S1_MA-SOW_(2015) - Hwa Chong Institution

Hwa Chong Institution

Scheme of Work 2015

Subject/Programme : Mathematics

Level : Secondary 1

Scheme of Work (incorporating GL-Matrix, Differentiation: italicised for SBGE, refer to Appendix for further differentiation in SSMT )

Learning outcomes are statements of what a student should know, understand and/or be able to demonstrate after completion of a process of learning.

OVERVIEW

Term 1

Foundation Skills (0.5 wk)

Unit 1: Overview (0.5 wk)

Arithmetic I (5 wk)

Unit 1: Prime Numbers, HCF & LCM (1.5 wk)

Unit 2: Integers, Rational Numbers & Real

Numbers (1.5 wk)

Unit 3: Approximation & Estimation (1 wk)

Unit 4: Applications of Mathematics in

Practical Situations (1 wk)

Algebra I (1.5 wk)

Unit 1: Basic Algebra & Algebraic

Manipulation (1.5 wk)

Formative Assessment 1

Term 2

Algebra I (5 wk)

Unit 2: Linear Equations, Algebraic Formula &

Simple Inequalities (4.5 wk)

Unit 3: Ratio, Rate and Speed (0.5 wk)

Coordinate Geometry I (2 wk)

Unit 1: Functions and Graphs (linear and quadratic)

(2 wk)


Term 3

Coordinate Geometry I (1 wk)

Unit 1: Functions and Graphs (linear and quadratic)

(1 wk)

Statistics I (1 wk)

Unit 1: Statistical Data Handling (0.5 wk)

Unit 2: Averages of Statistical Data (0.5 wk)

Geometry I (4 wk)

Unit 1: Basic Geometry (0.5 wk)

Unit 2: Triangles, Quadrilaterals and Polygons (1 wk)

Unit 3: Geometrical Constructions (0.5 wk)

Unit 4: Perimeter and Area of Plane Figures (1 wk)

Unit 5: Volume and Surface Area of Solids (1 wk)

Trigonometry I (1 wk)

Unit 1: Pythagoras’ Theorem (1 wk)


Sets (2 wk)

Term 4

Unit 1: Set Notations (1 wk)

Unit 2: Venn Diagrams (1 wk)

Revision (1 wk)

EOY Exam (70%)

Summative Assessment

Common Test 1 (10%) Term 2 Week 7

Topics

(a) Prime Numbers, HCF & LCM

(b) Integers, Rational Numbers & Real Numbers

(c) Approximation & Estimation

(d) Applications of Mathematics in Practical

Situations

(e) Basic Algebra & Algebraic Manipulation

(f) Linear Equations, Algebraic formula & Simple

Inequalities

(g) Ratio, Rate, and Speed

Summative Assessment

Common Test 2 (10%) Term 2 Week 7

Topics

(a) Functions and Graphs (Linear and Quadratic)

(b) Statistical Data Handling

(c) Averages of Statistical Data

(d) Basic Geometry

(e) Triangles, Quadrilaterals and Polygons

(f) Geometrical Constructions

(g) Perimeter and Area of Plane Figures

(h) Volume and Surface Area of Solids

All Topics

1



Time allocated

In Wks/hrs

0.5 weeks

Time frame

Term 1

Week 1

In Wks/hrs

1.5 weeks

Time frame

Term 1

Week 1 to

Week 3

Content/ Learning Outcomes

Core:

Foundation Skills (Unit 1/Overview)

At the end of the topic, students will be able to

1.

know the overview of the Secondary

Sch Mathematics Programme – framework, expectations, assessment plan and requirements

2.

know the locations of Mathematics

Resources in HCI a.

school network b.

school library

3.

know the effective Mathematics study skills

4.

use MS Office Equation Editor or

MathType in BOTH MS Word and MS ppt

Core:

Arithmetic I (Unit 1/Prime Numbers, HCF

& LCM)


1.

differentiate between prime numbers and composite numbers, factors and



Connection:

Investigate how prime numbers are used in the area of number theory, computing and cryptography.

Practice:

Comment on how prime numbers

Learning Activities Assessment/ Feedback Resources

Parallel Curriuclum

Practice:

Explain the differences and similarities in the mathematics processes of primary and secondary school mathematics.

Identity:

Reflect on their role as learners in mathematics, relate to their aspirations when they grow up.

Set targets in their learning.

Suggestions:

Blended learning and

collaborative learning –

Teachers share their perception of Maths with students.

Use a primary school topic such as Ratio & rate for collaboration

Students exchange email addresses and mobile numbers in class, divide into groups as they will be later engaged in home-based internet surfing after sch.

