Preface to the book
Identification and calculation
Space and graphics
solve problems
Algebraic preliminary
Statistics and probability
other
Book one
Understanding of numbers within 20
Introduced in three paragraphs.
1-5 and the understanding of 0: the meaning of reading and writing numbers, cardinal number and ordinal number, size comparison, the composition of numbers, the meaning of addition and subtraction, and oral calculation.
6- 10 understanding of numbers: reading, writing and counting; The order, composition, size comparison and ordinal significance of numbers; Oral addition and subtraction, continuous addition and subtraction, addition and subtraction (oral)
Understanding of the number 1 1-20: number, reading, order and size, writing number, unit and decimal digits, addition and corresponding subtraction of 10; Carry addition within 20 (the method of supplementing ten is the main method, and the diversity of algorithms is advocated).
Emphasis and difficulty: basic concepts, skills, sense of symbols, preliminary sense of numbers, carry addition and verbal calculation.
Know cuboid, cube, cylinder and sphere: intuitively know and initially perceive the characteristics of objects.
Understand rectangle, square, triangle and circle: intuitively understand these plane figures and initially perceive their characteristics.
Graphic assembly. Perception of the complex process from simple graphics to complex graphics.
Scenario addition and subtraction application problems: find the total number, find the remainder, (Figure 4), scenario addition and subtraction, addition and subtraction mixed application problems.
Intuitively penetrate one application problem with more (less) numbers than another.
Emphasis and difficulty: learn to interpret situations, find useful information, know the conditions and problems of application problems, initially complete the connection between the meaning of addition and subtraction and real life phenomena (abstraction and materialization), and master the "one picture and four formulas" of addition and subtraction problems.
Classification: Simple classification of specific things according to different standards.
Infiltrate simple statistics and charts (physical bar charts)
Emphasis and difficulty: diversity of classification standards
Understand the simple structure of clocks and watches, and know the hour and the half hour.
Book one and book two
Subtract by abdicating within 20 minutes: (I want to add and subtract)
The understanding of numbers within 100: counting, writing, numbers (10, 100), composition of numbers (10, 10) and size comparison.
Addition and subtraction within 100: add and subtract one digit from two digits (entry and abdication) and add and subtract ten digits. (oral calculation)
Emphasis and difficulty: abdication subtraction within 20; Add and subtract one digit for oral calculation (entry and abdication). Concepts of Numbers, Numbers and Bit Values
Location: (one-dimensional space) Up and down, left and right, front and back. (two-dimensional space) Up, down, left and right.
Graphic assembly: the process of mutual transformation of perceptual graphics
Emphasis and difficulty: understanding left and right position, initial two-dimensional space position.
Graphic addition and subtraction application problem: find the total number, the remainder, the partial quantity, and find the application problem that one number is more (less) than the other.
The mixed application of addition, subtraction and addition and subtraction
Emphasis and difficulty: continue to learn to interpret situations, find useful information, and complete the transformation from overall relationship to comparative relationship.
Find patterns: simple sorting rules (shape, color, quantity, etc. )
Statistics: through the process of collecting and sorting out data, fill in and describe simple statistical charts (bar statistical charts with one as one; Simple statistics).
Understand RMB: jiao yuan fen, promotion and polymerization rate, currency calculation.
Know the time: know the time and minutes of the timing unit, the propulsion rate 1 hour = 60 minutes, the reading and writing time and minutes,
Volume II
Addition and subtraction within 100: two-digit addition and subtraction (no advance and retreat, advance and retreat), writing calculation rules (the alignment of the same digit is reduced from one-digit addition and subtraction to the tenth digit), continuous addition, continuous subtraction, mixed pen calculation of addition and subtraction, and estimation of addition and subtraction.
Table multiplication: the meaning of multiplication, formula table, formula quadrature, multiplication and addition, multiplication and subtraction are divided into two steps.
Emphasis and difficulty: addition and subtraction rules (primary stage); Multiplication meaning, 99 formula table
Perception of line segments: intuitively identify line segments, measure the length of line segments and draw line segments.
A preliminary understanding of the angle: the name of each part, right angle and right angle of drawing; Penetrating acute and obtuse angles.
Observation objects: view, symmetrical figure and specular reflection figure.
Word expression application problem: find a number that is more (less) than a number, and add and subtract mixed application problems.
One-step calculation of multiplication: what is the sum of several identical addends and how many times a number is an application problem. Multiply, add and subtract application problems.
