CHAPTER 1 NUMBER BASES MATHEMATICS 5

Transcription

1 CHAPTER NUMBER BASES MATHEMATICS 5 Number Bases Students will be tauht to:. Underst use the concept of number in base two, eiht five. Students will be able to: (i) State zero, one, two, three,, as a number in base: a) two b) eiht c) five (ii) State the value of a diit of a number in base: a) two b) eiht c) five (iii) Write a number in base: a) two b) eiht c) five in exped notation. ACTIVITIES Use models such as a clock face or a counter which uses a particular number base. Number base blocks of twos, eihts fives can be used to demonstrate the value of a number in the respective number bases. For example: Discuss diits used place values in the number system with a particular number base. ICT Cooperative Conceptual Compare contrast Rational Accurate Emphasise the ways to read numbers in various bases. Examples : 0 2 is read as one zero one base two is read as seven two zero five base eiht is read as four three two five base five Numbers in base two are also known as binary numbers. Examples of numbers in exped notation : 00 2 = = = Exped notation

2 CHAPTER NUMBER BASES MATHEMATICS 5 Students will be tauht to: Students will be able to: iv) convert a number in base : a) two b) eiht c) five to a number in base ten vice versa. v) convert a number in a certain base to a number in another base. ACTIVITIES Number base blocks of twos, eihts fives can also be used here. For example, to convert 0 0 to a number in base two, use the concept of least number of blocks (2 3 ), tiles (2 2 ), rectanles (2 ) squares (2 0 ). In this case, the least number of objects needed here are one block, zero tiles, one rectanle zero squares. So, 0 0 = Discuss the special case of convertin a number in base two directly to a number in base eiht vice versa. For example, convert a number in base two directly to a number in base eiht throuh roupin of three consecutive diits. ICT Cooperative Identify patterns Identify relations Arrane sequentially Consistent Perform repeated division to convert a number in base ten to a number in other bases. For example, convert 74 0 to a number in base five : 5)74 5) ) ) ) = Limit conversion of numbers to base two, eiht five only. Students will be tauht to: Students will be able to: (vi) Perform computations involvin : a) addition b) subtraction of two numbers in base two Perform addition subtraction in the conventional manner. For example : Communicat ion Method of Evaluation Arrane sequentially Usin alorithm relationship Appreciatio n of technoloy Cooperation Prudence 2

3 CHAPTER 2 GRAPHS OF FUNCTIONS II MATHEMATICS 5 Graphs of functions Students will be tauht to: 2. Underst use the concept of raphs of functions. Students will be able to: (i) Draw the raph of a ; a) linear function; y = ax + b, where a b are constants b) quadratic function; 2 y = ax + bx + c, where a, b c are constants, a 0 c) cubic function : 3 2 y = ax + bx + cx + d, where a,b,c d are constants, a 0 d) reciprocal function : a y =, where a is a x constants, a 0. ACTIVITIES Explore raphs of functions usin raphin calculator or the Geometer s Sketchpad. Compare the characteristics of raphs of functions with different values of constants. For example : A Constructivism Mastery Self-access Concept constructivis m Compare contrast Analisin Mental visualization Relationship Punctuality Awareness Neatness Limit cubic functions to the followin forms: 3 y = ax 3 y = ax + b 3 y = ax + bx + c Students will be tauht to: (ii) Find from a raph : a) the value of y, iven a value of x b) the value(s) of x, iven a value of y. Students will be able to: iii) Identify: a) the shape of raph iven a type of function b) the type of function iven a raph c) the raph iven a function vice versa. B Graph B is broader than raph A intersects the vertical axis above the horizontal axis. As reinforcement, let students play a ame; for example, matchin card of raphs with their respective function. When the students have their matchin partners, ask them to roup themselves into four roups of types of functions. Finally, ask each roup to name the type of function that is depicted on the cards. ACTIVITIES - Mastery - Cooperative. - - Comparin & differentiatin - Classifyin - patterns - Accuracy - For raph of cubic function, limit to y = ax 3 y = ax 3 + b. For raph of quadratic function limit to y = ax 2 + b quadratic function which can be factorise to ( mx + n) ( px + q) where m.n.p POINTS q are inteers TO NOTE / 3

