Mathematics form-5

CHAPTER 1– NUMBER BASES MATHEMATICS 5

LEARNING LEARNING LEARNING SUGGESTED TEACHING & MORAL POINTS TO NOTE /
WEEKS GENERICS CCTS
AREA OBJECTIVES OUTCOMES LEARNING ACTIVITIES VALUES VOCABULARY
Number Bases Use models such as a clock face
or a counter which uses a ICT Systematic
Students will be able to: Conceptual Emphasise the ways to
Students will be particular number base. Contextual
taught to: Number base blocks of twos, learning Rational read numbers in various
(i) State zero, one, two, Compare bases.
eights and fives can be used to Cooperative
three,…, as a number in demonstrate the value of a and contrast Examples :
1. Understand and learning Accurate
base: number in the respective number • 1012 is read as “one
use the concept of
a) two zero one base two”
number in base two, bases.
b) eight
eight and five. • 72058 is read as
c) five
For example: “seven two zero five
2435 base eight”
(ii) State the value of a
• 43255 is read as “ four
digit of a number in base:
three two five base
a) two
five”
b) eight
c) five
Numbers in base two are
also known as binary
(iii) Write a number in
numbers.
base:
Examples of numbers in
a) two
expanded notation :
b) eight
• 101102= 1×24 + 0×23 +
c) five
2 4 3 1×22 + 1×21 + 0×20
in expanded notation.
• 3258 = 3×82 +2×81 +
5×80
Discuss • 30415 = 3×53 + 0×52 +
• digits used 4×51 + 1×50
• place values
in the number system with a Expanded notation
particular number base.

1

CHAPTER 1– NUMBER BASES MATHEMATICS 5

WEEKS GENERICS CCTS
Number base blocks of twos, ICT
eights and fives can also be used Contextual Perform repeated division
Students will be Students will be able to: Identify Systematic
here. For example, to convert learning to convert a number in
taught to: iv) convert a number in patterns Consistent
1010 to a number in base two, Cooperative base ten to a number in
base :
use the concept of least number learning other bases. For example,
a) two Identify
of blocks (23), tiles (22), convert 71410 to a
b) eight relations
rectangles (21) and squares (20). number in base five :
c) five
In this case, the least number of
to a number in base ten Arrange
objects needed here are one 5)714
and vice versa. sequentially
block, zero tiles, one rectangle 5)142---4
and zero squares. So, 1010 = 5) 28---2
v) convert a number in a
10102. 5) 5---3
certain base to a number
5) 1---0
in another base.
Discuss the special case of 0---1
converting a number in base two
directly to a number in base ∴ 71410 = 103245
eight and vice versa.
For example, convert a number Limit conversion of
in base two directly to a number numbers to base two,
in base eight through grouping eight and five only.
of three consecutive digits.

Students will be Students will be able to: Perform addition and subtraction Contextual Arrange Appreciatio
taught to: (vi) Perform computations in the conventional manner. Learning sequentially n of
involving : For example : technology
a) addition 1010 Communicat Using
b) subtraction + 110 ion Method algorithm Cooperation
of two numbers in of Learning and relation-
base two ship Prudence
Evaluation

2

CHAPTER 2 – GRAPHS OF FUNCTIONS II MATHEMATICS 5

WEEKS GENERICS CCTS
Graphs of Students will be taught Students will be able to: Explore graphs of functions using Constructivism Concept Punctuality Limit cubic functions to the
functions to: (i) Draw the graph of a ; graphing calculator or the constructivis following forms:
2.1 Understand and use a) linear function; Geometer’s Sketchpad. Mastery m Awareness 3
y = ax
the concept of graphs of y = ax + b , learning
functions. Compare the characteristics of Compare and Systematic 3
where a and b are y = ax + b
constants graphs of functions with different Self-access contrast
3
b) quadratic function; values of constants. For example : learning Neatness y = ax + bx + c
2 Analising
y = ax + bx + c ,
where a, b and c are Mental
constants, a ≠ 0 visualization
c) cubic function :
3 2 Relationship
y = ax + bx + cx + d ,
where a,b,c and d are
constants, a≠0 A
d) reciprocal function :
a
y= , where a is a
x
constants, a≠0.

