First, negative numbers:
1, get a preliminary understanding of negative numbers in familiar life situations, read and write positive numbers and negative numbers correctly, and know that 0 is neither positive nor negative.
2. Learn to express some practical problems in daily life with negative numbers, and experience the close relationship between mathematics and life.
I can learn to compare the sizes of positive numbers, 0 and negative numbers with the help of the number axis.
Second, the cylinder and cone
1. Know cylinders and cones and master their basic characteristics. Know the bottom, sides and height of a cylinder. Know the bottom and height of the cone.
2. Explore and master the calculation method of lateral area and surface area of cylinder and the calculation formula of volume of cylinder and cone, and use the formula to calculate the volume to solve simple practical problems.
3. By observing, designing and making cylinder and cone models, we can understand the relationship between plane graphics and three-dimensional graphics and develop students' spatial concept.
Third, the proportion.
1, to understand the meaning and basic properties of proportion, will be solution ratio.
2. Understanding the meaning of positive proportion and inverse proportion can help us find examples of positive proportion and inverse proportion in our life, and we can use the knowledge of proportion to solve simple practical problems.
3. Knowing the image with positive proportional relationship, you can draw an image on grid paper with coordinate system according to the given data with positive proportional relationship, and you can calculate or estimate the value of the other quantity in the image according to one of them.
If you know the scale, you will find the scale of the plan and the distance or actual distance on the map according to the scale.
5, understand the phenomenon of zoom in and out, can use the form of grid paper to zoom in or out simple graphics according to a certain proportion, and realize the similarity of graphics.
6. Infiltrate the thought of function, and let students be inspired by dialectical materialism.
Fourth, statistics.
1, can comprehensively use the learned statistical knowledge, accurately extract statistical information from statistical charts, and correctly interpret statistical results.
2, according to the information provided by the statistical chart, make a correct judgment or simple prediction.
Fifth, mathematical wide angle.
1, experience? Dove cage principle? A preliminary understanding of the inquiry process? Dove cage principle? Can you use it? Dove cage principle? Solve simple practical problems. 2. pass? Dove cage principle? Feel the charm of mathematics through its flexible application.
Sixth, sorting out and reviewing
1, the system grasps the basic knowledge about integers, decimals, fractions and percentages, negative numbers, ratios and proportions, and equations. Can skillfully perform four operations of integer, decimal and fraction, can estimate the addition, subtraction, multiplication and division of integer and decimal, and can use the simple algorithm learned to calculate reasonably and flexibly; Be able to solve the learned equations; Get into the habit of checking.
2, consolidate the appearance of commonly used units of measurement, grasp the progress between the units, and can simply rewrite.
3. Master the characteristics of geometry; Skillfully calculate the perimeter, area and volume of some geometric shapes and apply them; Consolidate simple drawing and measuring skills; Consolidating the understanding of axisymmetric graphics will draw a symmetrical axis of graphics and consolidate the understanding of translation and rotation of graphics; The position of an object can be determined by several pairs or according to the direction and distance, and the knowledge of proportion can be mastered and applied.
4, master the preliminary knowledge of statistics, can read and draw simple statistical charts, can make simple judgments and predictions according to the data, can find the possibility of some simple events, and can solve some practical problems in calculating the average.
5. Further feel the interrelation between mathematical knowledge and understand the role of mathematics; Master the common quantitative relations and problem-solving thinking methods, and be able to flexibly use the knowledge learned to solve some simple practical problems in life.
(A) the number of reading and writing
1. integer reading method: from high to low, read step by step. When reading level 110 million, first read according to the reading method of each level, and then add a at the end? Billion? Or? Wan? Words. The zeros at the end of each stage are not read, and only a few zeros of other digits are read.
2. Writing of integers: from high to low, writing step by step. If there is no unit on any number, write 0 on that number.
3. Decimal reading: When reading decimals, the integer part is read as an integer, and the decimal point is read as? Point? The decimal part reads the numbers on each digit from left to right in order.
4. Decimal writing: When writing decimals, the integer part is written as an integer, the decimal point is written in the lower right corner of each digit, and the decimal part is written on each digit in turn.
