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Hwa Chong Institution Subject/Programme : Mathematics

Scheme of Work 2015 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.

OVERVIEWTerm 1 Term 2 Term 3 Term 4

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)

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)

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)Unit 1: Set Notations (1 wk)Unit 2: Venn Diagrams (1 wk)

Revision (1 wk)

Formative Assessment 1 Formative Assessment 2Summative AssessmentCommon Test 1 (10%) Term 2 Week 7Topics(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

Formative Assessment 3Summative AssessmentCommon 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

EOY Exam (70%)All Topics

1


Scheme of Work 2015 Level : Secondary 1Time

allocated Content/ Learning Outcomes Parallel CurriuclumLearning Activities Assessment/ Feedback Resources

In Wks/hrs0.5 weeks

Time frameTerm 1 Week 1

Core:Foundation Skills (Unit 1/Overview)

At the end of the topic, students will be able to1. know the overview of the Secondary

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

2. know the locations of Mathematics Resources in HCIa. school networkb. school library

3. know the effective Mathematics study skills

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

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:

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

Online Resources:Some useful websites in Mathshttp://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/gcsebitesize/maths/

Print Resources:- S drive/ Maths/Resources/IP

MA S1/Fundamental Skill

- Brochures on Career in Mathematics

In Wks/hrs1.5 weeks

Time frameTerm 1 Week 1 to Week 3

Core:Arithmetic I (Unit 1/Prime Numbers, HCF & LCM)

At the end of the topic, students will be able to1. differentiate between prime numbers

and composite numbers, factors and multiples

2. apply prime numbers in real life3. prime factorize a composite number4. write composite numbers in product of

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

Practice:Comment on how prime numbers are used in computer security.Critique, in light ethical practices, how the system can be abused by hackers.

Suggestions:

Blended Learning:

Students explore online resources after classroom lessons

Suggestions:

Formative Assessment:Pop-quiz to access mastery of basic concepts and skills

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

Quiz on finding HCF of

Online Resources:http://www.algebrahelp.com/resources/tables/primes.jsphttp://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Finding prime factorshttp://www.algebrahelp.com/lessons/factoring/numbers/

2

http://www.algebrahelp.com/lessons/factoring/numbers/

http://www.algebrahelp.com/lessons/factoring/numbers/

http://www.onlinemathlearning.com/


http://www.bbc.co.uk/schools/gcsebitesize/maths/


http://www.purplemath.com/

http://www.nctm.org/

http://www.algebrahelp.com/resources/tables/primes.jsp

http://www.algebrahelp.com/resources/tables/primes.jsp



http://www.edublogs.org/

http://www.teachertube.com/

http://www.youtube.com/




factors in exponent form5. find square roots and cube roots by

prime factorization or with a calculator6. find LCM & HCF of two or more

numbers by any method7. apply LCM & HCF in problem solving in

real life

numbers:http://www.algebrahelp.com/worksheets/view/factoring/findgcf/numbers.quiz

Summative Assessment:Common Test 1, EOY Exam

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/IkenEdu/videos?flow=grid&view=0&sort=dahttp://www.youtube.com/watch?v=qzAa_azQUKw

Print Resources:- New Syllabus Mathematics 1

7th Edition by Shinglee Chapter 1 + eBook

- S drive/ Maths/Resources/IP MA S1/Arithmetic I

In Wks/hrs1.5 weeks


Core:Arithmetic I (Unit 2/Integers, Rational Numbers & Real Numbers)

At the end of the topic, students will be able to1. 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

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,

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

Imagine the world without number.

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 percentages

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

Suggestions:




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

VideosReal numbers http://www.youtube.com/watch?v=V6GnHfSaPaoIrrational numbers http://www.youtube.com/watch?v=q_wstDWjnKQMultiplying negative numbers http://www.youtube.com/watch?v=NtJy8uQVN7wReducing fractions

