Reading and Thinking: Processing Allowable Errors with Positive and Negative Numbers
1.2 Rational Numbers
1.2.1 Rational Numbers
1.2.2 The Axis
1.2.3 Opposite Numbers
1.2.4 Absolute Value
1.3 Addition and Subtraction of Rational Numbers
1.3.1 Addition of Rational Numbers
1.3.2 Subtraction of Rational Numbers
Experiment and Investigation: Fill in the Phantom Squares
Reading and Thinking: the Chinese were the First to Use Negative Numbers
1.4 Multiplying and Dividing Rational Numbers
1.4.1 Multiplying Rational Numbers
1.4.2 Multiplying and Dividing Rational Numbers
Observations and Conjectures: Mathematical Reasoning in Flopping Games
1.5 Multiplying Rational Numbers
1.5.1 Multiplying Rational Numbers
1.5.2 Scientific Notation
1.5.3 Approximating Numbers
Mathematical Activities: Activity 1 Keeping Accounts with Positive and Negative Numbers Activity 2 Communication Calculator Usage Activity 3 Collecting Big Data and Experiencing Scientific Notation and Approximate Numbers in Real Life
Chapter 2 Adding and Subtracting Whole Forms
2.1 Whole Forms
Reading and Reflecting: Conversation between the Number 1 and the Letter X
2.2 Adding and Subtracting Whole Forms
Information Technology (IT) Application: Spreadsheets and Data Calculation
Math activities: Activity 1 Spelling triangles and squares with matchsticks (observing patterns) Activity 2 Shopping (choosing options, sorting and discussing) Activity 3 Observing calendars (looking at charts to find patterns)
Chapter 3: Primary Equations
3.1 From Arithmetic to Equations
3.1.1 Primary Equations
3.1.2 Properties of Equations
Reading and Thinking: A History of Equations
3.2 Discussion of Solving Primary Equations (I) - Combining Like Terms and Shifting Terms
Experiments and Investigations: Infinitely Looped Decimals to Fractions
3.3 Discussion of Solving Primary Equations (II) - Removing Parentheses and Removing Denominators
3.4 Practical problems and quadratic equations
Mathematical activities: activity 1 shopping (number of money versus number of pieces) activity 2 statistics and quadratic equations in life activity 3 the arch bar principle and quadratic equations
Chapter 4: Preliminary Graphical Understanding
4.1 Colorful shapes
4.1.1 Geometric shapes
4.1.2 Points, Lines, Surfaces, and Bodies
Reading and Thinking: The Origins of Geometry
4.2 Straight Lines, Rays, and Line Segments
Reading and Thinking: Measurement of Length
4.3 Angles
4.3.1 Angles
4.3.2 Comparison of Angles and Operations
4.3.3 Remainder and Complementary Angles
4.4 Project-based learning: designing and making a rectangular shaped wrapping carton
Math activities: Activity 1 Make a model of a train car Activity 2 M?bius strip Activity 3 Make a pentagram
7th Grade Book (6 chapters)
Chapter 5 Intersecting and Parallel Lines
5.1 Intersecting Lines
5.1.1 Intersecting Lines<
5.1.2 Perpendicular lines
5.1.3 Congruent, interior, and congruent interior angles
Observations and conjectures: illusions when looking at diagrams
5.2 Parallel lines and their determination
5.2.1 Parallel lines
5.2.2 Determination of parallel lines
5.3 Properties of parallel lines
5.3.1 Properties of parallel lines
5.3.2 Propositions, theorems
Information technology application: exploring the relationship between the positions of two straight lines
5.4 Translations
Chapter 6: Right-angled coordinate system of the plane
6.1 Right-angled coordinate system of the plane
6.1.1 Ordered pairs of numbers
6.1.2 The plane Cartesian Coordinate System
Reading and Thinking: Representing Geographic Positions in Latitude and Longitude
6.2 Simple Applications of Coordinate Methods
6.2.1 Representing Geographic Positions in Coordinates
6.2.2 Representing Transformations in Coordinates
Chapter 7 Triangles
7.1 Lines Associated with Triangles
7.1. 1 Sides of Triangles
7.1.2 Heights, Midlines, and Angle Bisectors of Triangles
7.1.3 Stability of Triangles
Info & Tech App: Drawing a Diagram to Find a Pattern
7.2 Angles Associated with Triangles
7.2.1 Interior Angles of Triangles
7.2.2 Outer Angles of Triangles
Read and Think: Why Prove
7.3 Polygons and Their Interior Angle Sums
7.3.1 Polygons
7.3.2 Interior (Exterior) Angle Sums of Polygons
Read and Think: Trigonometric Sections of Polygons
7.4 Project Based Learning:Tessellations
Chapter 8 Systems of Binary Equations
8.1 Systems of Binary Equations
8.2 Elimination - Solving Systems of Binary Equations
8.3 Practical Problems and Systems of Binary Equations
Reading and Thinking:Ancient and Modern Representations of Systems of Primary Equations and Their Solutions
*8.4 Examples of Solutions to Systems of Ternary Equations
(Note: Content with * is optional for students who have the capacity to learn students to study.)
