The knowledge point of the sixth grade mathematics review: the reciprocity of numbers
1. Decimal component number: There are several decimals, so writing a few zeros after 1 as denominator and removing the decimal point after the original decimal point as numerator can reduce the number of quotation points.
2. Fractions become decimals: numerator divided by denominator. Those that are divisible are converted into finite decimals, and some that are not divisible are converted into finite decimals. Generally three decimal places are reserved.
3. A simplest fraction, if the denominator does not contain other prime factors except 2 and 5, this fraction can be reduced to a finite decimal; If the denominator contains prime factors other than 2 and 5, this fraction cannot be reduced to a finite decimal.
4. Decimal percentage: Just move the decimal point to the right by two places, followed by hundreds of semicolons.
5. Decimal percentage: Decimal percentage, just remove the percent sign and move the decimal point two places to the left.
6. Convert fractions into percentages: usually, first convert fractions into decimals (three decimal places are usually reserved when they are not used up), and then convert decimals into percentages.
7. Decimalization of percentage: First, rewrite percentage into component quantity and put forward a quotation that can be simplified to the simplest score.
Knowledge points of sixth grade mathematics: graphic calculation formula
1, square (c: perimeter s: area a: side length)
Perimeter = side length ×4 C=4a Area = side length× side length s = a× a.
2. Cube (V: volume A: side length)
Surface area = side length × side length× ×6 S Table =a×a×6
Volume = side length × side length × side length v = a× a× a.
3. rectangle (c: perimeter s: area a: side length)
Circumference = (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) surface area (length× width+length× height+width× height )× 2s = 2 (AB+ah+BH)
(2) volume = length× width× height V=abh
5. Triangle (S: area A: base H: height)
Area = bottom × height ÷2 s=ah÷2
Height of triangle = area ×2÷ base of triangle = area ×2÷ height
6. parallelogram (s: area a: bottom h: height)
Area = bottom × height s=ah
7. trapezoid (s: area a: upper bottom b: lower bottom h: height)
Area = (upper bottom+lower bottom) × height ÷2 s=(a+b)× h÷2.
8. Circle (s: area c: perimeter л d= diameter r= radius)
(1) perimeter = diameter× л = 2×л× radius C=лd=2лr
(2) area = radius × radius× л
9. Cylinder (V: volume H: height S: bottom area R: bottom radius C: bottom circumference)
(1) lateral area = bottom perimeter × height =ch(2лr or лd) (2) surface area = lateral area+bottom area ×2.
(3) Volume = bottom area × height (4) Volume = lateral area ÷2× radius.
Cone (v: volume h: height s: bottom area r: bottom radius)
Volume = bottom area × height ÷3
1 1, total number of copies/total number of copies = average.
12, the formula of sum and difference problem
(sum+difference) ÷2= large number (sum-difference) ÷2= decimal.
13 and the question of time
Sum ÷ (multiple-1) = decimal × multiple = large number (or sum-decimal = large number)
Mathematics learning methods and skills
First, a clear teaching objectives, develop a review plan
The total review capacity of mathematics in primary school graduating classes is large, the time span is long, and the forgetting rate of what they have learned is high. Before reviewing, teachers must study the textbook again to further understand the knowledge content and arrangement characteristics of the textbook, and also study the mathematics curriculum standards again, grasp the key points of teaching and mathematics knowledge, and conduct a comprehensive survey of students' knowledge, then determine the review objectives and make a review plan, which mainly includes: reviewing the main points, dividing into several classes and designing each class. For example, make a review plan for the unit "number operation": the first section reviews four calculation methods and their relationships, the second section reviews the algorithm, and the third section reviews the elementary arithmetic of integers and decimals. Only in this way can the review work be carried out in a planned and step-by-step manner. This logical progressive review method can fundamentally overcome the blindness and randomness of review, and the idea of simply reviewing textbooks as content, so that students can complete things according to the book.
Second, understand the learning situation and formulate review methods.
As the saying goes, "know yourself and know yourself, and you will win every battle." Although this sentence is used to direct marching and fighting, I think it is also suitable for guiding teaching. As an experienced teacher, we should first master students' every move, every word and deed, make timely adjustments to teaching work, reduce ineffective labor, and ensure that teaching activities do not deviate from the predetermined teaching objectives. There are many ways to understand the learning situation, such as "teaching observation", "talking with teachers and students" and "developing the second classroom method". In teaching practice, teachers can pay more attention to observation, sum up experience, use their brains and use various methods flexibly, so as to have a clear understanding of students' behavior, thoughts and feelings, learning situation and so on, so as to carry out teaching work in a targeted manner and improve the quality of classroom teaching.
Thirdly, combing knowledge and forming knowledge network.
After six years of mathematics study, most primary school graduates have mastered quite a lot of knowledge points. If they don't have a clear idea to help students, it's like a jumble of goods, which is particularly difficult to remember. Only by sorting it out and sorting it in an orderly way can it be clear at a glance. Therefore, in review, students should be guided to sort, classify and integrate the knowledge they have learned according to the key points of knowledge, the difficulties in learning and the weak links of students, so as to understand its context, communicate its vertical and horizontal relations and grasp the knowledge structure as a whole. The purpose of guiding students to organize themselves and promoting the systematization of knowledge is not only to build a complete knowledge network, but also to let students have a new understanding and improvement of what they have learned before while building a knowledge network. At the same time, we should pay attention to cultivate students' awareness of independent arrangement in the process of review and arrangement, and develop students' ability of independent learning. When reviewing, guide the students to divide the knowledge into blocks, organize it systematically, review it in blocks and memorize it one by one. If we find out the rules of each subclass, the memory effect will be greatly enhanced. Classify knowledge, present it in tabular form, refine it to each knowledge point, review it one by one, consolidate and strengthen it to achieve proficiency, and call it from block knowledge memory when using it, and the speed can also be accelerated. For example, in the part of space and graphics, the author built such a framework for students: point, line, surface and body. Points are: endpoint, vertex, starting point, vertical foot, etc. Lines include straight lines, rays, line segments, etc. There are rectangle, square, triangle, parallelogram, trapezoid, circle and so on. There are cuboids, cubes, cylinders and cones. Each knowledge point has its own meaning and characteristics. Through this logic, a knowledge situation combining with students' thinking rules is successfully constructed. Points are the basis of lines, which can be connected into lines, lines can form faces, and faces can be surrounded by bodies. The vertical line is actually the height of the face and body. These knowledge exist independently and are interrelated to form a system, which is convenient for students to master systematically.
Summarize the relevant articles on the basic knowledge points of mathematics in grade six;
★ Summary of the knowledge points reviewed at the end of the sixth grade mathematics.
★ Summary of Mathematics Knowledge Points in the Sixth Grade of Primary School
★ A Complete Collection of Mathematics Learning Methods and Skills in the Sixth Grade of Primary School
★ Sort out and summarize the knowledge points of the first volume of mathematics in the sixth grade.
★ Summary of knowledge points in the first volume of sixth grade mathematics
★ Summary of preliminary knowledge points of mathematical geometry in grade six
★ Summary of mathematical knowledge points in the first volume of the sixth grade
★ Review the knowledge points in the first volume of sixth grade mathematics.
★ Arrangement of basic knowledge points of primary school mathematics
★ Summary of important and difficult knowledge in sixth grade mathematics