3

http://www.youtube.com/watch?v=NtJy8uQVN7w

http://www.youtube.com/watch?v=NtJy8uQVN7w

http://www.youtube.com/watch?v=q_wstDWjnKQ

http://www.youtube.com/watch?v=q_wstDWjnKQ

http://www.youtube.com/watch?v=V6GnHfSaPao

http://www.youtube.com/watch?v=V6GnHfSaPao







http://www.youtube.com/watch?v=qzAa_azQUKw

http://www.youtube.com/watch?v=qzAa_azQUKw

http://www.youtube.com/user/IkenEdu/videos?flow=grid&view=0&sort=da



http://www.youtube.com/watch?v=Tr9FZUhfJR4

http://www.youtube.com/watch?v=Tr9FZUhfJR4

http://www.youtube.com/watch?v=3EFDOeFomYM

http://www.youtube.com/watch?v=3EFDOeFomYM

http://www.algebrahelp.com/worksheets/view/factoring/findgcf/numbers.quiz






addition and subtraction) on number6. 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 decimal13. compare two quantities by percentage14. increase/decrease quantity by a given

percentage15. apply percentage in real life context

such as simple and compound interest, discount, profit/loss, taxes & commission

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

Justify the use of the current system.

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 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

http://www.youtube.com/watch?v=HJo2Uw3Az-kImproper fraction and mixed number http://www.youtube.com/watch?v=Yfv6BON8qlgFractions and what are its useshttp://www.youtube.com/watch?v=0A3VfV0oIBoConverting Terminating Decimal Numbers to Fractions http://www.youtube.com/watch?v=qyTFvx_ZVOs

Learning positive and negative number: Powerup http://illuminations.nctm.org/Lesson.aspx?id=2413Simplifying ratios:http://www.algebrahelp.com/lessons/proportionbasics/Order of operations:http://www.algebrahelp.com/lessons/simplifying/oops/Learning rates: Paying for your bills http://illuminations.nctm.org/Lesson.aspx?id=2459Learning ratio and equivalent fractionhttp://illuminations.nctm.org/Lesson.aspx?id=2534


7th Edition by Shinglee Chapter 2, 8 & 9 + eBook


In Wks/hrs1 week

Core:Arithmetic I (Unit 3/Approximation &

Connection:Estimate the unit price of daily

Suggestions: Suggestions: Online Resources:http://www.nctm.org/

4


http://illuminations.nctm.org/Lesson.aspx?id=2534




http://www.algebrahelp.com/lessons/simplifying/oops/

http://www.algebrahelp.com/lessons/simplifying/oops/

http://www.algebrahelp.com/lessons/proportionbasics/




http://www.youtube.com/watch?v=qyTFvx_ZVOs

http://www.youtube.com/watch?v=qyTFvx_ZVOs

http://www.youtube.com/watch?v=0A3VfV0oIBo

http://www.youtube.com/watch?v=0A3VfV0oIBo

http://www.youtube.com/watch?v=Yfv6BON8qlg

http://www.youtube.com/watch?v=Yfv6BON8qlg

http://www.youtube.com/watch?v=HJo2Uw3Az-k

http://www.youtube.com/watch?v=HJo2Uw3Az-k





Estimation)

At the end of the topic, students will be able to1. 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 System5. apply simple operations (addition,

subtraction)on binary numbers

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.

Collaborative learningStudents 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




http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/




In Wks/hrs1 week


Core:Arithmetic I (Unit 4/Mathematics in Practical Situations)

At the end of the topic, students will be able to1. 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

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.

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

Practice:Critique the different types of car, housing loan packagesCritique 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

Suggestions:

Collaborative LearningFind 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.

Suggestions:

Formative assessment: Pop-quiz to access mastery of basic concepts and skills

Alternative formative assessment:Oral Presentation of the different types of loan packages by different financial institutions


Online resources:Various banks’ websitesHDB website

Print Resources:- Arithmetic of Life Insurance

(Unit 24, Teaching Sec Math by Alfred S. Posamentier)

- New Syllabus Mathematics 3 6th Edition by Shinglee Chapter 6

5









develop personal good habits of using money (preventing bankruptcy, taking calculated risks in investments)

In Wks/hrs1.5 week


Core:Algebra I (Unit 1/ Basic Algebra & Algebraic manipulation)

At the end of the topic, students will be able to1. trace and comment on the development

of Algebra2. use letters to represent quantities

3. interpret notations: , ,

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

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

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 make you a good algebra learner.

