? 43

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

involving indices

? Solving equations involving

indices

? Surds

? Calculations of

surds

? Rationalising

the denominator

of a fraction

? Solving equations involving

surds

博實(shí)樂(lè)“中外融通課程”

44?Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 2

Functions

21

2.1. Relations and

functions

? Relations

? Functions,domain,range

? Function notation

? Composite function

? Inverse function

? The modulus

function

? Monotonicity of

functions

? Where functions

meet

2.2 Quadratic

Functions

?Quadratic functions

? Transformation to

sketch

quadratics

? Axes intercepts

? Sketching quadratics for their

axes intercepts

? Graphs of quadratic functions

? Monotonicity of

quadratic

functions

? Solving quadratic

equation

graphically

? Practical maximum and

minimum

? Quadratic function and linear f

unction meet

Form Change,

Equivalence

Scientific and

technical

innovation

Representing

change and

equivalence in

a variety

of forms

has helped

human

apply their

understanding of

scientific

principles

Organization

skills-Use

appropriate

strategies for

organizing

complex information

Information literacy

skills-Process

data and report

results

Critical

thinking

skills-Revise

understanding based on

new evidence;

Transfer skillsApply skills

and knowledge

in unfamiliar

situations;

Self-management-organization-Use

appropriate

strategies for

organizing

complex situations.

IB learner profile

Reflective:

we can develop

our skills by

giving thoughtful

consideration to

our own learning, ideas and

experience. We

will reflect on our

work when we

assess our own

writing and that

of others.

Core competence

Critical thinking

Reason

2 B C D Criterion A: Knowing and

understanding

A test about functions will

be held.Questions will be

focused on functions such

as composite function,

inverse function, modulus

function, quadratic function

and their graphs.

Applying mathematics in

real-life context (Criterion

C, D)

Students will use quadratic

function to get the maximum profit.

A shopping mall is selling

shirts marked $58 for each,

it’s found the selling

amount will increase 100

while reducing $1, and the

original selling amount is

1000, to get the maximum

profit, what the selling

price should be?

service as action:

Take action by

giving a speech

to the primary

students about the

beauty of Math.

? 45

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 3

Exponential and

logarithms

36

Relationship Quantity, Change, Generalization Orien- tation in space and time Gener- alizing changes in quantity helps

establish

relationships that

can model

duration,

frequency

and variability

Collaboration

skills-Listen

actively to other

perspectives

and ideas.

Critical thinking skills-Consider ideas

from multiple

perspectives;

draw reasonable

conclusion and

generalizations;

Transfer skillsChange the

context of an

inquiry to gain

different perspectives

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Critical thinking

Problem-solving

2 A B Criterion A: Knowing and

understanding

A test about exponential

and logarithms will be

held. Questions will be

focused on calculating on

exponential and logarithms.

And also use the functions

properties to solve problems

Criterion B:

Investigation:

Investigate the product

rule, quotient rule, power

rule.

3.1 Exponential

and logarithms

? Simplifying

expressions

involving indices

? Evaluating

logarithms with

and without a

calculator

? Solve exponential equations

? Write and

solve exponential

equations from

real-life

situations

? Using natural

logarithms

? Drawing

graphs of

logarithmic

functions

? Finding the

inverse of an

exponential

function

? Identifying and

applying

博實(shí)樂(lè)“中外融通課程”

46?

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

function transformations on

graphs of logarithmic

functions

? Developing the

laws of

logarithms

? Using the law

of logarithms

to simplify expressions and

solve equations

? Proving the

laws of

logarithms

? Proving the

change of base

law

? Comparing the

increasing rate

of exponential

function, linear

function, logarithmic function

? 47

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 4

Geometry

27

4.1. Transformations

? Translations

? Reflections

?.Rotations

? Enlargements

and reductions

? Describing

combinations of

transformation

of a function

algebraically

and graphically

? Write the

equation of a

graph following one or more

transformations

4.2 Circular

measure

? Circular measure

? Length of an

arc

?.Area of a sector

Form Change,

Models

Orientation in

space and

time

Relationships model patterns

of change

that can

help clarify

ad predict

duration,

frequency

and variability

Critical thinking skills-Draw

reasonable

conclusions and

generalizations;

Creative thinking skills-create novel situation to authentic

problems;

Affective

skills- practice

being aware

of body-mind

connections

Media literacy skillsMake informed

choices about

personal viewing experience

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Inquisitive

Reflective

2 A Criterion A: Knowing and

understanding

A test about geometry will

be held. Questions will

be focused on calculating

on sector area, arc length,

and transformation. And

also use the transformation

properties to solve problems

service as action:

take action by

making our school

and community

more suitable.

博實(shí)樂(lè)“中外融通課程”

48?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 5

Probability

&

Statistics

81

Logic Representation,

System

Identities

and relationship

Understanding

health and

making

healthier

choices

result

from using

logical

representations and

systems

Communication

skills-Understand and use

mathematical

notation; use

and interpret a range

of discipline

specific terms

and symbols;

Collaboration

skills-Delegate

ad share responsibility for

decision-making

Organization

skills-Bring

necessary

equipment and

supplies to

class

Reflections

skills-Consider

ATL skills development what

can I already

do?

IB learner profile

Communicators:

Express ourselves confidently and creatively

in more than one

language and in

many ways, collaborate effectively, listening

carefully to the

perspectives of

other individuals

and groups.

Core Competence

Problem-solving

Critical thinking

2 A B CD Criterion A: Knowing and

understanding

A test about probability will

be held.

Questions will be focused

on probability using different ways of displaying data,

especially tree diagram

and Venn diagram. And

questions about sampling

with or without replacement

are also very important, and

last are questions about

permutation and combination.

Criterion B:

investigation

Investigating climate

change—using data

analysis and probability

to discuss the evidence of

the correlation between

the emission of greenhouse

gases and the rise in global

temperature

Criterion C, D:

Construct a tree diagram

for a three-day weather

forecast where the probability of rain on any day is

estimated from past data

service as action:

take action by

calculating the

probability to help

others to make

decisions

5.1 Probability

? Sampling,

lottery，random

sampling,

Stratified sampling,

population,

sample

? Statistics

terminology

? Quantitative

(numerical) data

? Grouped discrete data

? Continuous

data

? Measuring the

center

? Cumulative da

ta

? Measuring the

spread

? Box-andwhisker plots

? Statistics from

technology

? Standard deviation

? 49

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

? The normal

distribution

? Representation

data

? Measures of

central tendency

? .Measures of

variation

? Probability

using

2-dimensional

grid,

Venn diagram,

tree diagram，

two way tables

? Probability

distributions

? The binomial

distribution

? The geometric

distribution

? The normal

distribution

? Statistics from

technology

? Standard deviation

博實(shí)樂(lè)“中外融通課程”

50?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 6

Vectors

30

6.1 Vectors

? Directed line

segment

representations

? Vector equality

? Vector addition

and

subtraction

? Vectors in

component form

? Scalar multiplication

Parallelism of

vectors

? The scalar

product of two

vectors

? Position vector

? Vector geometry

? 3-dimensional

vectors

? Constant velocity problems

Form Space

Pattern

Personal and

cultural

expression

Understanding

patterns in

forms and

space can

enhance

creativity.

Transfer

skills-combine

knowledge,

understanding

and skills to

create products

or solutions

Reflective

skills-Consider

personal learning strategieswhat can I do

to become a

more efficient

and effective

learner?