4 CHAPTER 2 GRAPHS OF FUNCTIONS II MATHEMATICS 5 iv) Sketch the raph of a iven linear,quadratic,cubic or reciprocal function. - Graphs of function - Graph of linear function - Graph of quadratic function - Graph of cubic function - Graphs of reciprocal function For raph of cubic function, limit to y = ax 3 y = ax 3 + b Students will be tauht to: 2.2 Underst use the concept of the solution of an equation by raphical methods. Students will be able to: i) Find the point(s) of intersection of two raphs. (ii) Obtain the solution of an equation by findin the point(s) of intersection of two raphs. (iii) Solve problems involvin solution of an equation by raphical method. Explore usin raphin calculator or the Geometer s Sketchpad to relate the x- coordinate of a point of intersection of two appropriate raph to the solution of a iven equation. Make eneralization about the point(s) of intersection of the two raphs. - Self access - Coopera tive - Constru ctivisme - relation - Mental visualization (i)identifyin patterns. (ii)identifyin relations. (iii)reconiz in representi n. (iv)represe ntin interpret in data. - - Neatness - Precise -Rationale -Dilience - -Accuracy - To sketch a raph - To draw a raph Use the traditional raph plottin exercise if the raphin calculator or the Sketchpad is unavailable. Involve everyday problems. ACTIVITIES 4

5 CHAPTER 2 GRAPHS OF FUNCTIONS II MATHEMATICS 5 Students will be tauht to: 2.3 Underst use the concept of the reion representin in inequalities in two variables Students will be able to: i) Determine whether a iven point satisfies : y = ax + b or y > ax + b or y < ax + b ii) Determine the position of a iven point relative to the equation y = ax + b iii) Identify the reion satisfyin y > ax + b or y < ax + b iv) Shade the reions representin the inequalities a) y > ax + b or y < ax + b y ax + y ax + b b) b or v) Determine the reion which satisfies two or more simultaneous linear inequalities. Discuss that if one point in a reion satisfies y > ax + b or y < ax + b, then all point in the reion satisfies the same inequalities. Use the Sketchpad or raphin calculator to explore points relative to a raph to make eneralization about reions satisfyin the iven inequalities. Enquirydiscovery Constructivis m patterns Determinati on Makin inferences For Objectives 2.3, include situations involvin x = a, x a, x > a, x a, x < a reion dashed line Emphasise that: - For the reion representin y > ax + b or y < ax + b,the line y = ax + b is drawn as a dashed line to indicate that all points on the line are not in the reion. - For the reion representin or y ax + b y ax + b y = ax + b, the line is drawn as a solid line to indicate that all points on the line y = ax + b are in the reion. Solid line 5

6 CHAPTER 3 TRANSFORMATIONS III MATHEMATICS 5 3. TRANSFORM ATIONS III Students will be tauht to: 3. Underst use the concept of combination of two transformations. Students will be able to: i. Determine the imae of an object under combination of two isometric transformations. ACTIVITIES Relate to transformations in real life situations such as tessellation patterns on walls, ceilins or floors Constructivi sm relations Characterizi n Determinati on Accuracy Bein with a point, followed by a line a object ii. Determine the imae of an object under combination of a. two enlarements. b. an enlarement an isometric transformation. Explore combined transformation usin the raphin calculator, the eometer s Sketchpad, or the overhead projector transparencies. Mastery Comparin Differentiati n Interpretin Relation Rules Reulations Self Confidence Neatness Limit isometric transformations to translations, reflections rotations. iii. Draw the imae of object under combination of two transformations. Investiated the characteristics of object its imae under combined transformation Multiple Intellience theory Drawin Diarams Relation iv. State the coordinates of the imae of a point under combined transformation. Constructivi sm Relation Arranin Sequentially Dilience Accuracy Consistent Combined transformation. 6

7 CHAPTER 3 TRANSFORMATIONS III MATHEMATICS 5 v. Determine whether combined transformation AB is equivalent to combined transformation BA ACTIVITIES Multiple Intellience Comparin Differentiati n Relation Rational Cautious Equivalent vi. Specify two successive transformation in a combined transformation iven the object the imae Carry out projects to desin patterns usin combined transformations that can be used as decorative purposes. These projects can then be presented in classroom with the students describin or specifyin the transformations involved. Mastery Patterns Relation Loical Reasonin Hardworkin Specify Representin Interpretin Data vii. Specify a transformation which is equivalent to the combination of two isometric transformations. Use the Sketchpad to prove the sinle transformation which is equivalent to the combination of two isometric transformations. Mastery ICT Usin Analoies Workin Out Mentally Honesty Cooperation Limit the equivalent 7