Suggestions:

Blended learning:


Suggestions:



Quiz on factorization of expressionshttp://www.algebrahelp.com/worksheets/view/factoring/findgcf/terms.quiz

Quiz on simple factorizationhttp://www.algebrahelp.com/worksheets/view/factoring/gcf.quiz

Quiz on expansionhttp://www.algebrahelp.com/worksheets/view/simplifying/distribution.quiz


Online Resources:http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Simplifying multiplied algebraic expression http://www.youtube.com/watch?v=6fGa5NrJ3l8Simplifying mixed algebraic expression http://www.youtube.com/watch?v=guqtvxoj8a0Number Patternhttp://www.youtube.com/watch?v=4HjLfAxK2NoSimplifying Algebraic expressionshttp://www.algebrahelp.com/lessons/simplifying/Simplifying like terms in expressionshttp://www.algebrahelp.com/lessons/simplifying/combiningliketerms/Distributive law in expansionhttp://www.algebrahelp.com/lessons/simplifying/distribution/


7th Edition by Shinglee Chapter 4 & 7 + eBook

- S drive/ Maths/Resources/IP MA S1/Algebra I

6

http://www.algebrahelp.com/lessons/simplifying/distribution/

http://www.algebrahelp.com/lessons/simplifying/distribution/

http://www.algebrahelp.com/lessons/simplifying/combiningliketerms/



http://www.algebrahelp.com/lessons/simplifying/

http://www.algebrahelp.com/lessons/simplifying/

http://www.youtube.com/watch?v=4HjLfAxK2No

http://www.youtube.com/watch?v=4HjLfAxK2No

http://www.youtube.com/watch?v=guqtvxoj8a0

http://www.youtube.com/watch?v=guqtvxoj8a0

http://www.youtube.com/watch?v=6fGa5NrJ3l8

http://www.youtube.com/watch?v=6fGa5NrJ3l8







http://www.algebrahelp.com/worksheets/view/simplifying/distribution.quiz



http://www.algebrahelp.com/worksheets/view/factoring/gcf.quiz



http://www.algebrahelp.com/worksheets/view/factoring/findgcf/terms.quiz






where a is a constant

12. add and subtract algebraic fractions with

linear denominator, e.g.In Wks/hrs4.5 weeks


Core:Algebra I (Unit 2/Linear Equations, Algebraic formula & Simple Inequalities)

At the end of the topic, students will be able to1. differentiate between equations and

identities, equations and expressions2. solve simple linear equations involving

one unknown3. solve simple linear equations involving

fractional and decimal coefficients4. solve simple fractional equations that

can be reduced to linear equation e.g.

5. change the subject in given formula in linear form

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

7. construct formula from word problem8. apply linear algebraic equations and

solve problems in real life9. use inequality symbols <, >, and 10. represent simple linear inequalities (e.g.

x a ) on the number line11. 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

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

learning.

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

Suggestions:



Quizzes :http://www.algebrahelp.com/worksheets/view/equationbasics.quizhttp://www.algebrahelp.com/worksheets/view/proportionbasics.quizhttp://www.algebrahelp.com/worksheets/view/simplifying/combiningliketerms.quiz


Online Resources:http://www.algebrahelp.com/lessons/equationbasics/http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Equation Calculator & Solverhttp://www.algebrahelp.com/calculators/equation/




7

http://www.algebrahelp.com/calculators/equation/

http://www.algebrahelp.com/calculators/equation/







http://www.algebrahelp.com/lessons/equationbasics/

http://www.algebrahelp.com/lessons/equationbasics/

http://www.algebrahelp.com/worksheets/view/simplifying/combiningliketerms.quiz



http://www.algebrahelp.com/worksheets/view/proportionbasics.quiz



http://www.algebrahelp.com/worksheets/view/equationbasics.quiz






represent solutions on number line14. form and solve simple linear inequalities

from given word problemsIn Wks/hrs0.5 weeks


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

At the end of the topic, students will be able to1. recap the concept of ratios and speed

learnt in primary school2. 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 map6. understand rate and use speed as an

example of rates7. differentiate between ratio and rate8. solve problems in ratio, rate and

proportion in daily life context9. solve problems in speed, uniform speed

and average speed10. conversion of units(eg km/h to m/s)

