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Review materials of the second volume of mathematics in the fifth grade of primary school I. Graphic transformation

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.

Second, 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, 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 prime number or 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.

Three, cuboids and cubes

1. Features of cuboids and cubes: Cuboids have six faces, each of which is a rectangle. A special set of faces is 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 sides of a cube = 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: The ratio of adjacent units of square centimeter, square decimeter and square meter 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 is expressed by 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: The propulsion rate of the adjacent units of cubic centimeter, cubic decimeter and cubic meter 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 high-order units into low-order units, and multiply the number of high-order units by the propulsion rate;

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

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

13. unit of volume: liters and milliliters of l and ml1l =1000ml1l =1000m3cm31ml =1cm3.

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.

Fourth, 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 on average, and the number representing such a part is called decimal 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. Basic Properties of Fraction: The numerator and denominator of a fraction are multiplied or divided by the same number 0 at the same time, except that the size of the fraction remains unchanged, which is called the basic properties of the 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, generally speaking, these two numbers are also prime numbers except that the composite number is a multiple of the prime number.

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.

5. Addition and subtraction of fractions

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.

Six, 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.

The review data of the second volume of mathematics in the fifth grade of primary school is 1. Because 2×6= 12, we say that 2 and 6 are factors of 12, and 12 is a multiple of 2 and 6. You can't just say who is a multiple or a factor.

2. Find the factors of a number, and find them one by one by multiplication. Generally, when writing, they are arranged from small to large.

3. Find the multiple of a number and multiply it by 1, 2, 3, 4. ...

4. The minimum factor of a number is 1, and the maximum factor is itself. The number of factors of a number is limited.

5. The minimum multiple of a number is itself. Without the maximum multiple, the multiple of a number is infinite.

6. Numbers 0, 2, 4, 6 and 8 are multiples and even numbers of 2.

7. Among natural numbers, numbers that are multiples of 2 are called even numbers, and 0 is even numbers. Numbers that are not multiples of 2 are called odd numbers.

8. Numbers with numbers of 0 or 5 are multiples of 5.

9. The number of 0 is a multiple of 2 and 5.

10. The sum of each bit of a number is a multiple of 3, and this number is a multiple of 3.

1 1. A number with only 1 and its own two factors is called a prime number or prime number, and a number with other factors besides 1 and itself is called a composite number. 1 is neither prime nor composite.

12. Integers are classified according to the number of factors: 1, prime number and composite number. Integers are classified according to whether they are multiples of 2: odd and even.

13. Decomposition of a composite number into several prime numbers is called prime factorization. Prime factor divided by short division, what is the prime factor of 36?

14. The smallest prime number is 2, the smallest composite number is 4, the smallest odd number is 1, the smallest even number is 0, the smallest number is a multiple of 2, 5 and 3 is 30, and the smallest three digits are 120.

15. Odd number plus odd number equals even number. Odd plus even equals odd. Even number plus even number equals even number.

16.A is a multiple of c and b is a multiple of c, so the sum of a+b is a multiple of c, c is a factor of a+b sum, the difference between a and b is a multiple of c, and c is a factor of a-b difference.

17. 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. The straight line where the crease lies is called the symmetry axis.

18. Axisymmetric graphic features: the distance between the corresponding point and the axis of symmetry is equal, and the connecting line of the corresponding point is perpendicular to the axis of symmetry.

19. A cuboid has six faces. Each face is a rectangle, or there may be two opposite faces that are square, and the opposite faces are equal in size and exactly the same.

20. A cuboid has 12 sides, which are divided into three groups, and four sides are equal in length.

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