IB learner profile

Principled:

Act with integrity and honesty,

with a strong

sense of fairness

and justice, and

with respect for

the dignity and

rights of people

everywhere.

Core Competence

Inquiring

Reflective

2 A Criterion A: Knowing and

understanding

A test about advanced Vector will be held. Questions

will be focused on basic

calculation, application.

service as action:

take action by

making our school

or local community more sustainable.

? 51

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 7

Advanced

trigonometry

35

7.1 Advanced

trigonometry

? Radian measure

? The unit circle

? The relationship between sin

and cos

? The multiples

of 30° and 45°

? Trigonometric

functions

? Simplifying

trigonometric

expression

? Trigonometric

equations

? Negative and

complementary

angle formula

? Further

trigonometric

identities

? Application of

trigonometry

Relationship Measure- ment, Space,

Equivalence

Orientation in

space and

time

Generalizing and

applying

relationship

between

measurements in

space can

help define

where and

when

Critical

thinking

skills-Gather

and organize relevant

information to

formulate an

argument,

TransferApply skills

and knowledge

in unfamiliar

situations;

Creative-thinking

skills-Make

unexpected

or unusual

connections

between objects

and ideas.

draw reasonable

conclusions and

generalizations

Affective

skills- Practice

positive thinking

IB learner profile

Thinkers：

Use critical and

creative thinking

skills to analyze

and take responsible action on

complex problem.

Core Competence

Reason

Critical thinking

2 A B C D Criterion A: Knowing and

understanding

A test about advanced

trigonometry will be held.

Questions will be focused

on radians, sine rule and

cosine rule, trigonometric

identities, triangle area,

trigonometric functions.

Criterion B C:

Investigation:

1. A unit circle has a radius

of 1 unit. Find the circumference of a unit circle in

terms of

2. Find the formula for and

Criterion C D

Use the periodic property

of trigonometric function

to find out the appropriate time for a ship passes

through a bay.

service as action:

take action by

making our school

or local community more sustainable or measure

the height of the

small hill.

博實(shí)樂(lè)“中外融通課程”

52?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 8

Algebra 2

40

8.1 Straight-line

graphs

? Problems involving length of a

line and midpoint

? Parallel and

perpendicular

lines

? Equations of

straight lines

? Areas of rectilinear figures

? Converting

from a non-linear

equation to linear

form

? Converting from

a linear form to

anon-linear equation

8.2.Inequalities

? Interval notation

? Linear inequalities

? Modulus inequalities

? Sign diagrams

? Non-linear

inequalities

? Solving cubic

inequalities

graphically

? Linear programming

? Solving real-life

problems

From Equivalence,

Models

Identities

and Relationship

Modelling with

equivalent

forms of

representation can

improve

decision

making

Communication-Organize

and depict

information

logically;

Critical thinking-Use models

and simulations

to explore complex systems

and issues

Transfer-Apply skills and

knowledge

in unfamiliar

situations

Information literacy

skill-evaluate

and select

information

sources and

digital tools

based on their

appropriateness to specific

tasks.

IB learner profile

Reflective:

we can develop

our skills by

giving thoughtful

consideration to

our own learning, ideas and

experience. We

will reflect on our

work when we

assess our own

writing and that

of others.

Core Competence

Reflective

Inquisitive

2 A C D Criterion A: Knowing and

understanding

A test about solving

inequalities will be held.

(Solving linear inequalities,

quadratic inequalities,

rational inequalities algebrally and graphically)

Criterion C D:

Students should design a

plan for a party limit money.(Students need to design

several plans containing

different materials such

as fruits, candies, cookies

etc, and compare them to

choose the best one.)

Service as action:

Take action

by designing a

suitable plan for

preparing for a

party with limit

materials

? 53

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 9

Calculus

63

Relationship Quantity, Measure- ment Global- ization and sustainability Quantities and mea- surements illustrate

the relationships

between

human-made

system and

communities.

Critical-thinking skills- Draw

reasonable

conclusions and

generalizations;

Communication-Organize

and depict

information

logically;

IB learner profile

Inquirers：

Nurture our curiosity, developing

skills for inquiry

and research,

knowing how

to learn independently and

with others.

Core Competence

Reflective

Critical thinking

2 A B Criterion A: Knowing and

understanding

A test about differentiation

and integration will be hold.

It will be based on chain

rule, product rule, quotient

rule, tangent, normal, maximum or minimum value,

trigonometric functions.

Criterion B: Investigation

In this task student will

need to investigate how to

calculate the area of different region.

service as action:

Take action by

giving a speech

to the primary

students about

development of

math

9.1 Differentiation

? The gradient

function

? The chain rule

? The product

rule

? The quotient

rule

? Tangents and

normals

? Small increments and

approximations

? Rates of

change

? Second derivatives

? Stationary

points

? Practical

maximum and

minimum problems

? Derivatives

of exponential

functions

? Derivatives

of logarithmic

functions

? Derivatives

of trigonometric

functions

? Further

博實(shí)樂(lè)“中外融通課程”

54?Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

applications of

differentiation

9.2 Integration

? Differentiation

reversed

? Indefinite

integrals

? Integration of

functions of the

form

? Integration

of exponential

functions

? Integration of

sine and cosine

functions

? Integration of

functions of the

form and

? Further indefinite integration

? Definite integration

? Further definite integration

? Area under a

curve

? Area of regions

bounded by a

line and a curve

? Applications of

differentiation in

kinematics

? Applications

of integration in

kinematics

? 55

高中數(shù)學(xué)課程圖

4 Course Assessment

4.1 External assessment (Each criterion 25%)

Criterion A: knowledge and understanding

Criterion B: investigation

Criterion C: communication

Criterion D: Applying mathematics in real-life

4.2 Internal assessment

Criterion A: knowledge and understanding

5 Teaching Sources

5.1 Books:

1. Mathematics for the international student MYP 4. Michael Haese Sandra Haese

Mark Humphries Edward Kemp Pamela Vollmar. ISBN: 978-921972-49-2

2. Mathematics for the international student MYP 5. Michael Haese Sandra Haese

Mark Humphries Edward Kemp Pamela Vollmar. ISBN: 978-921972-53-9

3. Cambridge IGCSE and O Level Additional Mathematics Coursebook Second

edition. ISBN: 978-1-108-41166-0

4. Cambridge International AS&A Level Mathematics: Pure Mathematics 1

Coursebook. ISBN:978-1-108-40714-4

5. Cambridge International AS&A Level Mathematics: Probability & Statistics 1

Coursebook. ISBN:978-1-108-40730-4

5.2 Reference

1. Advanced Level Mathematics Pure Mathematics 1 Huhg Neill and Douglas

Quadling. ISBN: 978-0-521-53011-8

2. Cambridge IGCSE Maths STUDENT’S BOOK. ISBN: 978-0-00-825779-8.

博實(shí)樂(lè)“中外融通課程”

56?

5.3 Websites

1. www.myib.org

2. http://10.166.1.163/( 廣東碧桂園學(xué)校教學(xué)資源網(wǎng) )

3. https://cie.fraft.org

4. https://bgy.managebac.com/login

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CMYP Mathematics

Curriculum Map

（2022version）

Complied by Guangdong Country Garden Senior High Section

博實(shí)樂(lè)“中外融通課程”

58?