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

Understand and use ratio in similarity

Suggestions:

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


Online Resources:

Simplifying ratios:http://www.algebrahelp.com/lessons/proportionbasics/Learning rates: Paying for your bills http://illuminations.nctm.org/Lesson.aspx?id=2459Learning ratio and equivalent fractionhttp://illuminations.nctm.org/Lesson.aspx?id=2534




In Wks/hrs3 weeks

Time frameTerm 2 week 6 to term 3 week 1

Core:Coordinate Geometry I (Unit 1/Coordinate Geometry, Functions and Linear Graphs)

At the end of the topic, students will be able to1. plot points in the 4 quadrants of the

Cartesian plane2. 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

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 to part variation

Practice:Apply graphical skills to other areas of Science and Humanities

Suggestions:

Blended learning


Experiential learning

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

Suggestions:Formative Assessment:Pop-quiz to access mastery of basic concepts and skills


Quiz on coordinateshttp://www.algebrahelp.com/worksheets/view/graphing/points.quizQuiz on reading points


Functions http://www.youtube.com/watch?v=Imn_Qi3dlns

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

Graphing Straight Lines/

8

y ax b

http://www.youtube.com/watch?v=RrrYInyIEGo

http://www.youtube.com/watch?v=RrrYInyIEGo

http://www.youtube.com/watch?v=Imn_Qi3dlns

http://www.youtube.com/watch?v=Imn_Qi3dlns







http://www.algebrahelp.com/worksheets/view/graphing/points.quiz












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

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 lines10. give equations of lines with same

intercept11. Draw graphs of quadratic functions12. Name the line of symmetry in a

quadratic graph13. Give the coordinates of the intercepts in

a quadratic graphs14. Interpret problems with 2

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

-Geographyaffect 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 linear function.

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

(c) study how the graphs

and

change when a, b, and c vary.

http://www.algebrahelp.com/worksheets/view/graphing/readpoints.quizQuiz on plotting points and drawing lineshttp://www.algebrahelp.com/worksheets/view/graphing/pointslines.quizQuiz on determine slope from a graphhttp://www.algebrahelp.com/worksheets/view/graphing/slope.quizFurther Quiz on drawing line with gradient-intercept formhttp://www.algebrahelp.com/worksheets/answers/graphing/slopeintercept.quiz


Quadratic Functions Quizzes:- http://quiz.econ.usyd.edu.au/

mathquiz/linear/index.php- http://quiz.econ.usyd.edu.au/

mathquiz/quadratics/index.php



- S drive/ Maths/Resources/IP MA S1/Geometry I

Time allocated Content/ Learning Outcomes Parallel Curriuclum

Learning Activities Assessment/ Feedback Resources

In Wks/hrs0.5 weeks


Core:Statistics I (Unit 1/Statistical Data Handling)

At the end of the topic, students will be able to1. Collect, classify and tabulate 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).

Suggestions:

Blended learning:Students explore the online resources in iVLE on Statisticand also find out in the internet the usage of statistics in the

Suggestions:

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


9







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

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

http://www.algebrahelp.com/worksheets/answers/graphing/slopeintercept.quiz



http://www.algebrahelp.com/worksheets/view/graphing/slope.quiz



http://www.algebrahelp.com/worksheets/view/graphing/pointslines.quiz



http://www.algebrahelp.com/worksheets/view/graphing/readpoints.quiz






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

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 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.

real world

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



Data handling http://www.youtube.com/watch?v=hKHgqqk4NbEPresentation 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


7th Edition by ShingleeChapter 15 + eBook

- S drive/ Maths/Resources/IP MA S1/Statistic I

In Wks/hrs0.5 weeks


Core:Statistics I (Unit 2/Averages of Statistical Data)At the end of the topic, students will be able to1. Find the mean of a set of data2. Find the median of a set of data3. Find the mode of a set of data4. Evaluate the purposes and

appropriateness of the use of mean, median and mode

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

Suggestions:

Blended learning:Students explore the online resources in iVLE on Statisticand also find out in the internet the measures of central tendencies in the real world

Experiential learningTeachers to show reports on 2013 Singapore’s haze situation and have the students to discuss the use of 3 hr average

