GENERAL MATHEMATICS SS1 FIRST TERM
This scheme of work contains week, topic , content , teacher’s and students activities as well as instructional resources which are very vital for your lesson planning. please be guided.
1 NUMBER BASES (I)
i. Decimal base (Base 10) and other bases e.g. base 2(binary)
base 7 (days of the week) etc.
ii. Conversion from Base 10 to other bases, conversion from
other bases to base 10.
Teacher:
i. Guides students to realize other bases other than binary (base2) and denary (base 10)
ii. Guides students to convert the following:
one base to the other, are numbers with decimal fraction to base 10.
Students:
Mention other base such as 4, base 5(quandary), base 8(octal) base 16 (Hexadecimal).
Convert decimal fractions to base 10 and one base to another base.
Instructional Resources:
Charts showing the conversion from one
base (except base 2) to another base.
2 NUMBER BASES (II)
i. Problem solving, addition, subtraction, multiplication and
division of number in the various bases.
ii. Conversion of decimal fraction
in one base to base 10.
iii. Apply number base system to computer programming.
Teacher:
Guides students to perform mathematical operations of: addition, subtraction, multiplication and division.
Students:
Perform the mathematical operations.
Instructional Resources:
As in week one above.
3 . MODULAR ARITHMETIC
i. Revision of addition, division, multiplication and subtraction of integers.
ii. Concept of modular arithmetic
iii. Addition, subtraction and
Teacher:
Guides students to revise the mathematical
operations of integers
-to define modular arithmetic and uses
activities to develop the concept. To add, subtract, divide and multiply inmultiplication operations in modular arithmetic.
iv. Application to real life
situations.
modular arithmetic.
Teacher :To appreciate its application to shift duty,
menstrual chart, name of market days.
Students:
-Define modular arithmetic
-Perform the mathematical operations in modular arithmetic
-Appreciate the concept of modular arithmetic and apply in daily life.
Instructional Resources:
Modular arithmetic charts, samples of shift
duty chart, menstrual chart.
4 INDICES
i. Laws of indices and their applications e.g.
a. ax x ay = ax+y
b. ax /ay = ax-y
c. (ax)y = axy
ii. Application of indices, simple indicial/exponential equations.
Teacher:
Guides students to represent numbers in indices and gives examples.
Explains laws of indices with examples, drill students on problem solving.
Students:
-Study the laws of indices and solve related problems.
-Study the steps in indicial equation and solve exercises.
5 STANDARD FORM (AX10n)
i. Writing numbers in index form
ii. Adding two numbers and writing the results in standard
form.
iii. Subtracting one number from the other in standard form.
iv. Multiplying numbers in standard form
v. Dividing numbers in standard form including square root of
such numbers.
Teacher:
Guides students to convert numbers to standard form with emphasis on the values of ‘A’ and ‘n’.
Students:
-Convert numbers to standard form
-Convert long hand to short hand notation. (i.e. ordinary form to standard form and standard form to ordinary form)
Instructional Resources:
Charts of standard form and indices.
6. LOGARITHMS (I)
i. Deducing logarithm from
indices and standard form i.e. if
Teacher:
Guides students to learn logarithm as inverse
of indices with examples.y=10x, then x=logy10
ii. Definition of logarithm e.g. log101000=3
iii. Graph of y=10x using x=0.1, 0.2,………..
-Define logarithm and find the various values of expressions like logaN
plot the graph of y=10x and read the required values.
-to find logarithm of a number (characteristics, mantissa, differences and locate decimal points) and the antilogarithm.
Students:
Deduce the relationship between indices and
logarithms.
Define logarithm and find the various values of expressions like logaN numbers plot the graph of y=10x
Find the logarithm and antilogarithm of numbers greater than 1.
Instructional Resources:
Indices/logarithms chart, definition chart of logarithm, graph board with graph of y=10x, graph book etc.
7. LOGARITHM (II)
Calculations involving multiplication and division.
Teacher:
Guides students to read logarithm and antilogarithm table in calculation involving multiplication and division.
Students:
Read the tables and solve problems involving multiplication and division.
Instructional Resources:
Logarithm table chart and Antilogarithm table chart made of flex banner logarithm table booklet.
8 LOGARITHM (III)
i. Calculations involving power and roots using the logarithm
tables.
ii. Solving practical problems using logarithm tables relating to capital market.
iii. Explain the concept of capital
Teacher:
-Guides students to read logarithm and antilogarithm tables in calculations involving powers and roots.
-Explain meaning of capital market.