CMYPCurriculum

Subject Mathematics Grade G1& G2 Level HL2

Subject Code Credit 8 Duration 2 years

TeachingHours 720 Contributor

Tao Xiaojun

Nathan

Wang Ying

Wang Baishi

Liu Xinhua

Zhong Yi

Wang Runmei

Completed

Date 2022.9

1 Course Introduction

1.1 Introduction

Neglect of mathematics works injury to all knowledge, since he who is ignorant of it

cannot know the other sciences or things of the world.

Roger Bacon（1214-1294）

The study of mathematics is a fundamental part of a balanced education. It promotes a

powerful universal language, analytical reasoning and problem-solving skills that contribute

to the development of logical, abstract and critical thinking. Mathematics can help make

sense of the world and allows phenomena to be described in precise terms. It also promotes

careful analysis and the search for patterns and relationships, skills necessary for success

both inside and outside the classroom. Mathematics, then, should be accessible to and

studied by all students.

Studying mathematics, however, should be more than simply learning formulae or

rules. Students should not have the impression that all of the answers to mathematics can be

found in a book but, rather, that they can be active participants in the search for concepts

and relationships. In that light, mathematics becomes a subject that is alive with the thrill

of exploration and the rewards of discovery. At the same time, that new knowledge may then

be applied to other situations, opening up even more doors for students. MYP mathematics

promotes both inquiry and application, helping students to develop problem-solving

techniques that transcend the discipline and that are useful in the world outside school.

? 59

高中數(shù)學(xué)課程圖

An MYP mathematics programme should be tailored to the needs of students, seeking

to intrigue and motivate them to want to learn its principles. Students should see authentic

examples of how mathematics is useful and relevant to their lives and be encouraged to

apply it to new situations. Mathematics provides the foundation for the study of sciences,

engineering and technology. However, it is also evident in the arts and is increasingly

important in economics, the social sciences and the structure of language. Students in

the MYP are encouraged to use ICT tools to represent information, to explore and model

situations, and to find solutions to various problems. These are skills that are useful in a

wide range of arenas. MYP mathematics aims to equip all students with the knowledge,

understanding and intellectual capabilities to address further courses in mathematics, as

well as to prepare those students who will use mathematics in their studies, workplaces and

lives in general.

1.2 Aims

The aims of all MYP subjects state what a teacher may expect to teach and what a

student may expect to experience and learn. These aims suggest how the student may be

changed by the learning experience. The aims of MYP mathematics are to encourage and

enable students to:

1. enjoy mathematics, develop curiosity and begin to appreciate its elegance and

power

2. develop an understanding of the principles and nature of mathematics

3. communicate clearly and confidently in a variety of contexts

4. develop logical, critical and creative thinking

5. develop confidence, perseverance, and independence in mathematical thinking and

problem-solving

6. develop powers of generalization and abstraction

7. apply and transfer skills to a wide range of real-life situations, other areas of

knowledge and future developments

8. appreciate how developments in technology and mathematics have influenced each

other

博實(shí)樂(lè)“中外融通課程”

60?

9. appreciate the moral, social and ethical implications arising from the work of

mathematicians and the applications of mathematics

10. appreciate the international dimension in mathematics through an awareness of the

universality of mathematics and its multicultural and historical perspectives

11. appreciate the contribution of mathematics to other areas of knowledge

12. develop the knowledge, skills and attitudes necessary to pursue further studies in

mathematics

13. develop the ability to reflect critically upon their own work and the work of others.

2 Course Structure

1.Quadratic equation with one

unknown

2.Quadratic functions

3.Inverse proportional

4.Indices

5.Radicals

6.Sets and Venn diagrams

7.Financial mathematics

8.Sequence and series

9.Functions

10.Exponential and logarithms

11.Inequalities and graphs

12.Factors and polynomial

13.Permutation and

Combination

1.Special

parallelogram

2.Similar figures

3.Circle

4.Measurement

5.Coordinate

Geometry

6.Transformation

7.Vectors

8.Straight-line

graphs

9.Circular

measure

1.Trigonometry

in right-angled

triangle

2.Trigonometry

in non-rightangled triangle

3.Advanced

trigonometry

1.Probability

2.Statistics

Algebra

CMYP Mathematics HL2

Geometry Trigonometry Probability

and Statistics

Calculus

1.Differentiation

2.Integration

? 61

高中數(shù)學(xué)課程圖

3 Course Content

G1

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 1

Real numbers

27

0.1.Indices

? Evaluating

indices

? Scientific

notation

? Rational indices

1.2 Radicals

? Radical and

surds

? Simplifying

radicals

? Simplest radical form

? Adding and

subtracting radicals

? Multiplications

involving

radicals

? Division by

radicals

1.3 Proportion

? Direct proportion

? Inverse proportion

Form Simplification;

Change

Globalization

and sustainability

Changing

to simplified forms

can help

with analyzing the

effects of

consumption and

conservation

Critical thinking skills-Analyze complex

concepts and

projects into

their constituent parts and

synthesize

them to create

something new;

Communication

skills-preview

and skim texts

to build understanding;

IB learner profileThinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core Competence

Inquisitive

Reason

1 A B C Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

calculation of radical, and

indices

Investigation:

The sum, difference,

product and quotient of

irrational numbers (criterion B, C)

In this task, students will

investigate whether the

sum, difference, product and quotient of two

irrational numbers (also

one irrational number, one

rational) could be rational

number. And make conclusions of the conditions to

make a rational number.

service as action:

Take action by

mapping a Mind

map of the development of number

system for the

junior students

博實(shí)樂(lè)“中外融通課程”

62?Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 2:

Algebra

63

Form Patterns,

Space

Equivalence,

Scientific and

technical

innovation

Representing

patterns

with

equivalent forms

can lead

to better

systems,

models and

methods

Reflection

skills-Identify

strengths and

weakness of

personal learning strategies.

Critical-thinking skills-Applying existing

knowledge to

generate new

ideas or process, Propose

and evaluate

a variety of

solutions;

Reflection-Draw

reasonable

conclusions and

generalizations

Transfer

skills-Inquire

in different

contexts to

gain a different

perspective

IB learner profileCaring:

Show empathy,

compassion and

respect, act to

make a positive

difference in the

lives of others

and in the world

around us.

Core Competence

Inquiring

Reflective

2 A C D Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple

to complex to challenging (in both familiar and

unfamiliar situations), all

based on linear equation

and inequalities, quadratic

equations

Applying mathematics in

real-life contexts (criteria

C, D)

In this task, You decide

that instead of taking

vitamin and mineral supplements you will get your

calcium and vitamin A by

drinking milk and orange

juice. An ounce of milk

contains 38 mg of calcium

and 56μg (micrograms)

of vitamin A; an ounce of

orange juice contains 5 mg

of calcium and 60 μg of

vitamin A. Determine how

many ounces of milk and

orange juice you would

need to drink daily in order

to meet your minimum

requirement of 550 mg of

calcium and

service as action:

Take action by tutoring classmates.