8 CHAPTER 3 TRANSFORMATIONS III MATHEMATICS 5 ACTIVITIES viii. Solve problems involvin transformation. a. How to make a frieze or strip pattern. b. Constructin a kaleidoscope. Mastery ICT Find all possible solution Usin Analoies Sharin Rational Dilience Drawin Diaram Workin out Mentally 8

9 CHAPTER 4 MATRICES MATHEMATICS 5 Matrices Students will be tauht to: 4. underst use the concept of matrix. Students will be able to: i) form a matrix from iven information. ACTIVITIES Represent data in real life situations, for example, the price of food on a menu, in table form then in matrix form. Constructivis m Arranin sequentially Collectin hlin data Neatness systematic Emphasize that matrices are written in bracket. Matrix, row matrix, column matrix, square matrix ii) Determine : a) the number of rows b) the number of columns c) the order of a matrix iii) Identify a specific element in a matrix. Use students sittin positions in the classroom by rows columns to identify a student who is sittin in a particular row in a particular column as a concrete example. Mastery patterns patterns Accurate Emphasize that a matrix of order m x n is read as an m by n matrix Use row number column number to specify the position of an element. 4.2 Underst use the concept of equal matrices. i) Determine whether two matrices are equal. ii) Solve problems involvin equal matrices. Discuss equal matrices in terms of : a) the order b) the correspondin elements Mastery Usin alorithm relationship Comparin differentiatin Accurate Equal matrices Includin findin values of unknown elements. 9

10 CHAPTER 4 MATRICES MATHEMATICS 5 ACTIVITIES 4.3 Perform addition subtraction on matrices. i) Determine whether addition or subtraction can be performed on two iven matrices. ii) Find the sum or the difference of two matrices. iii) Perform addition subtraction on a few matrices. Relate to real life situations such as keepin scores of metals, tally or points in sport. Self-access Constructivi sm Mastery Communicat ion method of Comparin differentiati n Usin alorithm relationship Problem solvin Cooperation Rationale Confidence Limit to matrices with not more than three rows three columns. iv) Solve matrix equation involvin addition subtraction Multiple intelliences Mastery Future studies Usin alorithm relationship Analyzin Makin inferences Problem solvin Include findin values of unknown elements/matrix equation 4.4 perform multiplication of a matrix by a number. i) Multiply a matrix by a number. ii) Express a iven matrix as a multiplication of another matrix by a number. iii) Perform calculation on matrices involvin addition, subtraction scalar multiplication. Relate to real life situations such as in industrial productions Mastery Constructivis m Self-access Evaluatin Usin alorithm relationship Conceptuali ze findin all possible solutions systematic Multiplyin a matrix by a number is known as scalar multiplication 0

11 CHAPTER 4 MATRICES MATHEMATICS 5 iv) Solve matrix equations involvin addition, subtraction scalar multiplication. ACTIVITIES Self-access Constructivis m Self-access Evaluatin problems solvin Include findin the values of unknown elements 4.5 Perform multiplication of two matrices i. Determine whether two matrices can be multiplied state the order of the product when the two matrices can be multiplied. ii. Find the product of two matrices iii.solve matrix equations involvin multiplication of two matrices. Relate to real life situations such as findin the cost of a meal in a restaurant. For matrices A B, discuss the relationship between AB BA. Constructi vism ICT Cooperati ve Identifyin patterns Arranin sequentiall y Reconizi n representin Makin eneralizati on classifyin Determin ation Systemat ic Consiste nt Dilience Neatness The number of columns of first matrix must be same with the number of rows of second matrix. The order of the matrices : (m x n) x (n x s) = (m x s) Limit to matrices with not more than three rows three columns. Limit to two unknown elements.