Chapter 9 Inequalities and Systems of Inequalities
9.1 Inequalities
9.1.1 Inequalities and Their Solutions
9.1.2 Properties of Inequalities
Reading and Thinking: Comparing Sizes by the Method of Differentials
9.2 Practical Problems and Primary Inequalities
Experimenting and Thinking: Is the Water Level Raised or Lower
9.3 Groups of Primary Inequalities
Reading and Thinking: analyzing matches using inequalities
Mathematical Activities (Activity 1 Standard of Living Survey; Activity 2 Guess the Number Game; Activity 3 Finding the Maximum of an Area with a Mini-Experiment.)
Chapter 10 Collecting, Organizing and Describing Data
10.1 Statistical Investigations
Experiment and Investigation: How many beans are in a bottle
10.2 Histograms
Information Technology Application: Drawing Statistical Graphs Using Computers
10.3 Project Learning:Talking about Water Conservation from Data
Mathematical Activities ( Activity 1 Reading Statistical Charts in Life; Activity 2 Estimating the Average Height of the Class Using Simple Random Sampling; Activity 3 Who has the Fastest Response; Activity 4 Tossing a Coin)
Grade 8 (5 Chapters)
Chapter 11 Congruent Triangles
11.1 Congruent Triangles
11.2 Conditions for Congruence in a Trigonometrical Form
Reading and Think: Congruent and Congruent Triangles
11.3 Properties of Angle Bisectors
Chapter 12 Axis Symmetry
12.1 Axis Symmetry
12.2 Making Axis Symmetric Figures
12.2.1 Making Axis Symmetric Figures 12.2.2 Representing Axis Symmetry in Coordinates
IT application: exploring the properties of axial symmetry
12.3 Isosceles Triangles
12.3.1 Isosceles Triangles 12.3.2 Isosceles Triangles
Experiment and Exploration: inequality between sides and angles in triangles
Mathematical Activities: Activity 1 Artistic Characters and Axial Symmetry Activity 2 Mirrors, Reflections, and Axial Symmetry Activity 3 Equal Line Segments in Isosceles Triangles
Chapter 13 Real Numbers
13.1 Square Roots
13.2 Cubic Roots
13.3 Real Numbers
Reading and Thinking: Why It's Not Rational
Chapter 14 Primary Functions
14.1 Variables and Functions
14.1.1 Variables 14.1.2 Functions 14.1.3 Graphing Functions
Information Technology Application: Graphing Functions on a Computer
14.2 Primary Functions
14.2.1 Simple Functions 14.2.2 Primary Functions
Reading and Reflecting: How Scientists Measure the Age of the Earth
14.3 Equations (Sets) and Inequalities in Functional Perspective
14.3.1 Primary Functions and Quadratic Equations 14.3.2 Primary Functions and Quadratic Inequalities 14.3.3 Primary Functions and Quadratic Equations (Sets)
14.4 Topics for Study Choosing a Program
(Question 1 Which kind of lamps to use to save fuel? Question 2 How to rent a car? Problem 3 How to transfer water?)