2.1. Algebraic

expansion

? The distribution law

? The product

(a+b)(c+d)

? Difference of

two squares

? Perfect square

expansion

? Further expansion

2.2 Linear

equations and

inequalities

? Linear equations

? Rational equations

? Linear inequalities

2.3 Quadratic

equations

? Equations of

the form x2=k

? The Null Factor Law

? Solution by

factorization

? 63

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

? Completing the

square

? Problem solving

? The sun and

product of the

roots

2.4 Quadratic

functions

? The expression

of quadratic

functions

? The graph of

quadratic

functions

? The properties

of quadratic

functions

? Application of

quadratic

functions

? Quadratic

functions and

quadratic

equations

博實(shí)樂(lè)“中外融通課程”

64?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 3: Set

and Venn

diagrams

27

3.1.Set

? Sets, universal

set, empty set

? Special Number sets

? Interval notation

? Complement of

a set, element

? Venn diagrams

? Union and

intersection

? Number in

regions

? Problems solving with Venn

Diagrams

Form Change,

Equivalence

Scientific and

technical

innovation

Representing

change and

equivalence in

a variety

of forms

has helped

human

apply their

understanding of

scientific

principles

Collaboration

skills-Listen

actively to other

perspectives

and ideas.

Critical thinking skills-Consider ideas

from multiple

perspectives;

draw reasonable

conclusion and

generalizations;

Transfer skillsChange the

context of an

inquiry to gain

different perspectives

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Critical thinking

Problem-solving

2 A CD Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

set , Venn diagram.

Applying mathematics in

real-life contexts: (criteria

C, D)

In this task, students

become part of a task force

to analyze and report on the

problems associated with

the numbers of students

of each part and to make

a decision about the class

setting. For there are 107

students in MYP G1, they

all study at least one of the

subjects Physics, Chemistry, or Biology. 70 are

studying Physics, 62 are

studying Chemistry, and

48 are studying Biology. 28

are studying Physics and

Chemistry, 25 are studying

Chemistry and Biology, 30

are studying Physics and

Biology.

service as action:

Take action by tutoring classmates.

? 65

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 4

Geometry

45

4.1. Coordinate

geometry

? The distance

between two

points

? Midpoints

? Gradient

? Parallel and

perpendicular

lines

? The equation of

a line

? Graphing lines

from equations

? Finding the

equation of a line

? Perpendicular

bisector

? Distance from a

point to a line

? 3-dimensional

coordinate

geometry

4.2 Special parallelogram

? Rhombus

? Rectangle

? Square

Form Change

Model

Personal and

cultural

expression

Form is

helpful

to create,

develop

or change

things

Communication

skills-organize

and depict

information

logically

Critical

thinking

skills-Revise

understanding

based on new

information and

evidence

IB learner profileReflective:

Thoughtfully

consider the

world and our

own ideas and

experience. Work

to understand

our strengths

and weakness in

order to support

our learning and

personal development.

Core Competence

Critical thinking

Reflective

1 CD Unit Test:

Applying mathematics in

real-life contexts: (criteria

C, D)

Students are to imagine

they are living in a village

in a developing country.

They are given the task of

designing a container to

transport water from a well

to their village situated one

kilometer away. Students are to write a report

justifying their design and

detailing how much water

they need to transport.

service as action:

Take action by

giving a speech to

the primary students about some

famous mathematicians

博實(shí)樂(lè)“中外融通課程”

66?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 5

Circle and

Similar

54

5.1 Circle

? Basic knowledge

of circle

? The relationship

between angle

of circumference

and angle of

center

? Equation of

circles

? Line and circle

? Proving Chords

of a circle

theorem

? Proving Radius-tangent

theorem

? Proving Tangents from an

external point

? Regular polygons in circle

? Arc length and

sector area

5.2 Congruence

and similarity

? Similarity

? Problem solving

? Using similar

triangles to prove

other geometric

results

? Area of similar

objects

? Volume of similar objects

Logic Justification Person- al and

cultural

expression

Logic can

justify

generalizations

that increase our

appreciation of the

aesthetic

Critical-thinking: Draw

reasonable

conclusions and

generalizations;

Test generalizations and

conclusions;

Collaboration

skills- Encourage others to

contribute.

Reflection

skills-Consider

content what do

I learn about

today?

Creative-thinking

skills—Make

unexpected or

usual connections between

objects and/or

idea

IB learner profileInquirers：

Nurture our curiosity, developing

skills for inquiry

and research,

knowing how

to learn independently and

with others.

Core Competence

Critical thinking

Problem-solving

2 A CD Unit Test:

(Criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

circle and similarity.

Applying mathematics in

real-life contexts: (criteria

C, D)

Use the properties of similarity to measure the height

of the flag in our school.

Students need to write the

design plan clearly, and

think about the accuracy.

And they can use at least

two methods to check their

accuracy.

Study the national flag

carefully and create a similar national flag, students

should labeled the stars

and the length carefully,

and find out the beauty of

the design.

service as action:

Take action by

giving a speech

to the primary

students about the

beauty of Math.

? 67

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 6

Perimeter, area

andvolume

18

6.1. Geometry

? Length and perimeter

? Area

? Surface area for

3D shape

? Volume for 3D

shape

? Capacity

? Understanding

and using

coordinates in

three

dimensions

? Using the distance, section

and midpoint

formulae in

three dimensions

Relationship Space Measure- ment Person- al and cultural

expression

Generalizing relationship

between

measurements

enables the

construction and

analysis of

activities

for ritual

and play

Critical thinking skills-Analyze complex

concepts and

projects into

their constituent parts and

synthesize them

to create new

understanding;

Creative-thinking

skills-Apply existing

knowledge to

generate new

ideas, products

or process;

Communication skills-Use

and interpret

a range of

discipline-specific terms and

symbols

Organization

skills-keep an

organized and

logical system

of information

files/notebook.

IB learner profile

Principled:

Act with integrity and honesty,

with a strong

sense of fairness

and justice, and

with respect for

the dignity and

rights of people

everywhere.

Core Competence

Inquiring

Reflective

1 BCD Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

trigonometry

Investigation: (criterion B)

In this task, students will

need to investigate the

perimeter and area of a

region constructed by three

semi-circles ( two small

ones in a big one, and the

sum of the radius of the two

small ones equals to the big

one)

service as action:

Take action by

giving a speech to

the primary students about some

famous mathematicians

博實(shí)樂(lè)“中外融通課程”

68?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit7

Trigonometric

ratios in

right-angled triangles and

non-right

angled

triangle

trigonometry

54

7.1 Trigonometric

ratios

? Labelling right

angled

triangles

? The trigonometric ratios

? Finding side

lengths

? Finding angles

? Problem solving with

trigonometry

? Bearing

? 3-dimensional

problem

solving

? The unit circle

? The area of a

triangle

? The sine rule

? The cosine

rule

? Problem solving using the

sine and cosine

rule

Relationship Measure- ment, Models Scien- tific and technical

innovation

Generalizing relationships

between

measurements

can lead

to better

models and

methods

Critical thinking skills-Propose and evaluate a variety of

solutions, draw

reasonable

conclusions and

generalizations

Creative-thinking

skills-Apply existing

knowledge to

generate new

ideas, products

or process;

Organization

skills-set

goals that are

challenging and

realistic

Transfer skillsChange the

context of an

inquiry to gain

different perspectives

IB learner profileThinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core Competence

Inquiring

Reflective

2 AB C D Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

trigonometry

Investigation: (criterion B)

In this task, students will

need to investigate the sine

rule. First the students will

measure all the angles and

side lengths, and compare

their ratios of the side

length and sine value of

the corresponding angles to

get a general rule and then

justify the rule using circle

theorem.

