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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
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
|
KLB Mathematics Book Three Pg 98-99
|
|
| 2 | 2 |
Commercial Arithmetic
|
Simple interest
|
By the end of the
lesson, the learner
should be able to:
Calculate simple interest Solve complex simple interest problems Apply simple interest to real-world situations |
Q/A on advanced simple interest concepts
Discussions on practical applications Solving complex interest problems Demonstrations of real-world scenarios Explaining business applications |
Calculators, real-world problem sets
|
KLB Mathematics Book Three Pg 98-101
|
|
| 2 | 3 |
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
|
KLB Mathematics Book Three Pg 102-106
|
|
| 2 | 4 |
Commercial Arithmetic
|
Compound interest
|
By the end of the
lesson, the learner
should be able to:
Calculate the compound interest Solve advanced compound interest problems Compare simple and compound interest |
Q/A on advanced compounding scenarios
Discussions on investment comparisons Solving complex compound problems Demonstrations of comparison methods Explaining investment decisions |
Calculators, comparison worksheets
|
KLB Mathematics Book Three Pg 102-107
|
|
| 2 | 5 |
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
|
|
| 2 | 6 |
Commercial Arithmetic
|
Depreciation
Hire purchase |
By the end of the
lesson, the learner
should be able to:
Calculate the depreciation value of items Apply depreciation methods Solve depreciation problems |
Q/A on depreciation concepts and methods
Discussions on asset value decreases Solving depreciation calculation problems Demonstrations of depreciation methods Explaining business depreciation |
Calculators, depreciation charts
Calculators, hire purchase examples |
KLB Mathematics Book Three Pg 109
|
|
| 2 | 7 |
Commercial Arithmetic
|
Hire purchase
|
By the end of the
lesson, the learner
should be able to:
Find the hire purchase Solve complex hire purchase problems Calculate total costs and interest charges |
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, complex hire purchase worksheets
|
KLB Mathematics Book Three Pg 110-112
|
|
| 3 | 1 |
Commercial Arithmetic
|
Income tax and P.A.Y.E
|
By the end of the
lesson, the learner
should be able to:
Calculate the income tax Calculate the P.A.Y.E Apply tax calculation methods |
Q/A on tax system concepts
Discussions on income tax and P.A.Y.E systems Solving tax calculation problems Demonstrations of tax computation Explaining taxation principles |
Income tax tables, calculators
|
KLB Mathematics Book Three Pg 112-117
|
|
| 3 | 2 |
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
|
|
| 3 | 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 Solve complex arc length problems Apply arc concepts to real situations |
Q/A on advanced arc applications
Discussions on practical arc measurements Solving complex arc problems Demonstrations of real-world applications Explaining engineering and design uses |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 124-125
|
|
| 3 | 4 |
Circles: Chords and Tangents
|
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
|
|
| 3 | 5 |
Circles: Chords and Tangents
|
Parallel chords
|
By the end of the
lesson, the learner
should be able to:
Calculate the perpendicular bisector Find the value of parallel chords Apply parallel chord properties |
Q/A on parallel chord concepts
Discussions on perpendicular bisector properties Solving parallel chord problems Demonstrations of construction techniques Explaining geometric relationships |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 129-131
|
|
| 3 | 6 |
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
|
|
| 3 | 7 |
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
|
|
| 4 | 1 |
Circles: Chords and Tangents
|
Intersecting chords
|
By the end of the
lesson, the learner
should be able to:
Calculate the length of intersecting chords Solve complex intersection problems Apply advanced chord theorems |
Q/A on advanced intersection scenarios
Discussions on complex chord relationships Solving challenging intersection problems Demonstrations of advanced techniques Explaining sophisticated applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 135-139
|
|
| 4 | 2 |
Circles: Chords and Tangents
|
Chord properties
|
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
|
|
| 4 | 3 |
Circles: Chords and Tangents
|
Tangent to a circle
|
By the end of the
lesson, the learner
should be able to:
Construct a tangent to a circle Understand tangent properties Apply tangent construction methods |
Q/A on tangent definition and properties
Discussions on tangent construction Solving basic tangent problems Demonstrations of construction techniques Explaining tangent characteristics |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 139-140
|
|
| 4 | 4 |
Circles: Chords and Tangents
|
Tangent to a circle
|
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 |
Q/A on tangent calculations
Discussions on tangent measurement Solving tangent calculation problems Demonstrations of measurement methods Explaining tangent applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 141-142
|