12 CHAPTER 4 MATRICES MATHEMATICS Underst use the concept of identity matrix. i) Determine whether a iven matrix is an identity matrix by multiplyin it to another matrix. ACTIVITIES Bein with discussin the property of the number as an identity for multiplication of numbers. Makin eneralizati on Rational Identity matrix is usually denoted by I is also known as unit matrix. Identity matrix unit matrix. ii) Write identity matrix of any order. iii) Perform calculation involvin identity matrices. Discuss:. an identity matrix is a square matrix. there is only one identity.matrix for each order. Discuss the properties:. AI = A. IA = A Constructi vism Identifyi n patterns Systemati c Limit to matrices with no more than three rows three columns. 4.7 Underst use the concept of inverse matrix. (i) Determine whether a 2 x 2 matrix is the inverse matrix of another 2 x 2 matrix. a) (ii) Find the inverse Relate to the property of multiplicative inverse of numbers. For example : 2x2 = 2 x2 = In the example, 2 is the multiplicative inverse of 2 vice versa. Use the method of solvin simultaneous linear equations to show that not all square matrices have inverse matrices. For Cooperativ e Constructi vism Mastery Solvin problems Comparin Identifyin patterns relations Neatness Cooperati on Neatness Systemati c The inverse of matrix A is denoted by A. Emphasize that: If matrix B is the inverse of matrix A, then matrix A is also the inverse of matrix B, AB = BA = I Inverse matrices can only exist for square matrices, but not all square matrices have inverse matrices. 2

13 CHAPTER 4 MATRICES MATHEMATICS 5 matrix of a 2 x 2 matrix usin : b) the method of solvin simultaneous linear equations a formula. ACTIVITIES example, ask student to try to find the inverse matrix of Usin matrices their respective inverse matrices in the previous method to relate to the formula. Express each inverse matrix as a multiplication to the oriinal matrix discuss how the determinant is obtained Constructi vism Mastery Communi cation method of Comparin Identifyin patterns relations Cooperati on Neatness Systemati c Steps to find the inverse matrix : Solvin simultaneous linear equations 2 p q 0 = 3 4 r s 0 p + 2r =, 3p + 4r = 0 q + 2s = 0, 3q + 4s = p q where r s is the inverse matrix. Usin formula a b For A =, c d d A = ad bc c ad bc b ad bc a ad bc or 3

14 CHAPTER 4 MATRICES MATHEMATICS 5 ACTIVITIES d b A = ad bc c a when ad bc 0. ad bc is known as the determinant of the matrix A. 4.8 Solve simultaneous linear equations by usin matrices (i) Write simultaneous linear equations in matrix form. p (ii) Find the matrix q in a b p h = c d q k Usin the inverse matrix. Relate to equal matrices by writin down the simultaneous equations as equal matrices first. For example: Write 2x + 3y = 3 4x y = 5 As equal matrices: 2x + 3y 3 = 4x y 5 which is then expressed as: 2 3 x 3 = 4 y 5 Discuss why: The use of inverse matrix is necessary. Relate to solvin linear equations of type ax = b It is important to place the inverse matrix at the riht place on both sides of the equation. Mastery Constructi vism Multiple Intellience s Constructi vism Identifyin Patterns Identifyin Relations Rational Systemati c Neatness A - does not exist if the determinant is zero. Prior to use the formula, carry out operations leadin to the formula. Limit to two unknowns. Simultaneous linear equations ap + bq = h cp + dq = k in matrix form is a b p h = c d q k Where a, b, c, d, h k are constants, p ad q are constants, p q are unknowns. A a c b p = A d q h k 4

15 CHAPTER 4 MATRICES MATHEMATICS 5 (iii) Solve simultaneous linear equations by the matrix method. (iv) Solve problems involvin matrices. ACTIVITIES Relate the use of matrices to other areas such as in business or economy, science etc. Carry out projects involvin matrices usin the electronic spreadsheet. Cooperati ve Selfaccess Mastery ICT Identifyin Patterns Identifyin Relations Represent in & Interpretin Data Rational Systemati c Neatness Rational Systemati c Neatness a b Where A =. c d The matrix method uses inverse matrix to solve simultaneous linear equations. Matrix method 5