Applying mathematics in

real life: (criteria C, D)

In this task, students need

to find out the area of a

polygon with given lengths.

They can divide the polygon into small triangles and

find out the area of each.

service as action:

Take action by

giving a speech to

the primary students about some

famous mathematicians

? 69

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 8

Probability

& Statistics

45

Relationship Represen- tation Quantity Orien- tation in space and

time

How quantities are

represented can help

to establish

underlying

relationship and

trends in a

population

Communication

skills—Understand and use

mathematical

notation;

Affective

skills-Practise

strategies to

reduce stress

and anxiety.

Information literacy

skills-Process

data and report

results

Information literacy

skills-Process

data and report

results.

Media literacy

skills- understand the

impact of media

representations

and modes of

presentation

IB learner profile

Communicators:

Express ourselves confidently and creatively

in more than one

language and in

many ways, collaborate effectively, listening

carefully to the

perspectives of

other individuals

and groups.

Core Competence

Inquiring

Problem-solving

2 A C D service as action:

Take action by

giving a speech

to the primary

students about

development of

math

8.1 Probability

? Experimental

probability

? Probability

from data

? Life table

? Sample space

? Theoretical

probability

? Using 2-dimensional grids

? Compound

events

? Events and

Venn diagrams

? Expectation

8.2 Statistics

? Types of data

? Discrete numerical data

? Continuous

numerical data

? Range, mean,

median, mode,

IQR,

five-number

summary

? Cumulative

data

Unit Test:

(criterion A)

In this task, students will

answer a wide range of

questions, from simple

to complex to challenging (in both familiar and

unfamiliar situations), all

based on probability and

statistics.

(criteria C, D)

The managers of a large

factory, which has around

10000 workers, would

like to know more about

the commuting times of

their staff.

1 Explain why it might not

be sensible to ask every

single employee.

2 The managers decide

to conduct a survey of a

sample of the employees.

They brainstorm a number

of ideas for ways of gathering the information.

a They could ask each

employee individually as

they arrived at work.

博實(shí)樂(lè)“中外融通課程”

70?

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

? Measuring the

spread of a data

set

? Box-andwhisker plots

? Standard deviation

? The normal

distribution

? Scatter plots

? Correlation

? Measuring

correlation

? Line of best fit

b They could put up a

notice asking employees

to respond by email.

c They could ask one

person in each department

to estimate an average

commuting time for that

department.

d They could ask every

200th person on the company’s staff list, having

sorted it alphabetically.

e They could ask every

200th person on the company’s staff list, having

sorted it by salary.

f They could put every

employee’s name into a

bag and draw out

50 names at random.

Comment on each of these

ideas. Explain how useful

you think the surveys

would be for finding out

representative information

about the commute

times of the factory’s

employees.

? 71

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core Competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 9

Financial

mathematics

27

9.1 Financial

mathematics

? Converting

between different

currencies

? Recognizing

conversions in

real-life contexts

? understanding

the meaning

of different rates

and commission

charges

? Appreciation

and depreciation

? Simple and

compound interest

? Personal loans

Relationship Quantity, Measure- ment Global- ization and sustainability Quantities and mea- surements illustrate

the relationship

between

human-made

systems

and communities

Communication skillsMake effective

summary notes

for studying;

Collaboration

skills-Give and

receive meaningful feedback

Media literacy skillsSeek a range

of perspectives

for multiple and

varied sources

Critical-thinking skills-Draw

reasonable

conclusions and

generalizations

IB learner profileThinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core Competence

Problem-solving

Reflective

2 AB Unit Test: (criterion A)

In this task, students will

answer a wide range of

questions, from simple to

complex to challenging (in

both familiar and unfamiliar situations), all based on

linear patterns of change

and how they can be represented. Questions will focus

on representing lines in a

variety of forms, graphing

lines, finding the equation

of a linear pattern and applying these skills to solve

real-life problems. The test

will be done individually in

class during one period.

Investigation: Gradient of a

Line (criterion B)

In this task, students will

invest amount of money

(either simple interestor

compound interest with

different rate), they need to

choose a suitable plan for

this investment.

service as action:

Take action by

giving a speech

to the primary

students about

development of

math

博實(shí)樂(lè)“中外融通課程”

72?

G2

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 1

Algebra 1

63

Form Patterns,

generalization

Scientific and

technical

innovation

Different

forms can

be used to

generalize

and justify

patterns

Critical-thinking

skills-Identify

trends and

forecast possibilities; Draw

reasonable

conclusions and

generalizations;

Communication

skills-Understand and use

mathematical

notation

Media literacy skillsSeek a range

of perspectives

for multiple and

varied sources

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Inquisitive

Reflective

2 A B C D Criterion A: Knowing and

understanding

A test about sequence will

be held.

Questions will be focused

on the general term, sum

for both arithmetic and

geometric sequence, and

infinity sum of geometric

sequence with |r|<0. And

determine whether a value

is a term of sequence.

Criterion B C:

Investigation:

Investigate a sequence to

find the general term and

test, justify, and prove the

formula

Criterion C D: Applying in

real-life context.

There are two plans about

a deposit. One follows a

arithmetic sequence while

the other follows geometric

sequence, students should

calculate the interest and

determine which one better.

service as action:

Take action by

giving a speech

to the primary

students about the

beauty of Math.

1.1. Sequence

? Arithmetic

sequence

? Geometric

sequence

? Arithmetic

series

? Geometric

series

? Infinite geometric series

1.2 Simultaneous

equations and

quadratics

? Simultaneous

equations (one

linear and one

non-linear)

? Roots of quadratic equations

? Intersection of

a line and a

curve

1.3 Permutation

and Combination

? Factorial notation

? Permutation

? Combination

? Pascal’s

triangle

? The binomial

? 73

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

theorem

1.4 Factors and

polynomials

? Adding, subtracting and

multiplying

polynomials

? Division of

polynomials

? The factor

theorem

? Cubic expressions and

equations

? The reminder

theorem

1.5 Indices and

surds

? Simplifying

expressions

involving indices

? Solving equations involving

indices

? Surds

? Calculations of

surds

? Rationalizing

the denominator

of a fraction

? Solving equations involving

surds

博實(shí)樂(lè)“中外融通課程”

74?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 2

Functions

36

2.1. Relations and

functions

? Relations

? Functions,

domain, range

? Function notation

? Composite function

? Inverse function

? Simple piecewise function

? The modulus

function

? Monotonicity of

functions

? Where functions

meet

2.2 Quadratic

Functions

?Quadratic functions

? Transformation

to sketch

quadratics

? Axes intercepts

? Sketching quadratics for their

axes intercepts

? Graphs of quadratic functions

? Monotonicity of

quadratic

functions

? Solving quadratic equation

graphically

? Practical maximum and

minimum

? Quadratic function and linear f

unction meet

Form Change,

Equivalence

Scientific and

technical

innovation

Representing

change and

equivalence in

a variety

of forms

has helped

human

apply their

understanding of

scientific

principles

Organization

skills-Use

appropriate

strategies for

organizing

complex information

Information literacy

skills-Process

data and report

results

Critical thinking

skills-Revise

understanding based on

new evidence;

Transfer skillsApply skills

and knowledge

in unfamiliar

situations;

Self-management-organization-Use

appropriate

strategies for

organizing

complex situations.

