SMK Batu Lintang Yearly Plan – Mathematics Form 5 Week Learning Objectives Pupils will be taught to..... Learning Outcomes Pupils will be able to… Suggested Teaching & Learning activities/Learning Skills/Values Points to Note Topic /Learning Area : 1. NUMBER BASES – 1 1/2 weeks 6/1 15/1 – 14/1 Cuti Umum (Maulidur Rasul) 1. Understand and use the concept of number in base two, eight and five. (i) State zero, one, two, three, …, as a number in base: a) two b) eight c) five (ii) State the value of a digit of a number in base: a) two b) eight c) five (iii) Write a number in base: a) two b) eight c) five in expanded notation Use models such as a clock face or a counter which uses a particular number base. Discuss - Dicuss digits used - Place values in the number system with a particular number base. Skill : Interpretation, observe connection between base two, eight and five. Use of daily life examples Values : systematic, careful, patient Emphasis the ways to read numbers in variours bases. Give examples: Numbers in base two are also know as binary numbers. Expanded notation Give examples 1
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SMK Batu LintangYearly Plan – Mathematics Form 5
Week Learning ObjectivesPupils will be taught to.....
Learning OutcomesPupils will be able to…
Suggested Teaching & Learning activities/Learning Skills/Values Points to Note
Topic /Learning Area : 1. NUMBER BASES – 1 1/2 weeks
6/1 – 15/1
14/1 Cuti Umum(Maulidur Rasul)
1. Understand and use the concept of number in base two, eight and five.
(i) State zero, one, two, three, …, as a number in base:
a) two b) eight c) five
(ii) State the value of a digit of a number in base:
a) two b) eight c) five(iii) Write a number in base: a) two b) eight c) five in expanded notation
Use models such as a clock face or a counter which uses a particular number base.
Discuss- Dicuss digits used- Place valuesin the number system with a particular number base.
Skill : Interpretation, observe connection between base two, eight and five.
Use of daily life examples Values : systematic, careful, patient
Emphasis the ways to read numbers in variours bases. Give examples:
Numbers in base two are also know as binary numbers.
Expanded notationGive examples
(iv) Convert a number in base: a) two b) eight c) five to a number in base ten and vice versa.
(v) Convert a number in a certain base to
Use number base blocks of twos, eights and fives.
Discuss the special case of converting
Perform repeated division to convert a number in base ten to a number in other bases.Give examples.
Limit conversion of numbers to
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Week Learning ObjectivesPupils will be taught to.....
Learning OutcomesPupils will be able to…
Suggested Teaching & Learning activities/Learning Skills/Values Points to Note
a number in another base.
(vi) Perform computations involving : a) addition b) subtration of two numbers in base two
a number in base two directly to a number in base eight and vice versa.
Skill : Interpretation, converting numbers to base of two, eight, five and then.
Use of daily life examples Values : systematic, careful, patient
base two, eight and five only.
The usage of scientific calculator in performing the computitations.
Topic /Learning Area : 2 : Graphs of Functions II --- 3 weeks
Catatan: 29/1 4/2 Cuti Tahun Baru Cina 29/1, 3/2, 4/2 Cuti Gantian
30/1 Cuti Peristiwa 14/2 Cuti Peristiwa (Chap Goh Mei)
16/1 - 29/15/2 – 7/210/2 – 13/2
2.1 Understand and use the concept of graphs of functions
(i) Draw the graph of a: a) linear function : y = ax + b, where a and b are
constant; b) quadratic function
y=ax2+bx+c , where a, b and c are
constans, a≠0
c) cubic function :
y=ax3+bx2+cx+d where a, b, c and d are
constants, a≠0 d) reciprocal function
Explore graphs of functions using graphing calculator or the GSP
Compare the characteristic of graphs of functions with different values of constants.
Values : Logical thinking
Skills : seeing connection, using the GSP
Questions for 1..2(b) are given in the form of ( x+a ) ( x+b )=0 ; a and b are numerical values.