|
| 4 | 5 |
Circles: Chords and Tangents
|
Properties of tangents to a circle from an external point
Tangent properties |
By the end of the
lesson, the learner
should be able to:
State the properties of tangents to a circle from an external point Apply external tangent properties Solve external tangent problems |
Q/A on external tangent concepts
Discussions on tangent properties Solving external tangent problems Demonstrations of property applications Explaining theoretical foundations |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 142-144
|
|
| 4 | 6 |
Circles: Chords and Tangents
|
Tangents to two circles
|
By the end of the
lesson, the learner
should be able to:
Calculate the tangents of direct common tangents Find direct common tangent properties Apply two-circle tangent concepts |
Q/A on two-circle tangent concepts
Discussions on direct tangent properties Solving direct tangent problems Demonstrations of construction methods Explaining geometric relationships |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 148-149
|
|
| 4 | 7 |
Circles: Chords and Tangents
|
Tangents to two 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
|
|
| 5 | 1 |
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 internal contact properties Apply contact circle concepts |
Q/A on circle contact concepts
Discussions on internal contact properties Solving internal contact problems Demonstrations of contact relationships Explaining geometric principles |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 151-153
|
|
| 5 | 2 |
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
|
|
| 5 | 3 |
Circles: Chords and Tangents
|
Circle contact
|
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
|
|
| 5 | 4 |
Circles: Chords and Tangents
|
Angle in alternate segment
|
By the end of the
lesson, the learner
should be able to:
Calculate the angles in alternate segments Apply alternate segment theorem Understand segment angle properties |
Q/A on alternate segment concepts
Discussions on segment angle relationships Solving basic segment problems Demonstrations of theorem application Explaining geometric proofs |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 157-160
|
|
| 5 | 5 |
Circles: Chords and Tangents
|
Angle in alternate segment
|
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
|
|
| 5 | 6 |
Circles: Chords and Tangents
|
Circumscribed circle
|
By the end of the
lesson, the learner
should be able to:
Construct circumscribed circles Find circumscribed circle properties Apply circumscription concepts |
Q/A on circumscription concepts
Discussions on circumscribed circle construction Solving circumscription problems Demonstrations of construction techniques Explaining circumscription applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 165
|
|
| 5 | 7 |
Circles: Chords and Tangents
|
Escribed circles
|
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
|
|
| 6 | 1 |
Circles: Chords and Tangents
|
Centroid
|
By the end of the
lesson, the learner
should be able to:
Construct centroid Find centroid properties Apply centroid concepts |
Q/A on centroid definition and properties
Discussions on centroid construction Solving centroid problems Demonstrations of construction techniques Explaining centroid applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 166
|
|
| 6 | 2 |
Circles: Chords and Tangents
|
Orthocenter
|
By the end of the
lesson, the learner
should be able to:
Construct orthocenter Find orthocenter properties Apply orthocenter concepts |
Q/A on orthocenter concepts
Discussions on orthocenter construction Solving orthocenter problems Demonstrations of construction methods Explaining orthocenter applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 167
|
|
| 6 | 3 |
Circles: Chords and Tangents
Matrices |
Circle and triangle relationships
Introduction and real-life applications |
By the end of the
lesson, the learner
should be able to:
Solve comprehensive circle-triangle problems Integrate all circle and triangle concepts Apply advanced geometric relationships |
Q/A on comprehensive geometric understanding
Discussions on integrated relationships Solving complex geometric problems Demonstrations of advanced applications Explaining sophisticated geometric principles |
Geometrical set, calculators
Old newspapers with league tables, chalk and blackboard, exercise books |
KLB Mathematics Book Three Pg 164-167
|
|
| 6 | 4 |
Matrices
|
Order of a matrix and elements
Square matrices, row and column matrices Addition of matrices |
By the end of the
lesson, the learner
should be able to:
Determine the order of given matrices Identify matrix elements by position Use correct notation for matrix elements Distinguish between different matrix types |
Q/A on matrix structure using grid drawings
Discussions on rows and columns using classroom seating Solving element location using coordinate games Demonstrations using drawn grids on blackboard Explaining position notation using class register |
Chalk and blackboard, ruled exercise books, class register
Paper cutouts, chalk and blackboard, counters or bottle tops Counters or stones, chalk and blackboard, exercise books |
KLB Mathematics Book Three Pg 169-170
|
|
| 6 | 5 |
Matrices
|
