| SCHEME OF WORK FORM FOUR MATHEMATICS TERM ONE YEAR |
WK
NO. |
L/NO |
TOPIC / SUBTOPIC |
LESSON / SPECIFIC
OBJECTIVES |
TEACHING / LEARNING
ACTIVITIES |
MATERIALS
/
RESOURCES |
REFERE-
NCES |
REMARKS |
| 1 |
1 |
MATRICES & TRANSFORMA-TIONS
Definition of a transformation.
Reflection in the
y-axis. |
By the end of the lesson, the learner should be able to:
Define a transformation.
Obtain image of an object by reflection in the y-axis. |
Questioning to review position vectors;
Drawing objects and their images on the Cartesian plane;
Inferring the matrix of transformation for
reflection in the y-axis.
Written exercise.
|
Geo – board,
Graph papers,
mirrors. |
KLB BK IV
Pgs 1-2 |
|
| 2 |
Reflection in the
x-axis. |
Obtain image of an object by reflection in the x-axis. |
Drawing object and image on the Cartesian plane;
Inferring the matrix of transformation for
reflection in the x-axis.
Written exercise.
|
Geo – board,
Graph papers,
mirrors. |
KLB BK IV
Pgs 2 – 3 |
|
| 3 |
Reflection in the
Lines y = x,
y = – x and other lines. |
Obtain image of an object by reflection in a given line.
Obtain the object given its image and line of reflection.
|
Review equation of a line;
Draw the line y = x;
Reflect an object in the line
y = x;
Infer the matrix of transformation
Written exercise.
|
Geo – board,
Graph papers,
mirrors. |
KLB BK IV
Pgs 2-3 |
|
| 4 |
Rotation matrix.
(positive angle) |
Obtain image of an object by rotation through a positive angle.
Obtain the object given its image and positive rotation angle.
|
Guided discovery;
Worked example;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 3-4 |
|
| |
5 |
Rotation matrix.
(negative angle) |
Obtain image of an object by rotation through a negative angle.
|
Guided discovery;
Worked example;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 3-4 |
|
| |
6 |
The unit circle. |
Use the unit circle to identify a transformation represented by a given matrix. |
Guided discovery;
Worked example;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 9-13 |
|
| |
7 |
Finding matrix of transformation. |
Find matrix of transformation given an object and image.
Describe the transformation fully. |
Review simultaneous equations and matrix multiplication;
Worked examples;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 6-8 |
|
| 2 |
1 |
Enlargement matrix. |
Identify an enlargement matrix.
Perform operations involving enlargement matrices.
|
Review scale factor and centre of enlargement;
Worked examples;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 11-12 |
|
| |
2 |
Two successive transformations. |
Perform two successive transformations. |
Guided discovery of order of operation;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 16-17 |
|
| |
3 |
Several successive transformations. |
Perform several successive transformations. |
Previous exercise review;
Guided discovery of order of operation;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 16-17 |
|
| |
4 |
Combined matrix of transformations. |
Find combined matrix of several transformations. |
Previous exercise review;
Guided discovery of order of operation;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 21-22 |
|
| |
5 |
Inverse of a transformation matrix. |
Identify the identity matrix.
Determine the inverse of a transformation matrix. |
Worked examples using several methods;
Supervised practice;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 24-26 |
|
| |
6 |
Inverse of several transformation matrices. |
Determine the inverse of several combined transformation matrices. |
Worked;
Supervised practice;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 24-26 |
|
| |
7 |
A.S.F. and determinant of a transformation matrix. |
State the relation between A.S.F. and determinant of a transformation matrix. |
Finding area of object, image, ASF;
Guided discovery;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 26-27 |
|
| 3 |
1 |
Shear transformation.
(x-axis invariant) |
Identify a shear transformation. (x-axis invariant)
Describe a shear fully. |
Drawing object and image under a shear transformation;
Oral exercise;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 28-32 |
|
| |
2 |
Shear transformation.
(y-axis invariant) |
Identify a shear transformation. (y-axis invariant)
Describe a shear fully. |
Drawing object and image under a shear transformation;
Oral exercise;
Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 28-31 |
|
| |
3 |
Finding shear matrix. |
Find shear matrix given the object and image. |
Worked examples;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 31-2 |
|
| |
4 |
One-way stretch.
(x-axis invariant) |
Describe a one-way stretch.
(x-axis invariant)
Find the scale factor of a stretch. |
Guided discovery;
Worked examples and discussion.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 32-34 |
|
| |
5 |
One-way stretch.
(y-axis invariant) |
Describe a one-way stretch.
(y-axis invariant).
Find the scale factor of a stretch. |
Guided discovery;
Worked examples and discussion.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 32-34 |
|
| |
6 |
Isometric and non-isometric transformation. |
Classify transformations as either isometric or non-isometric. |
Review types of transformations;
Probing questions on size and shape of objects and images.
|
|
KLB BK IV
Pg 35 |
|
| |
7 |
Test / mixed exercise. |
|
|
Past exam papers. |
|
|
| 4 |
1 |
STATISTICS II
Mean and assumed mean.
(frequency 1) |
Find mean of ungrouped data using an assumed mean.