Statistics: Take one as two bar charts.
Learn to fill in statistical tables, draw statistical charts (1 for 2 units), read data and analyze data.
Focus: Discuss the method of collecting data (orthographic drawing), which can be drawn in the form of one to two.
Difficulties: understanding with one-to-two strategy, how to represent singular (semi-grid data), and analyzing data.
Probability: the perception of simple arrangement, combination and possibility permeates modern mathematical thought. (Mathematical Wide Angle)
Length unit: meters and centimeters; 1m = 100cm； Simple calculation of correlation quantity; Measure the length of the line segment.
Volume II
Intra-table division: average division meaning, division meaning (equal division, including division), division formula reading and writing ability, division formula name knowledge. Quotient of formula, one number and three formulas, multiplication and addition, multiplication and subtraction.
Emphasis and difficulty: the meaning of division and the formula of quotient.
Understanding of numbers within 10,000;
Understanding of numbers within (1) 1000 (2) Understanding of numbers within 10000.
Key points: number reading and writing (there is no reading and writing method of 0 in the middle of the number), number sequence table (single digit-ten thousand digits), the meaning of numbers and the decimal relationship between adjacent numbers, the composition of numbers (hundreds and tens of digits) and size comparison.
Understanding of divisor.
Add and subtract integer hundred and integer thousand by oral calculation.
10000 plus or minus two digits (and within 1 00) by mouth, plus or minus several hundred dozen by pen (if the key ten digits are full or insufficient, enter 1 or back 1 to a hundred), and estimate the addition and subtraction (which can be estimated in combination with specific conditions) )
Translation and rotation: the phenomenon of translation and rotation will be judged, and a figure will be drawn after several squares are translated. Difficulty: Draw a figure after translating a few squares.
Preliminary understanding of acute angle and obtuse angle: knowing acute angle and obtuse angle will judge whether an angle is acute or obtuse, and will draw acute angle and obtuse angle.
Two-step graphics application problems: addition, subtraction, subtraction (or the sum of one number MINUS two numbers) (parenthesis) application problems; Application problems of multiplication, addition and subtraction (comprehensive formulation).
One-step division application problem: equal division, including division, one number is several times the other number application problem.
Two-step application problem of multiplication and division (comprehensive formulation)
Emphasis and difficulty: continue to learn to interpret scenarios, find useful information, and find intermediate problems. Function of parentheses and recursive format.
Simple compound statistical table. Through the comprehensive process from simplex to duplex, understand and draw the structure of duplex statistics table. Difficulties: title comprehension
Bar chart with one as five.
Record with orthographic method, master drawing with five-grid statistical chart, and put forward prediction and rationalization suggestions. Difficulties: Prediction and Suggestions
Grams and kilograms: grams and kilograms know each other, knowing 1 kg = 1000 grams. Calculation of related quantity.
Three volumes
Addition and subtraction within 10,000 (2): calculation of two-digit numbers (continuous carry), addition and subtraction of three-digit numbers (continuous carry and continuous abdication), and calculation of addition and subtraction.
Division with remainder: vertical division in the table, vertical division with remainder and the meaning of remainder, and the relationship between remainder and divisor.
Multi-digit times one digit: oral calculation, integer times one digit, oral calculation, estimation and pen calculation (multiplication of multi-digit times one digit, no carry, continuous carry, with zeros in the middle and at the end of the factor).
Preliminary understanding of scores: understanding scores, comparing scores, understanding scores, comparing scores with denominator scores.
Simple calculation of fractions: simple addition and subtraction of fractions with the same denominator, 1 minus several fractions.
Key points: the meaning of division with remainder, division with remainder is calculated vertically; Algorithms and algorithms for multiplying multiple digits by one digit; Know fractions and fractions, read and write simple fractions, know the name and size of fractions, and simply add and subtract fractions with the same denominator.
Difficulties: continuous carry addition and continuous abdication subtraction in three-digit addition and subtraction.
Understanding of graphics: a preliminary understanding of quadrangles and parallelograms.
Graphic measurement: Know the perimeter and calculate the perimeter of rectangle and square.
Emphasis and difficulty: master the characteristics of rectangles and squares, and correctly calculate the perimeters of rectangles and squares.
One-step application problems: remainder division, multiple digits multiplied by one digit, addition and subtraction, multiple (less) digits application problems; Find an application problem whose number is multiple.