-Solve related problems and other real life problems. market operation
iv. Use logarithm tables in multiplying the large numbers
involved in capital market operation.
Students
Read the tables and solve problems involving multiplication and division, and solve problems related to real life problems.
Instructional Resources:
Logarithm tables chart, logarithm table booklet etc.
9 DEFINITION OF SETS
i. Set notation – listing or roster method, rule method, set builder notation
ii. Types of sets: e.g. universal set, empty set, finite set and
infinite set, subset, disjoint set, power set etc.
Teacher:
Guides students to:
-define set
-define types of sets
-write down set notations
-use the objects in the classroom, around the school and within home to illustrate sets.
Students:
Define set, use set notations
Identify types of sets.
Instructional Resources:
Objects in the classroom, sets of students,
set of chairs, mathematical sets, other
instrument etc.
10 SET OPERATIONS
i. Union of sets and intersection of sets complement of sets.
ii. Venn diagram
iii. Venn diagram and application up to 3 set, problems
Teacher:
Guides students to explain and carry out set operations:
-explains Venn diagram, draws, interprets and uses diagram.
-applies Venn diagram to real life problems.
Students:
Carry out set operations, draw, interpret and use Venn diagrams.
Instructional Resources:
As in week nine above.
11 SIMPLE EQUATIONS
i. Change of subject of formulae
ii. Formula involving brackets, roots and powers.
iii. Subject of formula and substitution.
Teacher:
Guides students in the process involved in changing the subject in a formula and carries out substitution.
Students:
Follow the process involved in changing subject in a formula and substitute in the formula.
Instructional Resources:
Charts displaying processes involved in change of subject in a formula.
Charts displaying the various types.
12 SIMPLE EQUATION AND VARIATIONS
i. Revision of simultaneous linear equation in two (2)
unknown
ii. Types and application of variations.
Teacher:
Revises solution of simultaneous equations in two unknowns.
Treats each type of variation with examples and solve problems in variation.
Students:
Solve problems involving all types of variations.
Instructional Resources
As in week 11 above.
13 Revision/Examinations
14 Examinations
GENERAL MATHEMATICS SS ONE SECOND TERM
WEEK TOPIC / CONTENT ACTIVITIES
1 FACTORISATION OF QUADRATIC EXPRESSION OF THE FORM ax2+bx+c where a, b, c are constants
i. Factorising quadratic expression of the form ax2+bx+c
ii. Factorising quadratic expression of the form ax2-bx+c
iii. Factorising quadratic expressions of the form ax2+bx-c
iv. Factorising quadratic expressions of the form ax2-bx-c
v. Solving quadratic equation of the form ax2+bx+c = 0 using
Teacher:
i. Illustrates the factorization of quadratic expressions using:
(a) Grouping (b). factor methods
ii. Teacher leads students to factorize quadratic expressions written in the different forms.
Students:
-Factorize quadratic expressions using the methods.
-Factorize the different forms given.
Instructional Resources:
Quadratic expressions and factors chart.
Sharing at least six expressions each of the factorization method. form ax2+bx+c, ax2-bx+c, ax2+bx-c and ax2bx-c (could be in flex banners).
2 APPROXIMATION
i. Rounding up and rounding down of numbers to significant
figures, decimal places and nearest whole numbers.
ii. Application of approximation to everyday life
iii. Percentage error.
Teacher:
Gives students two roots and leads them to form a quadratic equation.
Students:
Use the roots given to construct quadratic equation.
Instructional Resources:
Given values, in integer and fractions
incomplete table showing various numbers and approximation to various significant figures, decimal places etc. to be completed in class as illustration
3 QUADRATIC EQUATIONS(III)
i. Plotting graph in which one is quadratic function and one is a linear function.
ii. Using an already plotted curve to find the solution of the various equations.
iii. Finding the gradient of a curve, the maximum value of y,
and minimum value of y and the corresponding values of x.
iv. Solving a comprehensive quadratic and linear equation
graphically.
v. Word problem leading to quadratic equations.
Teacher: Leads students to construct tables of values, drawsthe x and y axis, chooses scale, graduates the axis and plot the points. Identifies the maximum and minimum
values.
Students:Follow the teacher lead in plotting the graph, Follow the teacher leads and read the
roots . Also read the minimum and maximum values.
Instructional Resources:
Graph boards, graph books are mandatory.
4 LOGICAL REASONING (I)
i. Meaning of simple statement –open and close statements, true or false.
ii. Negation of simple statements
iii. Compound statements –conjunctions, disconjunctions,
Teacher:
a. Uses examples to explain simple statements.
b. State the true value of a statement
c. States simple statements and writes not or “it is not true that” a negation of simple statements implication, bi-implication with examples.
d. Guides students to write examples of compound statements and distinguishes them from simple statements.