16 CHAPTER 5 VARIATIONS MATHEMATICS 5 VARIATIONS Students will be tauht to: 5. Underst use the concept of direct variation Students will be able to: (i)state the chanes in a quantity with respect to the chanes in another quantity, in everyday life situations involvin direct variation. (ii)determine from iven information whether a quantity varies directly as another quantity. (iii)express a direct variation in the form of equation involvin two variables. ACTIVITIES Discuss the characteristic of the raph of y aainst x when y x. Relate mathematical variation to other area such as science technoloy. For example, the Charles Law or the mation of the simple pendulum. Self- access Communicati on Method of Leanin relations Makin eneralization Estimatin Rationale Tolerance Hardworkin Y varies directly as x if only if x y is a constant. If y varies directly as x, the relation is written as y x. For the cases n y x, limit n = 2, 3,. 2 (iv)find the value of a variable in a direct variation when sufficient information is iven. (v)solve problems involvin direct variations for the followin cases: y x ; 2 y x ; 3 y x ; For the cases n y x, n = 2, 3,, discuss the 2 characteristics of the raph of y n aainst x. If y x, then y = kx where k is constant of variation. y = kx y y = 2 x x Usin ;or 2 to et the solutions. 2 y x : Direct variation Quantity Constant of variation Variable. 6

17 CHAPTER 5 VARIATIONS MATHEMATICS Underst use the concept of inverse variations i) State the chanes in a quantity with respect to chanes in another quantity, in everyday life situations involvin inverse variation. ii) Determine from iven information whether a quantity varies inversely as another quantity. iii) Express a inverse variation in the form of equation involvin two variables. iv) Find the value of a variable in an inverse variation when sufficient information is iven. v) Solve problems involvin inverse variation for the followin cases: y ; y ; 2 x x y ; y 3 x 2 x ACTIVITIES Discuss the form of the raph of y aainst x when y x. Relate to other areas like science technoloy. For example, Boyle s Law. For the cases y, n = 2,3 n, discuss x 2 the characteristics of the raph of y aainst. n x Contructivism Communicati on method of Cooperative Makin inferences Representin interpretin data relations Problem Solvin Rational Rational Accuracy y varies inversely as x if only if xy is a constant. If y varies inversely as x, the relation is written as y x. For the cases y, limit n to 2,3 n x. 2 If y x, then k y = x where k is the constant of variation. Usin: k y = or x x x y = 2 y2 to et the solution. : Inverse variation 7

18 CHAPTER 5 VARIATIONS MATHEMATICS 5 ACTIVITIES 5.3 Underst use the concept of joint variation. i) Represent a joint variation by usin the symbol for the followin cases: a) two direct variations. b) two inverse variations. c) a direct variation an inverse variation. ii) Express a joint variation in the form of equation. iii) Find the value of a variable in a joint variation when sufficient information is iven. iv) Solve problems involvin joint variation. Discuss joint variation for the three cases in everyday life situations. Relate to other areas like science technoloy. For example: V I means the current I varies R directly as the voltae V varies inversely as the resistance R. Constructivism Cooperative Multiple intelliences Self access Mastery relations comparin differentiatin collectin hlin data usin analoies findin all possible solutions Cooperation Punctuality Rational For the cases n n y x z, y n n x z n x y, limit n to 2, n z 3, 2. Joint variation 8

19 CHAPTER 6 GRADIENT MATHEMATICS 5 Gradient area under a raph Students will be tauht to: 6. Underst use the concept of quantity represented by the radient of a raph. Students will be able to: (i) State the quantity represented by the radient of a raph. (ii) Draw the distancetime raph, iven ; a) a table of distance-time values. b) a relationship between distance time. ACTIVITIES Use examples in various areas such as technoloy social science. Compare differentiate between distance-time raph speed-time raph. Reconizin representin Comparin differentiati n Interpretin data Rationality Respect Limit to raph a straiht line. The radient of a raph represents the rate of chane of a quantity on the vertical axis with respect to the chane of another quantity on the horizontal axis. The rate of chane may have a specific name for example speed for a distance time raph. (iii) Find interpret the radient of a distance-time raph. Emphasis that: Gradient chane of distance = chane of time =speed Distance-time raph Speed-time raph 9

20 CHAPTER 6 GRADIENT MATHEMATICS 5 ACTIVITIES (iv) Find the speed for a period of time from a distance-time raph. Use real life situation such as travelin from one place to another by train or by bus. Include raphs which consist of a combination of a few straiht lines. For example: distance, s time, t (v) Draw a raph to show the relationship between two variables representin certain measurements state the meanin of its radient. Use examples in social science economy. 6.2 Underst the concept of quantity represented by the area under a raph. (i) State the quantity represented the area under a raph. (ii) Find the area under a raph. (iii) Determine the distance by findin the area under the followin types of speed-time raph: (a) v = k Discuss that in certain cases, the area under a raph may not represent any meaninful quantity. For example: The area under the distance-time raph. Discuss the formula for findin the area under a raph involvin; a straiht line which is parallel to the x-axis a straiht line in the form of Constructivis m Reconisin representin Respect Include speed-time acceleration-time raphs. Limit to raph of a straiht line of a combination of a few straiht lines. v represents speed, t represents time, h k are constants. 20

