Mathematics knowledge of grade five 1. Knowledge points of mathematics in the fifth grade of primary school

Summary of the knowledge points reviewed at the end of the first volume of mathematics in the fifth grade of primary school Unit 1 Decimal multiplication 1, decimal multiplication integer (p2,3): meaning-a simple operation to find the sum of several identical addends.

For example, 1.5*3 indicates how many times 1.5 is or the sum of three 1.5. Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.

2. Decimal times decimal (P4, 5): that is, what is the score of this number. For example: 1.5*0.8 is eight tenths of 1.5.

1.5* 1.8 is 1.8 times 1.5. Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.

Note: In the calculation results, the 0 at the end of the decimal part should be removed to simplify the decimal; When the number of decimal places is not enough, use 0 to occupy the place. 3. Rule (1)(P9): the product of a number (except 0) multiplied by a number greater than 1 is greater than the original number; A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.

4. There are generally three methods to find the divisor: (P 10) (1) rounding method; (2) into law; (3) Truncation method 5. Calculate the amount of money, and keep two decimal places, indicating that the calculation has reached the point. Keep one decimal place, indicating that the angle has been calculated.

6. The operation of (p11) four decimal places is the same as that of an integer. 7. Algorithm and nature: addition: additive commutative law: a+b=b+a addition rule: (a+b)+c=a+(b+c) subtraction: subtraction nature: a-b-c=a-(b+c) a-(b-c)=a-b+c multiplication: C. The significance of fractional division: knowing the product of two factors and one of them, and finding the operation of the other factor.

For example, 0.6÷0.3 means that the product of two known factors is 0.6, and one factor is 0.3 to find the other factor. 9. Calculation method of decimal divided by integer (P 16): decimal divided by integer and then divided by integer.

The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point.

If there is a remainder, add 0 and divide it. 10, (P2 1) The calculation method of division in which the divisor is a decimal number: first expand the divisor and the dividend by the same multiple to make the divisor an integer, and then calculate according to the rule of fractional division in which the divisor is an integer.

Note: If there are not enough digits in the dividend, make up the dividend with 0 at the end. 1 1, (P23) In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places as needed to obtain the approximate value of the quotient.

Division change of 12, (p24,25): ① Quotient invariance: divisor and divisor expand or shrink by the same multiple (except 0) at the same time, and the quotient remains unchanged. (2) The divisor remains the same, the dividend expands, and the quotient expands.

③ The dividend is constant, the divisor decreases and the quotient expands. 13, (P28) Cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals.

Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the cyclic part of 6.3232 ... is 32. 14, and the number of digits in the decimal part is a finite decimal, which is called a finite decimal.

The number of digits in the decimal part is infinite decimal, which is called infinite decimal. Unit 3 Observing the object 15, observing the object from different angles may lead to different shapes; When observing a cuboid or cube, you can see at most three faces from a fixed position.

Unit 4 Simple Equation 16, (P45) In a formula containing letters, the multiplication sign in the middle of the letters can be written as "?" , can also be omitted. The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.

17, a*a can write a? A or a, a is pronounced as the square of a, and 2a stands for a+a 18. Equation: An equation with an unknown number is called an equation.

The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. The process of solving an equation is called solving an equation.

19, principle of solving equation: balance. The equation still holds when the left and right sides of the equation add, subtract, multiply and divide the same number (except 0) at the same time.

20, 10 quantitative relationship: addition: sum = addend+addend = and-two addend subtraction: difference = minuend-Mei Mei = difference+Mei Mei = minuend-difference multiplication: product = factor * factor = product ÷ another factor division: quotient = 22, equation testing process: = ... a calculation process of solving equations.