(ii) Find from a graph :
a) the value of y ,
given a value of x B
b) the value(s) of x , Graph B is broader than graph A
given a value of y. and intersects the vertical axis above
the horizontal axis.
As reinforcement, let students
Students will be Students will be able to:
play a game; for example, - Mastery - Comparing - Accuracy For graph of cubic
taught to:
matching card of graphs with learning & - Systematic function, limit to y = ax3
iii) Identify:
their respective function. When differentiatin and y = ax3 + b. For
a) the shape of graph
the students have their matching - g graph of quadratic
given a type of
partners, ask them to group Cooperative - Classifying function limit to y = ax2 +
function
themselves into four groups of learning. - Identifying b and quadratic function
b) the type of function
types of functions. Finally, ask patterns which can be factorise to
given a graph
each group to name the type of - Contextual ( mx + n)
c) the graph given a
function that is depicted on the learning ( px + q) where m .n.p
LEARNING LEARNING function and vice versa.
LEARNING SUGGESTED TEACHING & MORAL POINTS TO NOTE /
WEEKS cards. GENERICS CCTS and q are integers

3


- Graphs of function
- Graph of linear function
- Graph of quadratic
function
iv) Sketch the graph of a - Graph of cubic function
given - Graphs of reciprocal
linear,quadratic,cubic or function
reciprocal function.
For graph of cubic
function, limit to y = ax3
and y = ax3 + b

Students will be taught Students will be able to: Explore using graphing - Self access - Identifying - Systematic - To sketch a graph
to: calculator or the Geometer’s learning relation - Neatness - To draw a graph
Sketchpad to relate the x- - Precise
2.2 Understand and i) Find the point(s) of coordinate of a point of - Mental
use the concept of the intersection of two intersection of two appropriate - Coopera visualization
solution of an graphs. graph to the solution of a given tive
equation by graphical (ii) Obtain the solution of equation. Make generalization learning (i)Identifyin
methods. an equation by finding about the point(s) of intersection - Constru g
the point(s) of of the two graphs. ctivisme patterns.
intersection of two (ii)Identifyin Use the traditional graph
graphs. g plotting exercise if the
(iii) Solve problems relations. graphing calculator or the
involving solution of an (iii)Recogniz Sketchpad is unavailable.
equation by graphical ing and
method. representi Involve everyday
ng. problems.
(iv)Represe -Rationale
nting -Diligence
and -Systematic
interpret -Accuracy
ing data.

WEEKS GENERICS CCTS

4


Students will be Students will be able to: Discuss that if one point in a Enquiry- Identifying Systematic For learning Objectives
taught to: i) Determine whether a region satisfies discovery patterns Determinati 2.3, include situations
2.3 Understand and given point satisfies : y > ax + b or Constructivis on involving
use the concept of the y = ax + b or y < ax + b , then all point in
m Making x = a, x ≥ a ,
region representing inferences
in inequalities in two
y > ax + b or the region satisfies the same x > a, x ≤ a,
variables y < ax + b inequalities. x<a
ii) Determine the
position of a given point region
relative to the equation
y = ax + b dashed line
iii) Identify the region
satisfying
y > ax + b or Emphasise that:
- For the region
y < ax + b representing
iv) Shade the regions Use the Sketchpad or graphing y > ax + b or
representing the
inequalities
calculator to explore points y < ax + b ,the line
relative to a
a) y > ax + b or graph to make generalization y = ax + b is
about regions satisfying the
y < ax + b given inequalities.
drawn as a dashed line to
indicate that all points on
b) y ≥ ax + b or
the line
y ≤ ax + b are not in the region.
- For the region
v) Determine the region representing
which satisfies two or y ≥ ax + b or
more simultaneous linear
y ≤ ax + b , the line
inequalities.
y = ax + b
is drawn as a solid line to
indicate that all points on
the line y = ax + b are
in the region.
Solid line

5

CHAPTER 3 – TRANSFORMATIONS III MATHEMATICS 5

WEEKS GENERICS CCTS
Students will be Students will be able to:
3. taught to: i. Determine the image Relate to transformations in real Constructivi Identifying Systematic Begin with a point,
TRANSFORM 3.1 Understand and of an object under life situations such as sm relations followed by a line and a
ATIONS III use the concept of combination of two tessellation patterns on walls, Determinati object
combination of two isometric transformations. ceilings or floors Contextual Characterizi on
transformations. Learning ng
Accuracy

ii. Determine the image Explore combined Mastery Comparing Rules and Limit isometric
of an object under transformation using the Learning and Regulations transformations to
combination of graphing calculator, the Differentiati translations, reflections
geometer’s Sketchpad, or the ng Self and rotations.
a. two overhead projector and Confidence
enlargements. transparencies. Interpreting
b. an Neatness
enlargement Identifying
and an isometric Relation
transformation.

iii. Draw the image of Investigated the characteristics Contextual Drawing
and object under of and object and its image Learning Diagrams Systematic
combination of two under combined transformation
transformations. Multiple Identifying
Intelligence Relation
theory

iv. State the coordinates Constructivi Identifying Diligence Combined
of the image of a point sm Relation transformation.
under combined Accuracy
transformation. Contextual Arranging
Learning Sequentially Consistent