They will each go to various websites to find resources related to the selected topic

Students used dropbox or other storage devices in internet to collect and edit data

Students present their work in class as a group in the next lesson and also critique on other’s group sharing

Suggestions:

Blended Learning:

Students explore online resources after classroom lessons

Suggestions:

As everyone is new to school, internet and resources, this is just a trial and error session for collaborative learning

No formative or summative assessment for this topic

Suggestions:

Formative Assessment:

Pop-quiz to access mastery of basic concepts and skills

Design a mind map/concept map/cheat sheet to reflect

Online Resources:

Some useful websites in Maths http://www.youtube.com/ http://www.teachertube.com/ http://www.edublogs.org/ http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/

Print Resources:

S drive/ Maths/Resources/IP

MA S1/Fundamental Skill

Brochures on Career in

Mathematics

Online Resources: http://www.algebrahelp.com/reso urces/tables/primes.jsp

http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/ http://www.onlinemathlearning.co

2



Time allocated

In Wks/hrs

1.5 weeks

Time frame

Term 1

Week 4 to

Week 5

Content/ Learning Outcomes multiples

2.

apply prime numbers in real life

3.

prime factorize a composite number

4.

write composite numbers in product of factors in exponent form

5.

find square roots and cube roots by prime factorization or with a calculator

6.

find LCM & HCF of two or more numbers by any method

7.

apply LCM & HCF in problem solving in real life

Learning Activities


Assessment/ Feedback


Resources

Parallel Curriuclum are used in computer security.

Critique, in light ethical practices, how the system can be abused by hackers.

Core:

Arithmetic I (Unit 2/Integers, Rational

Numbers & Real Numbers)


1.

understand and use real, rational, irrational, integer, whole, natural, prime, odd, even, positive, negative numbers

2.

understand and write numbers using different numeral system, e.g. Roman,

Egyptian, Babylonian, etc

Connection:

Interpret negative numbers in various contexts such as directions, elevation, angles, temperature.

Solve problems involving percentages relating to daily life such as GST, discount, profit and loss etc.

Relate negative numbers to

Suggestions:

Blended learning:

Individually, students use Sieve of Eratosthenes to look for prime numbers from 1 to 100

Select and re-write a newspaper article from morning reading programme, which avoids all mention of numbers or replace them by fractions or on their mastery of the concepts and skills

Quiz on finding HCF of numbers: http://www.algebrahelp.com

/worksheets/view/factoring/fi ndgcf/numbers.quiz

Summative Assessment:

Common Test 1, EOY

Exam

Suggestions:



Design a mind map/concept map/cheat sheet to reflect on their mastery of the concepts and skills

Summative Assessment: m/

Finding prime factors http://www.algebrahelp.com/lesso ns/factoring/numbers/

Division and Prime numbers http://www.youtube.com/watch?v

=3EFDOeFomYM

Factoring http://www.youtube.com/watch?v

=Tr9FZUhfJR4

Factors and HCF: http://www.youtube.com/user/Iken

Edu/videos?flow=grid&view=0&so rt=da http://www.youtube.com/watch?v

=qzAa_azQUKw


New Syllabus Mathematics 1

7 th Edition by Shinglee Chapter

1 + eBook


MA S1/Arithmetic I

Online Resources: http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/ http://www.onlinemathlearning.co

m/

Videos

Real numbers http://www.youtube.com/watch?v

=V6GnHfSaPao

3



Time allocated Content/ Learning Outcomes

3.

find the reciprocal and absolute value of a number

4.

draw and arrange real numbers

(including integers, fractions, decimals, etc) on the number line

5.

apply PEMDAS (parentheses, exponents, multiplication, division, addition and subtraction) on number

6.

work with fractions, decimals and recurring decimals with or without calculator

7.

convert recurring decimals into fractions and vice versa

8.

use unit fractions and continued

fractions

9.

solve word problems involving different types of numbers including fractions and decimals

10.

introduce percentage and reverse percentage

11.

express one quantity as a percentage of another

12.

percentage as fraction and also decimal

13.

compare two quantities by percentage

14.

increase/decrease quantity by a given percentage

15.

apply percentage in real life context such as simple and compound interest, discount, profit/loss, taxes & commission


Parallel Curriuclum economic growth and recession and consider its impact on our lives.

Imagine the world without number.

Practice:

Compare and contrast the different types of numeral systems in the history of mankind.

Justify the use of the current system. percentages

Select an advertisement in the morning reading programme and calculate the percentage of money saved

Design a poster using any one ancient number system with simple illustration of its meaning and usage

Use drawing or tree diagram to classify numbers

Students to use contradiction to explain why 2 is an irrational number

Students prepare their family budget in terms of percentage

Student to research on how the less fortunate families in

Singapore are helped by the government – compassion

Students to research on why we have GST and not heavier corporate and personal taxes



