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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 |
OPENER EXAMINATION |
|||||||
| 2 | 1-2 |
Quadratic Expressions and Equations
|
The quadratic formula
The quadratic formula Formation of quadratic equations Graphs of quadratic functions |
By the end of the
lesson, the learner
should be able to:
Solve quadratic expressions using the quadratic formula Apply quadratic formula to any quadratic equation Derive the quadratic formula Solve quadratic expressions using the quadratic formula Apply formula to complex coefficients Interpret discriminant values |
Q/A on formula derivation steps
Discussions on formula applications Solving equations using formula Demonstrations of derivation process Explaining formula structure Q/A on formula mastery Discussions on discriminant meaning Solving complex equations Demonstrations of discriminant analysis Explaining nature of roots |
Calculators, formula derivation charts
Calculators, discriminant interpretation guides Calculators, word problem templates Graph papers, calculators, plotting guides |
KLB Mathematics Book Three Pg 7-9
|
|
| 2 | 3 |
Quadratic Expressions and Equations
|
Graphs of quadratic functions
Graphical solutions of quadratic equation |
By the end of the
lesson, the learner
should be able to:
Draw graphs of quadratic functions Identify vertex and axis of symmetry Find intercepts from graphs |
Q/A on graph plotting techniques
Discussions on graph features Solving graphing problems Demonstrations of feature identification Explaining graph properties |
Graph papers, calculators, rulers
|
KLB Mathematics Book Three Pg 12-15
|
|
| 2 | 4 |
Quadratic Expressions and Equations
|
Graphical solutions of quadratic equation
|
By the end of the
lesson, the learner
should be able to:
Solve quadratic equations using the graphs Verify algebraic solutions graphically Estimate solutions from graphs |
Q/A on solution verification
Discussions on estimation techniques Solving complex graphical problems Demonstrations of verification methods Explaining accuracy in estimation |
Graph papers, calculators, estimation guides
|
KLB Mathematics Book Three Pg 17-19
|
|
| 2 | 5 |
Quadratic Expressions and Equations
Approximations and Errors |
Graphical solutions of simultaneous equations
Computing using calculators |
By the end of the
lesson, the learner
should be able to:
Draw tables for simultaneous equations Find the graphical solutions of simultaneous equations Solve systems involving quadratic and linear equations |
Q/A on simultaneous equation concepts
Discussions on intersection analysis Solving systems of equations Demonstrations of intersection finding Explaining solution interpretation |
Graph papers, calculators, intersection analysis guides
Calculators, operation guides |
KLB Mathematics Book Three Pg 19-21
|
|
| 2 | 6 |
Approximations and Errors
|
Computing using calculators
Approximation |
By the end of the
lesson, the learner
should be able to:
Solve basic operations using calculators Perform complex calculations accurately Verify calculator results |
Q/A on calculator accuracy
Discussions on verification methods Solving complex computational problems Demonstrations of result checking Explaining calculation verification |
Calculators, verification worksheets
Calculators, rounding charts |
KLB Mathematics Book Three Pg 26-28
|
|
| 2 | 7 |
Approximations and Errors
|
Estimation
Accuracy and errors |
By the end of the
lesson, the learner
should be able to:
Approximate values by truncation Estimate values using appropriate methods Compare estimation techniques |
Q/A on estimation strategies
Discussions on truncation vs rounding Solving estimation problems Demonstrations of truncation methods Explaining when to use different techniques |
Calculators, estimation guides
Calculators, error calculation sheets |
KLB Mathematics Book Three Pg 30
|
|
| 3 | 1-2 |
Approximations and Errors
|
Percentage error
Rounding off error and truncation error Propagation of errors |
By the end of the
lesson, the learner
should be able to:
Find the percentage error of a given value Calculate percentage error accurately Interpret percentage error results Find the propagation of errors in addition and subtraction Calculate combined errors Apply error propagation rules |
Q/A on percentage concepts
