Review materials for primary school mathematics and Chinese (volume 2 for sixth grade)

Mathematics syllabus

First grade

Teaching content

(1) Numbers and calculations

(1 ) understanding of numbers within 20. Addition and subtraction.

Count. The composition, order, size, reading and writing of numbers. Addition and continuous addition, continuous subtraction and mixed addition and subtraction questions.

(2) Understanding of numbers within 100. Addition and subtraction.

Count. ones digits, tens digits. The order, size, reading and writing of numbers.

Oral arithmetic for adding and subtracting whole tens to two-digit numbers and adding and subtracting one-digit numbers to two-digit numbers. Two-step addition and subtraction problems.

(2) Quantity and Measurement

Understanding of the clock face (full time).

Understanding and simple calculation of RMB.

(3) Preliminary knowledge of geometry

Intuitive understanding of cuboids, cubes, circles and balls.

Intuitive understanding of cuboids, squares, triangles and circles.

(4) Application problems

Relatively easy one-step calculation problems of addition and subtraction.

(5) Practical activities

Choose content that is closely related to life. For example, based on the number of boys and girls in the class and the distribution of the number of people in each group, what mathematical problems come to mind.

Teaching requirements

1. Count the number of different objects and gradually abstract numbers. Will distinguish several and which number. Master the composition of numbers within 10. Able to write numbers correctly and neatly.

2． Recognize the counting units "one" and "tens", and initially understand the meaning of numbers in the ones and tens places. Be able to count numbers within 100 proficiently and be able to read and write numbers within 100. Understand that numbers within 100 are composed of several tens and several ones. Master the order of numbers within 100 and compare the sizes of numbers within 100.

3． Know the meaning of addition and subtraction, the names of each part in addition and subtraction calculations, and the relationship between addition and subtraction. Be able to verbally calculate one-digit addition and corresponding subtraction proficiently, and be relatively proficient in verbally calculating addition and subtraction of whole tens and two-digit addition and subtraction of one-digit numbers. Able to calculate two-step problems of addition and subtraction.

4. Recognize the symbols "="">""<" and use these symbols to express the magnitude of numbers.

5． Know the clock face and tell the time. Get to know the RMB. We know that 1 yuan = 10 jiao, and 1 jiao = 10 cents. We must protect the RMB.

6． Able to answer relatively easy one-step calculation problems of addition and subtraction based on the meaning of addition and subtraction. Know the conditions and questions in the question, be able to list the calculation formula, indicate the name of the unit of the number, and dictate the answer.

7. Cultivate students' good habits of doing questions carefully, calculating correctly, and writing neatly.

8. Through practical activities, students can experience the close connection between mathematics and daily life.

Second grade

Teaching content

(1) Numbers and calculations

(1) Adding and subtracting two-digit numbers .

Add and subtract two-digit numbers. Addition and subtraction vertical forms. Two-step addition and subtraction problems.

(2) In-table multiplication and in-table division.

Initial understanding of multiplication. Multiplication table. Multiplication table. Vertical multiplication.

Preliminary understanding of division. Use multiplication tables to find quotients. Division vertical form. Division with remainder. Two-step calculation formula.

(3) How to read and write numbers within ten thousand.

Count. Hundreds, thousands, ten thousand. How to read, write and compare numbers.

(4) Addition and subtraction.

Addition, subtraction. Continuous addition. Check addition, use addition to check subtraction.

(5) Mixed operations.

First multiply and divide, then add and subtract. Two-step calculation formula. Parentheses.

(2) Quantity and measurement

Understanding of hours, minutes and seconds.

Understanding and simple calculation of meters, decimeters and centimeters.

Understanding of kilogram (kilogram).

(3) Preliminary knowledge of geometry.

Preliminary understanding of straight lines and line segments.

Initial understanding of angles. right angle.

(4) Application problems

One-step calculation problems of addition and subtraction.

One-step word problems for multiplication and division.

Relatively easy two-step calculation word problems.

(5) Practical activities

Content closely related to life. For example, if you investigate your home's spending on various items this week, what math questions come to mind.

Teaching requirements

1. Understand the counting units "hundred", "thousand" and "ten thousand", and know the decimal relationship between two adjacent counting units. Master the sequence of numbers within ten thousand, be able to read and write numbers, and compare numbers.