Math activities: activity 1 look at a statistical table to find a primary function; activity 2 look at several charging options for a telephone and choose the option that saves money? (Primary Functions and Primary Inequalities).
Chapter 15 Multiplication, Division, and Factoring of Integers
15.1 Multiplying Integers
15.1.1 Multiplying Powers of the Same Base 15.1.2 Multiplying Powers 15.1.3 Multiplying Cubes 15.1.4 Multiplying Entities
15.2 Multiplication Formulas
15.2.1 The Square Difference Formula 15.2.2 The Perfect Square Formula (Fill in Parentheses Rule)
Reading and Thinking: Yang Hui Triangle
15.3 Division of Integers
15.3.1 Division by Powers of the Same Base 15.3.2 Division of Integers
15.4 Factorization
15.4.1 Common Factorization 15.4.2 Formulaic Method
Observations and Conjectures: Factorization of type equations
Math activities: activity 1 Look at the equation to find the pattern (the perfect square formula); activity 2 Use the two formulas to perform simple operations.
Grade 8 Book (5 Chapters) Chapter 16: Fractions
16.1 Fractions
16.1.1 From Fractions to Fractions
16.1.2 Basic Properties of Fractions
16.2 Operations with Fractions
16.2.1 Operations with Fractions (Multiplication, Division, and Multiplication by a Fractional Formula)
16.2.2 Adding and Subtracting Fractions
16.2.3 Integer Exponential Powers (Positive Numbers Less Than 1 in Scientific Notation)
Reading and Thinking Can You Pour All the Water Out of a Container
16.3 Fractional Equations (Denominator Removal Method to Solve Fractional Equations)
Math Activities (Activity 1 Investigating the Properties of Proportions; Activity 2 Calculating Length; Activity 3 Designing a Mirror Frame .)
Chapter 17 Inverse Proportional Functions
17.1 Inverse Proportional Functions
17.1.1 Significance of Inverse Proportional Functions
17.1.2 Graphs and Properties of Inverse Proportional Functions
Information Technology Application: exploring the properties of inverse proportional functions
17.2 Applications of Inverse Proportional Functions
Reading and Think: Inverse Proportional Relationships in Life
Math Activities
Chapter 18 Pythagorean Theorem
18.1 Pythagorean Theorem
Reading and Thinking: Proof of the Pythagorean Theorem
18.2 Inverse Pythagorean Theorem
Math Activities
Chapter 19 Quadrilateral
19.1 Parallelograms
19.1.1 Properties of Parallelograms
19.1.2 Determination of Parallelograms
Reading and Thinking: the Law of Parallelograms
19.2 Special Parallelograms
19.2.1 Rectangles
19.2.2 Rhombuses
19.2.3 Squares
Experiments and investigations: tricky squares
19.3 Trapezoids
Observations and conjectures; special quadrilaterals in the planar right-angled coordinate system
19.4 Project Based Learning:Centers of Gravity
Math activities (Activity 1 Origami to make 60,30,15 degree angles; Activity 2 Golden Rectangles; Activity 3 Midpoint Quadrilaterals)
Chapter 20 Analysis of Data
20.1 Representation of Data
20.1.1 Mean
20.1.2 Median and Plurality
20.2 Fluctuations in Data
20.2.1 Polar Deviation
20.2.2 Variance
Information Technology Application: using a calculator to find several statistics
Reading and Thinking: Several measures of data fluctuation
20.3 Project-based Learning:Data Analysis in Physical Fitness Tests
Chapter 21 Quadratic Roots, Grade 9 (5 Chapters)
21.1 Quadratic Roots
21.2 Multiplying and Dividing Quadratic Roots
21.2 Adding and Subtracting Quadratic Roots
21.2 Quadratic Roots < /p>
Read and Reflect: Helen Chin's Jiu-Shao Formula
Chapter 22 Quadratic Equations
22.1 Quadratic Equations
22.2 Descending - Solving Quadratic Equations
22.2.1 Matching Methods 22.2.2 Formulaic Methods 22.2.3 Factorizing Methods 22.2.4 Relationship between roots and coefficients of quadratic equations
Reading and Thinking: The Golden Numbers
22.3 Practical Problems and Quadratic Equations
Experiments and Investigations:Calculation of the Number of Points for the First n Rows of a Triangular Dot Matrix
Mathematical Activities:Activity 1 Make a Cylinder; Activity 2 Encircle a Rectangle; Activity 3 Calculate the Rate of Change.