Limit cubic functions.Refer to CS.
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Week Learning ObjectivesPupils will be taught to.....
Learning OutcomesPupils will be able to…
Suggested Teaching & Learning activities/Learning Skills/Values Points to Note
y=ax , where a is a
constants, a≠0(ii) Find from the graph a) the value of y, given a value of x b) the value(s) of x, given a value of y(iii) Identify: a) the shape of graph given a type of function b) the type of function given a graph c) the graph given a function and vice versa(iv) Sketch the graph of a given linear,
quadratic, cubic or reciprocal function.
Play a game or quiz
For certain functions and some values of y, there could be no corresponding values of x.
Limit the cubic and quadratic functions.Refer to CS.
Limit cubic functions.Refer to CS.
2.2 Understand and use the concept of the solution of an equation by graphical method.
(i) Find the point(s) of intersection of two graphs
(ii) Obtain the solution of an equation by finding the point(s) of intersection of two graphs
(iii) Solve problems involving solution of an equation by graphical method.
Explore using graphing calculator of GST to relate the x-coordinate of a point of intersection of two appropriate graphs to the solution of a given equation. Make generalisation about the point(s) of intersection of the two graphs.
Use everyday problems.
Skills : Mental process
Use the traditional graph plotting exercise if the graphing calculator or the GSP is unavailable.
Involve everyday problems.
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Week Learning ObjectivesPupils will be taught to.....
Learning OutcomesPupils will be able to…
Suggested Teaching & Learning activities/Learning Skills/Values Points to Note
2.3 Understand and use the concept of the region representing inequalities in two variables.
(i) Determine whether a given point satisfies a) y=ax+b or y>ax+b or y<ax+b
(ii) Determine the position of a given point relative to the equation y=ax+b
(iii) Identify the region satisfying y>ax+b or y<ax+b
(iv) Shade the regions representing the inequalities
a) y>ax+b or y<ax+b b) y≥ax+b or y≤ax+b
(v) Determine the region which
satisfy two or more simultaneous linear inequalities.
Include situations involving x=a , x≥a , x>a , x≤a or x<a .
Values: Making conclusion, connection and comparison, careful
Emphasise on the use of dashed and solid line as well as the concept of region.
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Week Learning ObjectivesPupils will be taught to.....
Topic /Learning Area : 10. PLANS AND ELEVATIONS 2 weeks
17/2 - 21/2
24/2 - 28/2
10.1 Understand and use the concept of orthogonal projection.
i. Identify orthogonal projections.
ii. Draw orthogonal projections, given an object and a plane.
iii. Determine the difference between an object and its orthogonal projections with respect to edges and angles.
Use models, blocks or plan and elevation kit.Emphasise the different uses of dashed lines and solid lines.
Begin wth the simple solid object such as cube, cuboid, cylinder, cone, prism and right pyramid.
10.2 Understand and use the concept of plan and elevation.
i .Draw the plan of a solid object. ii. Draw-the front elevation-side elevation of a solid object
i. Draw the plan of a solid object.
iv. Draw-the front elevation- side elevation of a solid
Carry out activities in groups where students combine two or more different shapes of simple solid objects into interesting models and draw plans and elevation for thes models.
Use models to show that it is important to have a plan and at least two side elevation to construct a solid object.Carry out group project:Draw plan and elevations of buildings or structures, for example students’ or teacher’s dream home and construct a scale model based on the drawings. Involve real life situations such as in building prototypes and using actual home
Limit to full-scale drawings only.
Include drawing plan and elevation in one diagram showing projection lines.
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Week Learning ObjectivesPupils will be taught to.....
(iii) Draw the image of an object under combination of two transformations.
(iv) State the coordinates of the image of a point under combined transformations.
Give examples on the blackboard and students are asked to draw the image under 2 transformations
Tr. will state the coordinates of the image of a point under combined transformations.
