hwa chong institution (high school section) subject...

Hwa Chong Institution (High School Section) Subject: Mathematics Level: Secondary One

2011 Scheme of Work

Strands Curriculum of Core Curriculum of Connection Curriculum of Practice

Curriculum of Identity

Schedule Term 1 Week 1

Unit 1: Overview At the end of this unit, students will be

able to 1. Know the overview of the Sec 1

Mathematics Programme – framework, expectations, assessment plan and requirements

2. Know the Mathematics Resources in HCI a. IT resources b. Visit of high school

library/MaLRC c. Visit of college library

3. Know the effective Mathematics study skills

4. Demonstrate how to use MS Office Equation Editor or MathType in BOTH MS Word and MS ppt.

• Use of parabolic design in concentrated solar plant (CSP) and it benefit the earth and the environment

• Proving the quadratic formula using geometrical diagrams

• Using completing of square technique to find minimum and maximum in real life situations involving quadratic equations

• Adaptability (Communicating

with the students about the difference between primary and secondary mathematics, e.g. presentation of working in all assignments and assessments)

• Discipline • Respect • Perseverance

• Generalisation of Arithmetic, hence rules of operations in arithmetic will apply as well.

• PCM/Curriculum of Identity (Reflecting the role of a learner in mathematics, relating to their aspirations when they grow up, getting students to set expectations in their learning)

Processes (include pedagogies and indicate

Instructional Strategies: • Direct Instructions − Teachers

share their perception of


2011 Scheme of Work

infusion of ICT)

Mathematics with the pupils; teacher to explain in details the expectations and assessment programme including the Math Portfolio

• Student-centred – Working in pairs to find out the library resources on math; working in pairs, discuss about effective math study skills and research on famous mathematicians to find out what characterised these mathematicians

Thinking skills to be infused: • Information gathering • Investigating • Organising

Products (Assignments/ Tests/ Practicals)

ACE: • Poster or Web reports or brochures

on research on famous mathematicians/selected Mathematical topics can be display in class notice board, published as web and submit for ACE

• Rubrics for the performance assessment for all research work to be made known to all teachers and students to ensure consistency in grading and smoothness in follow-up work

Environment Resources Resources:

Library Books:


2011 Scheme of Work

• History of Famous Mathematicians • Brochures on Career in

Mathematics • Encyclopaedia • Non-print materials

Schedule Term 1 Week 2-3 Term 1 Week 4 - 6

Unit 1: Arithmetic I At the end of this unit, students will be able to 1. Understand and use real, rational,

irrational, integer, whole, natural, prime, odd, even, positive, negative numbers

2. Use inequality symbols <, >, ≤ and ≥

3. Apply PEMDAS (parentheses, exponents, multiplication, division, addition and subtraction) on the above number system

4. Work with fractions, decimals and recurring decimals

5. Use the calculator to evaluate calculations

6. Draw and arrange real numbers (including integers, fractions, decimals, etc) on the number line

7. Understand purpose and origin of complex numbers

8. Understand and write numbers using different numeral system, e.g. Roman, Egyptian, Babylonian, etc. (optional: as an introductory topic to Arithmetic / ACE)

9. Unit fractions, continued fractions Unit 2: Arithmetic II At the end of this unit, students will be

To expose students to the differences in numeral systems in the history of mankind, and why it has evolved to this day’s

To strengthen the concepts of Arithmetic learnt in primary school and introduce new arithmetic concepts


2011 Scheme of Work

able to 1. Apply prime factorisation to find

LCM & HCF to find factors, multiples, highest common factors, lowest common multiples, exponents, square and cube roots