Discussions on percentage error meaning Solving percentage error problems Demonstrations of percentage calculations Explaining error interpretation Q/A on error propagation concepts Discussions on addition/subtraction errors Solving error propagation problems Demonstrations of error combination Explaining propagation principles |
Calculators, percentage error worksheets
Calculators, error comparison charts Calculators, error propagation guides |
KLB Mathematics Book Three Pg 32-34
KLB Mathematics Book Three Pg 35-36 |
|
| 3 | 3 |
Approximations and Errors
|
Propagation of errors
Propagation of errors in multiplication |
By the end of the
lesson, the learner
should be able to:
Find the propagation of errors in addition and subtraction Apply error propagation to complex problems Verify error calculations |
Q/A on propagation mastery
Discussions on complex error scenarios Solving advanced propagation problems Demonstrations of verification methods Explaining error validation |
Calculators, verification worksheets
Calculators, multiplication error guides |
KLB Mathematics Book Three Pg 35-36
|
|
| 3 | 4 |
Approximations and Errors
|
Propagation of errors in multiplication
Propagation of errors in division |
By the end of the
lesson, the learner
should be able to:
Find the propagation of errors in multiplication Solve complex multiplication error problems Compare different error propagation methods |
Q/A on advanced multiplication errors
Discussions on complex error scenarios Solving challenging multiplication problems Demonstrations of method comparison Explaining optimal error calculation |
Calculators, method comparison charts
Calculators, division error worksheets |
KLB Mathematics Book Three Pg 36-37
|
|
| 3 | 5 |
Approximations and Errors
|
Propagation of errors in division
Word problems |
By the end of the
lesson, the learner
should be able to:
Find the propagation of errors in division Solve complex division error problems Verify division error calculations |
Q/A on division error mastery
Discussions on complex division scenarios Solving advanced division error problems Demonstrations of error verification Explaining accuracy in division errors |
Calculators, verification guides
Calculators, word problem sets, comprehensive review sheets |
KLB Mathematics Book Three Pg 37-38
|
|
| 3 | 6 |
Trigonometry (II)
|
The unit circle
|
By the end of the
lesson, the learner
should be able to:
Draw the unit circle Identify coordinates on the unit circle Understand the unit circle concept |
Q/A on basic circle properties
Discussions on unit circle construction Solving problems using unit circle Demonstrations of circle drawing Explaining unit circle applications |
Calculators, protractors, rulers, pair of compasses
|
KLB Mathematics Book Three Pg 41-42
|
|
| 3 | 7 |
Trigonometry (II)
|
Trigonometric ratios of angles greater than 90°
|
By the end of the
lesson, the learner
should be able to:
Find the trigonometric values of angles Calculate trigonometric ratios for obtuse angles Apply reference angle concepts |
Q/A on basic trigonometric ratios
Discussions on angle extensions Solving obtuse angle problems Demonstrations of reference angles Explaining quadrant relationships |
Calculators, protractors, rulers, pair of compasses
|
KLB Mathematics Book Three Pg 44-45
|
|
| 4 | 1-2 |
Trigonometry (II)
|
Trigonometric ratios of angles greater than 90°
Trigonometric ratios of negative angles Trigonometric ratios of angles greater than 360° Use of mathematical tables |
By the end of the
lesson, the learner
should be able to:
Find the trigonometric values of angles Solve problems with angles in different quadrants Apply ASTC rule for sign determination Find the trigonometric values of angles greater than 360° Apply coterminal angle concepts Reduce angles to standard position |
Q/A on quadrant properties
Discussions on sign conventions Solving multi-quadrant problems Demonstrations of ASTC rule Explaining trigonometric signs Q/A on angle reduction concepts Discussions on coterminal angles Solving extended angle problems Demonstrations of angle reduction Explaining periodic properties |
Calculators, quadrant charts
Geoboards, graph books, calculators Geoboards, graph books, calculators Mathematical tables, calculators |
KLB Mathematics Book Three Pg 46-47
KLB Mathematics Book Three Pg 49-51 |
|
| 4 | 3 |
Trigonometry (II)
|
Use of mathematical tables
Use of calculators |
By the end of the
lesson, the learner
should be able to:
Use mathematical tables to find tan Apply tables for all trigonometric functions Compare table and calculator results |