Common Test 1, EOY

Exam


Resources

Irrational numbers http://www.youtube.com/watch?v

=q_wstDWjnKQ

Multiplying negative numbers http://www.youtube.com/watch?v

=NtJy8uQVN7w

Reducing fractions http://www.youtube.com/watch?v

=HJo2Uw3Az-k

Improper fraction and mixed number http://www.youtube.com/watch?v

=Yfv6BON8qlg

Fractions and what are its uses http://www.youtube.com/watch?v

=0A3VfV0oIBo

Converting Terminating Decimal

Numbers to Fractions http://www.youtube.com/watch?v

=qyTFvx_ZVOs

Learning positive and negative number: Powerup http://illuminations.nctm.org/Less on.aspx?id=2413

Simplifying ratios: http://www.algebrahelp.com/lesso ns/proportionbasics/

Order of operations: http://www.algebrahelp.com/lesso ns/simplifying/oops/

Learning rates: Paying for your bills http://illuminations.nctm.org/Less on.aspx?id=2459

Learning ratio and equivalent fraction http://illuminations.nctm.org/Less on.aspx?id=2534

4



Time allocated

In Wks/hrs

1 week

Time frame

Term 1

Week 6

In Wks/hrs

1 week

Time frame

Term 1

Week 7

Content/ Learning Outcomes Parallel Curriuclum


Core:

Arithmetic I (Unit 3/Approximation &

Estimation)


1.

understand the need of using approximation and estimation in daily life

2.

use significant figures and write numbers in required significant figures or decimal places

3.

distinguish and explain significance of rounding and truncation errors

4.

define the Binary System

5.

apply simple operations (addition,

subtraction)on binary numbers

Core:

Arithmetic I (Unit 4/Mathematics in

Practical Situations)

At the end of the topic, students will be able to

1.

Solve problems involving profit and loss.

2.

Solve problems involving further examples of percentages.

3.

Solve problems involving simple interest.

4.

Solve problems involving compound

Connection:

Estimate the unit price of daily products for better budgeting.

Compare and make sense of the nutritional values of similar products.

Practice:

Explain how degree of accuracy is conveyed to the various audience (e.g. in economic growth, project funding, population, budget, housing, currency conversion).

Explore the use of different base system in various contexts such as time, computer systems, and

angle.

Connection:

Compare and contrast the traditional and modern views and perspectives on use of loans and credit

Understand the impact of the

2008 financial sub-prime loans which spiral into a global crisis; question on affordability of commodity

Suggestions:

Collaborative Learning

Find out the different types of interest rates offered by housing loans, car loas, etc, and determine which of these loans would be suitable for the different income groups.




Resources

Suggestions:

Collaborative learning

Students work in groups to estimate quantities in a variety of contexts, compare their estimates and share their strategies in determining the estimates

Students to compare the effects of rounding to different degrees of accuracy

Suggestions:





Common Test 1, EOY

Exam




2, 8 & 9 + eBook


MA S1/Arithmetic I


m/





MA S1/Arithmetic I

3 + eBook

Suggestions:

Formative assessment:


Alternative formative

assessment:

Oral Presentation of the different types of loan packages by different

Online resources:

Various banks’ websites

HDB website


Arithmetic of Life Insurance

(Unit 24, Teaching Sec Math by

Alfred S. Posamentier)



6

5



Time allocated

In Wks/hrs

1.5 week

Time frame

Term 1

Week 8 to

Week 9

Content/ Learning Outcomes interest.

5.

Solve problems involving hire purchase.

6.

Convert one currency to another in money exchange.

7.

Calculate simple taxation problems.

8.

Solve problems involving utilities bills.

9.

Solve problems involving personal and household finances.

10.

Interpret and use tables and charts in solving problems.

11.

Use different problem solving strategies to solve everyday life problems.

Core:

Algebra I (Unit 1/ Basic Algebra &

Algebraic manipulation)


1.

trace and comment on the development of Algebra

2.

use letters to represent quantities a

3.

interpret notations: ab , , 3 y b

3

 y

5

4.

identify polynomials, variables, coefficients and constant terms

5.

use basic conventions of algebraic notation to represent statements and relationships between variables

6.

translate simple real-world situations into algebraic expressions


Practice:

Critique the different types of car, housing loan packages

Critique on the current loan packages and create alternative loan packages for different income groups.

Identity:

Understand the importance of saving (household budgeting, long term financial planning) and develop personal good habits of using money (preventing bankruptcy, taking calculated risks in investments)

Connection:

Compare Algebraic method with methods used in primary school

(listing, drawing models)

Relate rules of operation associated with numerical fractions with those learnt in algebraic fractions

Practice:

Appreciate the use of algebra in problem solving in daily life

Discuss the contributions of Al-

Khwarizmi, the Mathematician who is known as the father of

Algebra and its impact on mathematics.

