(2025) the standard library for the new curriculum for compulsory mathematics is accompanied by reference answer one, filling in blank questions (20 points per cent) 1. 2025 editions of the curriculum standard for compulsory mathematics condensed “mathematic core” into “three sessions”, i. E. Looking at the real world with a mathematical perspective, thinking about the real world with a mathematical thinking. The new theme “ ” was added to the field of “numbers and algebras” at the primary level, with the aim of enabling pupils to experience abstract processes ranging from numbers to symbols. For the first time, the “statistical and probabilistic” component of the lower secondary stage was introduced to visualize the biases and peaks in the distribution of data. The course standards set out the principles for the design of the “problem chain”, emphasizing that the three-tiered gradient between the problems should be reflected. In the “integration and practice” event, students are required to complete the complete closure of the “question-formulation-reflecting improvement”. In the last year of the first grade, the module “assisting graphics” is designed to assist students in building stereographic images through three types of activities: in the sixth grade, the “ratio and ratio” module, the curriculum standard proposes to introduce the concept of positive ratio using the “ ” scenario to reinforce the early penetration of the concept of function. In the eighth grade, “one function”, the teacher shall direct the student through a four-part process of “ -indicative expression-image-characterism”. The “round” module for the ninth grade, with the addition of the “ ” expedition, allows students to discover the pathology by origami. The curriculum standards require that at least hours of classes, “mathematical games and appreciation”, be arranged every school year to feed the student's mathematical feelings. The “measurement” component of the second primary school cycle promotes consistency in the measurement of length, size and volume, with as the core unit. The “geometric certificate” of the beginning of the lower secondary school was advanced from the eighth grade to the grade in order to reduce the gradient of the certificate. The curriculum standard uses “ ” as the bottom line of the first cycle of training to ensure that pupils at the end of the second grade leave their mouths. In the “data awareness” dimension, students in the third school period should be able to determine the average, median, number of numbers applicable in different contexts. The curriculum standards set out a “ ” concept, emphasizing that learning is a continuation of learning rather than the end of learning. In the list of recommendations for reading “mathematical drawings” in primary schools, the proportion of originals in the country is no less than per cent. The “project learning” evaluation at the junior secondary level uses the three-pronged model “ +performance mission+end demonstration”. In the case of “interdisciplinary thematic learning”, given in the appendix to the curriculum standards, the “ ” project combines three subjects: mathematics, science and fine arts. A new “ ” module for teacher training focuses on upgrading the teacher's own core of mathematics. The curriculum standards suggest that classroom teaching boards should retain a “student generation” space of at least minutes to avoid teachers writing at once. [blank answer] 1. The real world is expressed in mathematical language in terms of 2. Quantities in 3. C. 4. Levels, coherence, openness 5. Solution to verify 6. Touch, roll, roll, roll and roll. 8. Situational perception of car at the same speed as 7. A. Observe experience b. Conjecture to validate c. Memory imitation of d. Expression 22. With regard to “mass sense” culture, the first paragraph advocates that a. Accurately calculates the standard unit for b. To convert c. Reasonable estimates of d. Complex measurement tools to use 23. Under the theme “calculation and operations”, what is moved from the whole to fourth grade? A. The initial recognition of b. Multiplication vertical c. The division of the d. Four hybrid operating sequences24. The curriculum standard suggests that the concept of “functions” in junior secondary schools first appeared as follows: a. Decomposition statistical chart b. Taxi billing table c. Square table d. Geometrical table d. 25. The following evaluation formula is most consistent with the concept of “learning integration”: a. At the end of the examination of b. Classrooms, feedback was given to c. Competition selection of d. The bottom line for integrating “mathematical culture” into the classroom is: a. 1 minute b. 1 hour in a book c. 1 hour in a school year d. No-compulsory provision 28. In the “comprehensive and practical” event, students need most of the support of their teachers: a. Standard answer b. Evaluation rule c. Extracurricular education d. Uniform template 29. Which of the following is the quality of learning standard for the first section of “data classification”? With regard to the "algemic reasoning", the objectives of the third paragraph were: a. Mastery of the weda theory b. Is equivalent to a symbol and gives reasons for c. Rereading the multiplication formula d. Rapidly caused decomposition [the answer to the question of choice] 21. C22. C23. A24. B25. B26. C27. B30. Biii, calculated and answered in a total of 30 points. (tip: a4-paper specification 21 x 29. 7 cm) [the answer] (1) v=x(21-2x) (29. 7-2x) (cm3) (2) guides v'=12x2-203. 6x+623. 7 and v'=0, x ≈3. 8 cm (dismissal of another), vmax≈3. 8x13. 4x22. 