Overall Physics Syllabus - Hwa Chong Institutionhsmath.wiki.hci.edu.sg/file/view/2015...
Transcript of Overall Physics Syllabus - Hwa Chong Institutionhsmath.wiki.hci.edu.sg/file/view/2015...
Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3
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
Algebra III (7 wk)Unit 1: Advanced Algebraic Manipulation (1 wk)Unit 2: Surds and Indices (1 wk)Unit 3: Equations and Inequalities (3 wk)Unit 4: Introduction to Relations & Functions (1 wk)Unit 5: Polynomials (1 wk)
Algebra III (3 wk)Unit 5: cont’d Polynomials (1 wk)Unit 6: Exponents & Logarithms (2 wk)
Relations and Functions (2.5 wk)Unit 1: Modulus Functions (0.5 wk)Unit 2: Power Functions + Standard Graphs (1 wk)Unit 3: Parabolas and Circles (1 wk)
Matrices (1 wk)
Coordinate Geometry II ( 3 wk) Unit 1: Points, Lines and Shapes (1.5 wk)Unit 2: Applications of Straight Line Graphs (1.5 wk)
Trigonometry III (4.5 wk)Unit 1: Further Trigonometry (1.5 wk)Unit 2: Trigonometric Functions (2 wk)Unit 3: Simple Trigonometric Identities and Equations (1 wk)
Revision (2 wk)
2 Class Tests (10%) (Topic are subjected to changes)
Term 1 Test 1: Week 4(a) Sec 2 Algebra(b) Advanced Algebraic Manipulation
Term 1 Test 2: Week 7(a) Surds and Indices(b) Equations and Inequalities
2 Class Tests (10%)(Topic are subjected to changes)
Term 2 Test 3: Week 4(a) Polynomials + Functions
Term 2 Test 4: Week 7(a) Exponents and Logarithms(b) Modulus Functions(c) Power Functions + Standard Graphs
2 Class Tests (10%)(Topic are subjected to changes)
Term 3 Test 5: Week 4(a) Parabolas and Circles(b) Points, lines and shapes(c) Applications of straight line graphs
Term 3 Test 6: Week 7(a) Further Trigonometry(b) Trigonometric Functions
EOY Exam (70%)All Topics
Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback ResourcesIn Weeks/hrs Core: Connection: Suggestions: Suggestions: Online Resources:
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources1 week
Time frameTerm 1 Week 1
Algebra III (Unit 1/Advanced Algebraic Manipulation)
At the end of the topic, students will be able to:1. Expand and factorise more complex
algebraic expressions.2. Change the subject of a formula with
involvement of roots.3. Add and subtract algebraic fractions
with quadratic denominators leaving answer as a single fraction in simplest
form. (e.g. or
)4. Solving equations involving rational
fractions.5. Manipulate algebraic formulae:
.6. Expand the expressions: (x y)3 and
(a+b+c)3.7. Extend expansion and factorisation
techniques to expressions where the basic unit of unknown is of higher power (x4-9), (x4-5x2+6).
8. Extend expansion and factorization to
expressions - SMTP
Apply the identities learnt in Sec 2
to more advanced problems.
Compare and contrast the concepts of equal identity/equality in Maths vs humanities.
Blended/Cooperative Learning:Students to be organized in expert groups, each group to watch one of the suggested videos and share with rest of group on what they learnt about the algebraic identities.
Experiential Learning:Use algebraic manipulatives to visualise algebraic identities of order 3.
- Formative assessment: Pop Quiz
- Alternative formative assessment: Students to present on what they have learnt from the videos to the rest of the class
- Summative assessment: Term 1 Test 1
Special Factoringhttp://www.purplemath.com/modules/specfact2.htm
Geometrical Interpretation of
http://www.youtube.com/watch?v=5x4gJPchSiYGeometrical Interpretation of
http://www.youtube.com/watch?v=9RHJt0GXLcY
In Weeks/hrs Core: Connection: Suggestions: Suggestions: Online Resources:2
Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources1 week
Time frameTerm 1 Week 2
Algebra III (Unit 5/Indices and Surds)*solving in integer solutions (rational to be discussed in unit 3*)At the end of the topic, students will be able to:1. Recognise surds and understand that
surds can be written in index form, or with radical signs and state the rules of surds
2. Perform arithmetical operations (addition, subtraction, and multiplication) on expressions involving simple surds in the numerator using properties of real numbers
3. Rationalise fractions involving surds in the denominator (without being instructed)
4. Solve problem sums involving surds5. Solve equations involving surds.6. Understand that by squaring an
equation involving surds, extraneous solutions may be introduced and the solutions need to be checked to ensure they still fulfil the original equation
7. Solve equations involving indices including substitution method
8. Recognize/identify/plot (different bases) basic graphs of exponential functions (for connection to population growth, compound i/r and etc), e.g. y=2x,
9. Solve challenging equations involving surds (surds within surds) - SMTP
Make sense of numbers in surd form and recognise that the quadratic formula gives the real roots of quadratic equations in various forms (integer, rational number and conjugate surds).