2. Write numbers in product of factors in exponent form (by prime factorisation)

3. Find the reciprocal and absolute value of a number

4. Solve word problems involving different types of numbers with fractions and decimals

5. Understand the concept of rate of work done, and solve work problems involving simple direct and inverse variations.

6. Understand significant figures and write numbers in required significant figures

7. Distinguish and explain significance of rounding and truncation errors

8. Define the Binary System 9. Apply simple operations

(addition, subtraction) binary numbers

10. Apply simple operations (multiplication, division) binary numbers

11. Understand operation systems and perform operations in defined systems

Processes (include

Thinking skills to be infused: • Classify


2011 Scheme of Work

pedagogies and indicate infusion of ICT)

• Generalise • Compare • Memorise • Compare • Analyse • Verify • Synthesise • Apply • Summarise • Specialise • Substitute • Create Instructional Strategies: • Direct instructions – drill and

practice, Socratic questioning • Student-centred instructions −

flexible grouping, concept mapping, problem solving

• Independent Study − homework, portfolio, research


• 1 written class test

• ACE idea: Graded pair work to produce either (i) a one-page report on any one ancient number system with simple illustration of its meaning and usage, or (ii) one page of the daily newspaper which avoids all mention of numbers (Appendix 1A)

• Graded oral presentation


o Discovering Mathematics Book 1Chap 1,2,3, 9, 10

o Discovering Mathematics Book 2


2011 Scheme of Work

Chap 1

SMO Resources: • Counting (Math Quiz Training) • Singapore Mathematical

Olympiads 1995-2005 Questions book

• Mathematics Teacher NCTM Calendar Problems 2001 to 2005

• Australian Mathematics Competition Book 1 (1978-1984), Book 2 (1985-1991), Book 3 (1992-1998)

• Mathematical Challenge by Tony Gardiner

• More Mathematical Challenge (Problems from UK Junior Mathematical Olympiad 1989-1995) by Tony Gardiner

• Senior Mathematical Challenge (The UK National Mathematical Contest 1988-1996) by Tony Gardiner

• Maths Challenge Book 1,2 & 3 by Tony Gardiner

• AMC8 Questions • Euler Student Problems –

Mathematical Challenge for Young Australians

Schedule Term 1 Week 6 -8

Unit 1: Basic Algebra At the end of this unit, students will be able to 1. Trace and comment on the

development of Algebra 2. Use letters to represent quantities 3. Identify polynomials, variables,


2011 Scheme of Work

coefficients and constant terms 4. Use basic conventions of algebraic

notation to represent statements and relationships between variables

5. Translate simple real-world situations into algebraic expressions

6. Demonstrate equivalence between algebraic expressions

7. Simplify algebraic expressions involving addition, subtraction, brackets, fractions (where either the denominator or numerator is a numeral and not algebraic expressions) and combinations of these

8. Evaluate algebraic expressions by substituting values for variables

9. Factorization of linear expressions of the form

( )ax ay az a x y z+ + = + + where a is a constant.

10. Addition and subtraction of algebraic fractions with linear

denominator, e.g.1 2

2 3x x+

− −

Processes (include pedagogies and indicate infusion of ICT)

Instructional Strategies: • Direct: Socratic questioning, drill

and practice • Student-centred: flexible grouping,

concept mapping, problem solving, model heuristic to algebraic approach

• Independent: research, homework,

To teach students to appreciate the use of algebra in solving of problems involving unknowns)


2011 Scheme of Work

portfolio

Thinking skills to be infused • Information gathering • Generalising • Focusing


Environment Resources Resources

o Discovering Mathematics Book 1 Chap 4 & 5

Library Books: • History of Famous Mathematicians • History of Algebra • Encyclopaedia Internet: • www.algebrahelp.com/resources/st

udytips.htm • www.algebrahelp.com/lessons

/equationbasics/ • www.mathsnet.net/algebra/index.h

tml CD-ROM: • CD-ROM: Pre Algebra

(CDR512/PRE) • CD-ROM: Algebra II

(CDR512/ALG) • CR-ROM: Math Blast (Pre

Algebra) (CDR512/MAT) • CD-ROM: Math Blast (Algebra)