5. How to read the spectrum: read the denominator before reading the spectrum? Share it? Then read the numerator, numerator and denominator as integers.
6. How to write the fraction: write the fraction first, then the denominator, and finally the numerator and the integer.
7. Reading method of percentage: When reading percentage, read the percentage first, and then read the number before the percentage symbol. When reading, read it as an integer.
8. How to write percentage: percentage is usually not written as a fraction, but a percentage sign is added after the original molecule? %? To show.
(2) The number of rewrites
A large multi-digit number is often rewritten as? Wan? Or? Billion? Number of units. Sometimes, if necessary, you can omit the number after a certain number and write it as an approximation.
1. exact number: in real life, for the convenience of counting, larger numbers can be rewritten into numbers in units of ten thousand or hundreds of millions. The rewritten number is the exact number of the original number. For example, put 1254300000.
The number rewritten in ten thousand years is 6.5438+0.2543 million; Rewritten into a number of 65.438+025.43 billion in units of hundreds of millions.
2. Approximation: According to the actual needs, we can also use a similar number to represent a larger number and omit the mantissa after a certain number. For example: 13024900 15 The mantissa after omitting 100 million is1300 million.
3. Rounding method: If the highest digit of the mantissa to be omitted is 4 or less, the mantissa is removed; If the digit with the highest mantissa is 5 or more, the mantissa is truncated and 1 is added to its previous digit. For example, omit
The mantissa after 34.59 million is about 350 thousand. After omitting 472509742 billion, the mantissa is about 4.7 billion.
4. Size comparison
1. Compare the sizes of integers: compare the sizes of integers, and the number with more digits will be larger. If the numbers are the same, view the highest number. If the number in the highest place is larger, the number is larger. The number in the highest bit is the same. Just look at the next bit, and the bigger the number, the bigger it is.
2. Compare the sizes of decimals: first look at their integer parts, and the larger the integer part, the larger the number; If the integer parts are the same, the tenth largest number is larger; One tenth of the numbers are the same, and the number with the largest number in the percentile is the largest.
3. Compare the scores: the scores with the same denominator and the scores with large numerator are larger; For numbers with the same numerator, the score with smaller denominator is larger. If the denominator and numerator of a fraction are different, divide the fraction first, and then compare the sizes of the two numbers.
(3) the number of mutual
1. Decimal component number: There are several decimals, so writing a few zeros after 1 as denominator and removing the decimal point after the original decimal point as numerator can reduce the number of quotation points.
2. Fractions become decimals: numerator divided by denominator. Those that are divisible are converted into finite decimals, and some that are not divisible are converted into finite decimals. Generally three decimal places are reserved.
3. A simplest fraction, if the denominator does not contain other prime factors except 2 and 5, this fraction can be reduced to a finite decimal; If the denominator contains prime factors other than 2 and 5, this fraction cannot be reduced to a finite decimal.
4. Decimal percentage: Just move the decimal point to the right by two places, followed by hundreds of semicolons.
5. Decimal percentage: Decimal percentage, just remove the percent sign and move the decimal point two places to the left.
6. Convert fractions into percentages: usually, first convert fractions into decimals (three decimal places are usually reserved when they are not used up), and then convert decimals into percentages.
7. Decimalization of percentage: First, rewrite percentage into component quantity and put forward a quotation that can be simplified to the simplest score.
(4) Divisibility of numbers
1. Usually a composite number is decomposed into prime factors by short division. Divide this complex number by a prime number until the quotient is a prime number, and then write the divisor and quotient in the form of multiplication.
2. The way to find the greatest common divisor of several numbers is to divide the common divisors of these numbers continuously until the quotient obtained is only the common divisor of 1, and then multiply all the common divisors to get the product, which is the greatest common divisor of these numbers.
3. The way to find the least common multiple of several numbers is to divide by the' common divisor' of these numbers (or some of them) until they are coprime (or pairwise coprime), and then multiply all the divisors and quotients to get the product, which is the least common multiple of these numbers.