Justify the existence of irrational numbers.
Relate the operations of surds and rationalisation of denominator to the three algebraic identities learnt in Sec 2 (e.g.
).
Justify the use of exponential graphs to population growth, radioactivity decay, half-life, compound interest etc.
Practice:Using graphing tools or software such as Microsoft Excel to model bacteria growth using exponential graph.
Collaborative Learning: Investigate how squaring an equation would lead to extraneous solutions.
- Formative assessment: Pop Quiz
- Alternative formative assessment: Open Ended Tasks on Surds (One Equals to Zero and Other Mathematical Surprises Pg 12-13, 18 - 22)
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 57
- Summative assessment: Term 1 Test 2
History of Surdshttp://www.mathsisgoodforyou.com/AS/surds.htm
Hotel Infinityhttp://www.mathsisgoodforyou.com/artefacts/hilberthotel.htm
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 2
In Weeks/hrs3 week
Time frame
Core:Algebra III (Unit 3/Equations and Inequalities)
At the end of the topic, students will be able
Connection:Explore the use of equations and inequalities in business problems, physics and decision making
Suggestions:Experiential Learning:Use a spreadsheet or graphing software to
Suggestions:- Formative
assessment: Pop Quiz
Online Resources:Simultaneous Equationshttp://www.youtube.com/
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback ResourcesTerm 1 Week 3 to 5
to:1. Solve quadratic equations using (1)
factorization (2) completing the square (3) formula [emphasis on completing the square where the x2 coeff is not 1. – working is essential]
2. Understand that the quadratic formula is derived from the quadratic equation form by completing the square method
3. Solve linear and non-linear simultaneous equations
4. Discuss the geometrical significance of the algebraic solution of simultaneous equations with the use of suitable IT tools,
5. Discuss the number of solutions of a pair of simultaneous linear and non-linear equations (i.e. there may be 2 solutions, 1 solution or no solution),
6. Solve word problems involving linear and non-linear equations.
7. Relationships between the roots and coefficients of a quadratic equation
8. Understand that different discriminant give rise to different types of solutions for a quadratic equation:(a) two real roots(b) two equal roots(c) no real roots
and related conditions for a given line to:(a) intersect a given curve(b) be a tangent to a given curve(c) not intersect a given curve
9. Apply conditions for to be always positive (or always negative)
10.Transform to the form
Explore biographies of Mathematicians such as Diophantus, Al-Kharizmi, Abu Kamil Babylonian tablets and reflect on how these mathematicians pursue their passion and their role in fulfilling societal needs at that time.
Practice:Model the trajectory path of an object in the air or the stopping distance of a car using quadratic function.
(a) investigate the relationship between the number of points of intersection and the nature of solutions of a pair of simultaneous equations, one linear and one quadratic.
(b) explain how the roots of the equation
are related to the sign of
.(c) show graphically why
there are no real solutions to a quadratic equation
when
is negative.(d) investigate how the
positions of the graph
vary with the sign of
, and describe the graph
when .(e) Examine the solution of
a quadratic equation and that of its related quadratic inequality
(e.g.
and ), and describe both solutions and their relationship.
- Alternative formative assessment: Mathematical Modelling Task on Marshall Cavendish Pg 33
- Alternative formative assessment: Open Ended Tasks on Quadratics (One Equals to Zero and Other Mathematical Surprises Pg 8 – 11, 31 - 35)
- Performance Task – Paper Helicopter ASMS
- Summative assessment: Term 1 Test 2
watch?v=SZ4x-HzhaKoSimultaneous Equations and Intersections of Graphshttp://www.purplemath.com/modules/syseqgen.htm
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 1
- Math Through the Ages
- New Syllabus Mathematics 7th Edition by ShingleeChapter 1
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
and use it to (i) sketch the graph
11.Transform to the form
and use it to (i) sketch the graph
12.Understand that quadratic function can be expressed in many forms. The values of a, b, and c or h and k or p and q gives different information about the quadratic function.