Students:
i. Gives examples of the non examples of simple statements writes the true value of a given statements.
ii. Negates some simple statement using ‘not’ or ‘it is not true that’.
iii. Write examples of compound statements.
Instructional Resources:
Charts showing examples of simple statement, true and false statements, negation of statements.
5 LOGICAL REASONING (II)
i. Logical operations and symbols
– Truth value table – compound statement, Negation (NA),
conditional statement, bin-conditional statement.
Teacher:
Leads students to list the five logical operations and their symbols.
-Leads students to construct truth value for
each operation.
Students:
List the five logical operations with symbols
and construct truth value chart for each.
Instructional Resources:
Truth table chart etc.
6 .MENSURATION OF SOLID SHAPES (I)
i. Length of arc of a circle with practical demonstration, using
formula
ii. Revision of plane shapes –perimeter of sector and segment
iii. Area of sector and segment.
Teacher:
Guides students to find the length of arcs of circle using cut card board practically, deduces the formula and apply it in solving problems.
-cuts out sectors and segment, solve exercises.
-guides students to cut a circle into sectors and measure the angles.
-cut out triangle from a sector.
Students:Practice the practical demonstration.
Participate in deducing the formula and applyit to solve problems carry out teacher
activities.
Follow the teacher instruction to carry out the
activities.
Instructional Resources:
Cardboard paper, rope, string, scissors,
drawings on cardboard showing various arcs
(minor and major arcs in a circle).
7 MENSURATION OF SOLIDSHAPES (II)
i. Relationship between the sector of a circle and the surface area of a cone.
ii. Surface area of solids – cube, cuboids, cylinder, cone, prism,
pyramids.
Teacher:
-Guides students to cut out a sector and folding sector into a cone.
-Leads students to determine the relationship between the sector of a circle and the surface area of a cone.
-Revise the areas of the plane shapes that formed the listed solids and lead students to find their surface areas.
Students:
-Follow the teacher in carrying out the activities and observe the relationships
-Participate in the revision of the areas of the solids.
Instructional Resources:
Cut out papers, (sectors and segments) etc.
8 MENSURATION OF SOLID SHAPES (III)
i. Volume of solids – cube, cuboids, cylinder, cone, prism,
pyramids, frustum of cone and pyramids.
ii. Surface area and volume of compound shapes.
Teacher:
-Revise the area of the listed solids and lead students to find their volumes, show model of fraction of cones pyramids and solve problems.
-Lead students to solve problems on surface area and volume of compound shapes.
Students: Participate in the revision of the areas and volume of the solids.
-Solve problems on compound shapes.
Instructional Resources:Shapes of cube, cuboids, cylinder, cone, prism, pyramids, lampshade and buckets asfrustum as cone etc.
9 CONSTRUCTION (I)
i. Lines, line segments, bisection of a line segment e.g. horizontal,
vertical, inclined lines etc.
ii. Construction and bisection of angles e.g. 180°, 90°, 45°, 22° 60o, 30°, 150°, 75°, 135o, 105°, 165°etc.
iii. Construction of triangles
iv. Construction of quadrilaterals.
Teacher: -Lists out steps for drawing a line segment and how to bisect line segment.
-Leads students to construct special angles with the steps involved in bisection of angles.
Inspect them.
Students: List out triangle, draw a line and bisect, construct the given angles and bisect them.
Instructional Resources
Whiteboard, mathematical set, students
mathematical set. Teacher’s construction
instruments mandatory.
10 LOCUS OF MOVING POINTS
i. Equidistant from 2 intersecting
straight lines
ii. Equidistant from 2 points
iii. Equidistant from a fixed pointetc.
iv. Construction of locus
equidistant from a given straight
line.
Teacher:
Guides students to list and explain the steps
involved in constructing locus of moving
points equidistance from:
i. Two intersecting straight lines
ii. Two given points
iii. One point
iv. A given straight line on the
chalkboard using chalkboard
mathematical set .
Inspects students constructing.
Students:
-Attempts to list and explain the steps
involved, write down the steps listed and
explained by the teacher and ask questions.Students: Follow teacher’s demonstration on the
chalkboard by carrying out similar activities in
their exercise book with their mathematical
sets.Participate in the teacher’s re-
demonstration and take special notes of the
salient steps.