21 CHAPTER 6 GRADIENT MATHEMATICS 5 ACTIVITIES (uniform speed) (b) v = kt (c) v = kt + h (d) a combination of the above. y= kx + h a combination of the above. For example: Speed, v (v) Solve problems involvin radient area under a raph. time, t area under a raph acceleration-time raph uniform speed 2

22 CHAPTER 7 PROBABILITY II MATHEMATICS 5 Probability II Students will be tauht to: 7.Underst use the concept of probability of an event. Students will be able to: 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 involvin probability of an event. ACTIVITIES Discuss equiprobable sample throuh concrete activities bein with simple cases such as a. toss a fair coin b. ive a TRUE or FALSE question. Find the probability. Use tree diarams to obtain sample space for tossin a fair coin or tossin a fair die activities. The raphin calculator may also be used to simulate these activities. Discuss event that produce (a) P(A) =. Tossin a fair coin. P( Head) + P(Tail) =. (b) P(A) = 0 Climbin up the twin tower. Drillin exercise. Mastery Makin inference Workin out mentally Findin all possible solutions. Findin all possible solutions. Determinati on Cooperation Rational Limit to sample space with equally likely outcomes. Equally likely A sample space in which each outcome is equally likely is called equiprobable sample space. The probability of an outcome A, with equiprobable sample space S, is P(A)= n(a) n(s) Use tree diaram where appropriate. Include everyday problems makin predictions. 22

23 CHAPTER 7 PROBABILITY II MATHEMATICS Underst use the concept of probability of the complement of an event. (i)state the complement of an event in : a) words b) set notation (ii) Find the probability of the complement of an event ACTIVITIES Discuss equiprobable sample space throuh activities such as findin the consonants vowels from the word iven. Include events in real life situations such as winnin or losin a ame passin or failin an exam. Constructivism relations Findin all Possible solutions Makin inferences Cooperation Equity Rationale Precise 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 Underst use the concept of probability of combined event i) List the outcomes for events : a) A or B as elements of set A B ii) Find the probability by listin the outcomes of the combined event : a) A or B Example i: A coin is tossed twice consecutively. List the probability for each combined event a) Q = An event to et the numbers at the first o or both times showin the pictures Q = { NP, NN, PP} b) R = An event to et the picture at the second toss or both times showin the number. R= {NP, PP, NN } Mastery Enquiry Discovery Drawin diarams Estimatin Patterns Relations Findin all possible solutions Tolerance Determination Consistent Event Combined event Consecutively Toss Example ii: Find the probability by listin the outcomes of the combined event a) S = { NP, NN, PN, PP} n(s) = 4 Q = { NP, NN, PP} n(q) = 3. 23

24 CHAPTER 7 PROBABILITY II MATHEMATICS 5 (i) list the outcomes for events A B as elements of set A B ACTIVITIES P(Q) = n( Q) n( S) = 4 3. Ask D one student to toss 2 coins at the same time. D2 2. Fill in the outcomes. A G A {A,A} {A,G} G {G,A} {G,G} relations Findin all possible solution Drawin diaram Cooperation Rational Combined event 3. List the outcomes for different event A A = {(A,A)} A G = {(A,G), (G,A)} G G = { (G,G)} 4. State the relationship between &. A A = A A A G = A G G G = G G 5. The total number of the event n(a A) = n(a G) = 2 n(g G) = 24

25 CHAPTER 7 PROBABILITY II MATHEMATICS 5 (ii) Find the probability by listin the outcomes of the combined event A B ACTIVITIES. Split the class into the roup 2. Each roup will be iven one coin one dice. 3. List out all the possible combination when toss the coin dice at the same time { (A,), (A,2), (A,3), (A,4), (A,5), (A,6) (G,), (G,2), (G,3), (G,4), (G,5), (G,6)} relations Findin all possible solution Drawin diaram Cooperation Rational Combined event 4. Find the probability of ettin a when rollin a coin is A. P(A ) = 2 5. Introduce a tree diaram 6. Based on tree diaram, find the probability of :- (a) ettin A (b) ettin P(A) = 2 P() = 6 7. The probability to ettin A can be written as P(A ) = P(A) P() = 2 6 = 2 25