= the right side of the equation, so X=… is the solution of the equation. Unit 5 Polygon area 23, formula: rectangle: perimeter = (length+width) * 2- length = perimeter ÷2- width; Width = perimeter ÷2- long letter formula: C=(a+b)*2 area = length * wide letter formula: S=ab square: perimeter = side length *4 letter formula: C=4a area = side length * side length letter formula: S = parallelogram area = bottom * high letter formula: S=ah triangle. Height = area *2÷ letter formula: S=ah÷2 trapezoidal area = (upper bottom+lower bottom) * height ÷2 letter formula: S =(a+b)h÷2- upper bottom = area *2÷ height-lower bottom, lower bottom. Height = area *2÷ (upper bottom+lower bottom) 24. Derivation of parallelogram area formula: shear and translation 25. Derivation of triangle area formula: rotating parallelogram can be transformed into rectangle; Two identical triangles can be combined into a parallelogram, and the length of the rectangle is equivalent to the base of the parallelogram; The base of parallelogram is equivalent to the base of triangle; The width of the rectangle is equivalent to the height of the parallelogram; The height of parallelogram is equivalent to the height of triangle; The area of a rectangle is equal to that of a parallelogram and twice that of a triangle. Because the area of a rectangle is equal to the length * width, and the area of a parallelogram is equal to the bottom * height.

Because parallelogram area = base * height, triangle area = base * height ÷226, the derivation of trapezoid area formula: rotation 27, the second derivation of triangle and trapezoid.

2. Fifth-grade students have little knowledge of mathematics.

A math joke 1. Once, her mother patiently inspired her to do arithmetic: "Ya Ya, have you learned to do subtraction?" Come on, let's see, how much is 4 MINUS 2? ""it's already two o'clock, mom. "

"That's right, good boy. So, what about 5 MINUS 5? " "Five minus five, minus five.

"Ya ya muttered," I won't, mom. "

"Son, you can't! Think about it, for example, you have five coins in your pocket, but suddenly, all five coins fall out. Tell me, what else do you have in your pocket? " Ya Ya blinked her eyes and said, "Did you drop it? Well, there is still a hole in my pocket! " "I always get 100 in arithmetic."

"That's because you learn well." "But I never listen in class."

"That's because you are smart. You will know to study hard when you come home from school." "Smart? A little, but after school, I am a person who deals with football. "

"Then you must have cheated in the exam." "I can't say that. I didn't copy books or peek at others. How can I be derailed? "

"Then what happened to you?" "I kicked Jim, the bookworm in front, in the chair." "If you don't, you won't. How can you be so naughty? "

"I kicked the first foot, and he stretched five fingers back with his hand." "What does this mean?" "The answer to the first question is 2+3."

"Oh ... what if you ask the 5*8 answer to the tenth question?" "It was after I kicked the tenth foot that he stretched out four fingers first and then clenched his fist immediately, so I knew the answer of 40." 3. The teacher announced the results: "Xiaohua scored 30 points, Xiaoming scored 20 points ..." Pig: I got 0 points! Dog: What should I do? Me too ... Pig: We both got the same score in the exam. Will the teacher think we cheated? Legend has it that one day, Zhuge Liang summoned his soldiers and said, "Which one of you chooses an integer from 1 to 1024 and keeps it in mind. I asked ten questions, only one' yes' or' no'.

After answering all ten questions, I will' calculate' the numbers in your mind. "ZhuGeLiangGang say that finish, a counselor stood up and said, he has chosen a good number.

Zhuge Liang asked, "Did you choose more than 5 12?" The counselor replied, "No." Zhuge Liang asked his advisers nine questions in succession, and all the advisers answered them one by one.

Zhuge Liang finally said, "The number you remember is 1." The counselor was surprised because he really chose this number.

Do you know how clever Zhuge Liang is? In fact, the method is very simple, that is, take half of 1024, and the tenth time is "1". According to this truth, you can find the required number by asking ten questions in a row.

3. Mathematical sayings 1. Wang Juzheng's Percentage China scientist Wang Juzheng has a proverb about experimental failure, which says, "There is still a 50% chance of success if you continue, or 100% failure if you don't do it." 2. Tolstoy's score When it comes to people's evaluation, Tolstoy compares people to a score.

