Yearly Plan – Mathematics Form 5 Week No Learning Objectives Pupils will be taught to..... Learning Outcomes Pupils will be able to… No of Periods Suggested Teaching & Learning activities/Learning Skills/Values Points to Note Learning Area : NUMBER BASES -- 2 weeks First Term 1 1. Understand and use the concept of number in base two, eight and five. 2/1/2012-8/1/2012 (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 1 1 2 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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(v) Convert a number in a certain base to a number in another base.
(vi) Perform computations involving :
a) addition b) subtration of two numbers in base two
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Discuss the special case of converting 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
Limit conversion of numbers to base two, eight and five only.
The usage of scientific calculator in performing the computitations.
Topic 2 : Graphs of Functions II --- 3 weeks
32.1 Understand and
use the concept of graphs of functions
16/1/2012-22/1/2012
(i) Draw the graph of a: a) linear function : y = ax + b, where a and b are constant; b) quadratic function , where a, b and c are constans, c) cubic function : , where a, b, c and d are constants,
d) reciprocal function
, where a is a
constants,
2 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 ; a and b are numerical values.
(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.
CHINESE NEW YEAR
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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.
4 2.2 Understand and use the concept of the solution of an equation by graphical method.
30/1/2012-5/2/2012
(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
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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.
(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.
2 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.
220/2/2012-26/2/2012
(v) Determine whether combined transformation AB is equivalent to combined transformation BA.
3 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.
327/2/2012-29/2/2012
(vii) Specify a transformation which is equivalent to the combination of two isometric transformations.
(viii) Solve problems involving transformations.
5 Classroom activities – use GSP and CD-ROM (Multimedia Gallery)
6.1 Understand and use the concept of quantity represented by the gradient of a graph
25/4/2012-29/4/2012
30/4/2012-6/5/2012
(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
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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
7/5/2012-10/5/2012
11/5/2012-25/5/2012
26/5/2012-10/6/2012
(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
(iv) Solve problems involving gradient and area under a graph.
SECOND SCHOOL EXAMINATION
SCHOOL HOLIDAYS
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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. For example:
2 7.3 Understand use the concept of probability of combined event.
18/6/2012-24/6/2012
(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 combined events : (a) A or B (b) A and B
(iii) Solve problems involving probability of combined events.
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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 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
(i) Draw and label the eight main compass directions:
a) north, south, east, west
b) north – east, north – west, south – east, south – west
ii) 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.
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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.
place. Use a globe or map to name a place given its location.
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ii. Mark the location of a place
iii. Sketch and label the latitude and longitude of a given place.
iv.
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.
(iii)Find a latitude of a point given the latitude of another point and the distance between the two points along the same meridian.(iv) Find the distance between two points measured along the equator, given the longitude of both points.(v) Find the longitude of a point given the longitude of another point and the distance between the two points along the equator.
(vi) State the relation betwen the radius of the earth and the radius of a parallel of latitude.
(vii) State the relation between the length of an arc on the equatoq between two meridian and the lengthe of the corresponding arc on a parallel of latitude.
(viii) Find the distance between two points measured along a parallel of latitude.
(ix) Find the longitude of a point given the longitude of another point and the distance between the two points along a parallel of latitude.
(x) Find the shortest distance between two points on the surface of the earth.
(xi) Solve problems involving : (a) distance between two 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 between the radius of the earth and radii parallel of latitudes.
Find the distance between two cities or town 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 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.
1 10.1 Understand and use the concept of orthogonal projection.
9/7/2012-15/7/2012
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.
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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.
2 10.2 Understand and use the concept of plan and elevation.
16/7/2012-22/7/2012
i. Draw the plan of a solid object.
ii. Draw- the front elevation- side elevation
of a solid object
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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 plans.
Include drawing plan and elevation in one diagram showing projection lines.