Counting units and numbers
Counting units, numbers and decimal counting methods.
Rewrite Numbers (Omit)
1. Rewrite multiple numbers into "10,000" and "100 million"
Direct rewrite:
First, move the decimal point of the original number to the left by 4 or 8 places (the end of the decimal part is 0 to be crossed out), then add 10000 or 10000 million, and add "=" in the middle.
The omitted mantissa is rewritten as a divisor:
Omit the mantissa after 10,000 digits or 100 million digits by rounding, then add 10,000 digits or 100 million digits after the digit to get the approximate number, and add "√" in the middle.
2. Find the decimal approximation.
According to the requirements, wherever decimal places are reserved, the mantissa after this digit should be omitted by rounding, such as 1.5 ≈ 2, 1.4 ≈ 1. Use ""in the middle.
3. Reciprocity between false fraction and band fraction or integer. (from the network)
1. Turn a false fraction into a fraction: the denominator is unchanged, the integer obtained by dividing the numerator by the denominator is the integer part with the fraction on the left, and the remainder is the numerator.
2. Turn the band fraction into a false fraction: the denominator is unchanged, and the numerator is the product of the sum of the integer part and the denominator plus the original molecule.
3. Divide the band into integers: divider ÷ divider = divider/divider, and the divisible band is an integer.
Interoperability among fractions, decimals and percentages. (from the network)
Fractional decimals, that is, numerator divided by denominator, are decimals. When converted into percentages, it is to multiply decimals by 100 and then add a% sign after it, and vice versa.
For example, 1/4 is converted into decimal, that is, 1 divided by 4 = 0.25 is decimal, and then converted into percentage, that is, 0.25 * 100 = 25 plus% is 25%.
If 25% is converted to decimal, that is, the percentage sign is removed, now it is divided by 10025/ 100 = 0.25.
The component number of 0.25 is 25/ 100 and then simplified to 1/4.
Comparison of figures
Integer size comparison, decimal size comparison and fractional size comparison.
The nature of numbers
The basic properties of fractions and decimals and the changing law of decimal size caused by the movement of decimal position.
Understanding of numbers
Factor, multiple, odd number (jρ), even number, prime number, composite number, factorization prime factor, greatest common factor, least common multiple.
Significance and counting method of four operations
Addition meaning, subtraction meaning, multiplication meaning, division meaning, addition, subtraction, division, multiplication and check calculation.
Algorithms and simple methods, elementary arithmetic.
Additive commutative law, additive associative law, multiplicative commutative law, multiplicative associative law, multiplicative distributive law, properties of continuous reduction, properties of quotient invariance.
Subtraction property: a-(b+c) = a-b-ca-(b-c) = a-b+c.
Classification of operations: addition and subtraction are called first-order operations; Multiplication and division are called two-stage operations (abbreviated)
Composite application problem
Formulas and equations
equation
unit of measure
The speed of progress between length, area and volume, and their similarities.
Quality units and the progress between them
1 ton = 1000 kg = 1000 g.
Time unit exchange rate
Ratio and proportion
Positive proportion, inverse proportion, simplified proportion, proportion and fraction, division connection, proportion, proportion, solving application problems with proportion
Graphics and space
Graph, space, perimeter, area, lateral area, surface area, graph transformation, graph and position.
Statistics and possibilities
Statistical chart, average, median, mode, possibility
1. Analysis of the overall situation of students' mathematics academic performance: Judging from the results of the unified examination at the end of last semester, the average score of mathematics in the graduating class of our school was 78.6, with a passing rate of 92.4%, and the overall score was at the upper-middle level in the city. In order to further consolidate and improve the quality of mathematics teaching in our class, combined with the reality of our school, the following review strategies are formulated.
1, strengthen the leadership of the graduating class, and ask the school leaders to take overall responsibility in person. Closely combine the results of the graduating class with the comprehensive assessment results of the leaders, and give strong support in material resources, financial resources and time to ensure the smooth review of the graduating class.
2. Teachers are required to teach students in accordance with their aptitude, grasp both ends to promote the middle, and ensure that the gifted students learn well and the underachievers stay. Grasping both ends is to ensure the passing rate, and promoting the middle is to ensure the average score.
3. Make full use of the network teaching and research resources and advantages of our school, build a platform for final review and discussion, and have extensive exchanges with teachers and experts inside and outside the school to learn from each other's strengths; Broaden teachers' horizons and improve review efficiency and effect.
4. Combine work and rest, so that students can study in a relaxed and pleasant atmosphere. In the review stage, physical education class and music lessons should be kept to ensure that students have enough entertainment time.
Third, review time: June10-June 27th.
Fourth, review method: according to the arrangement and review of the teaching materials in the previous stage, as well as the actual situation of our students and the characteristics of the test proposition. The review method will be mainly based on the classification of test questions, and the learned knowledge will be divided into four sections: mathematical concepts and basic skills, operation questions, calculation and problem solving. Its main purpose is to improve students' comprehensive ability to use knowledge and answer various questions, and lay a good foundation for getting good grades in the final exam.
This kind of exercises are mainly reviewed by filling in the blanks, judging and choosing. He mainly examines students' ability to comprehensively apply concepts, properties, formulas and laws learned in primary schools. Therefore, on the basis of students' mastery and understanding of various concepts, properties, laws and formulas, teachers should pay attention to helping students understand the connections and differences of various concepts, laws and properties, and then carry out special exercises to let students see various types of questions, so as to improve their ability to answer such questions. The main review method is to carry out special exercises through comparison, analysis and comparison of typical examples.