Q/A on tangent table usage
Discussions on function relationships Solving comprehensive table problems Demonstrations of result verification Explaining table limitations |
Mathematical tables, calculators
Calculators, function guides |
KLB Mathematics Book Three Pg 55-56
|
|
| 4 | 4 |
Trigonometry (II)
|
Radian measure
Simple trigonometric graphs |
By the end of the
lesson, the learner
should be able to:
Convert degrees to radians and vice versa Apply radian measure in calculations Understand radian-degree relationships |
Q/A on angle measurement systems
Discussions on radian concepts Solving conversion problems Demonstrations of conversion methods Explaining radian applications |
Calculators, conversion charts
Calculators, graph papers, plotting guides |
KLB Mathematics Book Three Pg 58-61
|
|
| 4 | 5 |
Trigonometry (II)
|
Graphs of cosines
|
By the end of the
lesson, the learner
should be able to:
Draw tables for cosine of values Plot graphs of cosine functions Compare sine and cosine graphs |
Q/A on cosine properties
Discussions on graph relationships Solving cosine graphing problems Demonstrations of cosine plotting Explaining phase relationships |
Calculators, graph papers, plotting guides
|
KLB Mathematics Book Three Pg 63-64
|
|
| 4 | 6 |
Trigonometry (II)
|
Graphs of tan
The sine rule |
By the end of the
lesson, the learner
should be able to:
Draw tables for tan of values Plot graphs of tan functions Identify asymptotes and discontinuities |
Q/A on tangent behavior
Discussions on function domains Solving tangent graphing problems Demonstrations of asymptote identification Explaining discontinuous functions |
Calculators, graph papers, plotting guides
Calculators, triangle worksheets |
KLB Mathematics Book Three Pg 64-65
|
|
| 4 | 7 |
Trigonometry (II)
|
Cosine rule
Problem solving |
By the end of the
lesson, the learner
should be able to:
State the cosine rule Apply cosine rule to find solution of triangles Choose appropriate rule for triangle solving |
Q/A on cosine rule concepts
Discussions on rule selection Solving complex triangle problems Demonstrations of cosine rule Explaining when to use each rule |
Calculators, triangle worksheets
Calculators, comprehensive problem sets, real-world examples |
KLB Mathematics Book Three Pg 71-75
|
|
| 5 | 1-2 |
Surds
|
Rational and irrational numbers
Order of surds and simplification Simplification of surds practice Addition of surds |
By the end of the
lesson, the learner
should be able to:
Classify numbers as rational and irrational numbers Identify rational and irrational numbers Distinguish between rational and irrational forms Simplify surds using factorization Express surds in simplest form Apply systematic simplification methods |
Q/A on number classification concepts
Discussions on rational vs irrational properties Solving classification problems Demonstrations of number identification Explaining decimal representations Q/A on factorization techniques Discussions on factor identification Solving extensive simplification problems Demonstrations of step-by-step methods Explaining perfect square extraction |
Calculators, number classification charts
Calculators, surd order examples Calculators, factor trees, simplification worksheets Calculators, addition rule charts |
KLB Mathematics Book Three Pg 78
KLB Mathematics Book Three Pg 79-80 |
|
| 5 | 3 |
Surds
|
Subtraction of surds
Multiplication of surds |
By the end of the
lesson, the learner
should be able to:
Subtract surds with like terms Apply subtraction rules to surds Simplify surd subtraction expressions |
Q/A on subtraction principles
Discussions on surd subtraction methods Solving subtraction problems Demonstrations of systematic approaches Explaining subtraction verification |
Calculators, subtraction worksheets
Calculators, multiplication rule guides |
KLB Mathematics Book Three Pg 80
|
|
| 5 | 4 |
Surds
|
Division of surds
|
By the end of the
lesson, the learner
should be able to:
Divide surds of the same order Apply division rules to surds Simplify quotients of surds |
Q/A on division concepts
Discussions on surd division methods Solving division problems systematically Demonstrations of quotient simplification Explaining division techniques |
Calculators, division worksheets
|
KLB Mathematics Book Three Pg 81-82
|
|
| 5 | 5 |
Surds
|
Rationalizing the denominator
Advanced rationalization techniques |
By the end of the
lesson, the learner
should be able to:
Rationalize the denominator of fractions Apply rationalization techniques Simplify expressions with surd denominators |
Q/A on rationalization concepts
Discussions on denominator clearing Solving rationalization problems Demonstrations of conjugate methods Explaining rationalization importance |
Calculators, rationalization guides
Calculators, advanced technique sheets |
KLB Mathematics Book Three Pg 85-87
|
|
| 5 | 6 |
Further Logarithms
|
Introduction
Laws of logarithms |
By the end of the
lesson, the learner
should be able to:
Use calculators to find the logarithm of numbers Understand logarithmic notation and concepts Apply basic logarithmic principles |
Q/A on exponential and logarithmic relationships
Discussions on logarithm definition and properties Solving basic logarithm problems Demonstrations of calculator usage Explaining logarithm-exponential connections |
Calculators, logarithm definition charts
Calculators, logarithm law charts |
KLB Mathematics Book Three Pg 89
|
|
| 5 | 7 |
Further Logarithms
|
Laws of logarithms
|
By the end of the
lesson, the learner
should be able to:
Use laws of logarithms to solve problems Apply advanced logarithmic laws Combine multiple laws in calculations |
Q/A on law mastery and applications
Discussions on power and root laws Solving complex law-based problems Demonstrations of combined law usage Explaining advanced law techniques |
Calculators, advanced law worksheets
Calculators, challenging problem sets |
KLB Mathematics Book Three Pg 90-93
|
|
| 6 | 1-2 |
Further Logarithms
|
Logarithmic equations and expressions
Further computation using logarithms |
By the end of the
lesson, the learner
should be able to:
Solve the logarithmic equations and expressions Apply algebraic methods to logarithmic equations Verify solutions of logarithmic equations Solve problems involving logarithms Apply logarithms to numerical computations Use logarithms for complex calculations |
Q/A on equation-solving techniques
Discussions on logarithmic equation types Solving basic logarithmic equations Demonstrations of solution methods Explaining verification techniques Q/A on computational applications Discussions on numerical problem-solving Solving computation-based problems Demonstrations of logarithmic calculations Explaining computational advantages |
Calculators, equation-solving guides
Calculators, advanced equation worksheets Calculators, computation worksheets |
KLB Mathematics Book Three Pg 93-95
KLB Mathematics Book Three Pg 95-96 |
|
| 6 | 3 |
Further Logarithms
|
Further computation using logarithms
|
By the end of the
lesson, the learner
should be able to:
Solve problems involving logarithms Apply logarithms to intermediate calculations Handle multi-step logarithmic computations |
Q/A on intermediate computational skills
Discussions on multi-step processes Solving intermediate computation problems Demonstrations of systematic approaches Explaining step-by-step methods |
Calculators, intermediate problem sets
Calculators, advanced computation guides |
KLB Mathematics Book Three Pg 95-96
|
|
| 6 | 4 |
Further Logarithms
|
Problem solving
|
By the end of the
lesson, the learner
should be able to:
Solve problems involving logarithms Apply logarithms to computational applications Integrate logarithmic concepts systematically |
Q/A on integrated problem-solving
Discussions on application strategies Solving comprehensive computational problems Demonstrations of integrated approaches Explaining systematic problem-solving |
Calculators, comprehensive problem sets
Calculators, real-world application examples |
KLB Mathematics Book Three Pg 97
|
|
| 6 | 5 |
Commercial Arithmetic
|
Simple interest
|
By the end of the
lesson, the learner
should be able to:
Calculate simple interest Apply simple interest formula Solve basic interest problems |
Q/A on interest concepts and terminology
Discussions on principal, rate, and time Solving basic simple interest problems Demonstrations of formula application Explaining interest calculations |
Calculators, simple interest charts
Calculators, real-world problem sets |
KLB Mathematics Book Three Pg 98-99
|
|
| 6 | 6 |
Commercial Arithmetic
|
Compound interest
|
By the end of the
lesson, the learner
should be able to:
Calculate the compound interest Apply compound interest formula Understand compounding concepts |
Q/A on compound interest principles
Discussions on compounding frequency Solving basic compound interest problems Demonstrations of compound calculations Explaining compounding effects |