(v) Determine whether combined transformation AB is equivalent to combined transformation BA.
Using Maths exercise books (grids) Do exercises from the textbooks
(vi) specify two successive transformations in a combined transformation given the object and the image
Outdoor activity – students are brought to specific site of the school compound and ask to identify the two successive transformations : pictures should consist of an object and an image.
(vii) Specify a transformation which is equivalent to the combination of two isometric transformations.
Classroom activities – use GSP and CD-ROM (Multimedia Gallery)
To specify isometric transformation Different examples to be given Various problem solving questions to be
given
- limit to translation, reflation & rotation.
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Week Learning ObjectivesPupils will be taught to.....
Topic/Learning Area : 6. GRADIENT & AREA UNDER A GRAPH ---( 2 1/2 weeks)
Catatan:
16/6 – 27/6 6.1 Understand and use the concept of quantity represented by the gradient of a graph
(i) State the quantity represented by the gradient of a graph
(ii) Draw the distance-time graph, given:
a) a table of distance-time values
b) a relationship between distance and time
(iii) Find and interpret the gradient of a distance-time graph
(iv) Find the speed for a period of time from a distance-time graph
(v) Draw a graph to show the relationship between two variables representing certain measurements and state the meaning of its gradient
Use examples in various areas such as technology and social science
Use of daily life examples like speed of a car, Formula One Grand Prix, a sprinter
Compare and differentiate between distance-time graph and speed-time graph
Use real life situations such as traveling from one place to another by train or by bus.
Use examples in social science and economy, for example, the increase in population in certain years
Limit to graph of a straight line.
The gradient of a graph represents the rate of change of a quantity on the vertical axis with respect to the change of another quantity on the horizontal axis. The rate of change may have a specific name for example ‘speed’ for a distance-time graph.
Emphasise that: Gradient = change of distance Time = speed
Include graphs which consists of a combination of a few straight lines.For example,
6.2 Understand the concept of quantityrepresented by the area under a graph
(i) State the quantity represented by the area under a graph
(ii) Find the area under a graph
(iii) Determine the distance by finding the area under the following of speed-time graphs:a. v=k (uniform speed)b. v=ktc. v=kt + hd. a combination of the above
Discuss that in certain cases, the area under a graph
may not represent any meaningful quantity.
For example:
The area under the distance-time graph.
Discuss the formula for finding the area under a
graph involving:
A straight line which is parallel to the x-axis
A straight lien in the form of y=kx+ hA combination of the above.
Include speed-time and acceleration-time
graphs.
Limit to graph of a straight line or a
combination of a few straight lines.
V represents speed, t represents time, h and k
are constants.
Week Learning ObjectivesPupils will be taught to.....
(i) Sketch a great circle through the north and south poles.(ii) State the longitude of a given
point.(iii) Sketch and label a meridian with
the longitude given.(iv) Find the difference between two
longitudes
Model such as globes should be used.Introduce the meridian through Greenwich in England as the Greenwich Meridian with longitude 0°Discuss that: All points on a meridian have the
same longitude There are two meridians on a great
circle through both poles. Meridians with longitude x°E(or W)
and (180°- x°)W(or E) form a great circle through both poles.
Emphasise that longitude 180°E and longitue 180°W refer to the same meridian.
Express the difference between two longitudes with an angle in the range of 0° ≤ x ≤ 180°
9.2 Understand and use the concept of latitude
(i) Sketch a circle parallel to the equator.(ii) State the latitude of a given point.(iii) Sketch and label a parallel of
latitude.(iv) Find the difference between two
latitudes.
Discuss that all the points on a paralell of latitude have the same latitude.
Emphasise that o the latitude of the equator is 0°o latitude ranges from 0° to 90°N
( or S )Involve actual places on the earth.Express the diffrence between two latitudes with an angle in the range of 0° ≤ x ≤ 180°.