Identity:

Discuss what qualities would


Suggestions:





Resources Assessment/ Feedback financial institutions


Common Test 1, EOY

Exam

Suggestions:




Quiz on factorization of expressions http://www.algebrahelp.com

/worksheets/view/factoring/fi ndgcf/terms.quiz

Quiz on simple factorization http://www.algebrahelp.com

/worksheets/view/factoring/ gcf.quiz


m/

Simplifying multiplied algebraic expression http://www.youtube.com/watch?v

=6fGa5NrJ3l8

Simplifying mixed algebraic expression http://www.youtube.com/watch?v

=guqtvxoj8a0

Number Pattern http://www.youtube.com/watch?v

=4HjLfAxK2No

Simplifying Algebraic expressions http://www.algebrahelp.com/lesso ns/simplifying/

6




7.

introduce and solve number pattern and generalize the nth term of a simple number sequences using algebraic expression

8.

demonstrate equivalence between algebraic expressions

9.

evaluate and simplify algebraic expressions involving addition, subtraction, brackets, fractional coefficients and combinations of these

10.

simplify algebraic expressions or evaluate algebraic expressions by substituting values for variables

11.

expand and factorize linear expressions of the form ax ay az ( y z )

In Wks/hrs

4.5 weeks

Time frame

Term 2

Week 1 to

Week 5 where a is a constant

12.

add and subtract algebraic fractions with linear denominator, e.g.

x

1



2



Core:

Algebra I (Unit 2/Linear Equations, x

2



3

Algebraic formula & Simple Inequalities)


1.

differentiate between equations and identities, equations and expressions

2.

solve simple linear equations involving one unknown

3.

solve simple linear equations involving fractional and decimal coefficients

4.

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

 x



3 4

2



3; x

3



2



6

5.

change the subject in given formula in

Parallel Curriuclum make you a good algebra learner.

Connection:

Connect algebraic method to primary school methods (listing, drawing models).

Understand and explain the reasons why algebra fallacies occur.

Practice:

Apply concept and strategies of solving linear equations on new situations to solve simple equations.

Identity:

Discuss the passion shown by and the contributions of Amalie

Emmy Noether as a female





Resources

Quiz on expansion http://www.algebrahelp.com

/worksheets/view/simplifyin g/distribution.quiz


Common Test 1, EOY

Exam

Simplifying like terms in expressions http://www.algebrahelp.com/lesso ns/simplifying/combiningliketerms

/

Distributive law in expansion http://www.algebrahelp.com/lesso ns/simplifying/distribution/




4 & 7 + eBook


MA S1/Algebra I

Suggestions:

Guided independent learning

Students learn to form equations and solve it on their own with the help of the website to check answers

Blended learning


Experiential learning

Use graphic calculators to explore the graphical interpretation of solving linear equations and solving linear

Suggestions:




Quizzes : http://www.algebrahelp.com

/worksheets/view/equationb asics.quiz http://www.algebrahelp.com

/worksheets/view/proportion basics.quiz

http://www.algebrahelp.com

Online Resources: http://www.algebrahelp.com/lesso ns/equationbasics/ http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/ http://www.onlinemathlearning.co

m/

Equation Calculator & Solver http://www.algebrahelp.com/calcu lators/equation/




5 + eBook

7



Time allocated

In Wks/hrs

0.5 weeks

Time frame

Term 2

Week 5

Content/ Learning Outcomes linear form

6.

use the concept on changing subject to find unknown in a formula

7.

construct formula from word problem

8.

apply linear algebraic equations and solve problems in real life

9.

use inequality symbols <, >,  and 

10.

represent simple linear inequalities (e.g. x

 a ) on the number line

11.

using the number line to simplify linear inequalities involving ‘and’ and ‘or’

12.

perform the fundamental operations of addition, subtraction, multiplication, and division on linear inequalities

13.

simplify and solve simple linear inequalities in one variable and represent solutions on number line

14.

form and solve simple linear inequalities from given word problems

Core:

Algebra I (Unit 3/Ratio, Rate and Speed)


1.

recap the concept of ratios and speed learnt in primary school

2.

write and simplify ratios involving 2 or more quantities involving rational numbers

3.

use ratio to study scales in map and do scale drawing

4.

enlargement and reduction of plane figures using scale factor

5.

calculate linear and area scales in map

6.

understand rate and use speed as an example of rates

7.

differentiate between ratio and rate

8.

solve problems in ratio, rate and proportion in daily life context

Parallel Curriuclum mathematician during her times and reflect on how this is similar or different to your own math learning.

Connection:

Apply ratios to photography, map reading, ergonomics. Industrial design.

Understand and use ratio in similarity

Learning Activities inequalities




Resources

/worksheets/view/simplifyin g/combiningliketerms.quiz


Common Test 1, EOY

Exam


MA S1/Algebra I

Suggestions:

Use GSP/Geogebra to visualise ratios and compare linear to area ratios.