Two-step application problem: add and subtract mixed application problem, one number subtracts the product of two numbers, and the sum of two numbers multiplies one number.
Emphasis and difficulty: collect the information in the situation, choose to deal with relevant information, and understand the quantitative relationship of application questions.
Probability: Feel the possibility, describe the phenomena in life with "certainty", "possibility" and "impossibility", compare the magnitude of the possibility, infer some things in life according to statistical laws, and learn the relevant knowledge of permutation and combination from collocation knowledge. (Mathematical Wide Angle)
Emphasis: Experience the certainty and uncertainty of events and learn to describe some events in life with certainty, possibility and impossibility. Experience the possibility of events and make judgments and inferences.
Difficulties: the experience and regularity of uncertainty, the reasoning of reverse thinking.
Length unit: mm, decimeter, kilometer, 1 cm = 10 mm, 1 decimeter = 10 cm, 1 km = 1000 m, simple unit conversion.
Mass unit: understanding of tons, 1 ton =1000kg, simple unit conversion.
Time unit: hours, minutes, seconds, 1 minute = 60 seconds, after calculating the time.
Three volumes
Divider is the division of single digits: oral calculation (oral calculation of whole hundred and hundreds of numbers), estimation of dividing three digits by one digit, and written calculation (basic written calculation, check calculation of division, division of around 0).
Two-digit multiplication by two-digit multiplication: oral calculation (integer ten, integer hundred times integer ten), estimation and pen calculation (two-digit multiplication by two-digit multiplication without carry, carry).
Preliminary understanding of decimals: Understand decimals (common reading methods of decimals and decimals, the meaning and writing method of one and two decimals and size comparison), and simple addition and subtraction of decimals (addition and subtraction of one decimal).
Key points: divisor is the arithmetic and principle of oral calculation, estimation and pen calculation of one-digit division, and the arithmetic and principle of multiplying two digits by two digits. Have a preliminary understanding of decimals,
Simple decimal addition and subtraction.
The position of graphics: the qualitative understanding of eight directions (east, south, west, north, southeast, northeast, southwest and northwest).
Graphic measurement: knowing the area, calculate the area of rectangle and square.
Emphasis and difficulty: Know eight directions, describe the direction of objects with orientation words, and correctly calculate the areas of rectangles and squares.
One-step application problem: find the application problem of each copy, number of copies, multiple and multiple; Division application problem with remainder; Multiplication application problem of finding the total.
Two-step application problem: the sum of two numbers divided by a number, the sum of multiple numbers divided by a number (average) and the application problems of multiplication, addition, multiplication, subtraction and multiplication and division.
Problem solving: multiplication, division and subtraction.
Mathematical wide angle: overlapping problem, equivalent replacement.
Emphasis and difficulty: from the application problems with equal emphasis on graphics and text to the application problems with pure text narration, choose to deal with relevant information and understand the quantitative relationship of application problems.
Statistics: horizontal single bar chart, the bar chart whose starting cell is inconsistent with the number of units represented by other cells; Data analysis, general.
Key points: Understand the structure of horizontal simple bar chart, the applicability of sawtooth bar chart and the initial grid, make decisions and make reasonable suggestions.
Difficulties: Make decisions according to the statistical chart and put forward reasonable suggestions.
Time unit: year, month, day, 24-hour timing method and calculation of elapsed time.
Area unit: square meter, square decimeter and square centimeter, hectare and square kilometer, 1 square decimeter = 100 square centimeter, 1 square meter = 1 000 square meter, 1 hectare = 1000 square meter,/.
Four volumes
Understanding of large numbers (the improvement and expansion stage of positive integer reading and writing): the concept of counting unit, digits and series, digit sequence table, decimal counting method, reading and writing of numbers within 100 million and above 100 million, comparison of large numbers, rewriting of whole trillions, finding the divisor of large numbers, understanding of calculation tools and calculation with calculator.
Multiplying three digits by two digits (at the end of integer multiplication): oral calculation, written calculation, variation law of product, estimation and checking calculation.
Divider is the division of two digits (the last stage of integer division): oral calculation estimation, written calculation, change law of quotient and checking calculation.
Emphasis and difficulty: the concept distinction of numbers, the reading and writing of large numbers, and the calculation of divisors; The location of the product; Flexible trial quotient and positive definite quotient.
Angle measurement (from a mathematical point of view): the definition of ray, straight line, angle, protractor, drawing angle, understanding of special angle and their relationship.
