1. Simple and compound statement
2. Logical operation and truth tables
3. Conditional statements and indirect proofs.
Gives collection of simple and compound statement and guides students to distinguish them.
-Leads students to construct truth table chart for each of the given logical operations.
-Guides students to state the converse, inverse and contra positive operation of a given conditional statement.
Write examples of simple and compound statements:
-construct truth table chart for each of the five logical operations
-prove the converse, inverse and contra positive of a given conditional statement.
1. Linear inequalities in one variable
2. Linear inequalities in two variables
3. Range of values of combined inequalities
4. Graph of linear inequalities in two variables.
5. Maximum and minimum values of simultaneous linear inequalities and application of linear inequalities in real life situation.
- Uses scale balance to introduce inequality, and illustrate further using number line.
-leads students to solve problem on inequalities in one variable and two variables.
-guides students to combine the solution of two inequalities
-guides students to construct the table of values, plot the values and highlight the region that satisfies the inequality.
-locates the highest value and the lowest value.
Follow teacher illustration and find what should be added or subtracted to make the scale balance.
-combine the solutions of two inequalities
-construct the table of values, plot the values, highlight the region that satisfies inequalities and locate the maximum and minimum values.
Scale balance, number line chart, graph board, mathematical sets.
1. Angles suspended by a chord in a circle.
2. Angles subtended by chord at the centre.
3. Perpendicular bisectors of chords.
4. Angles in alternate segment
5. Cyclic quadrilaterals
- Leads students in constructing models to show angles subtended at the centre, perpendicular bisectors of chord and angles alternate segments.
-leads students in carrying out the formal proof of each one.
-leads students in solving practical problems using the models.
Participate in constructing models using cardboard paper
-draw diagrams of models and write down their observations against each model
-follow the teacher in deductive proof
-solve problems using the models.
Card board, cardboard showing chords and segments of a circle.
1. Proof of the theorem: the angle which an arc suspend at centre is twice the angle subtended at the circumference.
2. Proof of the theorem: the angles in same segment are equal.
3. Proof of the theorem: the angles in a semi-circle is one right angle.
4. Proof of the theorem: the opposite angles of a cyclic quadrilateral are supplementary.
5. Proof of the theorem: the tangent to a circle is perpendicular to the radius.
Leads students to review the format for proving Euclidean Geometry such as: Given: Required to prove: Construction, Proof, and Conclusion.
-leads students to prove the theorem by asking them to suggest reasons why certain conclusions should hold.
-demonstrates the solution of practical problems leading to the theorem.
Participate in the revision by mentioning the format along with the teacher.
-suggest reason for the conclusions arrived at each point in the process.
-solve problems given by the teacher.
Models of circle theorem.
1. Angle at centre is twice angle at the circumference of circle
2. Angles in the same segments are equal.
3. Angles in a semi-circle is 90o
4. Opposite angles of a cyclic quadrilateral are supplementary (i.e. when the opposite angles are added, they give 1800)
5. Tangent to a circle (i.e. Radius of a circle is perpendicular to the tangent of a circle).
-leads the students to measure the angles on the circumference and draw the diagram that represents their model.
-leads students to carry out the formal proof using the model to explain the steps involved.
Construct the models, measure, the angles on the circumference, draw the diagram and participate in the formal proof using inference from the drawing.
1. Derivation of sine rule and its application
2. Derivation of cosine rule and its applications.
Shows the chart of acute and obtuse angle
-leads students to use the charts to explain conventional methods of denoting vertices of triangles
-guides students to match corresponding sides to the corresponding angle of the triangle.
-leads students to identify angle 900 and proves the sine rule to arrive at the expression a = b = c
SinA SinB SinC
-applies the sine rule in solving problems
-shows students cosine rule chart
-guides students to derive the expression for the cosine rule and apply the rule in solving problems. E.g. (c2=a2+b2-2abCosC) and the likes
Study the two charts and follow teacher’s explanation on deriving the sine and the cosine rule.
-apply the rules in solving problem.
Acute angle chart and obtuse-angled triangle chart.
Angles of elevation and depression.
Guides students on how to draw angles of elevation and depression.
