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.
OVERVIEW
Term 1 / Term 2 / Term 3 / Term 4Foundation 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 2
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 / Formative Assessment 3
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 / EOY Exam (70%)
All Topics
Time allocated / Content/ Learning Outcomes / Parallel Curriuclum / Learning Activities / Assessment/ Feedback / Resources /
In Wks/hrs
0.5 weeks
Time frame
Term 1 Week 1 / 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 / 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 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/gcsebitesize/maths/
Print Resources:
- S drive/ Maths/Resources/IP MA S1/Fundamental Skill
- Brochures on Career in Mathematics
In Wks/hrs
1.5 weeks
Time frame
Term 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 to
1. differentiate between prime numbers and composite numbers, factors and 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 / 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 numbers:
http://www.algebrahelp.com/worksheets/view/factoring/findgcf/numbers.quiz
Summative Assessment:
Common Test 1, EOY Exam / Online Resources:
http://www.algebrahelp.com/resources/tables/primes.jsp
http://www.nctm.org/
http://www.purplemath.com/
http://www.bbc.co.uk/schools/gcsebitesize/maths/
http://www.onlinemathlearning.com/
Finding prime factors
http://www.algebrahelp.com/lessons/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/IkenEdu/videos?flow=grid&view=0&sort=da
http://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/hrs
1.5 weeks
Time frame
Term 1 Week 4 to Week 5 / Core:
Arithmetic I (Unit 2/Integers, Rational Numbers & Real Numbers)
At the end of the topic, students will be able to
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
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 / 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.
Practice:
Compare and contrast the different types of numeral systems in the history of mankind.
Justify the use of the current system. / 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
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 / 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
Summative Assessment:
Common Test 1, EOY Exam / Online Resources:
http://www.nctm.org/
http://www.purplemath.com/
http://www.bbc.co.uk/schools/gcsebitesize/maths/
http://www.onlinemathlearning.com/
Videos
Real numbers http://www.youtube.com/watch?v=V6GnHfSaPao
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/Lesson.aspx?id=2413
Simplifying 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=2459
Learning ratio and equivalent fraction
http://illuminations.nctm.org/Lesson.aspx?id=2534
Print Resources:
- New Syllabus Mathematics 1 7th Edition by Shinglee Chapter 2, 8 & 9 + eBook
- S drive/ Maths/Resources/IP MA S1/Arithmetic I
In Wks/hrs
1 week
Time frame
Term 1 Week 6 / Core:
Arithmetic I (Unit 3/Approximation & Estimation)
At the end of the topic, students will be able to
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 / 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. / 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:
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
Summative Assessment:
Common Test 1, EOY Exam / Online Resources:
http://www.nctm.org/
http://www.purplemath.com/
http://www.bbc.co.uk/schools/gcsebitesize/maths/
http://www.onlinemathlearning.com/
Print Resources:
- New Syllabus Mathematics 1 7th Edition by Shinglee Chapter 3 + eBook
- S drive/ Maths/Resources/IP MA S1/Arithmetic I
In Wks/hrs
1 week
Time frame
Term 1 Week 7 / 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 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 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) / 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. / 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
Summative Assessment:
Common Test 1, EOY Exam / Online resources:
Various banks’ websites
HDB 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
In Wks/hrs
1.5 week
Time frame
Term 1 Week 8 to Week 9 / Core:
Algebra I (Unit 1/ Basic Algebra & Algebraic manipulation)
At the end of the topic, students will be able to
1. trace and comment on the development of Algebra
2. 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