Common Test 1, EOY

Exam


Simplifying ratios: http://www.algebrahelp.com/lesso ns/proportionbasics/

Learning rates: Paying for your bills http://illuminations.nctm.org/Less on.aspx?id=2459

Learning ratio and equivalent fraction http://illuminations.nctm.org/Less on.aspx?id=2534




9 + eBook


8



Time allocated

In Wks/hrs

3 weeks

Time frame

Term 2 week

6 to term 3 week 1


9.

solve problems in speed, uniform speed and average speed

10.

conversion of units(eg km/h to m/s)

Core:

Coordinate Geometry I (Unit 1/Coordinate

Geometry, Functions and Linear Graphs)


1.

plot points in the 4 quadrants of the

Cartesian plane

2.

understand what are ordered pairs and use a graph of a set of ordered pairs as a representation of a relationship between two variables

3.

introduce function and how function can be represented by equations

4.

State the equation of a horizontal line and of a vertical line

5.

Draw and learn more about graphs of linear equations in the form y

 ax b

6.

understand the gradient of a linear graph as a ratio of the vertical change to the horizontal change (positive and negative gradients)

7.

understand what are intercepts in a linear graph

8.

derive the equations of given straight line graph

9.

give equations of parallel lines

10.

give equations of lines with same intercept

11.

Draw graphs of quadratic functions

12.

Name the line of symmetry in a quadratic graph

13.

Give the coordinates of the intercepts in a quadratic graphs

14.

Interpret problems with 2


Connection:

Explain the concept of ratio with

Coordinate Geometry – Gradient

Relate Coordinate Geometry to real life applications. e.g. contour mapping, positioning, map reading - latitude and longitude.

Relate y

 ax b to part variation

Practice:

Apply graphical skills to other areas of Science and Humanities

-Geography





Resources

MA S1/Algebra I

Suggestions:




Use Graphmatica or other graphing software to illustrate the geometrical meaning of solving linear equations

Use Excel to demonstration how the change of m and c can affect the appearance of graph

Play battleship game that involves the use of 2D

Cartesian coordinates to specify locations

Given examples of function machines in daily life and know how to represent the function in verbal, tabular, graphical and algebraic forms

Use a spreadsheet or graphing software to

(a) show graphically the relationship between the area of a square and the length of its axis, and explain that the relationship is a function, but not a

Suggestions:




Quiz on coordinates http://www.algebrahelp.com

/worksheets/view/graphing/ points.quiz

Quiz on reading points http://www.algebrahelp.com

/worksheets/view/graphing/r eadpoints.quiz

Quiz on plotting points and drawing lines http://www.algebrahelp.com

/worksheets/view/graphing/ pointslines.quiz

Quiz on determine slope from a graph http://www.algebrahelp.com

/worksheets/view/graphing/ slope.quiz

Further Quiz on drawing line with gradient-intercept form http://www.algebrahelp.com

/worksheets/answers/graphi ng/slopeintercept.quiz



m/

Functions http://www.youtube.com/watch?v

=Imn_Qi3dlns

The Cartesian Coordinate System http://www.youtube.com/watch?v

=RrrYInyIEGo

Graphing Straight Lines/

Quadratic Functions Quizzes:

http://quiz.econ.usyd.edu.au/m athquiz/linear/index.php

http://quiz.econ.usyd.edu.au/m athquiz/quadratics/index.php




6 + eBook


MA S1/Geometry I

9



Time allocated

Time allocated

In Wks/hrs

0.5 weeks

Time frame

Term 3

Week 2

Content/ Learning Outcomes unknowns/variables and Formulate a pair of linear equations in two variables and solve mathematical and real-life problems using graph


Learning Activities linear function.

(b) create linear and quadratic graphs and explore the characteristics.

(c) study how the graphs y

 ax b

and y

 ax

2  bx

 c change when a, b, and c vary.




Common Test 2, EOY

Exam


Resources

Assessment/ Feedback Resources


Core:

Statistics I (Unit 1/Statistical Data

Handling)


1.

Collect, classify and tabulate data

2.

Construct and interpret data from pictograms and bar graphs

3.

Construct and interpret data from pie charts

4.

Construct and interpret data from line graphs

5.

Evaluate the purposes and appropriateness of the use of different statistical diagrams

6. Explain why some statistical information or diagrams can lead to a misinterpretation of data


Connection:

Explain how data is used in survey.

Explore ways of data collection in research (for e.g. on internet, or data from past Cat 4 projects).

Relate experience in helping to conduct survey and discuss the factors of misrepresentation of data.

Practice:

Analyse statistical data e.g. climate, population etc, found in

Singapore websites, presenting data in different ways to optimize and communicate and convince people to agree to their findings or suggestions.