Calculators, compound interest tables
Calculators, comparison worksheets |
KLB Mathematics Book Three Pg 102-106
|
|
| 6 | 7 |
Commercial Arithmetic
|
Appreciation
|
By the end of the
lesson, the learner
should be able to:
Calculate the appreciation value of items Apply appreciation concepts Solve appreciation problems |
Q/A on appreciation concepts
Discussions on asset value increases Solving appreciation calculation problems Demonstrations of value growth Explaining appreciation applications |
Calculators, appreciation examples
|
KLB Mathematics Book Three Pg 108
|
|
| 7 |
MIDTERM EXAMINATION |
|||||||
| 8 | 1-2 |
Commercial Arithmetic
|
Depreciation
Hire purchase Hire purchase Income tax and P.A.Y.E |
By the end of the
lesson, the learner
should be able to:
Calculate the depreciation value of items Apply depreciation methods Solve depreciation problems Find the hire purchase Solve complex hire purchase problems Calculate total costs and interest charges |
Q/A on depreciation concepts and methods
Discussions on asset value decreases Solving depreciation calculation problems Demonstrations of depreciation methods Explaining business depreciation Q/A on advanced hire purchase scenarios Discussions on complex payment structures Solving challenging hire purchase problems Demonstrations of cost analysis Explaining consumer finance decisions |
Calculators, depreciation charts
Calculators, hire purchase examples Calculators, complex hire purchase worksheets Income tax tables, calculators |
KLB Mathematics Book Three Pg 109
KLB Mathematics Book Three Pg 110-112 |
|
| 8 | 3 |
Circles: Chords and Tangents
|
Length of an arc
|
By the end of the
lesson, the learner
should be able to:
Calculate the length of an arc Apply arc length formula Understand arc-radius relationships |
Q/A on circle properties and terminology
Discussions on arc measurement concepts Solving basic arc length problems Demonstrations of formula application Explaining arc-angle relationships |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 124-125
|
|
| 8 | 4 |
Circles: Chords and Tangents
|
Chords
Parallel chords |
By the end of the
lesson, the learner
should be able to:
Calculate the length of a chord Apply chord properties and theorems Understand chord-radius relationships |
Q/A on chord definition and properties
Discussions on chord calculation methods Solving basic chord problems Demonstrations of geometric constructions Explaining chord theorems |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 126-128
|
|
| 8 | 5 |
Circles: Chords and Tangents
|
Equal chords
|
By the end of the
lesson, the learner
should be able to:
Find the length of equal chords Apply equal chord theorems Solve equal chord problems |
Q/A on equal chord properties
Discussions on chord equality conditions Solving equal chord problems Demonstrations of proof techniques Explaining theoretical foundations |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 131-132
|
|
| 8 | 6 |
Circles: Chords and Tangents
|
Intersecting chords
|
By the end of the
lesson, the learner
should be able to:
Calculate the length of intersecting chords Apply intersecting chord theorem Understand chord intersection properties |
Q/A on chord intersection concepts
Discussions on intersection theorem Solving basic intersection problems Demonstrations of theorem application Explaining geometric proofs |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 132-135
|
|
| 8 | 7 |
Circles: Chords and Tangents
|
Chord properties
Tangent to a circle |
By the end of the
lesson, the learner
should be able to:
Solve comprehensive chord problems Integrate all chord concepts Apply chord knowledge systematically |
Q/A on comprehensive chord understanding
Discussions on integrated problem-solving Solving mixed chord problems Demonstrations of systematic approaches Explaining complete chord mastery |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 126-139
|
|
| 9 |
MID TERM BREAK |
|||||||
| 10 | 1-2 |
Circles: Chords and Tangents
|
Tangent to a circle
Properties of tangents to a circle from an external point Tangent properties Tangents to two circles |
By the end of the
lesson, the learner
should be able to:
Calculate the length of tangent Calculate the angle between tangents Apply tangent measurement techniques Solve comprehensive tangent problems Apply all tangent concepts Integrate tangent knowledge systematically |
Q/A on tangent calculations