13.Solve quadratic inequalities, and representing the solution on the number line
14. Solve inequalities of the form
.15. Discuss the difference between the
parabola vs catenary – SMTPIn Weeks/hrs1 week
Time frameTerm 1 Week 6
Core:Algebra III (Unit 4/Relations and Functions)At the end of the topic, students will be able to:1. Define the terms function (one-to-one,
many-to-one), relation (one-to-one, many-to-one, many-to-many, one-to many), domain, range and image.
2. Illustrate a relation using the arrow diagram.
3. Find the expression for inverse function.
4. Acquire the concept and skills needed for composite functions and their inverses – SMTP
Connection:Understand that sometimes it is possible to model data from a real world situation with a linear equation.
Understand that the operations (adding and subtracting functions) within the domain of the functions involved, are similar to that of real numbers.
Suggestions:Experiential Learning:Match graphs with functions (Maths Resource)
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 236
Summative assessment: Term 2 Test 3
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 4
In Weeks/hrs2 week
Time frame
Algebra III (Unit 5/Polynomials)
At the end of the topic, students will be able to:
Connection:Make connections between division of
polynomial and division of whole
Suggestions:
Experiential Learning:Use a spreadsheet or
Suggestions:- Formative
assessment: Pop Quiz
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback ResourcesTerm 1 Week 8 to Week 9 to Term 2 Week 1
1. Definition of polynomial.2. Multiplication and division of polynomial.3. Types of equations – identity vs
conditional equation.4. Equating two equivalent polynomials
and then comparing coefficients
5. Able to recognize quotient & remainder from a given identity.
6. Know the Division Algorithm (long division)
7. Define remainder theorem and know its limitation.
8. Apply reminder theorem to solve for unknowns in polynomial.
9. Able to revert back to the division algorithm to find the quotient and the remainder when the divisor is non-linear
10. Define factor theorem11. Use factor theorem to solve for
unknowns in polynomial.12. Apply factor theorem to factorise cubic
expressions and solve cubic equations (including unknown constants to test for understanding instead of using the calculator).
13. Understand that the degree of a polynomial equation tells them about the number of roots that the equation has
14. Sketch cubic graphs and understand that there is always 1 real root and conditions for possible solutions (1) 3 real distinct roots, (2) 1 real root, 2 repeated roots, (3) 1 real root, 2 imaginary roots (4) 3 repeated roots
15. Sketch polynomial graphs in product form of any order and using it to solve polynomial inequalities in product form.(guided SMTP + SBGE)
number, and express the division
algorithm as
.
Make connections between the Fundamental theorem of algebra (prime factors) and the factor theorem.
Explore biographies of Mathematicians Tartaglia Vs Cardano and reflect on how these mathematicians pursue their passion and their role in fulfilling societal needs at that time.
Practice:Relate cubic equations to design of roller coasters (consideration of max allowed speed) and link to integrated resorts.
Explore mathematical questions crafted using Chinese poetic verses in Arithmetic in Nine Sections.
graphing software to(a) investigate the graph of
a cubic polynomial and discuss(i) the linear factors of
the polynomial and the number of real roots; and
(ii) the number of real roots of the related cubic equation,with reference to the points of intersection with the x-axis
- Alternative formative assessment: Concept Map on the behavior of roots for Quadratic vs Cubic functions
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 89
- Summative assessment: Term 2 Test 3
Chapter 3
In Weeks/hrs2 week
Core:Algebra III (Unit 6/Exponents
Connection:Relate the solution of the equation
Suggestions:Experiential Learning:
Suggestions:- Formative
Online Resources:Richter Scale
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
Time frameTerm 2 Week 2 to Week 3
&Logarithms)
At the end of the topic, students will be able to:
1. Know functions and their graphs.
2. Know equivalence of
and that they are inverse functions. [Students must
also be aware and prove , e.g 10lg a = a]
3. Show that and
for any and .4. Understand and apply Laws of
logarithms:(1) product (2) quotient (3) power (4) change-of-base laws.
5. Understand that logarithmic laws can be used to simplify, solve exponential expressions/equations and vice versa.
6. Solve logarithmic and exponential equations.
7. Discuss the use of exponential and logarithmic functions to other disciplines via word problems (e.g. pH value, Richter scale of earthquakes, decibel scale for sound intensity, radioactive decay, population growth). Refer to Add Maths textbook (Scatter plot), pg 189 for e.g.]