Subtraction of matrices
Combined addition and subtraction |
By the end of the
lesson, the learner
should be able to:
Subtract matrices of the same order Apply matrix subtraction rules correctly Understand order requirements for subtraction Solve complex matrix subtraction problems |
Q/A on matrix subtraction using simple numbers
Discussions on element-wise subtraction using examples Solving subtraction problems on blackboard Demonstrations using number line concepts Explaining sign changes using practical examples |
Chalk and blackboard, exercise books, number cards made from cardboard
Chalk and blackboard, exercise books, locally made operation cards |
KLB Mathematics Book Three Pg 170-171
|
|
| 6 | 6 |
Matrices
|
Scalar multiplication
Introduction to matrix multiplication |
By the end of the
lesson, the learner
should be able to:
Multiply matrices by scalar quantities Apply scalar multiplication rules Understand the effect of scalar multiplication Solve scalar multiplication problems |
Q/A on scalar multiplication using times tables
Discussions on scaling using multiplication concepts Solving scalar problems using repeated addition Demonstrations using groups of objects Explaining scalar effects using enlargement concepts |
Beans or stones for grouping, chalk and blackboard, exercise books
Chalk and blackboard, rulers for tracing, exercise books |
KLB Mathematics Book Three Pg 174-175
|
|
| 6 | 7 |
Matrices
|
Matrix multiplication (2×2 matrices)
|
By the end of the
lesson, the learner
should be able to:
Multiply 2×2 matrices systematically Apply correct multiplication procedures Calculate matrix products accurately Understand result matrix dimensions |
Q/A on 2×2 matrix multiplication using simple numbers
Discussions on systematic calculation methods Solving 2×2 problems using step-by-step approach Demonstrations using organized blackboard layout Explaining product formation using grid method |
Chalk and blackboard, exercise books, homemade grid templates
|
KLB Mathematics Book Three Pg 176-179
|
|
| 7 | 1 |
Matrices
|
Matrix multiplication (larger matrices)
|
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
|
KLB Mathematics Book Three Pg 176-179
|
|
| 7 | 2 |
Matrices
|
Properties of matrix multiplication
|
By the end of the
lesson, the learner
should be able to:
Understand non-commutativity of matrix multiplication Apply associative and distributive properties Distinguish between pre and post multiplication Solve problems involving multiplication properties |
Q/A on multiplication properties using counterexamples
Discussions on order importance using practical examples Solving property-based problems using verification Demonstrations using concrete examples Explaining distributive law using expansion |
Chalk and blackboard, exercise books, cardboard for property cards
|
KLB Mathematics Book Three Pg 174-179
|
|
| 7 | 3 |
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
|
|
| 7 | 4 |
Matrices
|
Determinant of 2×2 matrices
|
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
|
KLB Mathematics Book Three Pg 183
|
|
| 7 | 5 |
Matrices
|
Inverse of 2×2 matrices - theory
|
By the end of the
lesson, the learner
should be able to:
Understand the concept of matrix inverse Identify conditions for matrix invertibility Apply the inverse formula for 2×2 matrices Understand singular matrices |
Q/A on inverse concepts using reciprocal analogy
Discussions on invertibility using determinant conditions Solving basic inverse problems using formula Demonstrations using step-by-step method Explaining singular matrices using zero determinant |
Chalk and blackboard, exercise books, fraction examples
|
KLB Mathematics Book Three Pg 183-185
|
|
| 7 | 6 |
Matrices
|
Inverse of 2×2 matrices - practice
|
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 |
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 |
Chalk and blackboard, exercise books, scrap paper for verification
|
KLB Mathematics Book Three Pg 185-187
|
|
| 7 | 7 |
Matrices
|
Introduction to solving simultaneous equations
|
By the end of the
lesson, the learner
should be able to:
Understand matrix representation of simultaneous equations Identify coefficient and constant matrices Set up matrix equations correctly Recognize the structure of linear systems |
Q/A on equation representation using familiar equations
Discussions on coefficient identification using examples Solving setup problems using systematic approach Demonstrations using equation breakdown method Explaining structure using organized layout |
Chalk and blackboard, exercise books, equation examples from previous topics
|
KLB Mathematics Book Three Pg 188-189
|
|
| 8 |
MIDTERM BREAK |
|||||||
| 9 | 1 |
Matrices
|
Solving 2×2 simultaneous equations using matrices
|
By the end of the
lesson, the learner
should be able to:
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 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, previous elimination method examples
|
KLB Mathematics Book Three Pg 188-190
|
|
| 9 | 2 |
Matrices
|
Advanced simultaneous equation problems
|
By the end of the
lesson, the learner
should be able to:
Solve complex simultaneous equation systems Handle systems with no solution or infinite solutions Interpret determinant values in solution context Apply matrix methods to word problems |