2． Master the arithmetic rules of addition and subtraction. Can use vertical expression to calculate relatively simple continuous addition problems. Be relatively proficient in verbally calculating addition and subtraction of two-digit numbers (the sum is within 100), and be able to verbally calculate the addition and subtraction of hundreds and thousands, as well as the addition and subtraction of hundreds and tens of hundreds or tens, and be able to use Swap the positions of the addends to check addition and use addition to check subtraction. Initial cultivation of students' habit of inspection and calculation.

3. Know the meaning of multiplication and division, the names of each part in the multiplication and division equations, and the relationship between multiplication and division. Know the multiplication formulas for product and quotient. Ability to calculate divisions with a remainder when the divisor is a single digit and the quotient is also a single digit.

4. Preliminarily master the order of mixed operations and be able to calculate two-step problems. Recognize parentheses.

5. Understand the units of length: meters, decimeters, and centimeters. Know the actual length of 1 meter and 1 centimeter. We know that 1 meter = 10 decimeters and 1 decimeter = 10 centimeters. A simple calculation of length will be performed.

6. Understand the mass unit kilogram (kilogram) and initially establish the quality concept of 1 kilogram.

7. Recognize the units of time: hours, minutes, and seconds. Know that 1 hour = 60 minutes and 1 minute = 60 seconds. Preliminarily establish the time concept of hours, minutes and seconds. Develop good habits of observing and cherishing time.

8． Be able to gradually recognize straight lines and line segments, and be able to measure the length of line segments and draw line segments (limited to centimeters).

9. Get a preliminary understanding of angles and right angles, and know the names of each part of an angle. Can use a set square to determine and draw right angles.

10． Able to solve one-step word problems of addition, subtraction, multiplication and division. Can solve relatively easy two-step calculation word problems step by step.

11. Through practical activities, students’ mathematical awareness is initially cultivated.

Third grade

Teaching content

(1) Numbers and calculations

(1) One-digit multiplication and division.

One multiplier is a one-digit multiplication (the other multiplier is generally no more than three digits). 0 multiplication. Multiply. Division is single digit division. 0 divided by a number. Use multiplication to check division. Continuous elimination.

(2) Two-digit multiplication and division.

One multiplier is a two-digit multiplication (the other multiplier is generally no more than three digits). Simple calculation with 0 at the end of the multiplier

Multiplication check. The divisor is the division of two digits.

A simple algorithm for continuous multiplication and division.

(3) Four mixed operations.

Three-step calculation formula questions. Use of parentheses.

(4) Preliminary understanding of fractions.

Preliminary understanding of fractions, how to read and write them. Look at the pictures to compare the sizes of the fractions. Simple addition and subtraction of fractions with the same denominator.

(2) Quantity and measurement

Understanding and simple calculation of kilometers (km) and millimeters.

Understanding and simple calculation of tons and grams.

Area unit.

(3) Preliminary knowledge of geometry

Characteristics of rectangles and squares. Perimeter of rectangles and squares.

Intuitive understanding of parallelograms.

The meaning of area. Area of ??rectangle and square.

(4) Application questions

Common quantitative relationships. Solve word problems with two-step calculations.

(5) Practical activities

Organize activities by contacting surrounding things. For example, record the weather conditions within 10 days, sort them into categories, and conduct simple analysis.

Teaching requirements

1. Master the arithmetic rules for multiplication and division of single-digit numbers and division of multiple digits (generally no more than three digits), and be able to calculate more skillfully. Ability to use multiplication to check divisions (including divisions with remainders).

2． Master the written arithmetic rules of multiplication and division of two-digit numbers, and be able to arithmetic multiplication and division. Multiplication is checked by swapping the positions of the multipliers. Able to multiply and divide single-digit numbers and divide two-digit numbers (the product is within 100). Able to verbally calculate multipliers and divisors of whole tens. Learn some simple algorithms.

3. Master the order of the four mixed operations and be able to calculate three-step problems. Parentheses will be used.

4. Have a preliminary understanding of fractions and can read and write simple fractions. Compares fractions with the same denominator. Initially learn to calculate the addition and subtraction of simple fractions with the same denominator.

5. Understand the units of length, kilometers (kilometers) and millimeters. We know that 1 kilometer = 1000 meters and 1 centimeter = 10 millimeters. Understand the mass units of tons and grams, and know that 1 ton = 1000 kilograms and 1 kilogram = 1000 grams. Simple calculations of length and mass will be made.

