Induction of mathematics knowledge points in the next semester of grade five

In primary school, we only knew how to play, but we didn't know how to summarize the knowledge points. In order to help students study better. The following is a summary of the knowledge points of mathematics in the fifth grade next semester, which I compiled for your reference only. Welcome to reading.

The mathematics knowledge points of the fifth grade in the next semester are summarized as 1. Axisymmetric figure: a figure is folded in half along a straight line, and both sides can completely overlap. Such a figure is called an axisymmetric figure, and this straight line is called an axis of symmetry.

2. Characteristics and properties of symmetrical figures: ① The distance from the symmetrical point to the symmetrical axis is equal; ② The line connecting the symmetrical points is perpendicular to the symmetry axis; ③ The figures on both sides of the symmetry axis have the same size and shape.

3. When an object rotates, we should grasp three points: ① the center of rotation; ② direction of rotation; ③ Rotation angle. Rotation only changes the position of the object, but not the shape and size of the object.

I. Factors and multiples

1, factor and multiple: If the integer A is divisible by B, then A is a multiple of B, and B is a factor of A. ..

2. How to find the factors of a number: the number of factors of a number is limited, the smallest is 1, and the largest is itself. The method is to look for it in sequence.

3. How to find the multiple of a number: the number of multiples of a number is infinite, the smallest is itself, and there is no maximum. When using the method, multiply the natural number in turn.

Features of multiples of 4, 2, 5 and 3: Numbers with 0, 2, 4, 6 and 8 are multiples of 2. A number with 0 or 5 is a multiple of 5. The sum of the numbers on each digit of a number is a multiple of 3, and this number is a multiple of 3.

5. Even and odd numbers: numbers that are multiples of 2 are called even numbers (0 is also even numbers), and numbers that are not multiples of 2 are called odd numbers.

6. Prime number and composite number: a number. If there are only two factors of 1 and itself, it is called a prime number, and the smallest prime number is 2. A number, if there are other factors besides 1 and itself, is called a composite number, and the smallest composite number is 4.

Second, cuboids and cubes.

1. Features of cuboids and cubes: a cuboid has six faces, each of which is a rectangle (especially a group of faces is a square), and the opposite faces are exactly the same; There are 12 sides, and the opposite sides are parallel and equal; There are eight vertices. A square has six faces, each face is a square, and all faces are exactly the same; There are 12 edges, all equal; There are eight vertices.

2. Length, width and height: the lengths of three sides intersecting at a vertex are called the length, width and height of a cuboid respectively.

3. The sum of the sides of a cuboid = (length+width+height) ×4? Sum of cube sides = side length × 12

4. Surface area: The total area of six faces of a cuboid or cube is called its surface area.

5. The surface area of a cuboid = (length× width+length× height+width× height )× 2s = (AB+AH+BH )× 2.

The surface area of a cube = side length × side length ×6 is expressed by letters: S=

6. Surface area unit: square centimeter, square decimeter, square meter? The propulsion rate of adjacent units is 100.

7. Volume: The size of the space occupied by an object is called the volume of the object.

8. cuboid volume = length × width × height? Expressed in letters: V=abh length = volume ÷ (width× height) width = volume ÷ (length× height)

Height = volume ÷ (length × width)

The volume of a cube = side length × side length× side length is expressed by letters: v = a× a× a.

9. unit of volume: cubic centimeter, cubic decimeter, cubic meter? The propulsion rate of adjacent units is 1000.

10, unified formula of cuboid and cube volume: cuboid or cube volume = bottom area × height V=Sh.

1 1, reciprocity of unit volume: change advanced units into low-level units, and multiply the number of advanced units by the rate of progress;

Gather low-level units into high-level units and divide the number of low-level units by the forward speed.

12. Volume: the volume of an object that a container can hold.

13. unit of volume: liters and milliliters (l and ml) 1L= 1000ml? 1L= 1000 cm3 1ml= 1 cm3.