(frequency 1) |
Simple worked examples;
Exposition of method involving an assumed mean;
Written exercise.
|
Calculator. |
KLB BK IV
Pgs 38-39 |
|
| |
2 |
Mean and assumed mean.
(frequency > 1) |
Find mean of ungrouped data using an assumed mean.
(frequency > 1) |
Simple worked examples;
Written exercise.
|
Calculator. |
KLB BK IV
Pg 40 |
|
| |
3 |
Mean of grouped data. |
Find mean of grouped data. |
Review previous exercise;
Completing table;
Worked examples. |
Calculator. |
KLB BK IV
Pgs 40-41 |
|
| |
4 |
Mean of grouped data.
(alternative methods) |
Find mean of grouped data.
(alternative methods) |
Completing table;
Worked examples.
Written exercise. |
Calculator. |
KLB BK IV
Pgs 40-46 |
|
| |
5 |
Median. |
Find median of grouped data. |
Worked examples;
Written exercise. |
Calculator. |
KLB BK IV
Pgs 46-7 |
|
| |
6 |
Quartiles. |
Find upper and lower quartiles. |
Exposition;
Worked examples;
Written exercise. |
Calculator. |
KLB BK IV
Pgs 47-8 |
|
| |
7 |
Deciles and Percentiles. |
Define a decile and percentile.
Find nth decile / percentile. |
Exposition;
Worked examples;
Written exercise. |
Calculator. |
KLB BK IV
Pgs 47-8 |
|
| 5 |
1 |
Cumulative frequency curve. |
Draw a cumulative frequency curve. |
Q/A to review upper and lower limits of class boundaries;
Complete a table by finding cumulative totals;
Draw an ogive.
|
Calculator, graph papers. |
KLB BK IV
Pgs 38-40 |
|
| |
2 |
Median and quartiles from an ogive. |
Estimate median and quartiles from an ogive. |
Probing questions to make inferences from an ogive.
|
Calculator, graph papers. |
KLB BK IV
Pgs 48-50 |
|
| |
3 |
Deciles and percentiles from an ogive. |
Estimate deciles and percentiles from an ogive. |
Probing questions to make inferences from an ogive.
|
Calculator, graph papers. |
KLB BK IV
Pgs 53-55 |
|
| |
4 |
Range, inter-quartile range and quartile deviation. |
Find range and inter-quartile range of a set of data. |
Exposition and oral exercise. |
Calculator. |
KLB BK IV
Pgs 55-56 |
|
| |
5 |
Mean absolute deviation. |
Determine mean absolute deviation. |
Exposition;
Worked examples. |
Calculator. |
KLB BK IV
Pgs 56-7 |
|
| |
6 |
Variance. |
Define variance.
Determine variance of a set of data. |
Exposition;
Worked examples. |
Calculator. |
KLB BK IV
Pgs 57-59 |
|
| |
7 |
Standard deviation. |
Determine standard deviation of a set of data. |
Exposition;
Worked examples;
Written exercise. |
Calculator. |
KLB BK IV
Pgs 59-60 |
|
| 6 |
1-4 |
Formulae for standard deviation. |
Use various methods of finding std deviation. |
Exposition;
Worked examples;
Written exercise. |
Calculator. |
KLB BK IV
Pgs 60-3 |
|
| |
5 |
LOCI
Definition of a locus. |
Define locus of a point. |
Illustrative examples;
Exposition of meaning of locus of a point.
|
Door, clock, see saw, etc. |
KLB BK IV
Pgs 66-7 |
|
| |
6 |
Sketching locus of a point. |
Sketch locus of a point. |
Oral exercise;
Supervised practice;
Written exercise. |
|
KLB BK IV
Pgs 67-8 |
|
| |
7 |
Perpendicular bisector locus.
(two dimensions) |
Describe perpendicular bisector locus.
(two dimensions) |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 68-9 |
|
| 7 |
1 |
Perpendicular bisector locus.
(three dimensions) |
Describe perpendicular bisector locus.
(three dimensions) |
Geometrical construction;
Guided discovery;
Supervised practice;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 69 |
|
| |
2 |
Locus of points at a given distance from a fixed point.
(two dim) |
Describe locus of points at a given distance from a fixed point. |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 70 |
|
| |
3 |
Locus of points at a given distance from a fixed point.
(three dim) |
Describe locus of points at a given distance from a fixed point. |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 71 |
|
| |
4 |
Locus of points at a given distance from a line.
(two dim) |
Describe locus of points at a given distance from a fixed point. |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 69 |
|
| |
5 |
Locus of points at a given distance from a line.
(three dim) |
Describe locus of points at a given distance from a fixed point. |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 70 |
|
| |
6 |
Angle bisector locus. |
Construct the angle bisector locus. |
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 70 |
|
| |
7 |
Constant angle locus. |
Construct constant angle locus. |
Probing questions to review angle properties of a circle;
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 72-4 |
|
| 8 |
1 |
Constant angle locus.
