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 to find what is eight tenths of 1.5. How much is 1.5× 1.8? It 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: × 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) Calculation method of division with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor an integer, and then calculate according to the rule of fractional division with divisor as 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 be written as 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. The area of the fifth unit polygon 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 the area of a parallelogram, which is equal to twice the area of a triangle. Because the area of rectangle = length × width, and the area of parallelogram = bottom × height. Because parallelogram area = base × height, triangle area = base × height ÷226. Derivation of trapezoid area formula: the second derivation method of rotation 27, triangle and trapezoid. The teacher said that two identical trapezoids can be combined into a parallelogram by reading books, as long as you know it. The base of parallelogram is equivalent to the sum of the upper and lower bases of trapezoid; The height of parallelogram is equivalent to the height of trapezoid; The area of parallelogram is equal to twice the area of trapezoid, because the area of parallelogram is equal to bottom× height, so the area of trapezoid is equal to (upper bottom+lower bottom )× height ÷228 and the areas of parallelogram with equal bottom and equal height are equal; Triangles with equal bases and equal heights have equal areas; The area of a parallelogram with equal base and equal height is twice that of a triangle. 29. The rectangular frame is drawn as a parallelogram with a constant perimeter and a smaller area. 30. Combination diagram: convert it into a simple diagram that has been learned and calculate it through addition and subtraction. Unit 6 Statistics and Possibility 3 1, Average = Total ÷ Total 32. The advantage of median is that it is not affected by too large or too small data, so it is more suitable to represent the approximate level of all data. Unit 7 Mathematics Wide Angle 33. Numbers can be used not only to indicate quantity and order, but also to encode. 34. Postal code: It consists of 6 digits, the first 2 digits represent the province (municipality directly under the central government or autonomous region) 05400 1, the first 3 digits represent the postal area, and the last 2 digits represent the county (city). The ID number is 18 digits130521kloc. Unit 1 multiples and factors (we only study multiples and factors within the range of natural numbers (except 0). ) 1, numbers like 0, 1, 2, 3, 4, 5, 6 are natural numbers. 2. Numbers like -3, -2,-1, 0, 1, 2,3 ... are integers. 3. Relationship between integer and natural number: Integer includes natural number. 4. Multiples and factors: for example, 4× 5 = 20, 20 is a multiple of 4 and 5, and 4 and 5 are factors of 20, and multiples and factors are interdependent. 5. Multiply: search in order from 1 time. 6. Characteristics of multiples of a number: ① The number of multiples of a number is infinite; (2) The minimum multiple is itself; ③ There is no maximum multiple. 7. Find a factor: find a numerical factor, preferably one-on-one, in an orderly way. 8. Features of a number factor: ① The number of factors of a number is limited; ② The minimum factor is1; The biggest factor is itself. Features of multiples of 9 and 2: Numbers in units of 0, 2, 4, 6 and 8 are multiples of 2. 10, odd number and even number: numbers that are multiples of 2 are called even numbers, and numbers that are not multiples of 2 are called odd numbers. According to whether a number is a multiple of 2, natural numbers can be divided into two categories: odd and even. 1 1 and multiples of 5: Numbers with 0 or 5 digits are multiples of 5. 12 and multiples of 3: the sum of the numbers on each digit is a multiple of 3, and this number is a multiple of 3. 13 is a multiple of 2 and a multiple of 5: a number with a unit of 0. It is both a multiple of 2 and a multiple of 3: ① The digits are numbers of 0, 2, 4, 6 and 8; ② The sum of digits on each number is a multiple of 3 and a multiple of 5: ① A number is a number of 0 or 5; ② The sum of digits on each number is a multiple of 3, a multiple of 2, a multiple of 3 or a multiple of 5: ① A number is a number of 0; ② The characteristic that the sum of numbers on each digit is a multiple of 3 and 9: the sum of numbers on each digit is a multiple of 9, and this number is a multiple of 9, 14, and prime number: a number has only two factors, 1 and itself, and this number is called a prime number. The smallest prime number is 2, which is an even number among unique prime numbers. Prime numbers within 100: 15, composite number: A number has other factors besides 1 and itself, and this number is called a composite number. 