IB learner profile

Reflective:

we can develop

our skills by

giving thoughtful

consideration to

our own learning, ideas and

experience. We

will reflect on our

work when we

assess our own

writing and that

of others.

Core competence

Critical thinking

Reason

2 B C D Criterion A: Knowing and

understanding

A test about functions will

be held.Questions will be

focused on functions such

as composite function,

inverse function, modulus

function, quadratic function

and their graphs.

Applying mathematics in

real-life context (Criterion

C, D)

Students will use quadratic

function to get the maximum profit.

A shopping mall is selling

shirts marked $58 for each,

it’s found the selling

amount will increase 100

while reducing $1, and the

original selling amount is

1000, to get the maximum

profit, what the selling

price should be?

service as action:

Take action by

giving a speech

to the primary

students about the

beauty of Math.

? 75

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 3

Exponential and

logarithms

36

Relationship Quantity, Change, Generalization Orien- tation in space and time Gener- alizing changes in quantity helps

establish

relationships that

can model

duration,

frequency

and variability

Collaboration

skills-Listen

actively to other

perspectives

and ideas.

Critical thinking

skills-Consider ideas

from multiple

perspectives;

draw reasonable

conclusion and

generalizations;

Transfer skillsChange the

context of an

inquiry to gain

different perspectives

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Critical thinking

Problem-solving

2 A B Criterion A: Knowing and

understanding

A test about exponential

and logarithms will be

held. Questions will be

focused on calculating on

exponential and logarithms.

And also use the functions

properties to solve problems

Criterion B:

Investigation:

Investigate the product

rule, quotient rule, power

rule.

3.1 Exponential

and logarithms

? Simplifying

expressions

involving indices

? Evaluating

logarithms with

and without a

calculator

? Solve exponential equations

? Write and

solve exponential

equations from

real-life

situations

? Using natural

logarithms

? Drawing

graphs of

logarithmic

functions

? Finding the

inverse of an

exponential

function

? Identifying and

applying

博實(shí)樂(lè)“中外融通課程”

76?

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

function transformations on

graphs of logarithmic

functions

? Developing the

laws of

logarithms

? Using the law

of logarithms

to simplify expressions and

solve equations

? Proving the

laws of

logarithms

? Proving the

change of base

law

? Comparing the

increasing rate

of exponential

function, linear

function, logarithmic function

? 77

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 4

Geometry

27

4.1. Transformations

? Translations

? Reflections

?.Rotations

? Enlargements

and reductions

? Describing

combinations of

transformation

of a function

algebraically

and graphically

? Write the

equation of a

graph

following one or

more

transformations

4.2 Circular

measure

? Circular measure

? Length of an

arc

?.Area of a sector

Form Change,

Models

Orientation in

space and

time

Relationships model patterns

of change

that can

help clarify

ad predict

duration,

frequency

and variability

Critical thinking

skills-Draw

reasonable

conclusions and

generalizations;

Creative thinking skills-create novel situation to authentic

problems;

Affective skillspractice being

aware of bodymind connections

Media literacy

skills-Make informed choices

about personal

viewing experience

IB learner profile

Thinker：

Exercise initiative in applying

critically and

creatively to

recognize an

approach complex issued, and

make reasoned,

ethical decisions,

to consider how

belonging relates

to location and

the impact on

local and global

communities.

Core competence

Inquisitive

Reflective

2 A Criterion A: Knowing and

understanding

A test about geometry will

be held. Questions will

be focused on calculating

on sector area, arc length,

and transformation. And

also use the transformation

properties to solve problems

service as action:

take action by

making our school

and community

more suitable.

博實(shí)樂(lè)“中外融通課程”

78?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 5

Probability

&

Statistics

30

Logic Representation,

System

Identities

and relationship

Understanding

health and

making

healthier

choices

result

from using

logical

representations and

systems

Communication

skills-Understand and use

mathematical

notation; use

and interpret a range

of discipline

specific terms

and symbols;

Collaboration

skills-Delegate

ad share responsibility for

decision-making

Organization

skills-Bring

necessary

equipment and

supplies to class

Reflections

skills-Consider

ATL skills development what

can I already

do?

IB learner profile

Communicators:

Express ourselves confidently and creatively

in more than one

language and in

many ways, collaborate effectively, listening

carefully to the

perspectives of

other individuals

and groups.

Core Competence

Problem-solving

Critical thinking

2 A B CD Criterion A: Knowing and

understanding

A test about probability will

be held.

Questions will be focused

on probability using different ways of displaying data,

especially tree diagram

and Venn diagram. And

questions about sampling

with or without replacement

are also very important, and

last are questions about

permutation and combination.

Criterion B:

investigation

Investigating climate

change—using data

analysis and probability

to discuss the evidence of

the correlation between

the emission of greenhouse

gases and the rise in global

temperature

Criterion C, D:

Construct a tree diagram

for a three-day weather

forecast where the probability of rain on any day is

estimated from past data

service as action:

take action by

calculating the

probability to help

others to make

decisions

5.1 Probability

? Experimental

probability,

? probability

from tabled data

? .Sample space,

theoretical

probability

? Using 2-dimensional grid,

Venn diagram,

tree diagram，

two way tables

? Compound

events

? Probabilities

with or without

replacement

? Conditional

probability

? Mutually

exclusive and

independent

events

? The product

and sum

principle

? Probabilities

using

permutations

? 79

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

and

combinations

5.2 Statistics

? Sampling,

lottery，random

sampling,

Stratified sampling,

population,

sample

? Statistics

terminology

? Quantitative

(numerical) data

? Grouped discrete data

? Continuous

data

? Measuring the

center

? Cumulative da

ta

? Measuring the

spread

? Box-andwhisker plots

? Statistics from

technology

? Standard deviation

? The normal

distribution

博實(shí)樂(lè)“中外融通課程”

80?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 6

Vectors

30

6.1 Vectors

? Directed line

segment

representations

? Vector equality

? Vector addition

and subtraction

? Vectors in

component form

? Scalar multiplication

Parallelism of

vectors

? The scalar

product of two

vectors

? Position vector

? Vector geometry

? 3-dimensional

vectors

? Constant velocity problems

Form Space

Pattern

Personal and

cultural

expression

Understanding

patterns in

forms and

space can

enhance

creativity.

Transfer

skills-combine

knowledge,

understanding

and skills to

create products

or solutions

Reflective

skills-Consider

personal learning strategieswhat can I do to

become a more

efficient and effective learner?

IB learner profile

Principled:

Act with integrity and honesty,

with a strong

sense of fairness

and justice, and

with respect for

the dignity and

rights of people

everywhere.

Core Competence

Inquiring

Reflective

2 A Criterion A: Knowing and

understanding

A test about advanced

Vector will be held. Questions will be focused on

basic calculation, application.

service as action:

take action by

making our school

or local community

more sustainable.

? 81

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 7

Advanced

trigonometry

35

7.1 Advanced

trigonometry

? Radian measure

? The unit circle?

? The relationship between sin

and cos

? The multiples

of 30° and 45°

? Trigonometric

functions

? Simplifying

trigonometric

expression

? Trigonometric

equations

? Negative and

complementary

angle formula

? Further

trigonometric

identities

? Application of

trigonometry

Relationship Measure- ment, Space,

Equivalence

Orientation in

space and

time

Generalizing and

applying

relationship

between

measurements in

space can

help define

where and

when

Critical thinking

skills-Gather

and organize relevant

information to

formulate an

argument,

Transfer- Apply skills and

knowledge

in unfamiliar

situations;

Creative-thinking

skills-Make

unexpected

or unusual

connections

between objects

and ideas.

draw reasonable

conclusions and

generalizations

Affective skillsPractice positive thinking

IB learner profile

Thinkers：

Use critical and

creative thinking

skills to analyze

and take responsible action on

complex problem.