Compare various representations and understand why a particular

Suggestions:

Blended learning:

Students explore the online resources in iVLE on Statistic and also find out in the internet the usage of statistics in the real world


Teachers to show how reports on Singapore’s population

Census can be found online and interpret a simple survey in the reports

Students form groups and do an online survey on an affective nature such as computer gaming, gambling etc and collect and present findings after June holidays

Students learn to use Microsoft

Suggestions:


Pop-quiz using iVLE resources to access mastery of basic concepts and skills



Common Test 2, EOY

Exam


m/

Data handling http://www.youtube.com/watch?v

=hKHgqqk4NbE

Presentation of data http://www.youtube.com/watch?v

=1xlAj_QkViw

Bar Graph http://www.youtube.com/watch?v

=gX9mAL8ixzI

Media Resources:

Mediacorp – ChannelNewsAsia -

IT Figures



10




In Wks/hrs

0.5 weeks

Time frame

Term 3

Week 2

Core:

Statistics I (Unit 2/Averages of Statistical

Data)


1.

Find the mean of a set of data

2.

Find the median of a set of data

3.

Find the mode of a set of data

4.

Evaluate the purposes and appropriateness of the use of mean, median and mode

In Wks/hrs Core:


Parallel Curriuclum representation is more suitable than others for a given situation.

Identity:

Discuss on integrity and understand under what circumstances that statistical data can be misused to mislead readers.

Connection:

Use existing online data and discuss the situations in which the different modes of central tendencies are used.

Use mean, mode, median to make sense of the skewness of the data

Practice:

Use statistical data e.g. climate, population etc, found in

Singapore websites and present them in different ways to convince others to agree to their findings or suggestions.

Compare various measures of central tendencies and understand why a particular measure is more suitable than others for a given situation

Identity:

Discuss how this unit has helped you to better manage data.

Connection:


Excel or other software they prefer to handle data, interpret data and draw charts and diagrams

Suggestions:

Blended learning:

Students explore the online resources in iVLE on Statistic and also find out in the internet the measures of central tendencies in the real world


Teachers to show reports on

2013 Singapore’s haze situation and have the students to discuss the use of 3 hr average vs the the 24 hr average as a means to measure the PSI.

Students to be organised into groups representing different countries (Singapore, Malaysia,

Indonesia), regions (N, S, E,

W), demographics (adult, children, elderly) and expressed their viewpoints and concerns on this issue

Suggestions:


Suggestions:


Pop-quiz using iVLE resources to access mastery of basic concepts and skills



Common Test 2, EOY

Exam

Suggestions:

-

7 th


Resources

Edition by Shinglee

Chapter 15 + eBook


MA S1/Statistic I


m/

Mean, Mode, Median http://www.youtube.com/watch?v

=h8EYEJ32oQ8

Mean, Mode, Median and the

Business Perspective http://www.ehow.com/info_12114

594_measurement-importantbusiness-perspective-modemean-median.html



7 th Edition by Shinglee

Chapter 13 + eBook


MA S1/Statistic I


11



Time allocated

0.5 weeks

Time frame

Term 3

Week 3


Geometry I (Unit 1/Basic Geometry)


1.

state the 5 axioms in Euclidean

Geometry

2.

define the basic geometric elements

(points, lines and angles)

3.

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

4.

identify angles formed by two parallel lines and a transversal

5.

identify and use corresponding, alternate and interior angles to find unknown angles

6.

Justify the use of the geometrical properties with reasons

In Wks/hrs

1 week

Time frame

Term 3

Week 4

Core:

Geometry I (Unit 2/Triangles,

Quadrilaterals and Polygons)


1.

construct 2-dimensional shapes using

Geometer’s Sketchpad / Fun with

Construction

2.

know properties of triangles and special quadrilaterals

3.

classify special quadrilaterals on the basis of their properties

4.

find angle sum of interior and exterior angles of any convex polygon


Connect to previous knowledge learned in primary school.

Relate to concept of alternate angles to angle of depression and angle of elevation.

Experiment sum of angles in triangle and treat this as a special case of angles on a straight line.

Explore the development of geometry and the Mathematicians behind all the development.

Practice:

Relate angles formed by parallel lines and transversal and investigate the different angles used in billiard games, or online games e.g. Angry Bird etc

Build a kaleidoscope using geometrical concepts.

Connection:

Organise 3-sided polygons and 4 sided polygons into the respective geometrical families.

Generalise the properties of polygons from triangles and quadrilaterals.

Show uniqueness of special polygons by supporting with minimum conditions

Practice:

Apply properties of polygons to




Design a poster on the timeline on the development of geometry and the

Mathematicians behind all the development.

Suggestions:

Collaborative learning

In groups, students draw triangles of different sizes and shapes and investigate the properties relating the three sides of a triangle, knowing the sum of two side is greater than the third side and also the longest side of a triangle is opposite the largest angle.

Use GSP or geometry software to explore properties of




Resources





Common Test 2, EOY

Exam http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/ http://www.onlinemathlearning.co

m/

Learn about lines: http://www.youtube.com/watch?v

=C-O_Kuuuv9c

Learn about angles: http://www.youtube.com/watch?v

=l_OuHtL7Bug




Chapter 10 + eBook


MA S1/Geometry I

Suggestions:





Common Test 2, EOY

Exam


m/




Chapter 11 + eBook


MA S1/Geometry I

12



Time allocated

In Wks/hrs

0.5 week

Time frame

Week 3 to week 4


5.

know properties of regular pentagon, hexagon, octagon and decagon

Core:

Geometry I (Unit 3/Geometrical

Constructions)


1.

know properties of perpendicular bisectors of line segments and angle bisectors

2.