6. Preliminarily master the characteristics of rectangles and squares. Can draw rectangles and squares on graph paper. Know the meaning of perimeter and be able to calculate the perimeter of rectangles and squares.

7. Know the meaning of area. Understand the units of area (square meters, square decimeters, square centimeters). Preliminarily establish the area concepts of 1 square meter, 1 square decimeter, and 1 square centimeter. Master the formulas for calculating the area of ??rectangles and squares.

8． Master common quantitative relationships. Learn to solve word problems with two-step calculations.

9. Through practical activities, students’ mathematical awareness is initially cultivated.

Fourth grade

Teaching content

(1) Numbers and calculations

(1) Reading and writing of numbers within 100 million.

The counting units are "hundred thousand", "million" and "ten million". Decimal relationship between adjacent counting units. How to read and write numbers within 100 million. Number size comparison. Approximate number in thousands.

(2) Addition and subtraction.

A simple algorithm for addition and subtraction of integers and hundreds.

The relationship between the various parts of the addition and subtraction equations. Find the unknown number X.

(3) Multiplication and division.

Changes in product. The constant nature of quotient. Simple arithmetic with 0's at the end of the dividend and divisor.

A simple algorithm for multipliers approaching whole tens and hundreds.

Find the relationship between the parts in the multiplication and division equations and find the unknown number X.

(4) Large number estimation ①. Introduction of abacus or calculator.

(5) Four mixed operations.

Square brackets. Three-step calculation formula.

(6) The relationship and operation laws of integers and their four arithmetic operations.

Natural numbers and integers. Decimal notation. Reading and writing.

The meaning of the four arithmetic operations. The relationship between addition and subtraction, multiplication and division. Integer division and division with remainder.

Laws of operation. Simple calculation.

(7) The meaning and properties of decimals. Addition and subtraction.

The meaning and properties of decimals. Comparison of decimal sizes. Shifting the decimal point causes the size of the decimal to change. Approximation of decimals.

Addition and subtraction. The law of addition generalizes to decimals.

(2) Quantity and measurement

Year, month and day. Ordinary years and leap years. century. 24-hour timekeeping.

Measurement of angles.

Area unit.

(3) Preliminary knowledge of geometry.

Measurement of straight lines. Measure distance (tool test, walking test, visual test).

Ray. Right angle, acute angle, obtuse angle, straight angle, circumferential angle ①. perpendicular. Draw vertical lines. parallel lines. Draw parallel lines.

Characteristics of triangles. The sum of the interior angles of a triangle.

(4) Preliminary knowledge of statistics

Simple data organization. A preliminary understanding of simple statistical charts. The meaning of average. Find the simple average.

(5) Application problems

Answer the application problems of two-step calculation. Solve relatively easy three-step calculation word problems.

(6) Practical activities

Organize activities by contacting surrounding things. For example, during the holidays, a student group organizes an inspection activity. According to the budget, how much activity fee does each person need to pay?

Teaching requirements

1. Understand the counting units "one hundred thousand", "million" and "ten million", and master the decimal counting method. Can read and write multiple digits according to the numerical level. Recognize natural numbers and integers. Able to write an approximate number by omitting the mantissa by rounding off a number as required.

2． Able to calculate orally the addition and subtraction of integers. Add and subtract hundreds and tens to hundreds and tens. Learn simple algorithms for addition and subtraction of numbers close to whole tens and whole hundreds, and be able to perform calculations flexibly. Preliminarily grasp the relationship between the various parts of addition and subtraction equations, and be able to find the unknown number x based on this relationship.

3. Check multiplication by swapping the positions of the multipliers. Know the invariant property of quotient. Able to verbally calculate multipliers and divisions of whole numbers. Learn some simple algorithms. Preliminarily grasp the relationship between the various parts of multiplication and division equations, and be able to find the unknown number x based on this relationship.

4. Understand the meaning of the four arithmetic operations, master the relationship between addition and subtraction, multiplication and division, so that students can receive enlightenment education from the perspective of dialectical materialism. Able to apply the laws of operation to perform some simple calculations. Four arithmetic operations with square brackets will be performed.

5. Understand the meaning and properties of decimals. Be relatively proficient in performing decimal addition and subtraction written calculations (the limit on the number of digits is the same as integer addition and subtraction) and simple oral calculations.