Core Competence

Reason

Critical thinking

2 A B C D Criterion A: Knowing and

understanding

A test about advanced

trigonometry will be held.

Questions will be focused

on radians, sine rule and

cosine rule, trigonometric

identities, triangle area,

trigonometric functions.

Criterion B C:

Investigation:

1. A unit circle has a radius

of 1 unit. Find the circumference of a unit circle in

terms of

2. Find the formula for and

Criterion C D

Use the periodic property

of trigonometric function

to find out the appropriate time for a ship passes

through a bay.

service as action:

take action by

making our school

or local community more sustainable or measure

the height of the

small hill.

博實(shí)樂(lè)“中外融通課程”

82?

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 8

Algebra 2

40

8.1 Straight-line

graphs

? Problems

involving length

of a line and

midpoint

? Parallel and

perpendicular

lines

? Equations of

straight lines

? Areas of rectilinear figures

? Converting

from a non-linear

equation to linear

form

? Converting

from a linear form

to anon-linear

equation

8.2.Inequalities

? Interval notation

? Linear inequalities

? Modulus inequalities

? Sign diagrams

? Non-linear

inequalities

? Solving cubic

inequalities

graphically

? Linear programming

? Solving real-life problems

? Important

inequalities

From Equivalence,

Models

Identities

and Relationship

Modelling with

equivalent

forms of

representation can

improve

decision

making

Communication-Organize

and depict

information

logically;

Critical thinking-Use models

and simulations

to explore complex systems

and issues

Transfer-Apply skills and

knowledge

in unfamiliar

situations

Information literacy

skill-evaluate

and select

information

sources and

digital tools

based on their

appropriateness to specific

tasks.

IB learner profile

Reflective:

we can develop

our skills by

giving thoughtful

consideration to

our own learning, ideas and

experience. We

will reflect on our

work when we

assess our own

writing and that

of others.

Core Competence

Reflective

Inquisitive

2 A C D Criterion A: Knowing and

understanding

A test about solving

inequalities will be held.

(Solving linear inequalities,

quadratic inequalities,

rational inequalities algebrally and graphically)

Criterion C D:

Students should design a

plan for a party limit money.(Students need to design

several plans containing

different materials such

as fruits, candies, cookies

etc, and compare them to

choose the best one.)

Service as action:

Take action by designing a suitable

plan for preparing

for a party with

limit materials

? 83

高中數(shù)學(xué)課程圖

Unit tittle,

Teaching

hours

Contents (subtopics, knowledge, skill) Key con- cept Related Concept Global context Statement of Inquiry ATL skills IB learner profile&Core competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

Unit 9

Calculus

63

Relationship Quantity, Measure- ment Global- ization and sustainability Quantities and mea- surements illustrate

the relationships

between

human-made

system and

communities.

Critical-thinking skills- Draw

reasonable

conclusions and

generalizations;

Communication-Organize

and depict

information

logically;

IB learner profile

Inquirers：

Nurture our curiosity, developing

skills for inquiry

and research,

knowing how

to learn independently and

with others.

Core Competence

Reflective

Critical thinking

2 A B Criterion A: Knowing and

understanding

A test about differentiation

and integration will be hold.

It will be based on chain

rule, product rule, quotient

rule, tangent, normal, maximum or minimum value,

trigonometric functions.

Criterion B: Investigation

In this task student will

need to investigate how to

calculate the area of different region.

service as action:

Take action by

giving a speech

to the primary

students about

development of

math

9.1 Differentiation

? The gradient

function

? The chain rule

? The product

rule

? The quotient

rule

? Tangents and

normals

? Small increments and

approximations

? Rates of

change

? Second derivatives

? Stationary

points

? Practical

maximum and

minimum problems

? Derivatives

of exponential

functions

? Derivatives

of logarithmic

functions

? Derivatives

of trigonometric

functions

? Further

applications of

differentiation

博實(shí)樂(lè)“中外融通課程”

84?

Unit tittle,

Teaching

hours

Contents (subtopics,

knowledge, skill)

Key

concept

Related

Concept

Global

context

Statement

of Inquiry

ATL skills

IB learner

profile&Core

competence

Academic

proficiency

Level

Subject

objectives Summative assessment

Connection to service as action or

Interdisciplinary

learning or international-mindedness or both

9.2 Integration

? Differentiation

reversed

? Indefinite

integrals

? Integration of

functions of the

form

? Integration

of exponential

functions

? Integration of

sine and cosine

functions

? Integration of

functions of the

form and

? Further indefinite integration

? Definite integration

? Further definite integration

? Area under a

curve

? Area of regions

bounded by a

line and a curve

? Applications of

differentiation in

kinematics

? Applications

of integration in

kinematics

? 85

高中數(shù)學(xué)課程圖

4 Course Assessment

4.1 External assessment (Each criterion 25%)

Criterion A: knowledge and understanding

Criterion B: investigation

Criterion C: communication

Criterion D: Applying mathematics in real-life

4.2 Internal assessment

Criterion A: knowledge and understanding

5 Teaching Sources

5.1 Books:

1. Mathematics for the international student MYP 4. Michael Haese Sandra Haese

Mark Humphries Edward Kemp Pamela Vollmar. ISBN: 978-921972-49-2

2. Mathematics for the international student MYP 5. Michael Haese Sandra Haese

Mark Humphries Edward Kemp Pamela Vollmar. ISBN: 978-921972-53-9

3. Cambridge IGCSE and O Level Additional Mathematics Coursebook Second

edition. ISBN: 978-1-108-41166-0

4. Cambridge International AS&A Level Mathematics: Pure Mathematics 1

Coursebook. ISBN:978-1-108-40714-4

5. Cambridge International AS&A Level Mathematics: Probability & Statistics 1

Coursebook. ISBN:978-1-108-40730-4

5.2 Reference

1. Advanced Level Mathematics Pure Mathematics 1 Huhg Neill and Douglas

Quadling. ISBN: 978-0-521-53011-8

2. Cambridge IGCSE Maths STUDENT’S BOOK. ISBN: 978-0-00-825779-8.

博實(shí)樂(lè)“中外融通課程”

86?

5.3 Websites

1. www.myib.org

2. http://10.166.1.163/( 廣東碧桂園學(xué)校教學(xué)資源網(wǎng) )

3. https://cie.fraft.org

4. https://bgy.managebac.com/login

Chinese and International Integrated

Curriculums for Bright Scholar

High School Section

CPRE-DP Mathematics

Curriculum Map

（2022version）

Complied by Guangdong Country Garden Senior High Section

博實(shí)樂(lè)“中外融通課程”

88?

CPRE-DP Curriculum Mapping

Subject Mathematics Level Pre-DP G2 Syllabus Code

Course Code Credit 8 Duration 1 year

Teaching

Hours

360

Designer

Tao Xiaojun，Nathan

Wang Ying，

Wang Baishi

Liu Xinhua，Zhong Yi

Wang Runmei

completed

Date

2022.9

1 Course Introduction

1.1 Introduction

Cambridge IGCSE Additional Mathematics and AS Probability & Statistics are

accepted by universities and employers as proof of essential mathematical knowledge and

ability.