Instructional materials: As shown in week 9Revision/Examinations Revision/Examinations
12 Examinations Examinations
GENERAL MATHEMATICS SS1 THIRD TERM
WEEK TOPIC / CONTENT ACTIVITIES
1 DEDUCTIVE PROOFS (I)
i. Types and properties of triangles
ii. Proofs of sum of angles in a
triangle is 180o
, the exterior angles
is equal to the sum of its two interior
opposite angles.
Teacher:
carrying out proofs in geometry, by
explaining the concepts of: given, required
to prove, construction, proof, conclusion.
Guides the students to prove the two
theorems on the board with necessary
diagrams.
Assists students to carryout practical
demonstrations, and to solve examples and
give students some task to solve and inspect
them.
Students:
Participate in discussing the format for
proving geometrical theorem, take special
note of the format, then write them down and
ask questions.
-Solve the task given.
Instructional Resources:
Cardboard paper, cutout of triangles,
protractor to verify and establish the truth
about the theorem.
2 DEDUCTIVE PROOFS (II)
i. Similar and congruent triangles
ii. Isosceles and equilateral
triangles.
Teacher:
Demonstrates on the chalkboard how to
prove the followings:
Angles of parallel lines, angles in a polygon,
congruent triangles, properties of
parallelogram, deductive reasoning and
axioms using relevant models of plane
shapes.
Students:
Participate in the teacher’s demonstrations
by contributing in making some deductions
and write down essential points agreed upon,
on angles of a polygon, congruent triangles.
etc.
Instructional Resources:
Parallel lines, congruent triangles, polygons,
cut out paper, protractors.
3 DEDUCTIVE PROOFS (III)
i. Properties of parallelogram and
related quadrilaterals.
ii. Intercept theorem
iii. Parallelogram of the same
base and between the same
parallel lines are equal in area.
Teacher:
properties of the riders using paper cutouts,
protractors, models of parallelogram,
polygon, congruent triangle etc.
Guides students to solve problems and help
them to reproduce arguments based on the
reasons (theorem or axioms).
Students:
Carry out practical demonstration of the
properties of the rides along with the teacher
using paper cutouts, construct models of
plane shapes. Apply deductive reasoning to
solve the given practical problems.
Instructional Resources:
As in week 2
4 POLYGON – TYPES
i. Sum of interior angles of any n-
sided polygon.
ii. Sum of exterior angles of any
polygon
iii. Problem solving on polygon.
Teacher:
As in week 2 and 3 above.
Students:
As in week 2 and 3 above
Instructional Resources:
As in week 2 and 3 above.
5 TRIGONOMETRY (I)
i. Basic trigonometric ratios, sine,
cosine and tangent with respect
to right-angled triangles.
ii. Trigonometric ratio of special
angles 30o, 45o, 60o.
iii. Deriving trigonometric ratios of
Teacher:
Shows students a chart of right angled-
triangle with a clearly marked angle.
Guides students to identify ratios forming
sine, cosine and tangent of the marked
angles. (verify the position of the marked
angles) 30o, 45o, 60o.
– Lead students to construct right angled-
triangles of 30o, 45o, 60o.
Guides students to use the above shapesto derive trigonometric ratios of 30o, 45o, 60o.
Students:
Study the chart; identify ratios forming cosine
and tangent of marked angle on the chart.
Draw right-angled triangles and use it to
solve problem involving calculation of
lengths, construct right-angled triangles of30o, 45o
and 60o.
Derive trigonometric ratios of 30o, 45o and
60o
under teacher’s supervision.
Instructional Resources:
Charts showing trigonometric ratios of a right
angled triangle, pencil and ruler, protractor,
cutout shapes of right angled triangles
showing angles 45o, 30oand 60o
respectively.
6 TRIGONOMETRY (II)
i. Solving problems involving use
of sine, cosine and tangent at
right-angled triangles.
ii. Application of trigonometric
ratios of 45o
, 30o
and 60o
to
solving problem without the use
of calculating aids.
Teacher:
i. Guides students to use sine, cosine and
tangents to solve problems involving
calculation of length, angles, angles of
elevation and depression etc.
ii. Leads students to draw right-angled
triangle of side 1 unit on the equal sides.
iii. Guides students on how to derive
trigonometric of ratio.
iv. Leads students to measure the two other
angles in the right angled triangle.
v. Lead students to obtain sine and cosines
of various angles using measured lengths.
Students:
Solve problems on practical application of
trigonometric ratios under guidance of
teacher.
Obtain sine and cosine of various angles.
Identify the relationship between the
trigonometric ratios and the measured 30o, 45o, 60o
– Lead students to construct right angled- triangles of 30o, 45o, 60o.