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

Parallel Curriuclum create tessellation, floor tiles etc.

Create an art piece on

Tessellation using GSP or other

IT tools.

Identity:

Research on Euclid, father of

Geometry and his approach to present facts from theory and produce them into the Elements and contrast with their approach in learning mathematics.

Connection:

Connect theoretical knowledge with construction skills.

Relate scale drawings to actual constructed figures.

Discover the properties involving angle bisector, perpendicular bisector of polygons

(parallelogram, rhombus etc.) – link to Sec 2 Plane Geometry and

Sec 3 Coordinate Geometry.

In Wks/hrs

1 week

Time frame

Term 3

Core:

Geometry I (Unit 4/Perimeter and Area of

Plane Figures)

At the end of the topic, students will be able

Connection:

Discuss the evolution of SI units and its impact on measurement.

Discuss how various parts of the

Learning Activities quadrilaterals and the sum of interior angles of different polygons drawn.




Resources

Suggestions:


Teachers to use online construction tools(such as

Geogebra) to demonstrate how to construct geometrical figures

Experiential learning:

Students to bring geometrical construction set to practice their drawing on worksheets

Suggestions:


Students find the area of different 2D figures manually

Suggestions:





Common Test 2, EOY

Exam

Suggestions:




m/ http://www.mathsisfun.com/geom etry/constructions.html http://www.onlinemathlearning.co

m/geometry-construction.html




Chapter 12 + eBook


MA S1/Geometry I

Online Resources: http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/schools/gcs ebitesize/maths/

13



Time allocated

Week 5 to


1.

convert between cm 2 and m 2

2.

find perimeter and area of simple geometrical figures including parallelogram & trapezium

3.

solve problems involving perimeter and area of composite plane figures

4.

solve problems in real-world contexts (including floor plans, surveying, navigation, etc) using geometry

5.

interpreting the solution in the context of the problem

6.

identifying the assumptions made and the limitations of the solution

In Wks/hrs

1 week

Time frame

Term 3 week

6

Core:

Geometry I (Unit 5/ Volume and Surface

Area of Solids)


1.

convert between cm 3 and m 3

2.

find the volume and surface area of 3D geometrical objects including cubes, cuboid, prism, cylinder, pyramid, cone and sphere

3.

solve problems involving volume and surface area of composite solids

Parallel Curriuclum world use SI units.

Distinguish between the different types of measurements used in real life applications such as area of HDB flat – psf vs psm, land use

- hectares vs km 2 .

Identify the height of parallelogram and trapezium as compare with height of rectangles and square.

Relate area of parallelogram with rectangle and hence trapezium with parallelogram

Practice:

Find or estimate perimeter and area of composite plane figures e.g. floor plans, fencing, boundaries of countries, rivers, lakes etc in daily life and know the relevance of these estimations.

Connection:

Estimate the sizes of containers

(Milo packets in various sizes,

Lipton pyramid tea, Toblerone – prism, 山楂饼 etc. in their daily life.

Use geometric models to connect between volumes of pyramid & prism, cone and cylinder

Practice:

Determine the optimal packaging shape to ensure minimum

Learning Activities and verify it with the actual area of interior calculated in GSP

Suggestions:






Resources



Common Test 2, EOY

Exam http://www.onlinemathlearning.co

m/

2-D and 3-D http://www.youtube.com/watch?v

=rMNa9wICWbo

Solid Shades: http://www.youtube.com/watch?v

=wZ3F16xcGRQ




Chapter 13 + eBook


MA S1/Geometry I

Suggestions:




Design a Maths trail in school regarding Geometry


m/

Volume of objects http://www.youtube.com/watch?v

=gNg77aqxiF8

Basic of Capacity http://www.youtube.com/watch?v

=TkXxn0bJ4r0

What is volume

14




In Wks/hrs

1 week

Time frame

Term 3

Week 7

Core:

Trigonometry I (Unit 1/Pythagoras’

Theorem)


1.

introduce Pythagoras theorem and some simple proofs

2.

find the length of a side of a rightangled triangle using Pythagoras’ theorem

3.

determine whether a triangle is rightangled using Pythagoras’ theorem

4.

solve problems involving Pythagoras’ theorem

5.

derive Pythagorean Triplets


Parallel Curriuclum wastage of space for packing of spherical and cylindrical objects.

Look into minimum wastage of material used in production for the same capacity.

Identity:

Discuss how, one as a global citizen, can help in reducing wastage of material used in packaging.