8. Sketch and understand the properties of logarithmic graphs vs exponential (of different bases) graphs. (aware the existence of asymptotes and indicate the intercepts and. Understand the properties of the 2 graphs exp/log - inverse of each other)
9. Solve challenging questions involving
to the graph to verify the existence of the solutions or to justify that the solution does not exist.
Trace the history of logarithms and appreciate the complexity of the logarithmic tables and how they have been programmed in calculators, computers.
Model real-life problems using exponential functions, such as the half-life function and heat and cooling function.
Use a spreadsheet or graphing software to(a) investigate the
characteristics of exponential and logarithmic graphs.
(b) display real-world data graphically and model with an appropriate exponential or logarithmic function.
Collaborative Learning:(a) Students to investigate
the cause and effect earthquakes that happened in the last 5 years for e.g. Sichuan Earthquake 2008, China, Tohoko Earthquake 2011, Japan, Christchurch Earthquake, New Zealand. Students to reflect on how they could help in the face of such natural disasters.
(b) Students to investigate the impact of Indonesian Tremors to Singapore.
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 189
Summative assessment: Term 2 Test 4
http://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_properties/v/richter-scale
Logarithms in the Real Worldhttp://www.youtube.com/watch?hl=en-GB&v=3oZPPIVC8MU&gl=SG
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 7
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
exponential and logarithmic functions.In Weeks/hrs0.5 week
Time frameTerm 2 Week 5
Core:Functions I(Functions and Modulus Functions)
1. Know and sketch the graph (reflection on the x-axis – no other
transformation yet) of where
is linear, quadratic, exponential/logarithmic or trigonometric (trigo in the later chapter).
2. Solve equations involving modulus functions (methods/skills – regions/squaring/substitution).
3. Understand that 4. Understand the difference between
and
Connection:Understand that an absolute value of x is its distance from 0 and the absolute of f(x) is its distance from the line y = 0.
Understand that the operations (adding and subtracting functions) within the domain of the functions involved, are similar to that of real numbers.
Suggestions:Experiential Learning:Match graphs with functions (Maths Rm Resource)
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 236
Summative assessment: Term 2 Test 4
Print Resources:Additional Mathematics 360 by Marshall Cavendish Chapter 4
In Weeks/hrs0.5 week1 week
Time frameTerm 2 Week 5/6
Core:Functions I (Standard Graphs + Transformation)
At the end of the topic, students will be able to:1. Sketch graphs illustrating direct and
indirect proportionality2. Sketch the power functions y=axn,
n = -2,-1,0,1,2,3 … or is rational. E.g.s
3. Identify the basic function and perform simple transformation (translation, reflection, stretch) of standard graphs including exponential, logarithmic,
Connection:Identify the basic unit and appreciate that new products are created as a result of successive transformations for product design, architecture
Compare transformations to point, line, rotational symmetry.
Suggestions:Experiential Learning:Use a spreadsheet or graphing software to(a) explore the
characteristics of the various functions.
(b) display real-world data and match it with appropriate functions (regression).
Collaborative Learning:Work in groups to match and justify sketches of graphs with their respective functions.
Suggestions:- Formative
assessment: Pop Quiz
- Performance Task: Students examine the problem of space-pollution caused by human-made debris in orbit to develop an understanding for functions and modeling at http://illuminations.nctm.org/lessonplans/9-12/debris/index.html
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 4
- Shinglee Textbook New Syllabus Mathematics 7th Edition Chapter 5
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
power, trigonometric functions (trigo to be discussed later). For graphs with asymptotes, students can relate the movements of the asymptotes to certain transformations
4. Introduce the notion of ,
5. Describe the transformations (at most 3 successive) that the functions have undergone and find the original function from resultant transformed function or vice versa.
6. Understand that 180o rotation about the origin as a successive reflections along the x and y axes
7. Explore the different ways of transformation given the original and end functions.
Summative assessment: Term 2 Test 4
In Weeks/hrs1 week
Time frameTerm 2 Week 7/8
Core:Functions I (Parabolas and Circles)
At the end of the topic, students will be able to:1. relate the graph of
to
to and that they are inverse functions of each other.