14. Calculation of volume: The calculation method of cuboid and cube container volume is the same as that of volume, but the length, width and height should be measured from the inside.

Third, the meaning and nature of the score

1, meaning of score: divide the unit "1" into several parts on average, and the number representing such one or several parts is called a score.

2. Decimal unit: divide the unit "1" into several parts to represent this. A partial number is called a fractional unit.

3. The relationship between fraction and division: in division, the dividend is equivalent to the numerator of the fraction, and the divisor is equal to the denominator, which is expressed in letters: a÷b= (b≠0).

4. True score and false score: the score with numerator less than denominator is called true score, and the true score is less than 1. Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions, which are greater than or equal to 1. Fractions consisting of integer parts and decimal parts are called decimal parts.

5. Mutualization of false score and score: false score is converted into score, numerator is divided by denominator, and the quotient obtained is integer part, remainder is numerator, and denominator remains unchanged. Turn the band fraction into a false fraction, multiply the integer part by the denominator and add the numerator as the numerator, and the denominator remains unchanged.

6. The basic nature of a fraction: 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 unchanged, which is called the basic nature of a fraction.

7. greatest common factor: some factors of several numbers are called their common factors, and the largest is called the greatest common factor.

8. Prime numbers: Two numbers whose common factor is only 1 are called prime numbers. Special methods to judge the coprime of two numbers: ① 1 is coprime with any natural number greater than 1. ②2 and any odd number are prime numbers. ③ Two adjacent natural numbers are prime numbers. ④ Two adjacent odd coprime. ⑤ Two different prime numbers are coprime. 6. When one number is a composite number and the other number is a prime number (except when the composite number is a multiple of a prime number), these two numbers are also prime numbers.

9. simplest fraction: A fraction whose numerator and denominator have only the common factor 1 is called simplest fraction.

10, approximation: it is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator.

1 1, the least common multiple: some multiples of several numbers are called their common multiples, and the smallest is called the least common multiple.

12. Comprehensive score: the score of different denominators is changed into the same denominator and the original score is equal, which is called comprehensive score.

13. Maximum common factor and minimum common multiple under special circumstances:

For two numbers in the (1) multiple relation, the greatest common factor is the smaller number and the smallest common multiple is the larger number. ② The greatest common factor of two prime numbers is 1, and the least common multiple is their product.

14, comparison of scores: scores with the same denominator, scores with large molecules are large, and scores with small molecules are small; Fractions with the same numerator have smaller scores with larger denominator and larger scores with smaller denominator.

15. Reciprocity between fractions and decimals: decimal fractions, in which one decimal represents a few tenths, two decimals represent a few percent, and three decimals represent a few thousandths ... If the decimal point is removed as a numerator, it can be simplified to the simplest fraction; Fractional decimal, numerator divided by denominator, with several decimal places reserved as required.

Fourth, the addition and subtraction of scores.

1, addition and subtraction of fractions with the same denominator: addition and subtraction of fractions with the same denominator, with the same denominator, only numerator addition and subtraction.

2. Addition and subtraction of fractions with different denominators: When fractions with different denominators are added or subtracted, they are divided first, and then calculated according to the addition and subtraction method of fractions with the same denominator.

3. The operation sequence of fractional addition and subtraction is the same as that of integer addition and subtraction. In an equation, if there are parentheses, count the inside of the parentheses first, and then count the outside of the parentheses; If only operations of the same level are included, it should be calculated from left to right.

Five, make a phone call

1, one by one method: the most time-consuming;

2. Grouping method: relatively saving time;

3. Simultaneous method: the most time-saving.

Expanding reading: the first volume of the first grade of the primary school Chinese text catalogue

Catalogue of the second volume of grade one

Catalogue of the first volume of grade two

Catalogue of the second volume of grade two

Catalogue of the first volume of grade three

Catalogue of the second volume of grade three

Catalogue of the first volume of the fourth grade

Catalogue of the second volume of the fourth grade