1 is neither a prime number nor a composite number, and the smallest composite number is 4. 16. According to the number of factors of a number, natural numbers can be divided into three categories. The area of the second unit pattern (1) is 1, rectangular perimeter = (length+width) ×2C=2(a+b)2, rectangular area = length× width S=ab3, square perimeter = side length× ×4C=4a4, and square area = side length× side length. Triangle base = area ×2÷ height a=2S÷h 10, triangle height = area ×2 1 square meter = 100 square decimeter = 10000 square centimeter unit 3 fraction 1, 2. Denominator: the number of shares representing the average score. Molecule: indicates the number of copies taken out. 3. Fraction unit: the unit "1" is divided into several parts on average, and the number representing such a part or parts is called a fraction. The number representing one of them is called the decimal unit of this fraction. 4. True fraction: The fraction with numerator less than denominator is called true fraction. The true score is less than 1. 5. False fraction: The fraction with numerator greater than or equal to denominator is called false fraction. False scores are all greater than or equal to 1. 6. With score: A score consisting of integer and true score is called with score. 7. False Fraction Fraction: The numerator is divided by the denominator, the quotient is the integer part with the fraction, and the remainder is the numerator with the fraction, and the denominator remains unchanged. 8. Integer into false fraction: use the specified denominator as the denominator, and use the product of integer and denominator as the numerator. 9. Turn the fraction into a false fraction: the denominator and numerator are multiplied by the integer part with the fraction respectively, and the denominator remains unchanged. 10, prime factor: every composite number can be written as the product of several prime numbers, where each prime number is a factor of this composite number, which is called the prime factor of this composite number. 1 1 means that a composite number is multiplied by a prime factor, which is called prime factor decomposition. For example, 12 = 2× 2× 3 12, and the common factor of several numbers is called the common factor of these numbers. The largest one of them is called their greatest common factor. 13 coprime: the common factor of two numbers is only 1. These two numbers are called coprime. Law of coprime: (1) adjacent natural numbers are coprime; (2) Adjacent odd numbers are prime numbers; (3) 1 is coprime with any number; (4) Two different prime coprime (5)2 and any odd coprime. The difference between prime number and coprime: prime number refers to a number, while coprime refers to the relationship between two or more numbers; These numbers themselves are not necessarily prime numbers, but the greatest common factor between them is 1, such as 8 and 9. 14. The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers. 15. The method of finding the maximum common factor and the minimum common multiple involves the maximum common factor and the minimum common multiple involves 16. A fraction in which the numerator and denominator are coprime is called simplest fraction, or a fraction in which the common factor of numerator and denominator is only 1 is called simplest fraction. 17, divisor: the numerator and denominator of a fraction are divided by the common factor at the same time, and the fractional value remains unchanged. This process is called division. The calculation result is usually expressed by the simplest fraction. 18, comprehensive score: divide the scores of different denominators by the scores of the same denominator, which is called comprehensive score. It is usually easier to use the least common multiple as the denominator of a fraction. 19. How to compare the scores: When the denominator is the same, the score with larger numerator is larger; When the numerator is the same, the fraction with small denominator is large; When the numerator and denominator are different, the total score will be compared again. 