26 CHAPTER 7 PROBABILITY II MATHEMATICS 5 (iii) Solve problems involvin probability of combined event. ACTIVITIES Use two-way classification tables of events from newspaper articles or statistical data to find probability of combined events. Ask students to create tree diarams from these tables. Example of a two-way classification table: MEANS OF GOING TO WORK Offic Car Bus Oth ers ers Men Wo men Discuss: situations where decision have to made based on probability, for example in business, such as determinin the value for specific insurance policy time the slot for TV advertisements the statement probability is the underlyin lanuae of statistics. ICT Mastery Self-access Relations Makin Generalizations Makin Inferences hypothesis Neatness Responsibility Emphasis that: knowlede about probability makin decisions predictions as based on probability is not definite or absolute. 26

27 CHAPTER 8 BEARING MATHEMATICS 5 8 BEARING Students will be tauht to : Students will be able to : ACTIVITIES 8. Underst use the concept of bearin (i) Draw label the eiht main compass directions: (a) north, south, east, west (b) north-east, northwest, south-east, south-west (ii) State the compass anle of any compass direction Carry out activities or ames involvin findin directions usin a compass, such as treasure hunt or scavener hunt. It can also be about locatin several points on a map Constructivi sm Cooperative Multiple intellience Makin connections Visualize mentally Makin connections Visualize mentally Cooperation Accuracy Neatness Carefulness North east South east North-west South-west Compass anle bearin Compass anle bearin are written in three-diit form, 000o to 360 o. They are measured in a clockwise direction from north. Due north is considered as bearin 000 o. For cases involvin derees minutes, state in derees up to one decimal point. (iii) Draw a diaram of a point which shows the direction of B relative to another point A iven the bearin of B from A Comparin differentiatin 27

28 CHAPTER 8 BEARING MATHEMATICS 5 (iv) State the bearin of point A from point b based on iven information ACTIVITIES Mastery Constructivi sm Self-access (Mathematic al-loical Verballinuistic) Makin connections Visualize mentally Rational Accuracy Carefulness Bein with the case where bearin of point B from point A is iven (v) Solve problems involvin bearin Discuss the use of bearin in real life situations. For example, in map readin naviation Constructivi sm Self-access (Mathematic al-loical Verballinuistic) Communicat ion Interpret Draw diarams Reconizin relationship Problem solvin Accuracy Rational Responsibili ty Appreciatio n 28

29 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS 5 EARTH AS A SPHERE Students will be tauht to: 9. Underst use the concept of lonitude. Students will be able to: (i) Sketch a reat circle throuh the north south poles. (ii) State the lonitude of a iven point. (iii) Sketch label a meridian with the lonitude iven. (iv) Find the difference between two lonitudes. ACTIVITIES Models such as lobes should be used. Introduce the meridian throuh Greenwich in Enl as the Greenwich Meridian with lonitude 0 0 Discuss that: (a) all points on a meridian have the same lonitude. (b) There two meridians on a reat circle throuh both poles. (c) Meridians with lonitudes x o E (or W) ( x 0 )W (or E) form a reat circle throuh both poles. Constructivis m patterns relations Understin Great circle Meridian Lonitude 9.2 Underst use the concept of latitude (i) Sketch a circle parallel to the equator. Usin any computer software to sketch a circle parallel to the equator. Constructivi sm Self-access Drawin diarams Rational Equator (ii) State the latitude of a iven point. Latitude Emphasize that * the latitude of the equator is 0 * latitude ranes from 0 to 90 N(or S) 29

