都立国際高校 年間授業計画／ Tokyo Metropolitan Kokusai High School Course Syllabus○ 科目基礎情報 ( Course information )開講年度( Academic year )令和6年度 ( 2024 年度 )開講学科

(Department)

国際学科国際バカロレアコース／IBDP(International Baccalaureate Diploma Programme)

教科(Subject Area)

Mathematics

科目(Subject)Mathematics: Applications and Interpretation Higher Level

学年･クラス(Grade･Class)

DP2単位数(Number of units)

6

使用教科書(Text Books)

Pearson Mathematics Applications and Interpretation

校外学習(Field trip)-○ 教科の目標 ( Goals of the subject area )【 知 識 及 び 技 能 】 ( Knowledge and Skills )Understand the basic concepts, principles and laws in mathematics, as well as the skills to mathematically interpret and express events.
【思考力、判断力、表現力等】 ( Ability to think, make judgements, express themselves )Develop the ability to examine events logically using mathematics, to recognize the essence of events and their relationships with other eventsand to examine them in an integrated and developed manner, and to express events concisely, clearly, and precisely using mathematicalexpressions.
【学びに向かう力、人間性等】 ( Motivation to learn, Humanity )Develop an attitude to recognize the advantages of mathematics and actively utilize mathematics, an attitude to think tenaciously and makejudgments based on mathematical arguments, an attitude to reflect on the process of problem solving and to deepen consideration, evaluationand improvement, and a basis for creativity.

○ 科目の目標 ( Goals of the subject )【知識及び技能】( Knowledge and Skills )【思考力、判断力、表現力等】【学びに向かう力、人間性等】( Motivation to learn, Humanity )( Ability to think, make judgements, express themselves )Understand the basic concepts, principles andlaws in mathematics, as well as the skills tomathematically interpret and express events.

Develop the ability to examine events logicallyusing mathematics, to recognize the essence ofevents and their relationships with other eventsand to examine them in an integrated anddeveloped manner, and to express events
concisely, clearly, and precisely using
mathematical expressions.

Develop an attitude to recognize the advantagesof mathematics and to make use ofmathematics, an attitude to think tenaciously andto make judgments based on mathematicalarguments, and an attitude to deepen
consideration, evaluation, and improvement bylooking back on the process of problem solving,as well as a basis for creativity.
Alottedhours○ 授業計画 ( Course schedule )単元の具体的な指導目標
Unit Objectives
Students will be able to

指導項目・内容
Topic / Contents

・make resonable estimates andbetter approximations.

・Number and algebra basics

・demonstrate an understanding of
the rules of exponents.

・Sequences and series

・Functions

・Modelling real-life phenomena
・use correct scientific notation.
・demonstrate a understanding of
the rules of logarithms.

・understand the concept of afunction, domain, range, and graph.
・use function notation.
・find composite functions incontext.
・find an inverse function, inlcudingdomain restriction.

１学期 ( 1st semester)・use piecewise functions.
・understand the graph of afunction.
・create a sketch from information
given ora context, includingtransferring a graph from screen topaper while determining key featuresof graphs using technology andfinding points of intersection ofcurves.

評価規準
Evaluation Criteria➊【Knowledge/Skills】
・Recall, select and use their knowledge ofmathematical facts, concepts and techniques
in a variety of familiar and unfamiliar contexts.
・Use technology accurately, appropriately andefficiently both to explore new ideas and tosolve problems.
❷【Ability to think/make judgements/express
themselves】
・Recall, select and use their knowledge ofmathematical skills, results and models in bothabstract and real-world contexts to solve
problems.
・Transform common realistic contexts into
mathematics; comment on the context; sketchor draw mathematical diagrams, graphs orconstructions both on paper and using
technology; record methods, solutions andconclusions using standardized notation; useappropriate notation and teminology.
・Construct mathematical arguments throughuse of precise statements, logical deduction
and interference and by the manipulation ofmathematical expressions.
・Investigate unfamiliar situations, both abstractand from the real world, involving organizing
and analyzing information, making conjectures,
drawing conclusions, and testing their validity.
❸【Attitude towards learning proactively】
・Be interested in mathematics, recognize theadvantages of mathematics, and try to apply
them to both abstract and real-world contexts
to solve problems.

知➊

思❷

態
❸

配当
時数

○○○

80○

○

・understand transformations ofgraphs (translations, reflections,vertical/horizontal stretches, andcomposite transformations)・use function to model real-life
phenomena.
・use the formulae for the nth term
for arithmetic and geometricsequences.
・use the formulae for the sum of nterms for arithmetic and geometricseries.
・use sigma notation for the sums ofsequences.
・use applications including
simple/compound interest,
population growth, annual
depreciation, and modelling as well
as solve problems using
amortisation and annuities using
technology.
End-Term Exam 1

4

単元の具体的な指導目標
Unit Objectives

指導項目・内容
Topic / Contents

Students will be able to・Geometry and trigonometry・find distances and midpoints
・Complex Numbers
・determine intersections of lines in aplane・Graph Theory

・use sine and cosine rules, find areasof triangles, and calculate volume andsurface areas of 3D solids