9.3 Understand the concept of locations of a place.
Use a globe or a map to find locations of cities around the world.Use a globe or map to name a place given its location.
i. State the latitude and longitude of a given place
ii. Mark the location of a placeiii. Sketch and label the latitude and
longitude of a given place.
A place on the surface of the earth is represented by a point.The, location of a place A at latitude x°N and longitude y°E is written ,as A(x°N, y°E).
9.4 Understand and use the concept of distance on the surface on the earth to solve problems.
(i) Find the length of an arc of a great circle in nautical mile, given the subtended angle at the centre of the earth and vice versa.(ii) Find the distance between two points measured along a meridian, given the latitudes of both points.
Use the globe to find the distance between two cities or town on the same meridian.Sketch the angle at the centre of the earth that is subtentded by the arc between two given points along the equator. Discuss how to find the value of this angle.Use models such as the globe to find relationship
Limit to nautical mile as the unit for distance.
Explain one nautical mile as the length of the arc of a great circle subtending a one minute angle at the centre of the earth.
Speed, v
time, t
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Between the radius of the earth and radii parallel of latitudes.
Find the distance between two cities or towns on the same parallel of latitude as a group project.
Use the globe and a few pieces of string to show how to determine the shortest distance between two points on the surface of the earth
Limit to two points on the equtor or a great circle through the poles.
Use knot as the unit for speeed in navigation and aviation
Topic/Learning Area :
8. BEARING --- 1 week
7/8 – 8/88.1. Understand and use the concept of bearing.
(i) Draw and label the eight main compass directions:
a) north, south, east, westb) north – east, north – west, south –
east, south – westii) State the compass angle of any
compass direction.
(iii) Draw a diagram of a point which shows the direction of B relative to another point A given the bearing of B from A.
(iv) State the bearing point A from point B based on given information.
(iii) Solve problems involving bearing.
Carry out the activities or games involving finding directions using a compass such as treasure hunt or scravenger hubt. It can also be about locating several points on a map, finding the position of students in class.
Discuss the use of bearing in real life situations. For example, a map reading and navigation.
Compass angle and bearing are written in three digit form, from 0000 to 3600. They are measured in a clockwise direction from north. Due north is considered as bearing 0000. For cases involving degrees up to one decimal point.
Week Learning ObjectivesPupils will be taught to.....
Topic/Learning Area : 7. PROBABALITY II --- 2 weeks
5/7 (Ganti 19/11 SPM), 12/7 (Ganti 20/11)
30/6 – 11/7 7.1 Understand and use the concept of probability of an event.
(i) Determine the sample space of an experiment with equally likely outcomes.
(ii) Determine the probability of an event with equiprobable sample space.
(iii)Solve problems involving probability of an event.
Discuss equiprobable sample space through concrete activities and begin with simple cases such as tossing a fair coin.Use tree diagrams to obtain sample space for tossing a fair coin or tossing or tossing a fair dice activities. The Graphing calculator may also be
used to simulate these activities.Discuss events that produce P(A) = 1 and P(A) = 0
Limit to sample space with equally likely outcomes.A sample space in which each outcomes is equally likely is called equiprobable sample space.The probability of an outcome A, with equiprobable sample space
S, is P(A) = Use tree diagram where appropriate.Include everyday problems and making predictions.
7.2 Understand and used the concept of probability of the complement of an event.
(i) State the complement of an event in :
(a) words (b) set notations (ii) Find the probability of
the complement of an event.
Include events in real life situations such as winning or losing a game and passing or failing an exam.
The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.
7.3 Understand use the concept of probability of combined event.
(i) List the outcomes for events: (a) A or B as elements of set A B
Use real life situations to show the relationship between
A or B and A B A and B and A B.