(contd) |
Construct constant angle locus. |
Probing questions to review previous exercise;
Geometrical construction;
Guided discovery;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 72-4 |
|
| |
2 |
Intersecting loci involving lines and angles. |
Construct intersecting loci involving lines and angles. |
Geometrical construction;
Supervised practice;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 72-4 |
|
| |
3 |
Circumcircle locus. |
Construct a circumcircle. |
Geometrical construction;
Supervised practice;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 78 |
|
| |
4 |
In-circle locus. |
Construct an in-circle locus. |
Geometrical construction;
Supervised practice;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 78 |
|
| |
5 |
Ex-circle locus. |
Construct an ex-circle locus. |
Geometrical construction;
Supervised practice;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 78 |
|
| |
6 |
Intersecting loci in plane figures. |
Construct intersecting loci in plane figures. |
Problem solving. |
Geometrical sets. |
KLB BK IV
Pgs 79-81 |
|
| |
7 |
Loci of inequalities. |
Draw locus of points that satisfy various inequalities. |
Q/A to review simple and compound inequalities;
Worked examples;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 81-2 |
|
| 9 |
1 |
Loci of inequalities.
(contd) |
Draw locus of points that satisfy various inequalities. |
Review previous exercise;
Further worked examples;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pg 83 |
|
| |
2 |
Locus involving chords. |
Construct locus involving chords. |
Worked examples;
Written exercise.
|
Geometrical sets. |
KLB BK IV
Pgs 96-97 |
|
| |
3 |
TRIGONOMETRY
III
Some trigonometric ratios. |
Rearrange
trigonometric expressions.
|
Exposition and worked examples;
Written exercise. |
Geometrical sets. |
KLB BK IV
Pgs 90-91 |
|
| |
4 |
Trigonometric identities. |
Prove some trigonometric identities. |
Problem solving. |
Geometrical sets. |
KLB BK IV
Pgs 100-1 |
|
| |
5 |
Period and amplitude of waves. |
Determine period and amplitude of waves. |
Exposition and worked examples. |
Geometrical sets. |
KLB BK IV
94-5 |
|
| |
6 |
Tables for trigonometric functions. |
Complete tables for trigonometric functions.
|
Exposition and worked examples. |
Calculator.
|
KLB BK IV
Pgs 96-7 |
|
| |
7 |
Graphs for trig. functions. |
Plot graphs for trigonometric functions.
|
Drawing graphs; supervised practice; make inferences from the graphs. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 96-7 |
|
| 10 |
1 |
Further graphs for trig. functions. |
Plot graphs for trigonometric functions.
|
Drawing graphs; supervised practice; make inferences from the graphs. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 96-7 |
|
| |
2 |
Transformations of waves. |
Describe some transformations of waves. |
Supervised practice;
Exposition and worked examples;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 96-97 |
|
| |
3 |
Waves with a phase angle.
(positive) |
Determine the phase angle (positive) for two waves. |
Guided discovery;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 97-8 |
|
| |
4 |
Waves with a phase angle.
(negative) |
Determine the phase angle (negative) for two waves. |
Guided discovery;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 97-8 |
|
| |
5 |
Trigonometric equations. |
Solve trigonometric equations. |
Q/A to review trig. ratios for complementary angles;
Worked examples;
Supervised practice;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 100-3 |
|
| |
6 |
Further trig. equations. |
Solve trigonometric equations. |
Exercise review;
Problem solving. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 100-3 |
|
| |
7 |
Graph of a trig. function and a line. |
Draw the graph of a trig. function and a line to solve an equation. |
Worked examples;
Supervised practice;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 100-3 |
|
| 11 |
1 |
Graphs of two trig. functions. |
Draw graphs of two trig. functions to solve some equations. |
Worked examples;
Supervised practice;
Written exercise. |
Geometrical sets, graph papers. |
KLB BK IV
Pgs 100-3 |
|
| |
2 |
THREE DIMENSIONAL GEOMETRY
Dimensions of figures. |
State the dimensions of figures.
Identify faces, edges, and vertices of common figures. |
Probing questions;
Oral exercise. |
Common planes and solids. |
KLB BK IV
Pgs 104-6 |
|
| |
3 |
Angle between a line and a plane. |
Identify the angle between a line and a plane. |
Exposition;
Oral exercise. |
Cuboid wire mesh. |
KLB BK IV
Pgs 106-7 |
|
| |
4 |
Finding the angle between a line and a plane. |
Find the angle between a line and a plane. |
Guided discovery;
Worked examples;
Written exercise.
|
Models of solids. |
KLB BK IV
Pgs 107-113 |
|
| |
5 |
Finding the angle between a line and a plane.
(contd) |
Find the angle between a line and a plane. |
Problem solving. |
Models of solids. |
KLB BK IV
Pgs 107-113 |
|
| |
6 |
Angle between two planes. |
Identify the angle between two planes. |
Q/A counting planes;
Exposition.
|
Models of solids. |
KLB BK IV
Pgs 113-118 |
|
| |
7 |
Angle between two planes.
(contd) |
Find the angle between two planes. |
Exposition;
Guided discovery;
Worked examples;
Written exercise.
|
Models of solids. |
KLB BK IV
Pgs 113-118 |
|
| 12
13 |
|
END OF TERM EXAMS |
|