Suggestions:

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


Summative Assessment:


Mean, Mode, Medianhttp://www.youtube.com/watch?v=h8EYEJ32oQ8

Mean, Mode, Median and the Business Perspective

10

http://www.youtube.com/watch?v=h8EYEJ32oQ8

http://www.youtube.com/watch?v=h8EYEJ32oQ8







http://www.youtube.com/watch?v=gX9mAL8ixzI

http://www.youtube.com/watch?v=gX9mAL8ixzI

http://www.youtube.com/watch?v=1xlAj_QkViw

http://www.youtube.com/watch?v=1xlAj_QkViw

http://www.youtube.com/watch?v=hKHgqqk4NbE

http://www.youtube.com/watch?v=hKHgqqk4NbE




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.

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

Common Test 2, EOY Exam

http://www.ehow.com/info_12114594_measurement-important-business-perspective-mode-mean-median.html



- S drive/ Maths/Resources/IP MA S1/Statistic I

In Wks/hrs0.5 weeks


Core:Geometry I (Unit 1/Basic Geometry)

At the end of the topic, students will be able to1. state the 5 axioms in Euclidean

Geometry2. 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

Connection: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.

Suggestions:

Blended learning:


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

Suggestions:




Online Resources:http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Learn about lines: http://www.youtube.com/watch?v=C-O_Kuuuv9cLearn about angles: http://www.youtube.com/watch?v=l_OuHtL7Bug




In Wks/hrs1 week

Time frame

Core:Geometry I (Unit 2/Triangles, Quadrilaterals and Polygons)

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

Suggestions:

Collaborative learning

In groups, students draw

Suggestions:

Formative Assessment:Pop-quiz to access mastery

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

11




http://www.youtube.com/watch?v=l_OuHtL7Bug

http://www.youtube.com/watch?v=l_OuHtL7Bug

http://www.youtube.com/watch?v=C-O_Kuuuv9c

http://www.youtube.com/watch?v=C-O_Kuuuv9c













Term 3 Week 4

At the end of the topic, students will be able to1. 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

5. know properties of regular pentagon, hexagon, octagon and decagon

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 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.

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

of basic concepts and skills



gcsebitesize/maths/http://www.onlinemathlearning.com/




In Wks/hrs0.5 week

Time frameWeek 3 to week 4

Core:Geometry I (Unit 3/Geometrical Constructions)

At the end of the topic, students will be able to1. 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

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.

Suggestions:

Blended learning

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:





http://www.mathsisfun.com/geometry/constructions.html

http://www.onlinemathlearning.com/geometry-construction.html


7th Edition by Shinglee

12


















Chapter 12 + eBook


In Wks/hrs1 week


Core:Geometry I (Unit 4/Perimeter and Area of Plane Figures)

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

1. convert between cm2 and m2

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

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

Discuss how various parts of the 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 km2 .

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.

Suggestions:

Blended learning:Students find the area of different 2D figures manually and verify it with the actual area of interior calculated in GSP

Suggestions:




Online Resources:http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/2-D and 3-D http://www.youtube.com/watch?v=rMNa9wICWboSolid Shades: http://www.youtube.com/watch?v=wZ3F16xcGRQ




In Wks/hrs1 week

Time frameTerm 3 week 6

Core:Geometry I (Unit 5/ Volume and Surface Area of Solids)

At the end of the topic, students will be able to1. convert between cm3 and m3

2. find the volume and surface area of 3D

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

Suggestions:

Blended learning:


Suggestions:


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

Online Resources:http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Volume of objects

13







http://www.youtube.com/watch?v=wZ3F16xcGRQ

http://www.youtube.com/watch?v=wZ3F16xcGRQ

http://www.youtube.com/watch?v=rMNa9wICWbo

http://www.youtube.com/watch?v=rMNa9wICWbo










geometrical objects including cubes, cuboid, prism, cylinder, pyramid, cone and sphere

3. solve problems involving volume and surface area of composite solids

between volumes of pyramid & prism, cone and cylinder

Practice:Determine the optimal packaging shape to ensure minimum 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.