6. Understand the time units of year, month and day, know ordinary years and leap years, and the number of days in each month. The time will be expressed using the 24-hour clock method.

7. Recognize rays and angles, know the size of angles, and be able to use a protractor to measure angles and draw angles according to specified degrees. Initial understanding of perpendiculars and parallel lines, and ability to use rulers and set squares to draw perpendiculars, parallel lines, rectangles and squares. Understand the characteristics of triangles. Know the sum of the interior angles of a triangle.

8． Understand land area units (hectares, square kilometers). Initially learn to use measuring tools to measure straight lines on the ground and measure short distances.

9. Initial understanding of simple statistical charts. Understand the process of collecting and organizing data. A preliminary understanding of the meaning of averages. Can find simple averages. Through statistical materials, students can understand the achievements of my country's socialist construction.

10． Can solve two-step calculation word problems. Can solve relatively easy three-step calculation word problems.

11. Combined with problem solving and calculation, students will further develop the habit of checking and checking calculations and a serious and responsible attitude.

12. Through practical activities, we cultivate students' ability to discover mathematical problems from the surrounding situations, use the knowledge they have learned to solve problems, and cultivate students' mathematical awareness.

Fifth grade

Teaching content

(1) Numbers and calculations

(1) Divisibility of numbers.

Characteristics of numbers that are divisible by 2, 5, and 3. Odd and even numbers. Prime and composite numbers. Table of prime numbers within 100. Factor the prime factors. Divisors and multiples. Common divisors and common multiples. Find the greatest common divisor. Find the lowest common multiple.

(2) Multiplication and division of decimals.

Multiplication and division. Approximate value of product and quotient. Repeating decimals. The laws of multiplication extend to decimals.

Four mixed arithmetic operations without counting (no more than three steps).

* (3) Use a calculator to perform large number calculations or explore relevant laws.

(4) The meaning and nature of fractions.

The meaning of fractions. Fractional unit. Comparison of fraction sizes. The relationship between fractions and division. True fractions and improper fractions. Mixed fractions. Basic properties of fractions. About points. Tongfen. Conversion of fractions and decimals.

(5) Addition and subtraction of fractions.

The meaning of adding and subtracting fractions. Addition and subtraction of fractions (excluding mixed numbers). The operational laws of addition extend to fractions. Mixed operations of fractions, decimal addition and subtraction.

(2) Preliminary knowledge of algebra

Use letters to represent numbers. Simple equation (ax±b=c, ax±bx=c). Solve word problems using equations.

(3) Quantity and measurement

Volume unit.

Singular numbers and plural numbers (complex numbers are generally not used to calculate area or volume).

(4) Preliminary knowledge of geometry

Characteristics of parallelograms and trapezoids. Areas of parallelograms, triangles and trapezoids. *Combined graphics.

Characteristics of cuboids and cubes.

Surface area of ??cuboids and cubes. The meaning of volume, the volume of cuboid and cube.

(5) Preliminary knowledge of statistics

Collection and classification of data. Simple statistical table. Find an average based on the data collected.

(6) Application questions

Encounter problems. Solve three-step calculation word problems.

(7) Practical activities

Organize activities based on the social situations that students are exposed to. For example, investigate the amount of water, electricity, gas and rent paid by 10 households in a certain month, or the annual output of various crops by 10 farmers, and ask some mathematical questions.

Teaching requirements

1. Know concepts such as integers, divisors and multiples, prime numbers and composite numbers, and understand the connections and differences between them. Master the characteristics of numbers divisible by 2, 5, and 3. Can decompose prime factors (generally no more than two digits). Able to find the greatest common divisor (limited to two numbers) and least common multiple (the comprehensive application of the above concepts is not required).

2． Be relatively proficient in decimal multiplication and division written calculations (the limit on the number of digits is the same as integer multiplication and division) and simple oral calculations. Can use rounding method to intercept the approximate values ??of products and quotients. Can perform mixed decimal arithmetic operations (no more than three steps).

3. Understand the meaning and basic properties of fractions. Able to compare fractions and perform reductions and general divisions more skillfully. Can convert fractions to decimals. Understand the meaning of adding and subtracting fractions. Master the calculation rules for adding and subtracting fractions, and be able to calculate addition and subtraction of fractions more skillfully. Correctly perform mixed operations of adding and subtracting fractions. Able to do simple addition and subtraction of fractions orally.