Discussions on tangent measurement Solving tangent calculation problems Demonstrations of measurement methods Explaining tangent applications Q/A on comprehensive tangent mastery Discussions on integrated applications Solving mixed tangent problems Demonstrations of complete understanding Explaining systematic problem-solving |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 141-142
KLB Mathematics Book Three Pg 139-147 |
|
| 10 | 3 |
Circles: Chords and Tangents
|
Tangents to two circles
Contact of circles |
By the end of the
lesson, the learner
should be able to:
Calculate the tangents of transverse common tangents Find transverse tangent properties Compare direct and transverse tangents |
Q/A on transverse tangent concepts
Discussions on tangent type differences Solving transverse tangent problems Demonstrations of comparison methods Explaining tangent classifications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 150-151
|
|
| 10 | 4 |
Circles: Chords and Tangents
|
Contact of circles
|
By the end of the
lesson, the learner
should be able to:
Calculate the radii of contact circles Understand external contact properties Compare internal and external contact |
Q/A on external contact concepts
Discussions on contact type differences Solving external contact problems Demonstrations of contact analysis Explaining contact applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 153-154
|
|
| 10 | 5 |
Circles: Chords and Tangents
|
Circle contact
Angle in alternate segment |
By the end of the
lesson, the learner
should be able to:
Solve problems involving chords, tangents and contact circles Integrate all contact concepts Apply comprehensive contact knowledge |
Q/A on comprehensive contact understanding
Discussions on integrated problem-solving Solving complex contact problems Demonstrations of systematic approaches Explaining complete contact mastery |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 154-157
|
|
| 10 | 6 |
Circles: Chords and Tangents
|
Angle in alternate segment
Circumscribed circle |
By the end of the
lesson, the learner
should be able to:
Calculate the angles in alternate segments Solve complex segment problems Apply advanced segment theorems |
Q/A on advanced segment applications
Discussions on complex angle relationships Solving challenging segment problems Demonstrations of sophisticated techniques Explaining advanced applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 160-161
|
|
| 10 | 7 |
Circles: Chords and Tangents
|
Escribed circles
Centroid |
By the end of the
lesson, the learner
should be able to:
Construct escribed circles Find escribed circle properties Apply escription concepts |
Q/A on escription concepts
Discussions on escribed circle construction Solving escription problems Demonstrations of construction methods Explaining escription applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 165-166
|
|
| 11 | 1-2 |
Circles: Chords and Tangents
Matrices |
Orthocenter
Circle and triangle relationships Introduction and real-life applications Order of a matrix and elements Square matrices, row and column matrices |
By the end of the
lesson, the learner
should be able to:
Construct orthocenter Find orthocenter properties Apply orthocenter concepts Define matrices and identify matrix applications Recognize matrices in everyday contexts Understand tabular data representation Appreciate the importance of matrices |
Q/A on orthocenter concepts
Discussions on orthocenter construction Solving orthocenter problems Demonstrations of construction methods Explaining orthocenter applications Q/A on tabular data in daily life Discussions on school exam results tables Analyzing bus timetables and price lists Demonstrations using newspaper sports tables Explaining matrix notation using grid patterns |
Geometrical set, calculators
Old newspapers with league tables, chalk and blackboard, exercise books Chalk and blackboard, ruled exercise books, class register Paper cutouts, chalk and blackboard, counters or bottle tops |
KLB Mathematics Book Three Pg 167
KLB Mathematics Book Three Pg 168-169 |
|
| 11 | 3 |
Matrices
|
Addition of matrices
Subtraction of matrices Combined addition and subtraction Scalar multiplication |
By the end of the
lesson, the learner
should be able to:
Add matrices of the same order Apply matrix addition rules correctly Understand compatibility for addition Solve matrix addition problems systematically |
Q/A on matrix addition using number examples