Guides students to use the above shapesto derive trigonometric ratios of 30o
, 45o, 60o.
Students:
Study the chart; identify ratios forming cosine
and tangent of marked angle on the chart.
Draw right-angled triangles and use it to
solve problem involving calculation of
lengths, construct right-angled triangles of
30o, 45oand 60o.
Derive trigonometric ratios of 30o,
, 45oand 60o
under teacher’s supervision.
Instructional Resources:
Charts showing trigonometric ratios of a right
angled triangle, pencil and ruler, protractor,
cutout shapes of right angled triangles
showing angles 45o, 30o and 60o
respectively.
6 TRIGONOMETRY (II)
i. Solving problems involving use
of sine, cosine and tangent at
right-angled triangles.
ii. Application of trigonometric
ratios of 45o, 30o and 60o to
solving problem without the use
of calculating aids.
Teacher:
i. Guides students to use sine, cosine and
tangents to solve problems involving
calculation of length, angles, angles of
elevation and depression etc.
ii. Leads students to draw right-angled
triangle of side 1 unit on the equal sides.
iii. Guides students on how to derive
trigonometric of ratio.
iv. Leads students to measure the two other
angles in the right angled triangle.
v. Lead students to obtain sine and cosines
of various angles using measured lengths.
Students:
Solve problems on practical application of
trigonometric ratios under guidance of
teacher.
Obtain sine and cosine of various angles.
Identify the relationship between the
trigonometric ratios and the measured values.
Instructional Resources:
Chart showing unit circle etc.
7 TRIGONOMETRY (III)
Trigonometric ratios related to
the unit circle
i. Draw graphs of sine from 0o≤ ө ≤ 360o
ii. Draw graphs of cosine from 0o ≤ ө ≤ 360o
Teacher:
Guides them to see the relationship between
calculated sine and cosine of trigonometric
ratios and the angles measured with
protractor in the unit circles.
Constructs table of values for 0o
≤ ө ≤ 360o
fie both sine and cosine, plots the points on
the graph board and draw the graphs.
Guides them on the activities to obtain
accurate values.
Leads them to obtain solution from graph
drawn.
Students:
Participates in the construction of table of
value for y and plotting of the points and
drawing of the graph.
Instructional Resources:
Graph board, graph book, pencils, and
mathematical sets. Mandatory.
8 STATISTICS
i. Revision on collection,
tabulation and presentation of
data.
ii. Construction of frequency
tables
iii. Bar charts and histogram
differentiate between bar chat
and histogram.
Teacher:
Guides students to:
-information on their age, number of children
in the families and other areas of life.
-tabulates data collected
-lists various forms of presentation of data
e.g. bar chart, pie chart.
-leads students to construct table from given
data; draw bar chart and histogram.
Students:
Submit objects like corks brought to class.
Tabulate into specific categories, list various
of presentation of dates, table from given
data.
Draw bar chart and histogram.
Instructional Resources:
Ages of students recorded on cardboard,
prices of goods, objects of different kinds.
Corks of soft drinks, posters containing real
life data.
Graph board, graph book.
9 STATISTICS (II)
i. Calculating the sectoral
component of pie chart.
ii. Drawing pie chart correctly.
iii. Interpreting the pie chart and
bar chart.
Teacher:
Leads students to calculate the angular
equivalent of the different frequency in a
given distribution using the idea of ratio and
proportion.
Guides students to draw pie chart using their
compass, and protractor.
Interpret the pie chart in terms of sectoral
angles.
Students:
Calculate sectoral angles, draw pie charts,
correctly to interpret data using the pie chart.
Instructional Resources:
Graph board, graph papers, a pair of
compass and protractor etc.
10 STATISTICS (III) GROUPED DATA
i. Drawing histogram
ii. Estimation of mode from
histogram.
Teacher:
Guides students to use frequency table to
draw histogram.
Leads students to construct table from given
data, construct group frequency table.
Guides students to use class boundaries to
draw histogram and how to read or estimate
mode from the histogram.
Students:
Participate in the activities with the teacher,
perform the instructions given by the teacher.
Draw histogram and estimate mode from the
histogram.
Construct frequency table of a grouped data.
Instructional Resources:
Graph board, graph papers etc.
11 STATISTICS (III)
Construction of frequency
polygon of a given distribution.
Teacher:
Guide the students to construct frequency
polygon of a given distribution.
Students:
Construct frequency polygon from a grouped
data.
Instructional Resources:
Graph board, graph papers etc.
12 Revision Revision
13 Examinations Examinations
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