Connection:

Explore and explain the history of ancient Egyptians and the significance of Pythagoras

Theorem in their daily life at that time (e.g construction, farming).

Relate measurement of LCD/LED screens (35 inch vs 37 inch) and the area in relation to aspect ratio.

Apply Trigonometry in the obstacle courses during National

Service trainings.

Discuss the efficiency of traffic systems using diagonal road crossing in Australia and in Japan

(Shibuya).

Investigate the instinctive nature of animals to get from point A to

B.

Suggestions:

Blended learning and

Collaborative learning with

Flipped Classroom

Pedagogy:

Students learn the history of

Pythagoras Theorem.




Resources


Common Test 2, EOY

Exam

Suggestions:





EOY Exam http://www.youtube.com/watch?v

=ayg5YEEWE9s




Chapter 14 + eBook



Chapter 10 + eBook


MA S1/Geometry I


m/

Use of Java applets to illustrate the interactive proofs http://www.iesmath.com/math/java/geo/pythago ras.html

http://sunsite.ubc.ca/LivingMathe matics/V001N01/UBCExamples/P ythagoras/pythagoras.html




Chapter 8 + eBook


MA S1/Trigonometry I

15




Time allocated

In Wks/hrs

1 week

Time frame

Term 4

Week 1


Core:

Sets (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 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 of 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 = 

A is a subset of B: A  B

A is a proper subset of B: A  B




Solve 3-dimensional real life problems using Pythagoras’

Theorem.

Identity:

Using the story of Pythagoras and his disciple, Hippasus, discuss the qualities that would make you a better learner.



Connection:

Appreciate the importance of hierarchical structure of various systems, (number (e.g. integers are subset of real numbers), geometry (e.g. squares are subset of parallelograms)).

Using visual representations to group information for purposeful interpretations of different sets.

Design a poster on the timeline on the development of Set Theory and the Mathematicians behind all the development.

Practice:

Understand the precision in using mathematical symbol as they use different set notations to represent different meaning and relationships.

Suggestions:


Set equality and subsets http://www.youtube.com/watch?

v=OYGYqRj9-ok&feature=c4overviewvl&list=PL20023FA07684B937

Defining sets http://www.youtube.com/watch?

v=GYlhVuGBl5E&feature=c4overviewvl&list=PL20023FA07684B937



Suggestions:





EOY Exam


Resources

Resources


m/




Chapter 10 + eBook


MA S1/Sets

16




A is not a subset of B: A Ш B

A is a not a proper subset of B: A  B

Time allocated

In Wks/hrs

1 week

Time frame

Term 4

Week 2


Core:

Sets (Unit 2/Venn Diagrams)

At the end of this unit, students will be able to use Venn diagram to

1.

represent the relations of different sets

2.

represent the intersection of sets, union of sets

3.

solve problems involving 2 sets

4.

solve problems involving 3 sets

5.

find maximum/minimum size of a set through logical deduction

6.

understand and apply De Morgan’s Laws for intersection and union of sets

7.

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

8.

discuss the contribution of George

Cantor to Set Theory

9.

comment on the history of development of Set Theory and Modern Mathematics


Suggested Curriculum of

Parallel/s

Practice:

Illustrate and interpret information from real life scenarios (e.g. subject combination, skills, hobbies) using

Venn diagram and set theory

Identity:

Discuss how the study of this unit might make one a better problem solver.






Suggestions:

Venn diagram http://www.youtube.com/watch?v=u

R70knMr2Hg&list=PL20023FA0768

4B937

Venn diagram union and intersection http://www.youtube.com/watch?v=u

R70knMr2Hg

Notes on Venn diagram http://www.cut-theknot.org/LewisCarroll/dunham.shtml

Suggestions:



Cheat Sheet/Mind map to reflect on their mastery of the concepts and skills

Prepare a poster using

Venn Diagram to create a overview of Sec 1 Maths syllabus

Prepare a poster using

Venn Diagram to study on the affective domain of classmates


EOY Exam


Resources

Resources

Online Resources: http://www.nctm.org/ http://www.purplemath.com/ http://www.bbc.co.uk/school s/gcsebitesize/maths/ http://www.onlinemathlearni

ng.com/


New Syllabus

Mathematics 2


Chapter 10 + eBook

S drive/

Maths/Resources/IP MA

S1/Sets

17

S1_MA-SOW_(2015) - Hwa Chong Institution

Scheme of Work (incorporating GL-Matrix, Differentiation: italicised for SBGE, refer to Appendix for further differentiation in SSMT )

Learning outcomes are statements of what a student should know, understand and/or be able to demonstrate after completion of a process of learning.

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S1_MA-SOW_(2015) - Hwa Chong Institution

Scheme of Work (incorporating GL-Matrix, Differentiation: italicised for SBGE, refer to Appendix for further differentiation in SSMT )

Learning outcomes are statements of what a student should know, understand and/or be able to demonstrate after completion of a process of learning.

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