1≈1126 cm3. (6 minutes) reading material: “for 40 people in a class in the sixth grade, a one-minute jump rope test averaged 120 under, 115 under and 110 under. A new student scored 120." to determine whether the following statements are correct and to state the reasons briefly. (1) the new average must remain at 120; (2) the new median must remain at 115; (3) the new mass must remain at 110. [answer 1] error. The total has increased from 4,800 to 4920, with 41 people and a new average of 120, but not “a certain” and a new average of 120 if the original average is not integer. (2) error. Both the 20th and 21st medians were 115, and after 120, the 21st place became 115 or 120, and if the 21st place 115 was squeezed to 22, the new median could be 117. (3) error. The number is the most frequent occurrence, adding a 120 may equal or exceed 110 times and the number may turn to 110 and 120 doubles or only 120 times. In the “exploring laws” course for the seventh grade (6 points), students find: 12+22+...+n2=n(n+1) (2n+1)/6. The teacher asked: can you spell it out in graphics? Please provide an intuitive description along the lines of "3d" with a short graphic text description. [the answer] treats 12- to n2 as a squared array of k2 points per layer. Disassembly the k-point array into a k "l" fold, each containing a k-point. Collapse all the cones in a mistangible direction along the space x axis, which can be codled into a tilted cone with a base of nx(n+1) and a high (2n+1). This is evidenced by the total number of points, i. E. The ratio of the pristine volume formula. (text description: overside view is a ladder, side view is triangulated, with no gaps in the whole.) 34. (6 minutes) a school study on the “trust carbon sinks on campus” project has measured annual chest growth data (in cm): 2. 1, 2. 3, 2. 0, 2. 4, 2. 2, 2. 5. (1) calculates average annual growth and differentials; (2) if carbon sinks are proportionally proportional to chest diameter squares, the percentage of carbon sinks absorbed in the sixth year is estimated to be higher than in the first year. [a answer] (1) = (2. 1+... +2. 5)/6 = 2. 25 cm; variance s2≈0. 032。(2) ratio coefficient k, sixth year carbon sinksk (2. 25+2. 1+2. 3+2. 0+2. 4+2. 2+2. 5), first year k(2. 1. 1), excess percentage =
(d62-d12)/d12
X 100% ≈
(15. 82-2. 12)/2. 12
X 100% ≈5569%. (note: simplified model with actual points required. 35. 6. Extension of the “round” module for the ninth grade: ab is the ⊙o diameter, c is the upper circle, cd ⊥ab is the d link to ac, bc. Evidence: cd2 = ad. Db, and how this conclusion relates to the “deepness” of photographs. In rtabc, the cd is tilted high, so cd2=ad. Db. For metaphors: the depth of the scene corresponds to the length of ad db in the "clear section" and the larger ab in the aperture diameter, the more obvious the background is, the more obvious the background (cd2) is, the more geometrical the conclusion is, the greater the diameter, the greater the depth of the depth of the landscape. Teaching design questions (15 minutes total) 36. Read and respond to the following material: a follow-up module for the second grade “additions and additions to the table”, which presents a “magic step” scenario: each step is 7 cm high, the elves jump up 3 levels, jump down 2 levels and jump up 4 levels [requests] (1) write the core chain of the subject (three questions, reflecting the level); (2) design a “secondary school” activity, highlighting the “multiplier-to-reverse calculation”; and (3) give learning evaluation points (two simple). [refer to answer] (1) the core chain: how many centimetres does the elf rise? How many times do you jump? If the steps are unknown, the same number rises by 63 centimetres and how high is the step? (equal thinking) (2) high school activities: “paper cup telephone ladders” - students stacked high with one-time cups, one-step per three cups, 7 cm high. Group cooperation: the target is given a height of 56 cm, assuming that it takes several steps and then applying multipliers to verify that the error exceeds one level. At the event, students are automatically divided by 56 ÷7 steps, tested by multiplication, and are perceived to be reversible. (3) element of the evaluation: whether the process of “known totals versus required quantities per mass” can be recorded in detached algorithms; and whether the “multipliers against each other” can be explained and their original estimates modified by physical operation. Case analysis (out of 15 minutes) 37. Watches the classroom footage: fourth grade “intra-triangular angles and” import links, teachers allow students to draw triangles each, cut the angles and square them, and then ask: “is all triangles so?” and i said, "i'm drawing a blunt angle triangle, and i can spell it flat." and b questions, "we've only got dozens of them, and if there's any exceptions?" and the teacher says, "well, let's see if there's any exceptions. Post-school research shows that only 12 per cent of students actually implement it, with no exceptions, but that students still have less than 70 per cent confidence in the conclusions. Please answer: (1) what are the reasonable factors in the teacher's approach? (3 minutes) (2) identifies major shortcomings and makes two suggestions for improvement. (6 minutes) (3) please design a “mathematical reasoning + technical validation” integration to increase the general acceptance of students. (6) [reference answers] (1) reasonable factors: respect for student experience and encouragement of large sample observations; use of information technology to extend classes; attention to student questioning spirit. (2) deficiencies and recommendations: less than one: the sample, though large, remains in “quantitative” accumulation and lacks “mass” reasoning; less than two: the task is too open and the lack of ladder guidance leads to low implementation. Recommendation 1: introduction of a “column-line corner” doctrine in the classroom immediately, with a parallel-line triangle to move the corner and complete the performance certificate; recommendation 2: after-school