2. sketch the graphs of
(a) parabolic
(b) .3. Perform simple transformation of these
graphs.4. Derive and define the equation of a
circle with centre (a, b) and radius r using the Pythagoras’ theorem, and the
Connection:Compare equation of circle with Pythagoras’ Theorem.
Relate the concept of loci of points equidistant from a fixed point to equation of circle.
Recognise concept of circles as a special class of ellipses.
Explore the use of parabolas in other discicplines (e.g. sciences parabolic motion) and in the real world.
Discuss how to solve geometry problems involving intersection of a parabola/circle and a straight line.
Suggestions:
Experiential Learning:Use a spreadsheet or graphing software to(a) explore the
characteristics of the various functions.
(b) investigate the graph of
when varies.
(c) display real-world data and match it with appropriate functions (regression).
Collaborative Learning:(a) Work in groups to
match and justify
Suggestions:- Formative
assessment: Pop Quiz
- Summative assessment: Term 3 Test 5
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 9
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
special case when the centre is at the origin.
5. Transform general form of equation of
circle to by completing the square method.
6. Compare the three cases where line meets circle (1) 2 distinct roots, (2) 2 repeated roots, (3) imaginary roots.
7. Find the intersection of two circles.
Practice:Determine centre of a broken circular wheel in archaeological studies
Find epicentre by solving 3 circle equations, detected from 3 satellite stations.
sketches of graphs with their respective functions.
In Weeks/hrs1 week
Time frameTerm 2 Week 9
Core:Algebra III (Matrices)
At the end of the topic, students will be able to:1. Present information in the form of a
matrix of any order,2. Define equal, zero, identity matrices.3. Find unknowns in equal matrices.4. Perform addition and subtraction on
matrices of same order, perform scalar multiplication.
5. Perform matrix multiplication on small order matrices.
6. Find determinant of a 2 2 matrix,7. Understand singular and non-singular
matrices,8. Find the inverse of a 2 2 non-singular
matrix by formula,9. Express a pair of simultaneous linear
equations in matrix form and solving the equations by inverse matrix method.
10. Solve word problems involving the sum and product of matrices and interpret the data in the given or computed matrices
Connection:Contrast the matrices operations with algebraic operations (e.g. AX = B is non-commutative whereas ax = b is commutative).
Practice:Create encrypted messages using matrices and decrypt messages using matrix operations.
Investigate the use of matrices in operation research
Discuss some applications of matrix multiplication, e.g. transformation matrices for movie making.
Discuss how the idea of matrices is being used in spreadsheets and how these programs are useful in their everyday lives.
Suggestions:
Experiential Learning:Use a graphing calculatorto input matrices and to compute inverse matrices – simplify decoding process.
Collaborative Learning:Students to get into groups and justify if two matrices can be multiplied by checking the orders of the matrices.
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Students to encode and decode using shift transformations (refer to NSA lesson plan) and present their work in an oral presentation
Summative assessment: Term 3 Test 1
Online Resources:Matrices Khan Academyhttp://www.khanacademy.org/math/algebra/algebra-matricesNSA lesson plan on encoding and decodinghttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/matrices_secret_weapon.pdf
In Weeks/hrs1.5 week
Core:Coordinate Geometry III (Unit 1/Points, Lines and Shapes)
Connection:Relate gradient to tangent ratio of the angle of inclination between the line
Suggestions:
Collaborative Learning:
Suggestions:- Formative
assessment: Pop
Online Resources:Descartes and Coordinate System
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback ResourcesTime frameTerm 3 Week 1 to Week 2
At the end of the topic, students will be able to:1. Given coordinates of two points
calculate, revise(a) mid-point(b) distance(c) gradient.
2. Prove squares, rectangles, parallelograms and other standard polygons.
3. Understand and solve problems involving collinear points.
4. Understand that they can compare the slopes of two lines and determine if the lines are parallel or perpendicular.
5. Understand gradient of a perpendicular
line using the relationship 6. Identify equations of parallel or
perpendicular lines.7. Find the equation of the circle passing
through three given points. (using perpendicular bisectors)
8. Formulate equations of lines passing through a given point and parallel or perpendicular to another given line.
9. Find equation of perpendicular bisector between two points.
10. Find the area of rectilinear figure given its vertices(Shoelace Formula).
11. Estimation of the gradient of a curve by drawing a tangent
and the positive direction of the x-axis
Deduce the relationship between the gradient of (a) two parallel lines, (b) two perpendicular lines.