4. Two numbers that become coprime relations: 1 and any natural number coprime; Two adjacent natural numbers are coprime; When the composite number is not a multiple of the prime number, the composite number and the prime number are coprime;
When the common divisor of two composite numbers is only 1, these two composite numbers are coprime.
(5) Approximate points and general points
Reduction method: divide the denominator by the common divisor of the denominator (except 1); Usually, we have to separate it until we get the simplest score.
General division method: first find the least common multiple of the denominator of the original fraction, and then turn each fraction into a fraction with this least common multiple as the denominator.
decimal
1. The meaning of decimals
The integer 1 can be divided into 10, 100 and 1000, which can be expressed in decimals.
One decimal place indicates a few tenths, two decimal places indicate a few percent, and three decimal places indicate a few thousandths.
Decimal system consists of integer part, decimal part and decimal part. The point in the number is called the decimal point, the number to the left of the decimal point is called the integer part, and the number to the right of the decimal point is called the decimal part.
In decimals, the series between every two adjacent counting units is 10. What is the highest decimal unit of the decimal part? One tenth? And the smallest unit of the integer part? One? The propulsion rate between them is also 10.
2. Classification of decimals
Pure decimals: Decimals with zero integer parts are called pure decimals. For example, 0.25 and 0.368 are pure decimals. With decimals: decimals whose integer part is not zero are called with decimals. For example, 3.25 and 5.26 are all decimals.
Finite decimals: The digits in the decimal part are finite decimals, which are called finite decimals. For example, 4 1.7, 25.3 and 0.23 are all finite decimals.
Infinite decimal: The digits in the decimal part are infinite decimal, which is called infinite decimal. For example: 4.33 3. 14 15926
Infinite acyclic decimal: the decimal part of a number with irregular arrangement and unlimited digits. Such decimals are called infinite cyclic decimals. For example:?
Cyclic decimal: the decimal part of a number, in which one or several numbers appear repeatedly in turn, is called cyclic decimal. For example: 3.555 0.033312.109109.
The decimal part of cyclic decimal is called the cyclic part of cyclic decimal. For example, what is the period of 3.99? 9 ? What is the cycle segment of 0.5454? 54? . Pure cyclic decimal: the cyclic segment starts from the first digit of the decimal part, which is called pure cyclic decimal. For example: 3.111.5656.
Mixed cycle decimal: the cycle section does not start from the first digit of the decimal part. This is called mixed cyclic decimal. 3. 1222 0.03333
When writing a cyclic decimal, for simplicity, the cyclic part of the decimal only needs one cyclic segment, and a dot is added to the first and last digits of this cyclic segment. If there is only one number in the circle, just click a point on it. For example: 3.777 short form 0.5302302 short form.
mark
The meaning of 1. score
Put the unit? 1? Divide into several parts on average, and the number indicating such a part or parts is called a score.
In the score, the middle horizontal line is called the dividing line; The number below the fractional line, called the denominator, represents the unit? 1? How many shares are divided equally; The number below the fractional line is called the numerator, indicating how many copies there are.
Put the unit? 1? Divide into several parts on average, and the number representing one part is called fractional unit.
2. Classification of scores
True fraction: The fraction with numerator less than denominator is called true fraction. The true score is less than 1.
False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1. With fraction: False fraction can be written as a number consisting of integer and true fraction, which is usually called with fraction. 3 Reduction and comprehensive score
Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called divisor. The denominator of a molecule is a fraction of a prime number, which is called simplest fraction.
Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.
4) Percentage
1. A number indicating that one number is a percentage of another number is called a percentage, also called a percentage or a percentage. Percentages are usually expressed as "%". The percent sign is a symbol indicating percentage.
Proportion refers to two equal expressions called proportion. In proportion, the product of two external terms is equal to two internal terms. This is called the basic nature of proportion.
According to the basic nature of proportion, if any three items in the proportion are known, another unknown item in this proportion can be found. Finding the unknown term in the proportion is called the solution ratio.
For example: x: 320 =1:1kloc-0/0x = 320? 1 x =320？ 10 x =32