① Understand the meaning and basic properties of fractions, compare the sizes of fractions, turn false fractions into fractions or integers, and transform integers and decimals into each other, and skillfully divide and divide.
Master the concepts of factors and multiples, prime numbers and composite numbers, odd numbers and even numbers, and the characteristics of multiples of 2, 3 and 5; Will find the greatest common factor and the least common multiple of two numbers in 100.
③ Understanding the meaning of the addition and subtraction of fractions, mastering the calculation method of the addition and subtraction of fractions and skillfully calculating simple addition and subtraction of fractions will solve simple practical problems about the addition and subtraction of fractions.
(4) Know the volume and its meaning and unit of measurement, know the conversion between units, and feel the practical significance of volume and unit of volume.
⑤ Explore and master the calculation methods of volume and surface area of cuboids and cubes, and explore some measurement methods of physical volume.
⑥ Can draw an axisymmetric figure on the grid paper and rotate the simple figure by 90 degrees; Appreciate the patterns in life, and flexibly use translation, symmetry and rotation to design patterns on square paper.
⑦ Understand the meaning of patterns through abundant examples, find a set of data patterns, and explain the practical significance of the results; According to specific problems, appropriate statistics can be selected to represent different characteristics of data.
⑧ Understand the composite broken-line statistical chart, and select the appropriate statistical chart to represent the data as needed.
basic concept
If a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is an axisymmetric graph.
In an axisymmetric figure, the distance between the opposite points on both sides of the axis of symmetry is equal.
The phenomenon that slides, baby carriages, through trains and speed skating all move along a straight line is called translation.
Ferris wheel, space shuttle, merry-go-round, these objects all move around a point or an axis. We call it rotation.
Translation and rotation are changes in the position of objects or figures. Translation means that an object moves in a straight line.
Rotation is the movement of an object around a point or axis.
2×6= 12, so 2 and 6 are factors of 12, and 12 is a multiple of 2 and 6. A number has more than one factor, the smallest is 1, and the largest is itself. Start with the smallest natural number 1, that is, start with the smallest factor and find all the way. In the process of searching, one by one, from small to uppercase.
The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple.
Numbers in units of 0, 2, 4, 6 and 8 are all multiples of 2.
Numbers that are multiples of 2 are called even numbers (0 is even), the smallest even number is 0, numbers that are not multiples of 2 are called odd numbers, and the smallest odd number is 1.
A number with 0 or 5 digits is a multiple of 5.
The sum of the digits of a number is a multiple of 3, so this number must be a multiple of 3.
The factor of a number is only 1 and itself. Such numbers are called prime numbers, and the smallest prime number is 2.
The factor of a number is only 1 and itself. Such numbers are called prime numbers, and the smallest prime number is 2.
A number has other factors besides 1 and itself. Such a number is called a composite number, and the smallest composite number is 4.
A cuboid has six faces, each of which is a rectangle (or two opposite faces are squares), and the opposite faces are exactly the same. 12 sides, and the four opposite sides are equal in length. Eight vertices. The lengths of three sides intersecting at a vertex are called length, width and height respectively.
A cube has six faces, each of which is square and the opposite faces are exactly the same. 12 sides are equal in length. Eight vertices. Cubes are special cuboids.
The total area of six faces of a cuboid or cube is called its surface area.
The surface area of a cuboid = (length× width+length× height+width× height) × 2.
Surface area of cube = side length × side length ×6= bottom area ×6
To calculate the surface area of a long cube, it is generally necessary to calculate the total area of six faces, but sometimes it is necessary to calculate its surface area according to actual needs. (Pay attention to the diversity of examination questions and methods)
The space occupied by an object is called its volume. Measure the length in units of length, measure the area in units of area, and measure the volume in unit of volume. Commonly used unit of volume are: cubic meter, cubic decimeter and cubic centimeter. A cube with a length of 1 cm and a volume of 1 cm. A cube with side length of 1 decimeter and volume of 1 cubic decimeter. A cube with length 1 m and volume 1 m3.
Cuboid volume = length × width × height, v = abh
Cube volume = side length × side length × side length, and v = a3 is pronounced as a cube.
Volume of long cube = bottom area × height, V =sh.
1 cubic decimeter = 1000 cubic centimeter, 1 cubic meter = 1000 cubic decimeter, and the propulsion rate between adjacent unit of volume is 1000.
The volume of boxes, oil drums, warehouses and other objects. The amount that can be accommodated is called their volume.