Discussions on element-wise addition using counters Solving basic addition using blackboard work Demonstrations using physical counting objects Explaining compatibility using size comparisons |
Counters or stones, chalk and blackboard, exercise books
Chalk and blackboard, exercise books, number cards made from cardboard Chalk and blackboard, exercise books, locally made operation cards Beans or stones for grouping, chalk and blackboard, exercise books |
KLB Mathematics Book Three Pg 170-171
|
|
| 11 | 4 |
Matrices
|
Introduction to matrix multiplication
Matrix multiplication (2×2 matrices) |
By the end of the
lesson, the learner
should be able to:
Understand matrix multiplication prerequisites Learn compatibility requirements for multiplication Apply row-by-column multiplication method Calculate simple matrix products |
Q/A on multiplication compatibility using dimensions
Discussions on row-column method using finger tracing Solving basic multiplication using dot product method Demonstrations using physical row-column matching Explaining order requirements using practical examples |
Chalk and blackboard, rulers for tracing, exercise books
Chalk and blackboard, exercise books, homemade grid templates |
KLB Mathematics Book Three Pg 174-176
|
|
| 11 | 5 |
Matrices
|
Matrix multiplication (larger matrices)
Properties of matrix multiplication |
By the end of the
lesson, the learner
should be able to:
Multiply matrices of various orders Apply multiplication to 3×3 and larger matrices Determine when multiplication is possible Calculate products efficiently |
Q/A on larger matrix multiplication using patterns
Discussions on efficiency techniques using shortcuts Solving advanced problems using systematic methods Demonstrations using organized calculation procedures Explaining general principles using examples |
Chalk and blackboard, large sheets of paper for working, exercise books
Chalk and blackboard, exercise books, cardboard for property cards |
KLB Mathematics Book Three Pg 176-179
|
|
| 11 | 6 |
Matrices
|
Real-world matrix multiplication applications
Identity matrix |
By the end of the
lesson, the learner
should be able to:
Apply matrix multiplication to practical problems Solve business and economic applications Calculate costs, revenues, and quantities Interpret matrix multiplication results |
Q/A on practical applications using local business examples
Discussions on market problems using familiar contexts Solving real-world problems using matrix methods Demonstrations using shop keeper scenarios Explaining result interpretation using meaningful contexts |
Chalk and blackboard, local price lists, exercise books
Chalk and blackboard, exercise books, pattern cards made from paper |
KLB Mathematics Book Three Pg 176-179
|
|
| 11 | 7 |
Matrices
|
Determinant of 2×2 matrices
Inverse of 2×2 matrices - theory |
By the end of the
lesson, the learner
should be able to:
Calculate determinants of 2×2 matrices Apply the determinant formula correctly Understand geometric interpretation of determinants Use determinants to classify matrices |
Q/A on determinant calculation using cross multiplication
Discussions on formula application using memory aids Solving determinant problems using systematic approach Demonstrations using cross pattern method Explaining geometric meaning using area concepts |
Chalk and blackboard, exercise books, crossed sticks for demonstration
Chalk and blackboard, exercise books, fraction examples |
KLB Mathematics Book Three Pg 183
|
|
| 12 | 1-2 |
Matrices
|
Inverse of 2×2 matrices - practice
Introduction to solving simultaneous equations Solving 2×2 simultaneous equations using matrices Advanced simultaneous equation problems |
By the end of the
lesson, the learner
should be able to:
Calculate inverses of 2×2 matrices systematically Verify inverse calculations through multiplication Apply inverse properties correctly Solve complex inverse problems Solve 2×2 simultaneous equations using matrix methods Apply inverse matrix techniques Verify solutions by substitution Compare matrix method with other techniques |
Q/A on inverse calculation verification methods
Discussions on accuracy checking using multiplication Solving advanced inverse problems using practice Demonstrations using verification procedures Explaining checking methods using examples Q/A on matrix solution methods using step-by-step approach Discussions on solution verification using substitution Solving 2×2 systems using complete method Demonstrations using organized solution process Explaining method advantages using comparisons |