Parallelogram and trapezoid: vertical and parallel, draw vertical lines, parallel lines, parallelogram and trapezoid features.
Emphasis and difficulty: the formation of spatial skills and spatial concepts such as quantity and painting.
Synchronization of multiplication and division exercises: one-step or two-step general questions;
Travel problem: the relationship between speed, time and distance.
Optimization problems: boiling water problem, pancake problem, unloading problem, countermeasures.
Emphasis and difficulty: the preliminary experience of operational thinking and countermeasures and their application in practical problems.
Composite bar chart: through the combination of two simple bar charts, the structure and production of vertical and horizontal composite bar charts, information reading, analysis and prediction.
Emphasis and difficulty: the structure, production and information reading and analysis of composite bar chart.
Four volumes
Four operations: sorting out and summarizing the operation sequence at the same level, two-stage mixed operation with brackets, three-step problem calculation and simple calculation.
The meaning and nature of decimals: the comparison of meaning, reading and writing, nature and size, as well as the changing law of decimal size caused by the movement of decimal point position, the mutual transformation of singular and composite numbers, and the calculation of divisor.
Decimal addition and subtraction: addition and subtraction pen calculation, addition and subtraction mixed calculation, simple calculation.
Emphasis and difficulty: the change law of decimal size caused by decimal meaning and decimal position movement, pen calculation and simple calculation.
Position and direction: quantitative description of direction, angle and length
Triangle: features (definition, part name, stability, trilateral relationship, triangular relationship), classification, and graphic assembly.
Emphasis and difficulty: describe and determine the position in a quantitative way; Triangular feature
Two-step and three-step compound problems: addition, subtraction, multiplication and division are two-step calculations at the same level, and the sum (difference) of two products and the sum (difference) of two quotients are generally two-step and three-step calculations;
Decimal addition and subtraction: continuous addition, continuous subtraction and mixed addition and subtraction.
Tree planting problem: non-closed three cases, square matrix problem
Emphasis and difficulty: understand the quantitative relationship, find intermediate problems and solve problems; Tree planting problem
Five algorithms of addition and multiplication are represented by letters.
Simple broken-line statistical chart: the structure and characteristics of simple broken-line statistical chart, which can read and make broken-line statistical chart and find and solve simple mathematical problems according to statistical chart.
Emphasis and difficulty: understand the characteristics of broken-line statistical chart, draw broken-line statistical chart and read the chart for analysis.
Book five
Decimal multiplication:
Decimal multiplication operation and algorithm; Small multiple problem; Multiplication checking calculation; Approximation of the product; Multiply, multiply and add, multiply and subtract; The law of integer multiplication is extended to decimals.
Decimal division:
The operation and algorithm of fractional division; Find the approximate value of quotient; Cyclic decimal; Explore the law with a calculator; Solve problems (double standardization, "one-step method" and "tailing method")
Key points and difficulties:
Master the calculation method of decimal multiplication and division; Approximation of product sum quotient; Related problems are solved.
Area of polygon:
The area of parallelogram, triangle, trapezoid and combination figure.
Emphasis and difficulty: explore and master the area calculation formula of parallelogram, triangle and trapezoid, and calculate the area of parallelogram, triangle and trapezoid.
Decimal multiplication:
One step, multiplication, multiplication and addition, multiplication and subtraction to solve problems.
Decimal division: continuous division to solve problems, problems related to the method of entering one, ending and divisor.
Polygon area: solving problems related to polygon area calculation.
Simple equation: solve the problem of addition and subtraction with equation; Multiplication and division method, calculation problems of slightly complex equations and their applications
Key points and difficulties:
Solving equations;
Solve problems related to the multilateral field
Simple equation: use letters to represent numbers, operation rules, calculation formulas and quantitative relations; The meaning and basic properties of the equation; Solve simple equations; Column equations solve some simple practical problems.
Key points and difficulties:
Solve simple equations; Column equations solve simple practical problems.
Statistics:
Median cognition; Find the middle value of a set of data
Key points and difficulties:
Understand the statistical significance of the median; Find the middle value of a set of data
Mathematical wide angle: digital coding
Five volumes
Factors and multiples:
Concepts of factor and multiple; Characteristics of multiples of 2, 3 and 5;
Prime numbers and composite numbers; Prime factorization.