6


WEEKS GENERICS CCTS
Equivalent
v. Determine whether Multiple Comparing Rational
combined transformation Intelligence and
AB is equivalent to Differentiati Cautious
combined transformation ng
BA
Identifying
Relation

vi. Specify two Carry out projects to design Mastery Identifying Systematic Specify
successive transformation patterns using combined Learning Patterns
in a combined transformations that can be used Hardworkin
transformation given the as decorative purposes. These Identifying g
object and the image projects can then be presented in Relation
classroom with the students
describing or specifying the Logical
transformations involved. Reasoning

Representin
g and
Interpreting
Data

vii. Specify a Use the Sketchpad to prove the Mastery Using Honesty Limit the equivalent
transformation which is single transformation which is Learning Analogies
equivalent to the equivalent to the combination of Cooperation
combination of two two isometric transformations. ICT Working
isometric transformations. Out
Mentally

7


WEEKS GENERICS CCTS

viii. Solve problems a. How to make a frieze or Mastery Find all Sharing
involving transformation. strip pattern. Learning possible
solution Rational
b. Constructing a ICT
kaleidoscope. Using Diligence
Analogies

Drawing
Diagram

Working out
Mentally

8

CHAPTER 4 – MATRICES MATHEMATICS 5

WEEKS GENERICS CCTS
Matrices Students will be Students will be able to: Represent data in real life Contextual Arranging Neatness Emphasize that matrices
taught to: i) form a matrix from situations, for example, the price learning sequentially and are written in bracket.
4.1 understand and given information. of food on a menu, in table form Constructivis systematic
use the concept of and then in matrix form. m Collecting Matrix, row matrix,
matrix. and column matrix, square
handling matrix
data

Emphasize that a matrix
of order m x n is read as
ii) Determine : Accurate ‘an m by n matrix’
a) the number of rows Mastery Identifying
b) the number of learning patterns
columns Use students sitting positions in
c) the order of a matrix the classroom by rows and
columns to identify a student Use row number and
iii) Identify a specific who is sitting in a particular row column number to specify
element in a matrix. and in a particular column as a the position of an
concrete example. Systematic element.
Identifying
patterns

4.2 Understand and i) Determine Discuss equal matrices in terms Mastery Using Systematic Equal matrices
use the concept of whether two of : learning algorithm Accurate
equal matrices. matrices are a) the order and
equal. b) the relationship
corresponding elements
ii) Solve Comparing Including finding values
problems and of unknown elements.
involving differentiatin
equal g
matrices.

9


WEEKS GENERICS CCTS

4.3 Perform addition i) Determine whether Relate to real life situations such Self-access Comparing Cooperation
and subtraction on addition or subtraction as keeping scores of metals, tally learning and
matrices. can be performed on two or points in sport. Constructivi differentiati Rationale
given matrices. sm ng
Mastery Confidence
ii) Find the sum or the learning Using
difference of two Communicat algorithm Systematic
matrices. ion method and
of learning relationship Limit to matrices with not
iii) Perform addition and more than three rows and
subtraction on a few Problem three columns.
matrices. solving

iv) Solve matrix equation
involving addition and Contextual Using
subtraction learning algorithm
Multiple and Include finding values of
intelligences relationship unknown elements/matrix
Mastery Analyzing equation
learning Making
Future inferences
studies Problem
solving

4.4 perform i) Multiply a matrix by a Relate to real life situations such Mastery Evaluating Multiplying a matrix by a
multiplication of a number. as in industrial productions learning number is known as
matrix by a number. Constructivis Using scalar multiplication
ii) Express a given matrix m algorithm
as a multiplication of Contextual and
another matrix by a learning relationship
number. Self-access
learning Conceptuali
iii) Perform calculation on ze and
matrices involving finding all systematic
addition, subtraction and possible
scalar multiplication. solutions

10


WEEKS GENERICS CCTS
iv) Solve matrix equations Self-access Evaluating Include finding the values
involving addition, learning and of unknown elements
subtraction and scalar problems
multiplication. Constructivis solving
m
Self-access
learning

4.5 Perform i. Determine whether two Relate to real life situations such • Constructi • Identifyin • Determin The number of columns
multiplication matrices can be as finding the cost of a meal in a vism g ation of first matrix must be
of two multiplied and state the restaurant. patterns same with the number of
matrices order of the product • ICT • Systemat rows of second matrix.
when the two matrices • Arranging ic
can be multiplied. • Cooperati sequentiall The order of the matrices
ve y • Consiste :
• Learning nt
• Recognizi (m x n) x (n x s)
ii. Find the ng • Diligence = (m x s)
product of and
two matrices representin • Neatness
g
For matrices A and B , discuss
the relationship between AB • Making Limit to matrices with
and BA. generalizati not more than three rows
iii.Solve matrix on and three columns.
equations
involving
multiplication • classifying Limit to two unknown
of two elements.
matrices.