Synthesise the different methods to find area of triangles learnt (1)
Shoelace method, (2) and extend these to finding the area of polygons.
Relate the concept of foot of perpendicular to finding shortest distance from point to line.
Relate estimation of gradient of tangent for speed-time graph to instantaneous speed in kinematics.
Explore and discuss ways of finding the area of a triangle (or polygon) with given vertices.
Discuss other ways of finding area of rectilinear figures.
Quiz
Alternative formative assessment:Concept Map of properties of lines in Coordinate Geometry
Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 162
Summative assessment:Term 3 Test 5
http://www.bookrags.com/research/descartes-and-his-coordinate-system-mmat-02/
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 6
- Shinglee Textbook New Syllabus Mathematics 7th Edition Chapter 4
In Weeks/hrs1.5 week
Time frameTerm 3 Week 2 to 3
Core:Coordinate Geometry III(Unit 2/Applications of Straight Line Graphs)
At the end of the topic, students will be able to:1. Distinguish between linear and non-linear relationships.2. Determine a linear relation based on
Connection:Justify the use of straight line graph in science experiment (e.g. oscillation of a pendulum (Hooke’s Law), relationship between resistance in circuit (Ohm’s Law), kinematics graphs.
Understand the purpose to convert
Suggestions:
Maths Journal:Use a table to explore some typical transformations of non-linear equation into a linear equation
Inquiry Learning:
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 8
Online resources:- Singapore data(http://data.gov.sg/
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
experimental results of two non-linearly related quantities.3. Convert non-linear equations into linear form.4. Derive the relationship between two variables given the straight line graphs.5. By applying linear law to obtain straight line graphs using experimental data, determine unknowns by reading from the graphs.6. Understand independent and dependent variables.7. Understand and identify outliers or incorrect readings.8. Expect to plot linear graph given set of experimental data (with no scale given – proper scale).
non-linear graphs to linear ones and how it is used to prove/justify the relationship between variables.
Practice:Model phenomena in Science or real world using an equation. For example, students can conduct simple Science experiments to collect data. Part (a) to find a formula (V = RI) for the resistance of a resistor.
Part (b) to find a formula () for the period of a pendulum.
Use suitable software to find out what happens when the non-linear equation has more than two unknown constants.
Plot the curve of best fit to fit a given set of data directly to decide the relationship between each set of unknowns.
Engage in simple Science experiments to collect data and analyse data using a straight line graph.
Exploratory Activity:Predict population growth using suitable linear function. (Textbook: Pg. 213)
Collaborative Learning:Working in groups, based on the data on water consumption per capita in Singapore for the past 10 years, students will plot graphs to predict future water consumption based on graph plotted using data from past years.
Identify and explain abnormal or inconsistent data.
Explore new water sources for Singapore
Pg 213
- Summative assessment: Term 3 Test 5
home.aspx)
- To convert non-linear relationships to linear form.(http://www.youtube.com/watch?v=pX6WlxP2eok)
- Applications of linear law(http://www.youtube.com/watch?v=Gvb6MLB_x6I)
In Weeks/hrs1.5 week
Time frameTerm 3 Week 4 to Week 5
Core:Trigonometry III (Unit 1/Further Trigonometry)At the end of the topic, students will be able to:1. Prove of Sine Rule and derive (guided)
the Cosine Rule on their own.2. Use the sine and cosine rules to
articulate the relationships between the sides and angles of a triangle, e.g. the lengths of the sides are proportional to sine of the corresponding angles, Pythagoras’ theorem is a special case of the cosine rule, etc.
Connection:Explore and discuss applications of Trigonometry to different fields like geography and astronomy, physics and engineering.
Relate concept of sine rule to congruency tests learnt in Sec 2Illustrate the ambiguous case of Sine Rule using construction/GSP and emphasise congruency tests learnt in Sec 2.
Suggestions:
Experiential Learning:Use Clinometer app on iPhone or Android phone to find the angle of elevation or depression of particular buildings
To organise a treasure hunt where treasures are located at different spots as a result of ambiguous case of sine
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Concept Map on connecting the areas of triangles from various topics for different types of triangles
Online Resources:Leaning tower of Pisahttp://www.clarku.edu/~djoyce/trig/apps.html
Applications of Trigonometryhttp://www.youtube.com/watch?v=wvmU7XKdt3w
Trigonometry in Real
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
3. Solve triangles through Sine Rule (including ambiguous case) & Cosine rule.
4. Use the formula for area of triangle (Heron’s formula).
5. Prove Heron’s formula – SMTP6. Find the perpendicular height of a
triangle using area of triangle (apart from using trigonometry)
7. Know and use the concept of bearings.8. Solve 2D and 3D problems.9. Compute angles of elevation and
depression, shortest distance, maximum angle elevation and understand that shortest horizontal distance would give maximum angle of elevation or depression.