Leads students to apply trigonometric ratio, sine and cosine rules to solve problems on angles of elevation and depression.
Draw the diagrams.
Solve problem on angles of elevation and depression.
Tree in the school compound, a student standing on a desk.
1. Definition and drawing of 4 cardinal, 8 cardinal points and 16 cardinal points
2. Notation for bearings cardinal notations N30oE, S45oN, 3 digits notations e.g. 075o, 350o etc.
3. Making sketches involving lengths and angles/bearing
4. Problem solving on lengths, angles and bearing.
Leads students to define bearing and draw 4, 8 and 16 cardinal points.
-leads students to mention the two types of bearing notation giving examples of each.
-leads students to do exercise on writing bearings.
-guides students to represent problems on bearing with diagram.
-leads students to use Pythagoras theorem, trigonometric ratios, sine and cosine rules etc to solve problems on bearing.
Mention the two types of notations and state their own examples
-draw diagram on word problem on bearing
-use the Pythagoras theorem, trigonometric ratios, sine and cosine rules to solve the problem.
Charts illustrating cardinal points, ruler, pencil, protractor, computer assisted instructional resources.
1. Throwing of dice, tossing of coin and pack of playing cards
2. Theoretical and experimental probability.
3. Mutually exclusive events.
Leads students to examine the coin, die and pack of cards, identify the number of faces of the coin, die and number of cards. Ask students to throw or toss the coin/die and note the outcome.
-Leads students to identify the die, the card and coin, pack of card as instruments of chance.
-Teacher explains theoretical and experimental probabilities and mutually exclusive events.
- Examine the coin, die and pack of cards.
-identify the number of faces of the coin and die and number of cards.
-throw or toss die/coin and record outcome and consequently define theoretical, experimental probabilities and mutually exclusive events.
Ludo, die, park of playing cards.
i. Independent events
ii. Complementary events
iii. Outcome tables
iv. Tree diagram/practical application of probabilities in health, business and population.
Leads students to define mutually exclusive independent and complementary events.
-Asks students to derive other examples on those types each.
-leads them to evolve the rules using the chart.
-to use the rule to solve problems on independent events and complementary events.
-to draw questions on probability etc.
Solve problems on selection with or without replacement
-study and copy the derived questions and approaches relevant to probabilities in practical situations.
-students solve the derived questions.
Cut a newspaper of stock market reports.
Annual reports of shares, published statistics on capital market.
1. Meaning and computation of mean, median and mode of ungrouped /discrete data
2. Explain meaning of dispersion and define-range, variance and standard deviation for ungrouped data.
3. Presentation of grouped figures
4. Class interval
5. Determination of class boundaries from class interval and class mark.
Revises mean, median, mode of set of numbers with students.
-leads students to calculate mean, mode of ungrouped frequency tables manually and with calculator.
-On computation of these measures
-determine class boundaries, class interval, mid-value etc.
Revise measures of central tendency calculate mean, median, mode under supervision of teacher.
-write scores of 50 students
-appreciate need for grouping
-calculate class boundaries, class interval and class mark.
Ages of students, poles of different height, different objects, and score chart showing grouped frequency table.
Grouped data (drawing and reading of histogram)
Asks students to suggest and write possible scores of 50 students in mathematics
-leads students to see need for grouping
-constructs grouped frequency table using specified intervals.
- Teaches the steps for calculating class boundaries, class interval and class mark.
- Suggest and write scores of 50 students and record the scores.
-appreciate need for grouping
-calculate class boundaries, class internal and class marks.
Poles of different heights, ages of large number of students, prices of goods in the market, objects etc.
1. Mean of grouped data
2. Median of grouped data
3. Mode of grouped data
Shows score charts that will lead to grouped frequency distribution to the students.
-guides students to identify the highest and lowest marks and construct class interval
-constructs grouped frequency table by using class interval.
- calculates the mean, median, mode of grouped data.
Study the score charts,
-identify the highest and lowest score
-follow the teacher’s guide to calculate the grouped frequency table.
Score chart containing marks of 50 students in a class ranging from 5 to 92, computer will be relevant software.