2011 Scheme of Work

(CDR512/MAT) • CD-ROM: Exploring Algebra

(CDRTR512/CHA) • Dynamic Maths Series: • Linear Equations / Quadratic

Equations (CDR510/JUN) • Enrichment 1-3: Divisibility Rules • Enrichment-1: Calendar • Enrichment-2: Prove yourself SMO Resources: • Factorisation (Math Quiz

Training) • Algebraic Expressions (Math

Quiz Training) • Simultaneous Equations (Math

Quiz Training) • Quadratic Equations in 1

Variables (Math Quiz Training) • Singapore Mathematical



• AMC8 Questions • Australian Mathematics

Competition Book 1 (1978-1984), Book 2 (1985-1991), Book 3 (1992-1998)



• Senior Mathematical Challenge


2011 Scheme of Work

(The UK National Mathematical Contest 1988-1996) by Tony Gardiner


• Euler Student Problems – Mathematical Challenge for Young Australians

Schedule Term 2 Week 1-2

Unit 2: Algebraic Formulae At the end of this unit, students will be able to 1. Construct formula from word

problem 2. Change the subject in given

formula in linear form 3. Use the skills in change of subject

to evaluate unknown in given algebraic formula

4. Solve number sequence (finding algebraic formula for the nth term)

5. Use and apply the formula governing speed, distance and time to solve word problems.




problem solving, model heuristic to algebraic approach

Thinking skills to be infused: • Generating • Analysing • Focusing


2011 Scheme of Work


1 Class Test


Discovering Mathematics Book 3 Chapter 1 Discovering Mathematics Book 1 Chapter 11 Internet http://www.mathsnet.net/algebra/index.html

Schedule Term 2 Week 2-3

Unit 3: Linear Algebraic Equations At the end of this unit, students will be able to 1. Solve simple linear equations

involving one unknown 2. Solve simple linear equations

involving fractional and decimal coefficients

3. solve simple fractional equations that can be reduced to linear equation e.g.

2 33; 6

3 4 2x x

x−

+ = =−

4. Form linear algebraic equations from given word problems

5. Solve challenging problems using algebraic skills

• To provide real life word problems for students to apply the concepts of algebra)


Thinking skills to be infused: • Analysing • Focusing • Generating


2011 Scheme of Work

infusion of ICT)

IT skills Use graphic calculators to explore the graphical interpretation of solving linear equations Instructional Strategies: • Direct: Socratic questioning, drill


pair work, problem solving, model heuristic to algebraic approach


1 Class Test


Discovering Mathematics Book 1 Chapter 6 Mathsoft Study Works, CD-ROM: • Algebra II CDR512/MAT • Math Blast (Algebra)

CDR512/MAT • Dynamic Maths Series: Linear

Equations CDR510/JUN

Internet • www.algebrahelp.com/lessons/wor

dproblems/basics/ • www.mathsnet.net/algebra/index.ht

ml


2011 Scheme of Work

S Drive • E1-Enrichment: Proving &

Solving • E2-Diophantus’ Riddle • E3-The Monkey and The Coconuts

Term 2 Week 4

Unit 4: Linear Inequalities At the end of this unit, students will be able to 1. Represent simple linear

inequalities (e.g. x a≥ ) on the number line

2. Using the number line to simplify linear inequalities involving ‘and’ and ‘or’

3. Perform the fundamental operations of addition, subtraction, multiplication, and division on linear inequalities

4. Simplify and solve simple linear inequalities of one variable

5. Form and solve simple linear inequalities from given word problems



and practice • Student-centred: Investigative

approach, flexible grouping, pair work, real life problem solving involving inequalities

Thinking skills to be infused: • Analysing, • Focusing • Generating


2011 Scheme of Work

IT skills Use graphic calculators and websites to explore the graphical interpretation of solving linear inequalities