An example of a situation is being chosen to be a member of an exclusive club with restricted
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(b) A and B as elements of set A B(ii) Find the probability by listing the outcomes of the combined events : (a) A or B (b) A and B
(iii) Solve problems involving probability of combined events.
conditions.Use tree diagram and coordinate planes to find all the outcomes of combined events.
Use two-way classification tables of events from newspaper articles or statistical data to find probability of combined events. Ask students to create tree diagrams from these tables. Example of a two-way classification table :
Means of going to workOfficers Car Bus OthersMen 56 25 83Women 50 42 37
Discuss : situations where decisions have to be
made on probability, for example in business, such as determining the value for aspecific insurance policy and time the slot for TV advertisements
the statement “probability is the underlying language of statistics”
Emphasise that : knowledge about probability is
useful in making decisions. prediction based on probability
is not definite or absolute.
Week Learning ObjectivesPupils will be taught to.....
Topic/Learning Area : 7. PROBABALITY II --- 2 weeks
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17/6-28/6
7.1 Understand and use the concept of probability of an event.
(i) Determine the sample space of an experiment with equally likely outcomes.
(ii) Determine the probability of an event with equiprobable sample space.
(iii)Solve problems involving probability of an event.
Discuss equiprobable sample space through concrete activities and begin with simple cases such as tossing a fair coin.Use tree diagrams to obtain sample space for tossing a fair coin or tossing or tossing a fair dice activities. The Graphing calculator may also be
used to simulate these activities.Discuss events that produce P(A) = 1 and P(A) = 0
Limit to sample space with equally likely outcomes.A sample space in which each outcomes is equally likely is called equiprobable sample space.The probability of an outcome A, with equiprobable sample space
S, is P(A) = Use tree diagram where appropriate.Include everyday problems and making predictions.
7.2 Understand and used the concept of probability of the complement of an event.
(i) State the complement of an event in :
(a) words (b) set notations (ii) Find the probability of
the complement of an event.
Include events in real life situations such as winning or losing a game and passing or failing an exam.
The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.
7.3 Understand use the concept of probability of combined event.
(i) List the outcomes for events: (a) A or B as elements of set A B (b) A and B as elements of set A B
(ii) Find the probability by listing the outcomes of the
Use real life situations to show the relationship between
A or B and A B A and B and A B.
An example of a situation is being chosen to be a member of an exclusive club with restricted conditions.Use tree diagram and coordinate planes to find all the outcomes of combined events.
Use two-way classification tables of events from newspaper articles or statistical data to find probability of combined events. Ask students to Emphasise that :
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combined events : (a) A or B (b) A and B
(iii) Solve problems involving probability of combined events.
create tree diagrams from these tables. Example of a two-way classification table :
Means of going to workOfficers Car Bus OthersMen 56 25 83Women 50 42 37
Discuss : situations where decisions have to be
made on probability, for example in business, such as determining the value for aspecific insurance policy and time the slot for TV advertisements
the statement “probability is the underlying language of statistics”
knowledge about probability is useful in making decisions.
prediction based on probability is not definite or absolute.
Topic/Learning Area : 8. BEARING --- 1 week
24/6 -28/68.1. Understand and use the concept of bearing.
(i) Draw and label the eight main compass directions:
a) north, south, east, westb) north – east, north – west,
south – east, south –
Carry out the activities or games involving finding directions using a compass such as treasure hunt or scravenger hubt. It can also be about locating several points on a map, finding the position of students in class.
Compass angle and bearing are written in three digit form, from 0000 to 3600. They are measured in a clockwise direction from north. Due north is considered as bearing 0000. For cases
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westii) State the compass angle
of any compass direction.
(iii) Draw a diagram of a point which shows the direction of B relative to another point A given the bearing of B from A.
(iv) State the bearing point A from point B based on given information.
(v) Solve problems involving bearing.
Discuss the use of bearing in real life situations. For example, a map reading and navigation.
involving degrees up to one decimal point.
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Week Learning ObjectivesPupils will be taught to.....