1. Mean deviation of grouped data
2. Standard deviation of grouped data.
3. Variance of grouped data and range
4. Calculation of standard deviation by using assumed or working mean (A).
Explains concept of variability or dispersion to the students.
-leads students on computation of these measures.
-explains terms including secondary market transaction.
Note: (The Secondary market also known as the aftermarket, is the financial market where previously issued securities and financial instruments such as stock, bonds, debentures are bought and sold)
Solve problems with the help of the teacher in groups, identify areas of application.
Posters containing some data from published statistics.
Posters showing areas of application of measure of dispersion.
i. Construction of cumulative frequency table to include class intervals, tally, frequencies, class boundaries.
ii. Drawing of histogram and frequency polygon
iii. Deduce frequency polygon from histogram
iv. Drawing of frequency polygon using mid-value and the frequency.
v. Review of (i-iv) by engaging the students with various class work.
Suggests 30 quantitative values less than 100. Writes down the values on board, leads students to construct cumulative frequency tables.
-constructs class boundaries of the cumulative frequency curve.
-draws the cumulative frequency curve using the upper class boundaries and the cumulative frequencies
-draws histogram and read from the graph.
Suggests values to teacher
-copy suggested values
-construct grouped frequency table
-construct cumulative frequency under teacher’s supervision
Cumulative frequency curve chart, graph board, graph book, pencil etc. (graph board is mandatory)
Guides students to plot the points of class boundaries and cumulative frequency on the graph.
-Uses free hands to join the points.
-shows students various ways of locating the points
-guides students to read quartiles, percentiles, deciles from the ogive
-plot points o the graph with teacher’s supervision.
-join points together to have the graph, determine, median, deciles, quartiles and percentiles from the graph (ogive)
Graph board, graph book, pencil etc.
i. Meaning of deciles
ii. Examples showing median and quartiles from graph
iii. More examples on interquartiles, range (quarter deviation) by using formula.
Guides students to calculate deciles, quartiles by formula.
-reads the values from the graph by writing the y – axis and x-axis.
-writes down the values.
Calculate deciles, quartiles, percentiles, decile etc.
Graph board, graph book.
1. Explain the meaning of median on a cumulative frequency curve, percentiles, quartiles, deciles.
2. Determination of median, deciles, quartiles and percentiles, by formula method.
Leads students to define median from cumulative frequency curve, deciles, quartiles and percentiles.
-guides students to draw Ogives of data and make interpretation
-calculates the mean, median and the mode of the grouped frequency table manually.
Calculate class boundaries
-plot cumulative frequency curves in graph paper, follow steps for estimated median, quartiles and percentiles from the graph under teacher’s supervision.
Graph board, graph book, ruler, pencil, published charts of cumulative frequency curve. Data from capital market, stock market used in previous lessons.
i. Rational and irrational numbers revision showing examples of surd.
ii. Simplification of surds
iii. Addition and subtraction of surds (stating the rule that guides addition and subtraction of similar surds)
iv. Multiplication and division of surds to include rationalization.
Guides students to:
-differentiate between rational and irrational numbers.
-performs the operations of addition and subtraction on surds
-conjugates binomial surds using the idea of difference of two squares.
Differentiate between rational and irrational numbers leading to the definition of surds
-perform and solve problems on addition, subtraction, multiplication and division of surds.
-verify the rules of the operation of mathematical operations
-apply the principles.
Charts showing addition, subtraction, multiplication, division and conjugate.
i. Conjugate of binomial surds.
ii. Simplification of surds including difference of two squares in the denominator.
iii. Application to solving triangles involving trigonometric ratio of special angles 30o, 60o and 45o.
iv. Evaluation of expression involving surds.
Guides students to conjugate binomial surds using the idea of difference of two squares.
Leads students to appreciate the application of surds to trigonometric ratios e.g.
sin 600 = 3/2
sin 450 = 1/2 etc.
Apply the principles of difference of two squares to the conjugate of surds expressions.
-relate surds to trigonometric ratios.
As in week 9 above.
Students: Dramatize their duties and obligations as citizens to the communities.
i. Meaning/definition of popular participation