Discovering Mathematics Book 1 Chapter 13

Term 2 Week 5-6

Unit 5: Algebra and Indices At the end of this unit, students will be able to 1. Define zero index 2. State the rules of indices for non-

negative integral indices 3. Apply rules of indices to simplify

simple indicial expressions 4. Apply rules of indices to simplify

algebraic expressions involving addition, subtraction & multiplication

5. Evaluate indicial expressions 6. Solve equations and problems

involving non-negative integral indices

7. Change the subject of an indicial formula (no involvement of roots)

8. Change the subject of an indicial formula (with involvement of roots) 9. Discuss the patterns in the last digit of powers of natural


2011 Scheme of Work

numbers 2, 3, … 8, 9 10. Find last digit of sums and differences of powers of natural numbers 11. Understand and use very large and very small numbers such as mega/million ( 610 ), giga/billion ( 910 ), tera/trillion ( 1210 ), micro ( 610− ), nano ( 910− ) and pico ( 1210− ) and know their examples 12. Write numerals in standard form

10na× where 1 10a≤ < 13. Perform arithmetic operations with

numerals in standard form 14. use of standard form

10 , 1 10nA A× ≤ < where n is an integer.


Thinking skills to be infused: • Generating • Analysis • Focusing


ACE/Assessment: • Units 4 & 5 tested in Class Test 3 • Pose problems involving indices

for others to solve


Discovering Mathematics Book 3 Chapter 1


2011 Scheme of Work

Mathsoft Study Works Enrichment-1: The Last digits Enrichment-2: The Prime number race Video on Indices

Term 3 Week 1

Unit 1: Data Analysis & Statistics in Real Life At the end of this unit, students will be able to 1. Identify and relate the usage of

statistics in the real world 2. Identify and use different ways to

collect data – experiments, survey – oral, online, print, observation, web-based data, etc

3. Identify a few ways of obtaining a good sample

4. Design a survey / questionnaire to collect data for a relevant purpose

5. Understand methods of data collection such as taking measurements and conducting surveys

6. Interpret bar graphs, pictograms, histograms, pie charts and line graphs

7. Calculate and interpret the three different measures of central tendencies, namely the mode, median and mean Interpret stem and leaf diagrams and dot diagrams


Instructional Strategies: • Student-centred: flexible grouping,

inquiry learning, project-based learning, problem solving, oral

• Interpret Reports of Singapore’s population Census on 1980, 1990 and 2000.

To apply knowledge of statistics in project work and analyse research results and data correctly and to look for loopholes


2011 Scheme of Work

infusion of ICT)

presentation • Independent: Research, homework • Experiential: Survey • Online Learning Package Thinking skills to be infused: • Organising • Analysing • Interpreting • Creative • Critical thinking IT Skills: • Use of Microsoft Excel or

Autograph or SPSS to handle data, interpret data and draw charts and diagrams.

• Use of Microsoft Excel or Autograph or SPSS to handle data, interpret data and draw charts and diagrams.

• Collect data of an affective nature, such as students’ response to computing gaming, smoking, etc.

• Survey and research on

Volunteerism


ACE • A coursework (project style)

incorporating all of the above topics

• Averages and representation of data tested in Term 3 Class Test 4


• “Statistics: Concepts and Controversies”: David S Moore, Part 1.

• Carry out some methods of data collection.

• “Statistics: Concepts and Controversies”: David S Moore,


2011 Scheme of Work

Chapter 1. • Conduct a simple and short online

survey as a group. • Statistics: Roger Fentem, Chapter

18. • “Understanding Statistics”:

Graham Upton and Ian Cook, Chapter 1.