Chapter 23 Rotation
23.1 Rotation of Figures
23.2 Centrosymmetry
23.2.1 Centrosymmetry 23.2.2 Centrosymmetric Figures 23.2.3 Co-ordinates of Points Symmetric about the Origin
Information Technology Application: Exploring the Properties of Rotation
23.3 Project-based Learning:Patterns Design
Reading and Thinking: Rotational Symmetry
Math activities: Activity 1 Draw a flower; Activity 2 Explore the relationship between the coordinates of points of symmetry symmetrical about the , axis.
Chapter 24 Circles
24.1 Circles
24.1.1 Circles 24.1.2 Diameters perpendicular to a chord 24.1.3 Arcs, chords, and circumferential angles 24.1.4 Circumferential angles
24.2 Relationships between the position of a point, a straight line, a circle, and a circle
24.2.1 Relationships between the position of a point and a circle 24.2.2 Relationships between a straight line and a circle Positional Relationships 24.2.3 Positional Relationships of Circles and Circles
24.3 Orthogonal Polygons and Circles
Reading and Thinking: Pi
24.4 Arc Lengths and Areas of Sectors
Experiments and Investigations:Designing a Runway
CHAPTER 25 PRELIMINARY PROBABILITY
25.1 Random Events and Probability
25.1.1 Random Events 25.1.2 Probability
25.2 Finding Probability by Enumeration
Reading and Thinking: Probability and Winning the Lottery
25.3 Estimating Probability by Frequency
Experiment and Investigation: Estimation of
25.4 Project Based Learning:Patterns of Arrangement of Letters on a Keyboard
Math Activities:Activity 1 Precipitation and statistical probability; Activity 2 Relationship between area and probability; Activity 3 Relationship between the order of drawing lots and probability.
Grade 9 Booklet (4 Chapters)
Chapter 26 Quadratic Functions
26.1 Quadratic Functions
Experiment and Investigation: Speculate on the relationship between the growth of a plant and its temperature
26.2 Quadratic Functions in a Functional Perspective
Information Technology Application: Explore the properties of quadratic functions
26.3 Practical Problems and Quadratic Functions
Chapter 27 Similarity
27.1 Similarity of Figures
27.2 Similar Triangles
27.2.1 Determination of Similar Triangles
27.2.2 Examples of Applications of Similar Triangles
27.2.3 Perimeter and Area of Similar Triangles
Observation and Conjecture: Wonderful Fractal Figures
27.3 Bitwise Similarity
Information Technology Application: Exploring the Properties of Bitwise Similarity
Mathematical Activities: Activity 1 Measuring the Height of a Flagpole; Activity 2 Bitwise Transformations and Artistic Characters.
Chapter 28 Acute Triangle Functions
28.1 Acute Triangle Functions
Reading and Thinking: an old trigonometry table
28.2 Solving Right Triangles
Maths activities: activity 1 Making a goniometer and measuring the height of a flag; activity 2 Measuring the height of a tower using a goniometer.
Chapter 29 Views and Projections
29.1 Projections
29.2 Three Views
Reading and Thinking: Generating and Applying Views
29.3 Project-based Learning:Making Three-Dimensional Models
Math Activities:Activity 1 Observe an object and draw a three-dimensional view; Activity 2 Design a geometry and make a model; Activity 3 Design and make a pencil holder.