11


WEEKS GENERICS CCTS
4.6 Understand and i) Determine whether a Begin with discussing the • Contextual • Making • Rational Identity matrix is usually
use the concept of given matrix is an property of the number 1 as an learning generalizati denoted by I and is also
identity matrix. identity matrix by identity for multiplication of on known as unit matrix.
multiplying it to another numbers. Identity matrix unit
matrix. matrix.

ii) Write identity matrix of Discuss:
any order. . an identity matrix is a square Limit to matrices with no
matrix more than three rows and
. there is only one identity • Constructi • Systemati three columns.
.matrix for each order. vism • Identifyi c
ng patterns
Discuss the properties:
. AI = A
iii) Perform calculation . IA = A
involving identity
matrices.

• Cooperativ • Solving • Neatness
e problems
learning
4.7 Understand and (i) Determine whether a 2 Relate to the property of • Constructi • Comparin • Cooperati The inverse of matrix A
use the concept of x 2 matrix is the inverse multiplicative inverse of vism g on −1
is denoted by A .
inverse matrix. matrix of another 2 x 2 numbers. • Mastery • Identifyin • Neatness Emphasize that:
matrix. For example : learning g • Systemati • If matrix B is the
−1 −1 patterns c
2x2 =2 x2 = 1 inverse of matrix A,
−1 and then matrix A is also
In the example, 2 is the
relations the inverse of matrix
multiplicative inverse of 2 and
vice versa. B, AB = BA = I
• Inverse matrices can
only exist for square
Use the method of solving matrices, but not all
simultaneous linear equations to square matrices have
show that not all square matrices inverse matrices.
a) (ii) Find the inverse
have inverse matrices. For

12


WEEKS GENERICS CCTS
matrix of a 2 x 2 matrix example, ask student to try to • Constructi • Comparin • Cooperati Steps to find the inverse
using : find the inverse matrix of vism g on matrix :
b) the method of solving  3 2 • Mastery • Identifyin • Neatness • Solving simultaneous
simultaneous linear 
 6 4 .
 learning g • Systemati linear equations
equations   • Communi patterns c
a formula. cation and  1 2  p q  1 0

 3 4  r
 = 
Using matrices and their method of relations
  s  0 1
  
respective inverse matrices in learning •
the previous method to relate to p + 2r = 1, 3 p + 4r = 0
the formula. Express each • q + 2 s = 0, 3q + 4 s = 1
inverse matrix as a  p q
multiplication to the original where   r s 
matrix and discuss how the  
determinant is obtained is the inverse matrix.
• Using formula

a b
For A = 
 c d ,

 
 d −b 
 
A =  ad − bc ad − bc 
−1
 −c a 
 
 ad − bc ad − bc 

or

13


WEEKS GENERICS CCTS
• • • 1  d − b
A−1 =  
ad − bc  − c a 
 
when ad − bc ≠ 0.
ad − bc is known as
the determinant
of the matrix A.
A -1 does not exist if
the determinant is zero.
Prior to use the
formula, carry out
operations leading to the
formula.
4.8 Solve (i) Write simultaneous Relate to equal matrices by • Mastery • Identifyin • Rational Limit to two unknowns.
simultaneous linear linear equations in matrix writing down the simultaneous Learning g Patterns Simultaneous linear
equations by using form. equations as equal matrices first. • Constructi equations
matrices For example: vism ap + bq = h
Write cp + dq = k
2 x + 3y = 13 in matrix form is
4x − y = 5  a b  p   h 
 c d  q  =  k 
    
As equal matrices:     
 2 x + 3y  13  Where a, b, c, d, h and k
 4x − y  =  5 
    are constants, p ad q are
   
constants, p and q are
which is then expressed as:
unknowns.
 2 3  x  13 
 4 − 1 y  =  5 
    
    
p Discuss why:
(ii) Find the matrix  
q • The use of inverse matrix is • Identifyin • Systemati
   a b  p  −1  h 
necessary. Relate to solving • Multiple g Relations c A −1 
in linear equations of type ax = b • Neatness  c d  q  = A  k 
   
Intelligence     
 a b  p   h  • It is important to place the s
 c d  q  =  k 
     inverse matrix at the right place • Constructi
    
on both sides of the equation. vism
Using the inverse matrix.