The Additional Mathematics syllabus is intended for high ability candidates who have

achieved, or are likely to achieve, Grade A*, A or B in the CIE Mathematics examination.

Successful Cambridge IGCSE Additional Mathematics and CIE candidates gain

lifelong skills, including:

? the further development of mathematical concepts and principles

? the extension of mathematical skills and their use in more advanced techniques

? an ability to solve problems, present solutions logically and interpret results

? a solid foundation for further study.

1.2 Aims

The aims are to enable candidates to:

? consolidate and extend their elementary mathematical skills, and use these in the

context of more advanced techniques.

? further develop their knowledge of mathematical concepts and principles, and use

? 89

高中數(shù)學(xué)課程圖

this knowledge for problem solving.

? appreciate the interconnectedness of mathematical knowledge.

? acquire a suitable foundation in mathematics for further study in the subject or in

mathematics related subjects.

? devise mathematical arguments and use and present them precisely and logically.

? integrate information technology (IT) to enhance the mathematical experience.

? develop the confidence to apply their mathematical skills and knowledge in

appropriate situations.

? develop creativity and perseverance in the approach to problem solving.

? derive enjoyment and satisfaction from engaging in mathematical pursuits, and gain

an appreciation of the beauty, power and usefulness of mathematics.

2 Course Structure

1.Quadratic equation with one

unknown

2.Quadratic functions

3.Inverse proportional

4.Indices

5.Radicals

6.Sets and Venn diagrams

7.Sequence and series

8.Functions

9.Exponential and logarithms

10.Inequalities and graphs

11.Factors and polynomial

12.Permutation and

Combination

1.Transformation

2.Vectors

3.Straight-line

graphs

4.Circular

measure

1.Trigonometry

in right-angled

triangle

2.Trigonometry

in non-rightangled triangle

3.Advanced

trigonometry

1.Probability

2.Statistics

Algebra

CPre-DPMathematics

Geometry Trigonometry Probability

and Statistics

Calculus

1.Differentiation

2.Integration

博實(shí)樂(lè)“中外融通課程”

90?3 Course outline

Timeline

Unit/ Theme/

Topic

Contents Objectives

Core Competency

Academic

Proficiency

Level

Teaching

Hours

ATL Skills Homework, Link to TOK,

IM, LP and CAS

9.5-9.18 Functions 0.1Types of

relations;

0.2Introduction to

functions;

0.3Composite

functions;

0.4

Inverse functions;

0.5Absolute

valued functions.

1.6 Sets

? understand the terms: function, domain, range (image

set), one-one function, inverse function and composition

of functions.

? use the notation f(x) = sin x,

f(x)=lg x (x > 0), f–1(x) and

f2(x) [= f (f(x))].

? understand the relationship between y = f(x) and y

= ( ) f x , where f(x) may be linear, quadratic or trigonometric.

? explain in words why a given function is a function or

why it does not have an inverse.

? find the inverse of a one-one function and form composite functions.

? use sketch graphs to show the relationship between a

function and its inverse.

? solve quadratic equations for real roots and find the

solution set for quadratic inequalities.

? Monotonicity of quadratic

functions

? Sets, universal set, empty set

? Special Number sets

? Interval notation

? Complement of a set, element

? Venn diagrams

? Union and intersection

? Number in regions

? Problems solving with Venn

Diagrams

Reason

Critical

thinking

Inquiring

Reflective

Problem-solving

2 18 Critical thinking skills-Analyze complex

concepts and

projects into

their constituent parts and

synthesize

them to create

something new;

Communication

skills-preview

and skim texts

to build understanding;

Homework

Assignment on textbook

and Past papers

TOK

Sometimes more than one

type of symbol might have

the same meaning such as

interval and set notation.

To what extent does the

language we use shape the

way we think?

IM

Over 2000 years age,

Babylonians and Egyptians used quadratics to

work with land area.

? 91

高中數(shù)學(xué)課程圖

Timeline

Unit/ Theme/

Topic

Contents Objectives

Core Competency

Academic

Proficiency

Level

Teaching

Hours

ATL Skills Homework, Link to TOK,

IM, LP and CAS

9.19-

9.30

Simultaneous

equations

and quadratics

2.1 Two

simultaneous

linear equations;

2.2 Non-linear

equations.

2.3 Quadratic

equations;

2.4 Quadratic

curve;

2.5 Completing

the

square;

2.6 Quadratic

inequality.

? solve simultaneous equations in two unknowns with at

least one linear equation.

? find the maximum or minimum value of the quadratic

function f : x

-

ax

2 + bx + c by any method.

? use the maximum or minimum value of f(x) to sketch

the graph or determine the range for a given domain.

? know the conditions for f(x) = 0 to have: (i) two real

roots,

(ii) two equal roots,

(iii) no real roots

and the related conditions for a given line to (i) intersect

a given curve,

(ii) be a tangent to a given curve,

(iii) not intersect a given curve.

? solve quadratic equations for real roots and find the

solution set for quadratic inequalities.

? know the difference of quadratic function, quadratic

equations with one unknown, and using quadratic functions to solve reality problems.

Reason

Critical

thinking

Reflective

Problem-solving

2 18 Reflection

skills-Identify

strengths and

weakness of

personal learning strategies.

Critical-thinking skills-Applying existing

knowledge to

generate new

ideas or process, Propose

and evaluate

a variety of

solutions;

Reflection-Draw

reasonable

conclusions and

generalizations

Homework

Assignment on textbook

and Past papers

TOK

How can you deal with the

ethical dilemma of using

mathematics to cause

harm, such as plotting the

course of a missile?

IM:

The Babylonians used

quadratics to find the area

of fields for agriculture

and taxation

博實(shí)樂(lè)“中外融通課程”

92?

Timeline

Unit/ Theme/

Topic

Contents Objectives

Core Competency

Academic

Proficiency

Level

Teaching

Hours

ATL Skills Homework, Link to TOK,

IM, LP and CAS

10.8-

10.16

Indices and

surds

3.1 Rules of indices and surds;

3.2 Exponential

equations;

3.3 Simplifying

surds.

? perform simple operations with indices and with surds,

including normalizing the denominator.

Inquiring

Reflective

2 9 Transfer skillsChange the

context of an

inquiry to gain

different perspectives

Homework

Assignment on textbook

and Past papers

TOK

Do you think that mathematics is just the manipulation of symbols under a

set of rules?

IM

French mathematician

Nicolas Chuquet created

his own notation for exponentials and might have

been the first to recognize

zero and negative exponents.

10.17-

10.30

Factors and

polynomials

4.1 Polynomial

identities;

4.2 Remainder

theorem;

4.3 Factor theorem;

4.4 Cubic

expressions.

? know and use the remainder and

factor theorems.

? find factors of polynomials.

? solve cubic equations.

Reason

Critical

thinking

Inquiring

Reflective

2 18 Collaboration

skills-Listen

actively to other

perspectives

and ideas.

Critical thinking skills-Consider ideas

from multiple

perspectives;

draw reasonable conclusion

and generalizations;

Homework

Assignment on textbook

and Past papers

TOK

Is zero the same as nothing?

IM

Greek mathematician

Heron discussed the root

of a negative in the first

century BC.