Chalk and blackboard, exercise books, scrap paper for verification
Chalk and blackboard, exercise books, equation examples from previous topics Chalk and blackboard, exercise books, previous elimination method examples Chalk and blackboard, exercise books, graph paper if available |
KLB Mathematics Book Three Pg 185-187
KLB Mathematics Book Three Pg 188-190 |
|
| 12 | 3 |
Matrices
|
Matrix applications in real-world problems
|
By the end of the
lesson, the learner
should be able to:
Apply matrix operations to practical scenarios Solve business, engineering, and scientific problems Model real situations using matrices Interpret matrix solutions in context |
Q/A on practical applications using local examples
Discussions on modeling using familiar situations Solving comprehensive problems using matrix tools Demonstrations using community-based scenarios Explaining solution interpretation using meaningful contexts |
Chalk and blackboard, local business examples, exercise books
|
KLB Mathematics Book Three Pg 168-190
|
|
| 12 | 4 |
Matrices
|
Transpose of matrices
Matrix equation solving |
By the end of the
lesson, the learner
should be able to:
Define and calculate matrix transpose Understand transpose properties Apply transpose operations correctly Solve problems involving transpose |
Q/A on transpose concepts using reflection ideas
Discussions on row-column interchange using visual methods Solving transpose problems using systematic approach Demonstrations using flip and rotate concepts Explaining properties using symmetry ideas |
Chalk and blackboard, exercise books, paper cutouts for demonstration
Chalk and blackboard, exercise books, algebra reference examples |
KLB Mathematics Book Three Pg 170-174
|
|
| 12 | 5 |
Formulae and Variations
|
Introduction to formulae
Subject of a formula - basic cases |
By the end of the
lesson, the learner
should be able to:
Define formulae and identify formula components Recognize formulae in everyday contexts Understand the relationship between variables Appreciate the importance of formulae in mathematics |
Q/A on familiar formulae from daily life
Discussions on cooking recipes as formulae Analyzing distance-time relationships using walking examples Demonstrations using perimeter and area calculations Explaining formula notation using simple examples |
Chalk and blackboard, measuring tape or string, exercise books
Chalk and blackboard, simple balance (stones and stick), exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 12 | 6 |
Formulae and Variations
|
Subject of a formula - intermediate cases
Subject of a formula - advanced cases |
By the end of the
lesson, the learner
should be able to:
Make complex variables the subject of formulae Handle formulae with fractions and powers Apply multiple inverse operations systematically Solve intermediate difficulty problems |
Q/A on complex rearrangement using systematic approach
Discussions on fraction handling using common denominators Solving intermediate problems using organized methods Demonstrations using step-by-step blackboard work Explaining systematic approaches using flowcharts |
Chalk and blackboard, fraction strips made from paper, exercise books
Chalk and blackboard, squared paper patterns, exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 12 | 7 |
Formulae and Variations
|
Applications of formula manipulation
Introduction to variation Direct variation - introduction |
By the end of the
lesson, the learner
should be able to:
Apply formula rearrangement to practical problems Solve real-world problems using formula manipulation Calculate unknown quantities in various contexts Interpret results in meaningful situations |
Q/A on practical applications using local examples
Discussions on real-world formula use in farming/building Solving application problems using formula rearrangement Demonstrations using construction and farming scenarios Explaining practical interpretation using community examples |
Chalk and blackboard, local measurement tools, exercise books
Chalk and blackboard, local price lists from markets, exercise books Chalk and blackboard, beans or stones for counting, exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 13 |
CLOSING EXAMINATION |
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| 14 |
MARKING AND CLOSING |
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