He said: "A person is like a score, his practical ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the score. "

1, the essence of mathematics is its freedom. Cantor) 2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. Cantor) 3. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity. However, no other concept needs clarification like infinity. Hilbert) 4. Mathematics is an infinite science. Hermanville 5. The problem is the core of mathematics. P.R. halmos 6. As long as a branch of science can ask many questions, it is full of vitality. No problem, indicating the termination or decline of independent development. Hilbert 7. Some beautiful theorems in mathematics have such characteristics: they are easy to sum up from facts, but the proofs are extremely profound. Gauss 3. Rybakov's Constants and Variables Russian historian Rybakov said in The Use of Time: "Time is a constant, but for diligent people, it is a' variable'. People who use' minutes' to calculate time spend 59 times more time than people who use' hours'. "

When talking about learning and exploration, Hua, a famous mathematician in China, pointed out: "To dare to do subtraction in learning is to subtract the parts that have been solved by predecessors and see if there are any unsolved problems, which need us to explore and solve." Edison, a great inventor, used a plus sign to describe genius. He said: "Genius = 1% inspiration +99% sweat."

6. dimitrov's symbol dimitrov, an internationally renowned worker movement activist, said in his evaluation of a day's work: "We should spend time thinking about what we have done in a day, whether it is' addition' or' subtraction'. If it is' addition', we will make progress; If it is'-',you have to learn from it and take measures. " 3. The aphorism written in Formula 7. Einstein Formula When talking about the secret of success, Einstein wrote a formula: A = X+Y+Z Y+Z.

And explained: A stands for success, X stands for hard work, Y stands for correct method, and Z stands for less empty talk. ""If you use a small circle to represent what you have learned and a big circle to represent what I have learned, then the area of the big circle is a little more, but the blank outside the two circles is our ignorance.

The bigger the circle is, the more ignorant faces its circumference contacts. "-Zhi Nuo Cauchy (A.L. Cauchy) People will die, but their actions will last forever. People will die, but achievements will last forever.

Laplace (1749–1827) is not well known. What we don't know is infinite. C. Hermite1822–1901) Abel left mathematicians enough to keep them busy for 500 years. When commenting on Abel, he once said: "What Abel left behind can keep mathematicians busy for 500 years.

"Poursin (Poisson, Simé on1781-1840)" Life is only good for two things, namely, discovering mathematics and teaching.

3. Summary of mathematics knowledge in primary school grades one to five (detailed)

Summary of teaching plan exercises of all subjects courseware in fifth grade of primary school; There are 12 sides, and the sides are equal in length; There are eight vertices.

2. Characteristics of a cube: a cube has six faces, all of which are squares, and all the faces are exactly the same; There are 12 sides with equal length; There are eight vertices. A cube can be regarded as a cuboid with equal length, width and height.

3. The length of three sides intersecting at a vertex is called the length, width and height of a cuboid. 4. The total length of 12 sides of a cuboid or cube is called the sum of their sides.

The sum of the sides of a cuboid = (length+width+height) *4, which can be expressed in letters as =C? Cuboid (a+b+h)4. The sum of sides of a cube = side length * 12, which can be expressed in letters as a cube = 12aC.

5. 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, which is expressed in letters as =(ab+ah+bh)2S? Cuboid.

The surface area of a cube = side length * side length *6, and a cube represented by letters as 2 =6aS. 6. The size of the space occupied by an object is called its volume.

Unit of volume is used to measure the volume. The commonly used unit of volume is cubic centimeter, cubic decimeter and cubic meter, which are expressed by letters as 3cm, 3dm and 3m. 33 1 1000 DCM？ ，33 1 1000mdm？ .

7. A cube with length 1 cm and volume 13cm. The volume of a fingertip is about 13cm.

A cube with a side length of 1 dm and a volume of 13dm. The volume of the chalk box is about 13cm.

A cube with a side length of 1 m and a volume of13 m. Use three pieces of wood with a length of 1 m to make a shelf at right angles to each other and put it in the corner. Its volume is 13cm.

8, cuboid volume = length * width * height, expressed in letters as =abhV cuboid. The volume of the cube = side length * side length * side length, expressed in letters as 3=aV cube.

Unified formula of cuboid and cube: column volume = bottom area * height. 9. The volume of an object that a container can hold is called its volume.