30 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS 5 (iii)sketch label a parallel of latitude. ACTIVITIES Discuss that all points on a parallel of latitude have the same latitude Parallel of latitude (iv) Find the difference between two latitudes. Carry out roup activity such as station ame. Each station will have different diaram the student will be ask to find the difference between two latitudes for each diaram. Cooperative Enquirydiscover y Communicati on method of Findin all possible solutions Loical reasonin Reconizin & interpretin data Cooperation Sharin Tolerance Involve actual places on the earth Express the difference between two latitudes with an anle in the rane of 0 x Underst he concept of location of a place. (i) State the latitude lonitude of a iven place. (ii) Mark the location of a place. (iii)sketch label the latitude lonitude of a iven place. Use a lobe or a map to find locations of cities around the world. Use a lobe or a map to name a place iven its location., Constructivis m, Communicati on Method of. Loical Reasonin, Relation, Reconizin Representin., Neatness, Public Spiritedness. A place on the surface of the earth is represented by a point. The location of a place A at latitude x N lonitude y E is written as A(x N, y E). 9.4 Underst use the concept of distance on the surface of the earth to solve problems (i) find the lenth of an arc of a reat circle in nautical mile, iven the subtended anle at the centre of the earth vice versa relations Rational 30

31 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS 5 (ii) find the distance between two points measured alon a meridian, iven the latitudes of both points. (iii) find the latitude of a point iven the latitude of another point the distance between the two points alon the same meridian. (iv) find the distance between two points measured alon the equator, iven the lonitudes of both points. ACTIVITIES Use the lobe to find the distance between two cities or town on the same meridian. Sketch the anle at centre of the earth that is subtended by the arc between two iven points alon the equator. Discuss how to find the value of this anle Contextu al Enquiry discovery Constructi vism Enquiry discover y Representin interpretin data Drawin diarams (v) find the lonitudes of a point iven the lonitude of another point the distance between the two points alon the equator. (vi) state the relations between the radius of the earth the radius of a parallel of latitude. (vii) state the relation between the lenth of an arc on the equator between two meridians the lenth of the correspondin arc on a parallel of latitude. Use models such as the lobe, to find relationships between the radius of the earth radii parallel of latitudes Cooperativ e Enquiry discovery Constructi vism Communic ation Method of relations relations Neatness Rational 3

32 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS 5 (viii) find the distance between two points measured alon a parallel of a latitude. ACTIVITIES Find the distance between two cities or towns on the same parallel of latitudes as a roup project. Mastery Cooperation Tolerance Sharin (ix) find the latitude of a point iven the lonitude of another point the distance between the points alon a parallel of latitude. (x) Find the shortest distance between two points on the surface of the earth. (xi) Solve problems involvin :- (a) distance between two points (b) travelin on a surface of the earth. Use the lobe a few pieces of strin to show how to determine the shortest distance between two points on the surface of the earth. Cooperati ve Multiple Enquiry discovery Self access Cooperati ve Self access Mastery Thinkin skills Drawin diarams Comparin & differentiatin Makin inferences Cooperation Sharin Tolerance Rational 32

33 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS 5 0.Plans Elevations Students will be tauht to : 0. Underst use the concept of orthoonal projection Students will be able to 0.. Identify orthoonal projection 0..2 Draw orthoonal projection,iven an object a plane 0..3 Determine the difference between an object ACTIVITIES Use models, blocks or plan elevation kit Mastery Comparin Differenti atin Visualizati on Identifyin relationshi p Accuracy Creative thinkin Systemati c Emphasize the different uses of dashed lines solid lines Bein with simple solid objects such as cubic, cuboids, cylinder, cone, prism riht pyramid Vocab Orthoonal projection 0.2 Underst use the Concept of plan elevation 0.2. Draw the plan of a solid Object Draw a) the front elevation b) side elevation of a solid object Carry out activities in roups where students combine two or more different shapes of simple solid objects into interestin models draw plans elevations for these models Mastery Self access Analyzin Synthesizi n Accuracy Creative thinkin Systemati c Self Confident Neatness Limit to full scale drawins only Include drawin plan elevation in one diaram showin projections lines 33

34 CHAPTER 0 PLANS AND ELEVATION MATHEMATICS Draw a) the plan b) the front elevation c) the side elevation of a solid object to scale Solve problems involvin plans elevation ACTIVITIES Use models to show that it is important to have a plan at least two side elevations to construct a solid object. Carry out roup project: Draw plan elevation of buildins or structures, for example students or teachers dream home construct a scale model based on the drawins. Involve real life situations such as in buildin prototypes usin actual home plans Constructi vism Identifyin Relationsh ip Dedicatio n Determina tion Vocab Plan Front elevation Side Elevation 34