• Discovering Mathematics Book 1 Chapter 16


• Various Statistics Books Additional Print Resources: (1) The Cartoon Guide to Statistics. (Library, MA LRC, 519GON, pp 1 - 26)

Term 3 Week 2-3

Unit 1: Pythagoras’ Theorem At the end of the unit, students should be able to 1. Find the length of a side of a right-

angled triangle using Pythagoras’ theorem

2. Determine whether a triangle is right-angled using Pythagoras’ theorem

3. Solve problems involving Pythagoras’ theorem

4. Derive Pythagorean Triplets

• Application of Trigonometry in the obstacle courses during reservist trainings

To apply Pythagoras’ Theorem in real-life problems, particularly in 3-dimensional situations


Thinking skills to be infused: • Deductive and inductive reasoning • Logical thinking • Analytical thinking


2011 Scheme of Work

IT Skills: • Use of GSP • Use of Graphmatica • Graphic Calculators


Environment Resources Material Resources:


• Geometry & Trigonometry for Calculus by Peter H. Selby (513 SEL)

• New Syllabus Mathematics 2 (Shinglee)

Media resources: CR-ROM: Trigonometry

(CDR514/TR1) Video: The Theorem of

Pythagoras (VT510/THE) • Project Mathematics Tape 1: Part 1

The Theorem of Pythagoras (VT510/PRO)

Term 3 Week 4-5

Unit 1: Mensuration At the end of this unit, students will be able to 1. State the 5 axioms in Euclidean

Geometry 2. Define the basic geometric

elements (points, lines and angles) 3. Convert between cm2 and m2, and

between cm3 and m3

Students act as logistics managers / operations managers in determining the optimal packaging shape/solid to ensure minimal wastage of space for packing of sphere-like/cylindrical-like objects such as tubes, balls, etc. To discuss why certain items are packed in different types of

Getting students to see things from different perspectives for two-dimensional shapes and three-dimensional solids


2011 Scheme of Work

Term 3 Week 5-8

4. Find perimeter and area of 2D objects including parallelogram & trapezium

5. Solve problems involving perimeter and area of composite plane figures

6. Find volume and surface area of 3D objects including cuboid, prism, cylinder, pyramid, cone and sphere

7. Solve problems involving volume and surface area of composite solids

8. Discuss the development of geometry

Unit 2: Geometrical Properties of Polygons 1. Construct 2-dimensional shapes

using Geometer’s Sketchpad / Fun with Construction

2. identify right, acute, obtuse and reflex angles, complementary & supplementary angles, vertically opposite angles, adj angles on a straight line, adj angles at a point, interior and exterior angles.

3. identify angles formed by two parallel lines and a transversal : corresponding, alternate and interior angles.

4. know properties of triangles and special quadrilaterals,

5. able to classify special quadrilaterals on the basis of their properties

6. find angles sum of interior and

packaging – other factors such as cost of production / stability to be discussed)


2011 Scheme of Work

exterior angles of any convex polygon.

7. know properties of regular penta, hexa, octa and decagon.

8. know properties of perpendicular bisectors of line segments and angle bisectors.

9. can construct of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors where appropriate.

10. Develop mathematical arguments about geometric relationships emphasising the two column proofs.

11. Solve problems using spatial reasoning, visualisation and geometric modelling

12. Pose problems involving geometrical properties of polygons


Instructional Strategies: • Direct: Socratic questioning • Student-centred: Inquiry Based,

Project Based, concept attainment, concept mapping

• Experiential: simulation of 2D/3D figures/objects using GSP or graphic calculators

Thinking skills to be infused: • Inductive reasoning • Deductive reasoning • Logical reasoning • Sequential reasoning


2011 Scheme of Work

• Visual/Spatial thinking • Empirical Proofs by means of GSP • Visual Proof with tangrams IT Skills: • GSP • Graphic Calculators


ACE/Assessment: • To be test under Class Test 5

(written) • Timeline on the development of

geometry and the contribution to mathematicians.

• Create “Tessellation Art” using GSP or other IT tools.