Unit of volume is generally used to measure volume. However, in order to measure the volume of liquids, such as medicine and gasoline, liters and milliliters are usually used. 1l (L) = 1000ml (mL), 1l (L) = 1 cubic centimeter (dm3), 1ml (mL)= 1 cubic centimeter (m3).
The calculation method of cuboid or cube container volume is the same as that of volume. But the length, width and height are measured from the inside of the container.
An object, some objects can be regarded as a whole, and a whole can use the natural number 1.
Commonly referred to as the unit "1". Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. Divide the unit "1" into several parts on average, and the number representing such a part is the decimal unit of the fraction.
The quotient of integer division can be expressed by a fraction, with the divisor as the denominator and the dividend as the numerator, and the divisor is equivalent to the fractional line in the fraction. Fraction is a number, division is an operation,
Fractions with numerator less than denominator are called true fractions. The true score is less than 1.
Fractions with numerator greater than or equal to denominator are called false fractions. False score is greater than or equal to 1.
Band scores are all composed of integer parts and fractional parts (real scores), and band scores are all greater than 1. When the numerator is a multiple of the denominator, the false fraction can be turned into an integer.
When the numerator is not a multiple of the denominator, divided by the denominator, the quotient is the integer part, and the remainder is the numerator of the decimal part, and the denominator remains unchanged.
The numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains the same.
1, 2,4 is the common factor of 16 and 12, which is called their common factor. Where 4 is the greatest common factor, which is called their greatest common factor. The product of all common prime factors of two numbers is the greatest common factor of these two numbers. When two numbers are multiples, the smaller number is their greatest common factor. When two numbers have only one common factor 1, their greatest common factor is also 1.
The numerator and denominator have only one common factor 1, and such a fraction is called the simplest fraction.
Changing a fraction into an equal fraction with smaller numerator and denominator is called divisor.
Using the greatest common factor of numerator and denominator, the simplest score is obtained by removing numerator and denominator respectively.
Two special cases of the least common multiple of two numbers: (1) When two numbers are multiples, the larger number is their least common multiple. (2) When two numbers have only one common factor 1, the product of these two numbers is their least common multiple.
Several fractions have the same denominator, which is called the common denominator.
Divide scores with different denominators into scores with the same denominator equal to the original score, which is called total score.
In general division, first find out the least common multiple of the original denominator as the common denominator, and then see how many times the denominator of the original fraction should be multiplied, and the numerator should be multiplied by the same number.
Decimal system is actually another form of fraction, and the denominator is 10, 100,1000 ...
When decimalizing a component number, the decimal number is first written as a fraction. There are several decimals, so write a few zeros after 1 as the denominator and remove the decimal point of the original decimal as the numerator. Pay attention to the quotation points of the contract.
Fractions into decimals Multiply the numerator and denominator of a fraction by the same number at the same time, and convert them into fractions with denominators of 10, 100,1000 ... and rewrite them into decimals. Or using the relationship between fraction and division, numerator is divided by denominator to get decimal. When it is not exhausted, it is necessary to keep a few decimal places according to the "four houses and five people" method.
Fraction addition and subtraction have the same meaning as integer addition and subtraction. When calculating the addition and subtraction of fractions with the same denominator, the denominator remains unchanged and only the numerator is added and subtracted. Note that the calculation result can be simplified to the simplest score. Molecules are all 0, and scores are all equal to O.
The addition and subtraction calculation method of fractions with different denominators is: divide first, and then calculate according to the addition and subtraction calculation method of fractions with the same denominator. Note that in order to make the calculation simple, the least common multiple of denominator should be chosen as the common denominator.
When calculating the mixed operation of addition and subtraction of scores, it can be done step by step or once.
The commutative law and associative law of integer addition are also applicable to fractional addition.
In a set of data, the number that appears most frequently is called the mode. Patterns can reflect the concentration of a set of data. In a set of data, there may or may not be multiple patterns.
The broken-line statistical chart can not only compare various quantities quickly, but also see the changes of quantities. The changing trend of two groups of data can be easily compared with the composite broken-line statistical chart. Attention should be paid to drawing legends when making composite broken-line statistical charts.
Some seemingly identical items are mixed together with different qualities, either light or heavy, which can be found quickly and accurately by using a balance. We call this problem finding defective products.
When using the balance to find defective products, divide the items to be tested into three parts and distribute them equally as much as possible to ensure that the defective products can be found, and the weighing times must be the least.