The significance and nature of music score;
The meaning of the score; True points and false points; The basic nature of the score; Reduced score, universal score and size comparison; Mutualization of Fractions and Decimals
Addition and subtraction of fractions:
Fraction addition and subtraction with denominator; Even increased or decreased; Addition and subtraction of fractions with different denominators; Fraction addition and subtraction mixed operation; The arithmetic of integer addition is extended to fractions.
Key points and difficulties:
Related concepts of factors and multiple units; Decomposition factor; The meaning and nature of music score; About points, general points; Fractional addition and subtraction.
Understanding of rectangles and cubes: characteristics of cuboids and cubes; Understand the surface area and volume; Calculate the surface area and volume of cuboids and cubes; Volume; The volume of an irregular object.
Key points and difficulties:
Characteristics of cuboids and cubes; Formation of the concepts of surface area and volume and related calculation.
Fractional addition and subtraction: a simple method to solve the problem of fractional addition and subtraction in one step or two.
Understanding of cuboids and cubes: solving the calculation problem of side length; Solution to the surface area calculation problem of cuboid and cube: solution to the volume calculation problem of cuboid and cube
Key points and difficulties:
Solve the problems related to the surface area and volume of cuboids and cubes.
Mode and compound broken line statistics:
The concept and significance of mode; The connection and difference of the three statistics; Composite broken line statistical chart.
Emphasis and difficulty: The significance of patterns in statistics will seek patterns. Understand and analyze the statistical chart of compound broken line.
Unit of measurement:
Unit of volume, unit of volume's understanding of the progress between unit of volume.
Mathematical Wide Angle: Discovering Defective Products
Liujuan
Fractional multiplication
Fractions are multiplied by integers, and fractions are multiplied by fractions; The law of multiplication is extended to fractions; Understanding of reciprocity.
decimal
Operational significance; Fractions divided by integers, integer fractions divided by fractions and fractional mixing operations.
per cent
The meaning of percentage and its reading and writing methods; Conversion between percentages, fractions and decimals.
Important and difficult
The operational significance, principle and law of fractional multiplication and division can be calculated flexibly.
Position (2D)
Use number pairs to represent the position of an object in a specific situation; Determine the position of the object with several pairs on the grid paper.
circle
Know the circle; The circumference and area of a circle.
Key points and difficulties:
Derivation and application of the formula of circumference and area of a circle.
Fractional multiplication problem solving
Find the fraction of a number; Find a solution to the problem of how much is more or less than a number.
Solving problems by fractional division.
Find a number by knowing its score; The problem of finding a number that is known to be larger or smaller than several fractions is solved (through the equation).
Application of ratio
The significance and nature of applying proportion will be solved (proportional distribution).
Percentage of problems solved
Solve the problems of percentage, discount, tax and interest rate; Find out how much one number is more or less than another; Find the percentage of a number, which is greater than or less than a number.
circle
Solution to the problem of calculating the circumference and area of a circle
Mathematical wide angle
The chicken and the rabbit are in the same cage.
Important and difficult
Analyze the meaning of the question and understand the quantitative relationship.
A formula for calculating the perimeter area of a circle with letters
C=πd or c=2πr
s=πr2
Fan statistics chart
Knowing the characteristics of fan-shaped statistical charts, we can read the necessary information from the charts.
compare
The meaning of ratio and ratio; Basic properties of ratio and simplified ratio.
Liujuan
negative number
Understanding of negative numbers; A complete number axis; Comparison of the size of numbers.
Important and difficult
Understanding of the meaning of negative numbers.
Cylinders and cones
Know cylinders and cones; Surface area and volume of cylinder; Volume calculation of cone.
Important and difficult
Master the characteristics of cylindrical cone, master the calculation formula and derivation process of surface area and volume.
Cylinders and cones
Calculation of surface area and volume of cylinder: a solution to the problem of cone volume calculation.
Proportional application
Solving problems by proportion (solving problems by positive and negative proportions).
Linear ruler
Solve the scale problem (find the actual distance, the distance on the map and the scale).
Mathematical wide angle
Dove cage principle
Important and difficult
Application of positive and negative proportion.
Formula for calculating the volume of cylindrical cone expressed by letters
v=sh=πr2
v= 1/3sh= 1/3πr2
A quantity expressed in positive and negative proportions.
Y/x = k (ok)
Or xy = k (ok)
statistics
It is recognized that we should not only pay attention to the external appearance of statistical charts, but also understand specific information to avoid making wrong judgments.
proportion
The significance and basic nature of proportion; The meaning of positive and negative proportion.
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