on their mastery of the concepts and skills

Design a Maths trail in school regarding Geometry


http://www.youtube.com/watch?v=gNg77aqxiF8Basic of Capacity http://www.youtube.com/watch?v=TkXxn0bJ4r0What is volume http://www.youtube.com/watch?v=ayg5YEEWE9s



- New Syllabus Mathematics 27th Edition by ShingleeChapter 10 + eBook


In Wks/hrs1 week


Core:Trigonometry I (Unit 1/Pythagoras’ Theorem)

At the end of the topic, students will be able to1. introduce Pythagoras theorem and

some simple proofs2. find the length of a side of a right-

angled triangle using Pythagoras’ theorem

3. determine whether a triangle is right-angled using Pythagoras’ theorem

4. solve problems involving Pythagoras’ theorem

5. derive Pythagorean Triplets

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

Suggestions:

Blended learning and Collaborative learning with Flipped Classroom Pedagogy:Students learn the history of Pythagoras Theorem.

Suggestions:



Summative Assessment: EOY Exam

Online Resources:http://www.nctm.org/http://www.purplemath.com/http://www.bbc.co.uk/schools/gcsebitesize/maths/http://www.onlinemathlearning.com/Use of Java applets to illustrate the interactive proofshttp://www.ies-math.com/math/java/geo/pythagoras.html

http://sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html



14




http://www.ies-math.com/math/java/geo/pythagoras.html

http://www.ies-math.com/math/java/geo/pythagoras.html







http://www.youtube.com/watch?v=ayg5YEEWE9s

http://www.youtube.com/watch?v=ayg5YEEWE9s

http://www.youtube.com/watch?v=TkXxn0bJ4r0

http://www.youtube.com/watch?v=TkXxn0bJ4r0

http://www.youtube.com/watch?v=gNg77aqxiF8

http://www.youtube.com/watch?v=gNg77aqxiF8




of animals to get from point A to 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.

- S drive/ Maths/Resources/IP MA S1/Trigonometry I

Time allocated Content/ Learning Outcomes Parallel Curriuclum


In Wks/hrs1 week


Core:Sets (Unit 1/Set Notations)

At the end of this unit, students will be able to1. 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 = Intersection of A and 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 BA is a proper subset of B: A B

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:

Blended learning

Set equality and subsets http://www.youtube.com/watch?v=OYGYqRj9-ok&feature=c4-overview-vl&list=PL20023FA07684B937

Defining sets http://www.youtube.com/watch?v=GYlhVuGBl5E&feature=c4-overview-vl&list=PL20023FA07684B937

Suggestions:



Summative Assessment:EOY Exam




- S drive/ Maths/Resources/IP MA S1/Sets

15







http://www.youtube.com/watch?v=GYlhVuGBl5E&feature=c4-overview-vl&list=PL20023FA07684B937



http://www.youtube.com/watch?v=OYGYqRj9-ok&feature=c4-overview-vl&list=PL20023FA07684B937






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

Time allocated Content/ Learning Outcomes

Suggested Curriculum of Parallel/s


In Wks/hrs1 week


Core:Sets (Unit 2/Venn Diagrams)

At the end of this unit, students will be able to use Venn diagram to1. represent the relations of different sets2. represent the intersection of sets, union

of sets3. solve problems involving 2 sets4. solve problems involving 3 sets5. find maximum/minimum size of a set

through logical deduction6. understand and apply De Morgan’s Laws

for intersection and union of sets7. 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

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=uR70knMr2Hg&list=PL20023FA07684B937

Venn diagram union and intersection http://www.youtube.com/watch?v=uR70knMr2Hg

Notes on Venn diagram http://www.cut-the-knot.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

Summative Assessment:EOY Exam


Print Resources:- New Syllabus

Mathematics 26th Edition by ShingleeChapter 10 + eBook

- S drive/ Maths/Resources/IP MA S1/Sets

16








http://www.cut-the-knot.org/LewisCarroll/dunham.shtml

http://www.cut-the-knot.org/LewisCarroll/dunham.shtml

http://www.youtube.com/watch?v=uR70knMr2Hg

http://www.youtube.com/watch?v=uR70knMr2Hg

http://www.youtube.com/watch?v=uR70knMr2Hg&list=PL20023FA07684B937



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