Unit of volume is generally used to measure volume, and the volume of liquid is usually measured in liters and milliliters, and expressed in letters as L and ml. 4 3 1 1Ldm？ ，3 1 1mlcm？ ， 1 1000Lml？ 10, the calculation method of cuboid or cube container is the same as that of volume.

But the length, width and height are measured from the inside of the container. 1 1, the volume of irregular objects can be calculated by drainage method.

The volume of the rising or falling part of the water surface is the volume of the object. The fourth single element 1. Meaning of the score 1. When measuring, dividing things or calculating, integer results are often not available. At this time, it is often expressed by scores.

2, an object, some objects, etc. It can be regarded as a whole, and this whole is divided into several parts on average, and such one or several parts can be expressed by fractions. If everything is divided equally, what is the unit "1"?

3. Divide the unit "1" into several parts on average, and the number representing one part is called fractional unit. The greater the denominator of a fraction, the smaller the decimal unit; The smaller the denominator of a fraction, the larger the fractional unit.

4. Relationship between fraction and division: fraction can represent the quotient of integer division; Divider in division is equivalent to numerator in fraction, divisor is equivalent to denominator in fraction, and symbol is equivalent to fractional line. =? Frequency divider Frequency divider, =? Molecule, numerator, denominator, denominator.

5. How to solve the problem that one number is a fraction of another number: calculate by division. =? When solving a problem, we must first make clear the unit "1" and the comparison quantity. Generally speaking, the unit "1" is followed by the word "yes" or "occupation" in the question. If these two words do not appear, we should judge the previous comparison quantity according to the meaning of the question, and then calculate the comparison quantity in the comparison with the competition unit according to the formula "65438".

6. When a low-level unit is divided into a high-level unit (expressed by a fraction), it is equal to the value of the low-level unit, and the ratio between the two units can be reduced to the simplest fraction. Second, the true score and false score are 1, the fraction with numerator less than denominator is called true score, and the true score is less than1; Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions, which are greater than 1 or equal to1; A fraction consisting of an integer part (excluding 0) and a true fraction is called a band fraction.

2. If the false fraction is converted into integer or fraction, the numerator should be divided by the denominator. When the numerator is a multiple of the denominator, 5 can be converted into an integer; When the numerator is not a multiple of the denominator, the number of components can be converted, the quotient is the integer part with a fraction, and the remainder is the numerator of the fractional part, and the denominator remains unchanged.

3. Turn the band fraction into a false fraction, use the original denominator as the denominator, and use the product of the denominator and the integer plus the original molecule as the numerator, which is expressed as:+=? Denominator integer numerator with fractional denominator III. Basic properties of fraction, reduced fraction, general fraction 1. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged. You can use the basic attributes of a fraction to divide or divide it, or change the denominator into a fraction with a specified denominator or numerator.

2. The common factor of two numbers is called their common factor. The greatest common divisor is called their greatest common divisor.

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 1. (Two numbers with only a common factor of 1 are called prime numbers) 3. To find the greatest common factor of two numbers, we can list the factors of these two numbers separately by enumeration, and then find the common factor. It can also be calculated by short division.

4, numerator denominator only common factor 1 is called simplest fraction. Turning a fraction into a fraction that is equal to it but smaller in numerator and denominator is called reduction.

The divisor can be divided by the common factor of the numerator denominator (except 1), by steps, or directly by the greatest common factor. The common multiple of two numbers is called their common multiple, and the smallest multiple is called their minimum common multiple.

Generally speaking, to find the multiple of a number, we can use enumeration method, graphic method, large number multiplication method and short division method. When two numbers are multiples, the big number is their least common multiple; The least common multiple of two prime numbers is their product.