Such as number and algebra, to help students understand the following knowledge.
(1) Write 950084000 yuan as a unit (), and the mantissa after omitting ten thousand digits is (). Distinguish between rewriting and ellipsis.
(2) 1.497 Keep the integer as (), one decimal place as () and two decimal places as (). The key is to make students understand that the zero after the decimal point cannot be removed.
(3) Divide a 3-meter-long iron wire into 7 segments on average, each segment is the ()/() segment of this iron wire, and each segment is () meters long. It is necessary to explain clearly to students the meaning of scores and the definition of how many units in each copy are one.
(4)0.75= 12 ( )=( ): 12=75/( )=( )%。 Help students understand the relationship among decimals, fractions, ratios and percentages, and let them master the solutions to such problems.
(5) Division of numbers is mainly carried out through practice on the basis of understanding various concepts. The tenth digit of a number is the smallest prime number, which is the smallest composite number, the percentile is the largest digit, one thousandth is a number divisible by 2 and 3 at the same time, and all other digits are 0. This number is written as () and accurate to the tenth place is ().
In the basic knowledge of algebra
(1) Find out how to represent numbers by letters. Write AX4.5A by multiplying the multiplication sign A by 4.5, and write AX4.5A by omitting the multiplication sign.
(2) Understand the difference between ratio and ratio. 1 ton: 250kg is the simplest integer ratio (): (), and the ratio is ().
(3) Reverse application of proportional property: If AX3=BX5, then A: B = (): () B: A = (): ()
(4) Understanding the concept of scale, such as a machine part with a length of 3 mm.. Measured on the drawing, its length is 2 1 cm, and the scale of this drawing is ().
Quantity and measurement
It is mainly to let students know the forward speed between two units of measurement and the actual quantity of one unit. For example, the area of (1) school playground is about 1.2 (). The volume of a container is 12 ().
(2)3 kg 50 g = () g 3.5 kg = () kg () g.
A rudimentary knowledge of geometry
What does the size of (1) angle have to do with? For example, an angle is 45 degrees. Xiao Ming looks at it with a magnifying glass. The angle is () degrees.
(2) the difference between area, perimeter and volume.
(3) The volume relationship between a cylinder and a cone with equal bottom and equal height.
Help students fill in the blanks, judge and choose multiple-choice questions after understanding the confusing knowledge points.
(2) Operation problem (June 16)
This kind of test questions is mainly reflected in the spatial graphics, which mainly examines the students' hands-on and practical ability. In the design of test questions, the common graphic calculation is changed to drawing as required, and the data is obtained through the operation of "drawing and quantity" before the relevant calculation is carried out. As in a rectangle
Draw a line segment and divide it into the largest isosceles right triangle and a
trapeziform
(1) The maximum angle of this trapezoid is () degrees.
(2) Please measure the relevant data and calculate the area of triangle and trapezoid respectively. Therefore, when reviewing this kind of test questions, we should strive to set out from the problem situation, establish a model, seek conclusions and apply the basic process of popularization.
(3) Calculation review (June1September-June 20th)
1, oral calculation review: pay attention to estimation and grasp the operation order.
Such as:1x 4/51x 4/51/9-1/9.
2. Solving Equation solution ratio: Note that addition and subtraction are mainly three digits, the multiplication factor does not exceed two digits, and the divisor in division does not exceed two digits. At the same time, let students master the basis of solving equations and proportions.
3, mixed operation, grasp the difficulty, elementary arithmetic does not exceed four steps, mixed operation has no decimals and fractions. Pay attention to the application of simple methods.
4. Formulaic calculation: pay attention to the application of column equation and arithmetic.
The key to reviewing the above questions at this stage is how to improve the calculation accuracy of students.
(3) Review of application problems (June 21-June 24)
First of all, teachers should understand that according to the basic requirements of Curriculum Standards, integer and decimal application questions should not exceed three steps, and percentage and fraction application questions should not exceed two steps. Secondly, the choice of application questions should pay attention to the connection with students' real life, and the presentation methods should be diversified and open, giving life factors to the application questions and adapting to the psychological needs of students' personality differences. If Party A, Party B and Party C take a taxi home, Party A will get off at 1/3. When the line reaches 2/3 of the whole journey, B gets off; C didn't get off until mid-point. The three of them paid the fare of 144 yuan. What do you think is the most reasonable payment method for Party A, Party B and Party C? Briefly explain why. Wait for the practice of the test questions.
1, composite application problem. The main feature is that the regularity is not strong. The key is to let students read the questions carefully and analyze and answer the questions with analytical methods.
2, column equation to solve application problems. Mainly train students to find the equivalent relationship in the problem, and then make equations.
3, scores, percentage application questions. Find out the quantity of the unit "1" and answer it in the way students like.
4. Solve application problems in proportion. Judge what proportion it is, then write the quantitative relationship and list the proportion.
5, geometry knowledge application questions. (1) When calculating the perimeter and area of a plane figure, you should memorize the calculation formula and pay attention to 1/2 when calculating the triangle area. Accuracy of calculating the circumference and area of a circle. (2) When calculating the surface area and volume of three-dimensional graphics, we should pay attention to the accuracy of calculating the surface area and volume of cuboids and cylinders while remembering the calculation formulas.