・Integral Calculus I・calculate sector areas and arc
lengths
・understand radian measure andconversions wih degrees
・understand trigonometric functions,the Pythagorean identity, and solve
equations in finite intervals
・use and create Voronoi diagrams
・be familiar with complex numbers,
their calculations, as vectors in thecomplex plane as well as powers androots of complex numbers and the useof complex numbers in STEM
applications

２学期 ( 2nd semester)・Matrix Algebra

・apply the Pythagorean theorem aswell as trigometric ratios in rightangled triangles

・be familiar with matrix algebra using
technology, including identitse,
inverses, eigenvectors, andcharacteristic polynomials・diagonalise 2x2 matrices, transform
points with matrices, and apply
transformations to fractals

・Differential Calculus

評価規準
Evaluation Criteria

知➊思❷

態❸

配当時数○○○

92○○➊【Knowledge/Skills】
・Recall, select and use their knowledge ofmathematical facts, concepts and techniques
in a variety of familiar and unfamiliar contexts.
・Use technology accurately, appropriately andefficiently both to explore new ideas and tosolve problems.
❷【Ability to think/make judgements/express
themselves】
・Recall, select and use their knowledge ofmathematical skills, results and models in bothabstract and real-world contexts to solveproblems.
・Transform common realistic contexts into
mathematics; comment on the context; sketchor draw mathematical diagrams, graphs orconstructions both on paper and using
technology; record methods, solutions andconclusions using standardized notation; useappropriate notation and teminology.
・Construct mathematical arguments throughuse of precise statements, logical deduction
and interference and by the manipulation ofmathematical expressions.
・Investigate unfamiliar situations, both abstractand from the real world, involving organizing
and analyzing information, making conjectures,
drawing conclusions, and testing their validity.
❸【Attitude towards learning proactively】
・Be interested in mathematics, recognize theadvantages of mathematics, and try to apply
them to both abstract and real-world contexts
to solve problems.

・understand transformations of graphs(translations, reflections,vertical/horizontal stretches, andcomposite transformations)・work with graphs and their features,use directed graphs, set up adjacency
matrices, construct transition
matrices, work with various paths andminimum spanning trees, use famous
problems like Route Inspection and thetravelling salesman
・understand limits as well asderivatives of gradients, as well as findderivatives using power, chain, andquotient/product rules
・understand the relationship of thefirst/second derivatives with graphs aswell as concavity and related tests, aswell as find tangent/normal, rate ofchange, and optimum solutions
・be familiar with integration as
antidifferetiation, finding area undercurves, motion problems as well as
techniques including substitution andthe trapezoidal rule as well as findvolumes of revolution around axes.

End-Term Exam 24単元の具体的な指導目標
Unit Objectives
Students will be able to・describe vectors use standard
notation and determine the vector
equations of lines as well as apply
vector equations to kinematic
models, find scalar and vector
products, and calculate the angle
between vectors in 3-dimensional
space (3-space)・be familiar with the concepts of
population, random sampling, othersampling techniques and theireffectiveness and bias, outliers, anddiscrete vs continuous data as wellas the reliability of data sources
・present data using tables,
histograms, cumulative frequency
tables, graphs

３学期 ( 3rd semester)・find measures of center andinterpret plots as well as compare
distriutions and effects of constantchanges of data
・be familiar with the concepts oftrial, outcomes, frequency, sample
spaces, events as well ascomplementary events, expected
number of occurrences, conditional
probability and independent events
as well as Venn diagrams, tree
diagrams, sample space diagrams,
and tables of outcomes to calculate
probabilities

指導項目・内容
Topic / Contents

・Vectors
・Descriptive Statistics
・Probability of Events
・Probability Distributions
・Inferential Statistics

評価規準
Evaluation Criteria➊【Knowledge/Skills】
・Recall, select and use their knowledge ofmathematical facts, concepts and techniques
in a variety of familiar and unfamiliar contexts.
・Use technology accurately, appropriately andefficiently both to explore new ideas and tosolve problems.
❷【Ability to think/make judgements/express
themselves】
・Recall, select and use their knowledge ofmathematical skills, results and models in bothabstract and real-world contexts to solve
problems.
・Transform common realistic contexts into
mathematics; comment on the context; sketchor draw mathematical diagrams, graphs orconstructions both on paper and using
technology; record methods, solutions andconclusions using standardized notation; useappropriate notation and teminology.
・Construct mathematical arguments throughuse of precise statements, logical deduction
and interference and by the manipulation ofmathematical expressions.
・Investigate unfamiliar situations, both abstractand from the real world, involving organizing
and analyzing information, making conjectures,
drawing conclusions, and testing their validity.
❸【Attitude towards learning proactively】
・Be interested in mathematics, recognize theadvantages of mathematics, and try to apply
them to both abstract and real-world contexts
to solve problems.

知➊

思❷

態❸

配当
時数

○○○

54

総授業時数
Total hours

234

・be familiar with continuous anddiscrete variables, findmean/variance of biomial, Poisson,and normal distributions as well as
apply understanding in determining
probabilities as well as determine
which distribution best describes
data・transform and combine data as
wel as calculate probabilities inMarkov chains with matrices
・draw inferences about apopulation and find unbiased
estimators of population parameters
・be familiar with reliability andvalidity, the central limit theorem,
and confdence intervals for theproportion and mean