14


WEEKS GENERICS CCTS
(iii) Solve simultaneous Relate the use of matrices to • Cooperati • Identifyin • Rational a b
linear equations by the other areas such as in business ve Learning g Patterns • Systemati Where A = 
c d .

 
matrix method. or economy, science etc. • Identifyin c
g Relations • Neatness
(iv) Solve problems Carry out projects involving The matrix method
involving matrices. matrices using the electronic uses inverse matrix
spreadsheet.
to solve simultaneous
• Self- • Represent
linear equations.
access ing & • Rational
Learning Interpreting • Systemati Matrix method
• Mastery • Data c
Learning • Neatness
• ICT •

15

CHAPTER 5 – VARIATIONS MATHEMATICS 5

WEEKS GENERICS CCTS
VARIATIONS Students will be taught Students will be able to: Contextual Identifying Rationale Y varies directly as x if and
to: (i)State the changes in a Learning relations y
5.1 Understand and use quantity with respect to the Systematic only if is a constant.
the concept of direct changes in another quantity, Self- access Making x
variation in everyday life situations Learning generalization Tolerance
involving direct variation.
Communicati Estimating Hardworking If y varies directly as x ,
(ii)Determine from given Discuss the characteristic of the on Method of the relation is written as
information whether a graph of y against x when y ∝ x . Leaning y ∝ x.
quantity varies directly as
another quantity. For the cases
Relate mathematical variation to
other area such as science and y ∝ xn , limit n = 2, 3,
(iii)Express a direct variation technology. For example, the
in the form of equation Charles’ Law or the mation of the
1
.
involving two variables. simple pendulum. 2
(iv)Find the value of a variable For the cases
in a direct variation when
sufficient information is y ∝ xn , If y ∝ x , then y = kx
given. 1 where k is constant of
n = 2, 3, , discuss the variation.
(v)Solve problems involving 2
direct variations for the
following cases: Usingy = kx ;or
y ∝ x; characteristics of the graph of y y1 y 2
n =
y∝x ; 2 against x . x1 x 2
y ∝ x3 ; to get the solutions.
1
VOCABULARY:
y ∝ x2 Direct variation
Quantity
Constant of variation
Variable.

16


WEEKS GENERICS CCTS
5.2 Understand and use i) State the changes in a Contructivism Making Rational y varies inversely as x if and
the concept of inverse quantity with respect to inferences Systematic only if xy is a constant.
variations changes in another Communicati
quantity, in everyday life on Representing If y varies inversely as x,
situations involving method of and the relation is written as
inverse variation. learning interpreting 1
Discuss the form of the graph of y data y∝ .
ii) Determine from given 1 1 Cooperative x
information whether a against when y∝ . learning Identifying For the cases
quantity varies inversely as x x relations 1
another quantity. Relate to other areas like science y , limit n to 2,3 and
and technology. For example, Rational xn
iii) Express a inverse Boyle’s Law. 1
variation Systematic .
in the form of equation 2
involving two variables. Accuracy 1 k
If y∝ , then y =
For the cases x x
iv) Find the value of a 1 1 where k is the constant of
variable in an inverse y∝ , n = 2,3 and , discuss variation.
variation when sufficient xn 2
information is given. the characteristics of the graph of y Using:
1 Problem k
v) Solve problems involving against . Solving • y= or
inverse variation for the xn x
following cases: • x1 y1 = x 2 y 2
1 1
y∝ ; y∝ 2 ; to get the solution.
x x
1 1
y∝ 3 ;y∝ 1
x VOCABULARY:
x2
Inverse variation

17


WEEKS GENERICS CCTS

5.3 Understand and use i) Represent a joint variation Discuss joint variation for the three Constructivism Identifying Cooperation For the cases
the concept of joint by using the symbol ∝ for cases in everyday life situations. relations 1
variation. the following cases: Cooperative Punctuality y ∝ xn zn , y ∝
a) two direct variations. Relate to other areas like science learning comparing x zn
n

b) two inverse variations. and technology. and Systematic
xn
c) a direct variation and an For example: Multiple differentiating and y∝ n , limit n to 2,
inverse variation. V intelligences Rational z
I∝ means the current I varies collecting and
3, 1
.
ii) Express a joint variation R Self –access handling data 2
in the form of equation. directly as the voltage V and varies learning
using Joint variation
inversely as the resistance R.
iii) Find the value of a analogies
variable in a joint variation
when sufficient finding all
information is given. possible
solutions
iv) Solve problems involving Mastery
joint variation. learning

18

Mathematics form-5

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Mathematics form-5