• Investigation on shapes and building

• Billiards and Geometry • Build a kaleidoscope


• Discovering Mathematics Book 1 Chapters 14 &15; chapters 7 & 8


• Cord Geometry Mathematics in Context

• Exploring Geometry with GSP • Discovering Geometry-An

Inductive Approach • Symmetry, Shape and Space. • Cancer and Mathematics

http://www.mste.uiuc.edu/dildine/cancer/cancer.html


2011 Scheme of Work

SMO Resources: • Geometric Problems (Math Quiz

Training) • Mathematics Teacher NCTM

Calendar Problems 2001 to 2005 • Singapore Mathematical



• AMC8 Questions • Australian Mathematics

Competition Book 1 (1978-1984), Book 2 (1985-1991), Book 3 (1992-1998)



• Senior Mathematical Challenge (The UK National Mathematical Contest 1988-1996) by Tony Gardiner


Euler Student Problems – Mathematical Challenge for Young Australians

Term 4 Week 1 - 2

Unit 1: Set Notations At the end of this unit, students will be able to 1. Understand empty or null set, finite

set, infinite set, universal set, equal

PCM/Curriculum of Practice (Students to solve real-life logical problems using Venn diagram and set theory)


2011 Scheme of Work

set, subset, complement of a set 2. Use set language and notation to

describe sets and represent relationships between sets as follows:

A = {x : x is natural number} B = {x: a < x ≤ b} D = {a, b, c…} 3. Understand and use the following

notations: Union of A and B = A ∪ B Intersection of A and B = A ∩ B Number elements in set A = n(A) “… is an element of …” ∈ “… is not an element of …” ∉ Complement of set A = A’ Empty set = ∅ or { } Universal set = ξ A is a subset of B: A ⊆ B A is a proper subset of B: A ⊂ B A is not a subset of B: A B A is a not a proper subset of B: A ⊄ B Unit 2: Venn Diagrams At the end of this unit, students will be able to 1. Use Venn diagram to represent the

relations of different sets 2. Use Venn diagram to represent the

intersection of sets, union of sets 3. Use Venn diagrams to solve

problems involving sets (not more than 2 sets)

4. Solve maximum/minimum size of


2011 Scheme of Work

a set through logical deduction. 5. Understand and apply De

Morgan’s Laws for intersection and union of sets

6. Relate sets to geometry, number systems and algebra (i.e. using Venn diagram to show the relationship between polygons, classification of numbers, and solution sets)

7. Define and write supersets 8. Use sets to solve syllogisms and

logic questions 9. Discuss the contribution of

George Cantor to Set Theory 10. Comment on the history of

development of Set Theory and Modern Mathematics


Instructional Strategies: • Direct: Socratic questioning • Student-centred: concept

attainment, concept mapping, flexible grouping, pair work, problem solving

• Independent: homework, research Thinking skills to be infused: • Information Gathering • Generating • Focusing • Analysing • Inductive reasoning • Deductive reasoning Logical reasoning

Products (Assignments/

ACE/Assessment: • Pop quiz on set notations and


2011 Scheme of Work

Tests/ Practicals)

description of sets • Online quiz on set notations and

description of sets • Pose problems involving sets for

classmates to solve • Oral presentation on contribution

of sets • Oral presentation on development

of Set Theory • Using Venn Diagram to create a

general overview of Sec 1’s syllabus


Textbooks: • New Additional Mathematics (Pan

Pacific) • Discovering Mathematics Book 2

Chapter 9 • Notes from GE branch Website: • NCTM illuminations lesson plan

site http://illuminations.nctm.org/lessonplans/9-12/reasoning/index.html

• Reasoning & Proof http://standards.nctm.org/document

/chapter7/reas.htm • Logic and Set Theory http://www.cis.yale.edu/ynhti/curri

culum/units/1980/7/80.07.04.x.html

• Venn Diagrams http://www.cut-the-

knot.com/LewisCarroll/dunham.sht


2011 Scheme of Work

ml Video: • Solution Sets and The Number

Line (VT510/SOL)

Tests: No. of class test per term: 2 No. of class tests per year: 6 Duration of class test: 1hr Format of class test paper: MCQ?%; Structured Questions ?%; Essay Questions ? %

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