4. Be able to use letters to express numbers, common quantitative relationships, operational laws and formulas. Have a preliminary understanding of the meaning of equations and be able to solve simple equations.

5. Understand common units of measurement and rates of change between units. Ability to perform simple conversions between singular numbers and plural numbers.

6. Understand the characteristics of parallelograms and trapezoids. Master the formulas for calculating the area of ??parallelograms, triangles and trapezoids.

7. Understand the characteristics of cuboids and cubes and calculate their surface areas. Know the meaning of volume and recognize commonly used units of volume (cubic meter, cubic decimeter, cubic centimeter, liter, milliliter). Master the formulas for calculating the volume of cuboids and cubes.

8． Initially learned to collect data and classify it, and be able to fill in simple statistical tables. An average is calculated based on the data collected. Through persuasive data and statistical materials, students can receive ideological education of loving the motherland and loving socialism.

9. Can solve three-step calculation word problems. Initially learn to formulate equations and solve word problems. Be able to initially apply the knowledge learned to solve some simple practical problems in life.

10． Through practical activities, we cultivate students' ability to discover mathematical problems from the surrounding situations, use the knowledge they have learned to solve problems, and cultivate students' mathematical awareness.

Sixth grade

Teaching content

(1) Numbers and calculations

(1) Multiplication and division of fractions.

The meaning of fraction multiplication. Multiply fractions. The laws of multiplication are extended to fractions. reciprocal.

The meaning of fractional division. Fraction division.

(2) Four mixed operations of fractions.

Four mixed operations on fractions.

(3) Percentage.

The meaning and properties of percentages. The meaning and fundamental properties of proportion. Solve the ratio. Directly proportional quantities and inversely proportional quantities.

(2) Ratio and Proportion

The meaning and nature of ratio. The meaning and fundamental properties of proportion. Solve the ratio. Directly proportional quantities and inversely proportional quantities.

(3) Preliminary knowledge of geometry

Understanding of circles. Pi. Draw a circle. Circumference and area of ??a circle. *Understanding of fan shape. A preliminary understanding of axisymmetric figures.

Understanding of cylinders. Surface area and volume of a cylinder. Understanding of cones. The volume of the cone. *Preliminary understanding of spheres and their radius and diameter.

(4) Preliminary knowledge of statistics

Statistical tables.

Bar chart, line chart, * sector chart.

(5) Application questions

Four application questions (including engineering problems) with fractions.

Practical application of percentages (including calculation of germination rate, qualification rate, interest rate, tax rate, etc.). scale. Allocate proportionally.

(6) Practical activities

Organize activities based on the social conditions that students are exposed to. For example, draw a floor plan of a bedroom in your home.

(7) Sorting and review

Teaching requirements

1. Understand the meaning of multiplication and division of fractions. Master the rules of calculation for multiplication and division of fractions. Can calculate fraction multiplication and division. Able to do simple multiplication and division of fractions orally. Can perform four mixed operations on fractions (no more than three steps).

2． Understand the meaning of percentages. Know how percentages are used in practice. Percentage calculations will be made.

3. Understand the meaning and nature of ratio. Able to find ratios and simplify ratios. Understand the meaning and basic properties of proportion. Understand proportions. Understand the meaning of direct and inverse proportions. Will determine whether two quantities are directly proportional or inversely proportional. Through proportional teaching, students can further receive enlightenment education from the perspective of dialectical materialism.

4. Know the circle. Can draw circles. Master the formulas for calculating the circumference and area of ??a circle. By introducing historical materials about pi, students can receive patriotism education.

5. Recognize cylinders and cones. The surface area of ??a cylinder and the volume of a cylinder and a cone can be calculated.

6. Be able to make simple statistical tables and use graphing to draw simple statistical charts. Some simple analysis of statistical charts will be conducted to enable students to receive education on national conditions. When drawing statistical charts, pay attention to neatness and beauty.

7. Able to solve fraction and percentage word problems (no more than two steps). Can use proportion knowledge to solve relatively easy word problems. Can read the scale on the map.

8． Through practical activities, students can have a preliminary understanding of the connection between mathematics and society, and further experience the application of mathematics.

9. Through systematic organization and review, we will consolidate and deepen our understanding of the mathematical knowledge learned in primary school. Be able to calculate reasonably and flexibly, choose simple solutions according to the specific circumstances of the problem, and use the knowledge learned to solve some simple practical problems in life.