Use circle properties to derive cosine rule.
Practice:Determinet the actual flight distance (geodesic path) using cosine rule.
Explore using software to check consistency of theoretical flight path vs actual flight path.
rule. Students to use Bearing app on iPhone or Android phone to locate the treasures.
Summative assessment: Term 3 Test 6
Lifehttp://www.youtube.com/watch?v=n1A2HqSXtGI
Print Resources:- New Syllabus
Mathematics 3, 7th Edition by Shinglee Chapter 6,7
In Weeks/hrs2 week
Time frameTerm 3 Week 6 to Week 8
Core: Trigonometry III (Unit 2/Trigonometric Functions)
At the end of the topic, students will be able to:1. Know the concept of unit circle.2. Know the six trigonometric functions for
angles of any magnitude (in degrees or radians) and the reciprocal relationship between trig functions, e.g. sec x and cos x and etc.
3. Distinguish between
and
.4. Know principal values (1 to 1 function)
of . – SMTP5. Know the exact values of the
trigonometric functions for special angles (0, 30, 45, 60, 90, 180 and in radians).
Connection:Discuss the relationships between sin A, cos A and tan A, with respect to the line segments related to a unit circle.
Relate the use of sine and cosine functions in sciences (e.g. tides, Ferris wheel and sound waves).
Understand that trigonometric functions, and their compositions gain significance when they are used to model waves and periodic behaviour.
Practice:Explore the historical development of trigonometry – from circle trigonometry to triangle trigonometry and its impact on the study of astronomy
Model natural phenomena – tides, heartbeat, music etc. using graphs of
Suggestions:
Experiential Learning:Use a Geogebra or GSP to(a) investigate the
relationship of sin A, cos A and tan A with respect to the unit circle.
(b) display the graphs of trigonometric functions and discuss their behaviour, and investigate how a graph (e.g.
) changes when a, b or c varies.
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 307
- Performance Task: Students to get into groups to find out the different ferris wheels for e.g. Singapore Flyer around the world and to use sine or cosine to its function
- Summative assessment: Term 3 Test 6
Online Resources:Trigonometric Functions and Unit Circlehttp://www.youtube.com/watch?v=rrXLl2WTKEc
Applications of Trigonometry – geography and astronomy, physics and Engineeringhttp://www.clarku.edu/~djoyce/trig/apps.html
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 11
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
6. Identify amplitude, periodicity (behaviour repeated over intervals of equal length) and symmetries related to sine, cosine and tangent functions.
7. Understand that they can translate periodic functions in the same way as they translate other functions.
8. Sketch graphs of
,
and
,
.
where can be , , ,
and relate to real life examples of sound waves with such patterns.
In Weeks/hrs1 week
Time frameTerm 3 Week 9
Core:Trigonometry III (Unit 3/Simple Trigonometric Identities and Equations)
At the end of the topic, students will be able to:1. Understand that the interrelationships
amongst the six basic trigonometric functions make it possible to write trigonometric expressions in various equivalent forms.
2. Derive and relate to Pythagoras’ theorem.
3. Use of ,
,
,
,
4. Simplify trigonometric expressions.
Connection:Make connections between solutions obtained from solving trigonometric equations and graphical method.
Discuss similarities and differences in solving algebraic equations and trigonometric equations.
Suggestions:- Formative
assessment: Pop Quiz
- Alternative formative assessment: Mathematical Modeling on Marshall Cavendish Pg 323
Print Resources:- Additional
Mathematics 360 by Marshall Cavendish Chapter 12
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Hwa Chong Institution Subject/Programme : MathematicsScheme of Work 2015 Level : Secondary 3Time Allocated Content/Learning Outcomes Parallel Curriculum Learning Activities Assessment/Feedback Resources
5. Solve simple trigonometric equations, including the use of trigo identities, in degrees. (angles can involve more than 1x, e.g. 2x-30o]
6. Prove simple trigonometric identities, including the use of trigo identities. (rigourous proving, > 5 steps – SMTP)
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