20. The basic nature of the score: the numerator and denominator of the score are multiplied or divided by the same number at the same time (except zero), and the size of the score remains unchanged. There are two explanations for the meaning of 2 1 and the fraction: ① Divide the unit "1" into four parts, which means three parts. ② Divide 3 into 4 parts on average, which is 1 part. Mathematics and Transportation: 1 Encountered problems: Basic formula: walking alone: speed × time = distance; Speed and × meeting time = two people walking * * * Distance A+ Distance B = Distance B * * * Travel expenses: ① Ticket purchase scheme: according to the number of people, price difference and group discount quantity. If there are only two options, A and B, choose the cheaper one. ② Car rental problem: solve the problem with list method. Two principles: use more low-priced seats and less empty seats. 3. Look at the picture to find the relationship: ① To understand the relevant information in the chart, we must analyze what the horizontal axis and the vertical axis represent respectively. (2) In the relationship between speed and time, draw a line upward, indicating that the speed increases; Parallel to the horizontal axis, it means driving at a constant speed; Draw a line down to indicate deceleration. (3) On the issue of time and distance, draw a line upward to indicate starting from somewhere; Parallel to the horizontal axis, indicating stillness; Draw the line down, indicating that you have returned to a place from the end. Unit 4 Fraction addition and subtraction 1, addition and subtraction of fractions with different denominators: divide the fractions with the same denominator first, and then calculate according to the addition and subtraction of fractions with the same denominator. 2. Requirements for calculation results: An offer can be converted into the simplest score, or a false score should be converted into the number of components. 3. Fractional decimal method: divide the numerator by the denominator and keep two decimal places. 4. Decimal method of components: depending on how many decimal parts there are, just add a few zeros after 1 as the denominator and remove the decimal point as the numerator to reduce the number of quotation points. Unit 5 graphic area (2) 1, and the method of finding the combined graphic area: (1) segmentation method: divide the graphic into basic graphics reasonably, and the sum of the basic graphic areas is the combined graphic area. (and) (2) Supplementary method: the missing part of the figure is supplemented to form several basic figures, and the basic figure area-supplementary figure area = combined figure area. 2. Estimation of irregular figure area: (1) grid counting method. (2) Irregular figures are regarded as approximate basic figures, and the area is estimated. Chicken and rabbit in the same cage: 1, list method. 2. Assumption 3. Laws in the grid of equations: omit the possibility of the sixth unit 1, use 1 to indicate that the event will definitely happen, use 0 to indicate that the event will definitely not happen, and use scores to indicate the possibility. 2. Design the activity plan. Floor tiles: 1, the floor area divided by the area of each floor tile = number of bricks laid 2, and the number of bricks needed per square meter multiplied by the floor area = number of bricks laid 3, as shown in Formula 4. Note: When converting the unit, the result is not to approximate the whole block number by one, but to write the number directly. (0.5 points for each small question, ***6 points) 0.125+7/8 =1/3+1/4 =1-1/9 = 5//kloc- 9 = 9.8 ÷ 0.01= 3.4+13 =1.08+1/2 = 5/8+1/4 = 4/5-0.2-. (2 points for each small question, ***6 points) 1x+1/5-4/35 = 272x3-6.75 = 33/43x-(1-3/7) =1/44, and the formula calculation. (3 points for each small question, 6 points * * *) 165 minus how many 2.5, leaving 17.5? ② The sum of half of a number and 20 is 120. Find this number. 5, graphic observation, calculation. (3 points for each small question, ***6 points)? Fifth, solve the problem. (5 points for each small question, ***30 points) 1. Xiaoming's mother goes to the supermarket to buy milk. There are three kinds of bottled milk. Which do you think is the most cost-effective? Why? ①250ml/2.00 yuan ②500ml/4.60 yuan ③ 1L/9.00 yuan ②. Spread a layer of 4 cm thick sand on a rectangular plot with a length of 45 meters and a width of 28 meters. If a car can only transport 3.5 cubic meters of sand at a time, how many times must the car transport it at least? 3. The wood length of a cuboid is1.2m.. If the saw is shortened by 2 decimeters, its volume will be reduced by 40 cubic decimeters. Find the volume of log block. 4. Dongdong's family has some eggs, including five numbers of 5, six numbers of 6 and 12 12, all of which are four watches. These eggs are known to be between 100 and 130. Do you know how many eggs Dongdong has?