of molecular multiplication is the numerator, and the product of denominator multiplication is the denominator.
What can be reduced is reduced first, and then calculated.
15, the fraction divided by an integer (except 0) is equal to the fraction multiplied by the reciprocal of this integer.
16, true fraction: the fraction with numerator less than denominator is called true fraction.
17, false score: the score with numerator greater than or equal to denominator is called false score, and the false score is greater than or equal to 1.
18, with fraction: A number consisting of integer and true fraction is called with fraction.
19, the basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0).
The size of the score remains the same.
20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
2 1, the number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B.
22. The basic nature of the ratio:
The two items before and after the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
23. What is proportion?
Two expressions with equal ratios are called proportions. For example, 3:6=9: 18
Complete set of commonly used formulas in primary school mathematics (unit conversion table)
(1) length unit conversion
1 km = 1 000m =1km =2 Li.
1 Li = 500m
1 m = 10 decimeter
1 decimeter =10cm
1 cm =10mm
1 m = 100 cm
1 decimeter = 100 mm
1m = 1000mm
(2) area unit conversion
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
1 m2 = 10000 cm2
1 dm2 = 10000 mm2
1 ha = 1 10,000 m2
1 km2 = 1000000 m2
1 km2 = 100 hectare
(3) conversion of volume (volume) units
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cm3 = 1000 cm3
1 l = 1 cubic decimeter
1L = 1000ml
1 ml = 1 cm3
(4) weight unit conversion
1 ton = 1000 kg
1 kg = 1 000g =1kg = 2kg
1 kg = 500g
(5) RMB unit conversion
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
(6) Time unit conversion
1 century = 100 year
1 year = 65438+ February.
The big month (3 1 day) includes: 1, 3, 5, 7, 8,10,65438+February.
Abortion (30 days) includes: April, June, September,165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
The first half of a normal year 18 1 day and the second half 184 days.
The first half of leap year 182 days and the second half 184 days.
In the quotient of non-whole hundred years, no remainder is leap year, and some remainder is average year.
In the whole hundred years, the quotient of 400 has no remainder that is leap year, and the remainder is average year.
1 day =24 hours
1 =60 points
Half an hour =30 minutes
A quarter of an hour = 15 minutes
1 min =60 seconds
Half a minute =30 seconds
1 =3600 seconds
A complete collection of commonly used formulas in primary school mathematics (calculation formula of quantitative relationship)
1, single output × quantity = total output
Total output/quantity = single output
Total output/single output = quantity
2. Speed × time = distance
Distance/speed = time
Distance/time = speed
3. Unit price × quantity = total price
Total price/unit price = quantity
Total price ÷ quantity = unit price
4. Work efficiency × working hours = total workload.
Total amount of work ÷ work efficiency = working hours
Total workload ÷ working time = working efficiency
5. Appendix+Appendix = Total
And-where one addend = the other addend
6. Negative-negative = difference
Negative difference = negative
Difference+Minus = Minus
7. Factor × factor = product (factor is not 0)
Product ÷ One factor = another factor.
8. Dividend bonus = quotient
Dividend = divisor
Quotient × Divider = Divider
9. Division with remainder
Divider = quotient ... remainder
Dividend = quotient × divisor+remainder
Table 2 1, Rectangular area of common formulas in primary school mathematics
= length × width, and the calculation formula is S=ab.
2. Square area
= side length × side length, and the calculation formula is S=a×a=a2.
3, rectangular perimeter
= (length+width) ×2, and the calculation formula is C=(a+b)×2.
4. Square perimeter
= side length ×4, calculation formula C=4a.
5, parallelogram area
= bottom × height, and the calculation formula is S=ah.
6. Triangle area
= bottom× height ÷2, and the calculation formula is S=a×h÷2.
7. Trapezoidal region
= (upper bottom+lower bottom) × height ÷2, and the calculation formula is S=(a+b)×h÷2.
8. cuboid volume
= length × width × height, and the calculation formula is V=abh.
9, the area of the circle
= pi× radius square, and the calculation formula is V=πr2.
10, cube volume
= side length × side length× side length, and the calculation formula is V=a3.
1 1, cuboid and cube volumes
It can be written as bottom area × height, and the calculation formula is V=sh.
12, the volume of the cylinder
= bottom area × height, and the calculation formula is V=sh.
Counting is the basic requirement of primary school mathematics learning.
Counting is the basic requirement of mathematics learning in primary schools, and children begin to learn counting from kindergarten. However, children are different from children, so the degree of learning is different.
Since all students who have received pre-school education can count successfully within 100, teachers should pay attention to how to solve the difficulties in the counting process. First, let students know the relationship between 1, 10 and 100, which will help students realize that "10" is the unit. The second step is to find a seat in the cinema to solve the difficulty of "full ten into one" when students score dozens. Designing exercises with numbers close to 10 will help students to calculate more correctly and lay a good foundation. The third step is to link numbers with numbers to improve students' counting ability.
Teachers start with what students like, guide students to cooperate in groups, use their hands and brains, encourage students to think independently, and advocate diversification of methods, so that students' personality can be publicized and their thinking can be trained. We should also pay attention to the students' existing life experience, let them tell dozens around them, and carry out a series of activities such as catching candy and guessing candy.
It is worth noting that the provisions in the outline have not received enough attention. There was a time when people talked a lot about creative thinking, but little about logical thinking. As we all know, in a sense, logical thinking is the basis of creative thinking, and creative thinking is often the simplification of logical thinking. As far as most students are concerned, it is difficult to develop creative thinking without good logical thinking training.
Therefore, how to implement the objective requirements of "Primary Mathematics Teaching Syllabus" and cultivate students' logical thinking ability in a planned and step-by-step manner is still a problem worthy of attention and serious study.
Modern teaching theory holds that the teaching process is not a simple process of imparting knowledge and learning, but a process of promoting students' all-round development (including the development of thinking ability). Judging from the process of mathematics teaching in primary schools, the mastery of mathematics knowledge and skills can not be separated from the development of thinking ability. On the one hand, in the process of understanding and mastering mathematical knowledge, students constantly use various thinking methods and forms such as comparison, analysis, synthesis, abstraction, generalization, judgment and reasoning;
On the other hand, when learning mathematics knowledge, it provides concrete contents and materials for using thinking methods and forms. In this way, we should never think that teaching mathematical knowledge and skills will naturally cultivate students' thinking ability. The teaching of mathematical knowledge and skills not only provides favorable conditions for cultivating students' thinking ability, but also needs to make full use of these conditions consciously in teaching and cultivate them in a planned way according to students' age characteristics in order to achieve the expected goals.
If we don't pay attention to this point, the arrangement of teaching materials is unconscious, and the teaching method violates the principle of stimulating students' thinking. Not only can it not promote the development of students' thinking ability, but it may also gradually develop students' bad habits of memorizing.
As far as the students in our class are concerned, when they first came to our class, their counting ability was different. Some of them can count to one hundred, while others can hardly count to ten. It can be seen that in the kindergarten stage, numbers leave different impressions in your mind. So I brought a small group of several people to help these students improve and make progress.
At the same time, it also adopted a "one-on-one" counseling method; Teaching in connection with things in real life can take things we often see, such as various fruits, the blackboard eraser in the classroom and so on. In short, it is something we often contact.
Counting activities have laid a good foundation for helping students count more correctly and understand the meaning of counting correctly. Only in this way can the future teaching be carried out and the future teaching be carried out smoothly. Therefore, I attach great importance to students' counting ability in the teaching process, hoping to make them improve.