6. Change the scores of different denominators into the same score equal to the original score.

4. Sort out the knowledge points of mathematics concepts in the first to fifth grades of primary schools.

Basic formula: 1 * number of shares per share = total number of shares/number of shares = 2 1 multiple * multiple = multiple1multiple = 1 multiple 3 speed * time = quantity = total price. Working time = total amount of work ÷ working time = working efficiency 6 factor = product ÷ one factor = another factor 9 Divider ÷ Divider = quotient divider ÷ quotient = divisor quotient * Divider = divider calculation formula for primary school mathematical figures: 1 square c perimeter S area A side length perimeter = side length * 4 c 6 volume = side length * side length * side length V=a*a*a 3 rectangle c perimeter s area a side length perimeter = (length+width) *2 C=2(a+b) area = length * width S=ab 4 cuboid v: volume s: area a: length b: width h: height (1). Volume = length * width * height V=abh 5 triangle s area a bottom h high area = bottom * height ÷2 s=ah÷2 triangle height = area * 2 bottom triangle bottom = area * 2 height 6 parallelogram s area a bottom h high area = bottom * height s=ah 7 trapezoid s area a top bottom b bottom. H÷2 8 circular S area c perimeter π d= diameter r= radius (1) perimeter = diameter *π=2*π* radius C=πd=2πr (2) area = radius * radius *n 9 cylinder V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter (1) lateral area = bottom perimeter * height (2) surface area = lateral area+bottom area *2 (3) volume = bottom area * height (4) volume = lateral area ÷2* radius 10 cone v: volume h: height. Bottom area r: bottom radius and volume = bottom area * height ÷3 sum difference problem formula: total number ÷ total number = average (sum+difference) ÷2= large number (sum-difference) ÷2= decimal and multiple problem ÷ (multiple-1)= decimal. Multiply = large number (or decimal+difference = large number) Tree planting problem 1 Tree planting problem on the non-closed line can be mainly divided into the following three situations: (1) If trees are planted at both ends of the non-closed line, Then: number of plants = number of segments+1= total length ÷ plant spacing-1 total length = plant spacing * (number of plants-1) plant spacing = total length ÷ (number of plants -65438 and then: number of plants = number of segments-/kloc. Number of plants and spacing between plants = total length ÷ number of plants profit and loss problem (surplus+deficit) ÷ difference between two distributions = number of shares participating in distribution (large surplus-small surplus) ÷ difference between two distributions = number of shares participating in distribution (large deficit-small deficit) ÷ difference between two distributions = number of shares participating in distribution; meeting distance = speed * meeting. Catch-up Time Catch-up Time = Catch-up Distance ÷ Speed Difference Speed Difference = Catch-up Distance ÷ Catch-up Time Water Problem Downstream Speed = Still Water Speed+Current Speed = (Downstream Speed+Current Speed) ÷2 Water Speed = (Downstream Speed-Current Speed) ÷2 Concentration Problem Solute Weight+100 Concentration = solute weight ÷ concentration = solution weight profit and discount problem profit = selling price-cost profit rate = profit \ 100% (discount interest = principal * interest rate * after-tax interest of time = principal * interest rate * time *( 1-20%) sum of side lengths: cuboid side length = (. The circumference of a circle is proportional to its diameter; The circumference of a circle is proportional to the radius; The area of a circle is proportional to the square of its radius; Common quantitative relationship: 1. Distance = speed * time and speed = distance ÷ time and time = distance ÷ speed ÷ total work = work efficiency * working time ÷ total work efficiency = unit price * quantity ÷ unit price = total price ÷ total output = single output * output per unit area = total output. 00600 1 ha = 100 ha 1 ha = 100 m2 1 km2 = 100000 m2 1 ha =1ha. 1 cm2 = 100 mm2 unit of volume: 1 cubic kilometer = 1000000 m3 1 m3 = 1000 m3/m3. M =1l1cc =1ml1l =1000 ml weight unit:1t =1000 kg1000 kg. Average year =366 days (leap year), first quarter =3 months, one month =30 days (up, middle and down), one month = 30 days (down), one month =3 1 day (up), one week =7 days, one day =24 hours, one hour. 1 1 month (four months) Special achievements: = 0.5 = 50% = 0.25 = 25% = 0.75 = 75% = 0.2 = 20% = 0.4 = 40% = 0.6 = 60% =.