Q/A on complex systems using special cases
Discussions on solution types using geometric interpretation Solving challenging problems using complete analysis Demonstrations using classification methods Explaining geometric meaning using line concepts |
Chalk and blackboard, exercise books, graph paper if available
|
KLB Mathematics Book Three Pg 188-190
|
|
| 9 | 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
|
|
| 9 | 4 |
Matrices
|
Transpose of matrices
|
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
|
KLB Mathematics Book Three Pg 170-174
|
|
| 9 | 5 |
Matrices
|
Matrix equation solving
|
By the end of the
lesson, the learner
should be able to:
Solve matrix equations systematically Find unknown matrices in equations Apply inverse operations to solve equations Verify matrix equation solutions |
Q/A on equation solving using algebraic analogy
Discussions on unknown determination using systematic methods Solving matrix equations using step-by-step approach Demonstrations using organized solution procedures Explaining verification using checking methods |
Chalk and blackboard, exercise books, algebra reference examples
|
KLB Mathematics Book Three Pg 183-190
|
|
| 9 | 6 |
Formulae and Variations
|
Introduction to formulae
|
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
|
KLB Mathematics Book Three Pg 191-193
|
|
| 9 | 7 |
Formulae and Variations
|
Subject of a formula - basic cases
|
By the end of the
lesson, the learner
should be able to:
Make simple variables the subject of formulae Apply inverse operations to rearrange formulae Understand the concept of subject change Solve basic subject transformation problems |
Q/A on inverse operations using number examples
Discussions on formula rearrangement using balance method Solving basic subject change problems using step-by-step approach Demonstrations using see-saw balance analogy Explaining inverse operations using practical examples |
Chalk and blackboard, simple balance (stones and stick), exercise books
|
KLB Mathematics Book Three Pg 191-193
|
|
| 10 | 1 |
Formulae and Variations
|
Subject of a formula - intermediate 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
|
KLB Mathematics Book Three Pg 191-193
|
|
| 10 | 2 |
Formulae and Variations
|
Subject of a formula - advanced cases
Applications of formula manipulation |
By the end of the
lesson, the learner
should be able to:
Make variables subject in complex formulae Handle square roots and quadratic expressions Apply advanced algebraic manipulation Solve challenging subject transformation problems |
Q/A on advanced manipulation using careful steps
Discussions on square root handling using examples Solving complex problems using systematic approach Demonstrations using detailed blackboard work Explaining quadratic handling using factoring |
Chalk and blackboard, squared paper patterns, exercise books
Chalk and blackboard, local measurement tools, exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 10 | 3 |
Formulae and Variations
|
Introduction to variation
|
By the end of the
lesson, the learner
should be able to:
Understand the concept of variation Distinguish between variables and constants Recognize variation in everyday situations Identify different types of variation |
Q/A on variable relationships using daily examples
Discussions on changing quantities in nature and commerce Analyzing variation patterns using local market prices Demonstrations using speed-time relationships Explaining variation types using practical examples |
Chalk and blackboard, local price lists from markets, exercise books
|
KLB Mathematics Book Three Pg 194-196
|
|
| 10 | 4 |
Formulae and Variations
|
Direct variation - introduction
|
By the end of the
lesson, the learner
should be able to:
Understand direct proportionality concepts Recognize direct variation patterns Use direct variation notation correctly Calculate constants of proportionality |
Q/A on direct relationships using simple examples
Discussions on proportional changes using market scenarios Solving basic direct variation problems Demonstrations using doubling and tripling examples Explaining proportionality using ratio concepts |
Chalk and blackboard, beans or stones for counting, exercise books
|
KLB Mathematics Book Three Pg 194-196
|
|
| 10 | 5 |
Sequences and Series
|
Introduction to sequences and finding terms
|
By the end of the
lesson, the learner
should be able to:
Define sequences and identify sequence patterns Find next terms using established patterns Recognize different types of sequence patterns Apply pattern recognition systematically |
Q/A on number patterns from daily life
Discussions on counting patterns using classroom arrangements Solving pattern completion problems step-by-step Demonstrations using bead or stone arrangements Explaining sequence terminology and pattern continuation |
Chalk and blackboard, stones or beans for patterns, exercise books
|
KLB Mathematics Book Three Pg 207-208
|
|
| 10 | 6 |
Sequences and Series
|
General term of sequences and applications
|
By the end of the
lesson, the learner
should be able to:
Develop general rules for sequences Express the nth term using algebraic notation Find specific terms using general formulas Apply sequence concepts to practical problems |
Q/A on rule formulation using systematic approach
Discussions on algebraic expression development Solving general term and application problems Demonstrations using position-value relationships Explaining practical relevance using community examples |
Chalk and blackboard, numbered cards made from paper, exercise books
|
KLB Mathematics Book Three Pg 207-208
|
|
| 10 | 7 |
Sequences and Series
|
Arithmetic sequences and nth term
|
By the end of the
lesson, the learner
should be able to:
Define arithmetic sequences and common differences Calculate common differences correctly Derive and apply the nth term formula Solve problems using arithmetic sequence concepts |
Q/A on arithmetic patterns using step-by-step examples
Discussions on constant difference patterns and formula derivation Solving arithmetic sequence problems systematically Demonstrations using equal-step progressions Explaining formula structure using algebraic reasoning |
Chalk and blackboard, measuring tape or string, exercise books
|
KLB Mathematics Book Three Pg 209-210
|
|
| 11 | 1 |
Sequences and Series
|
Arithmetic sequence applications
|
By the end of the
lesson, the learner
should be able to:
Solve complex arithmetic sequence problems Apply arithmetic sequences to real-world problems Handle word problems involving arithmetic sequences Model practical situations using arithmetic progressions |
Q/A on practical applications using local business examples
Discussions on salary progression and savings plans Solving real-world problems using sequence methods Demonstrations using employment and finance scenarios Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, local employment/savings examples, exercise books
|
KLB Mathematics Book Three Pg 209-210
|
|
| 11 | 2 |
Sequences and Series
|
Geometric sequences and nth term
|
By the end of the
lesson, the learner
should be able to:
Define geometric sequences and common ratios Calculate common ratios correctly Derive and apply the geometric nth term formula Understand exponential growth patterns |
Q/A on geometric patterns using multiplication examples
Discussions on ratio-based progressions and formula derivation Solving geometric sequence problems systematically Demonstrations using doubling and scaling examples Explaining exponential structure using practical examples |
Chalk and blackboard, objects for doubling demonstrations, exercise books
|
KLB Mathematics Book Three Pg 211-213
|
|
| 11 | 3 |
Sequences and Series
|
Geometric sequence applications
|
By the end of the
lesson, the learner
should be able to:
Solve complex geometric sequence problems Apply geometric sequences to real-world problems Handle population growth and depreciation problems Model exponential patterns using sequences |
Q/A on practical applications using population/growth examples
Discussions on exponential growth in nature and economics Solving real-world problems using geometric methods Demonstrations using population and business scenarios Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, population/growth data examples, exercise books
|
KLB Mathematics Book Three Pg 211-213
|
|
| 11 | 4 |
Sequences and Series
|
Arithmetic series and sum formula
|
By the end of the
lesson, the learner
should be able to:
Define arithmetic series as sums of sequences Derive the sum formula for arithmetic series Apply the arithmetic series formula systematically Calculate sums efficiently using the formula |
Q/A on series concepts using summation examples
Discussions on sequence-to-series relationships and formula derivation Solving arithmetic series problems using step-by-step approach Demonstrations using cumulative sum examples Explaining derivation logic using algebraic reasoning |
Chalk and blackboard, counting materials for summation, exercise books
|
KLB Mathematics Book Three Pg 214-215
|
|
| 11 | 5 |
Sequences and Series
|
Geometric series and applications
|
By the end of the
lesson, the learner
should be able to:
Define geometric series and understand convergence Derive and apply geometric series formulas Handle finite and infinite geometric series Apply geometric series to practical situations |
Q/A on geometric series concepts using multiplication examples
Discussions on convergence and formula applications Solving geometric series problems including infinite cases Demonstrations using geometric sum patterns Explaining convergence using practical examples |
Chalk and blackboard, convergence demonstration materials, exercise books
|
KLB Mathematics Book Three Pg 216-219
|
|
| 11 | 6 |
Sequences and Series
|
Mixed problems and advanced applications
|
By the end of the
lesson, the learner
should be able to:
Combine arithmetic and geometric concepts Solve complex mixed sequence and series problems Apply appropriate methods for different types Model real-world situations using mathematical sequences |
Q/A on problem type identification using systematic analysis
Discussions on method selection and comprehensive applications Solving mixed problems using appropriate techniques Demonstrations using interdisciplinary scenarios Explaining method choice using logical reasoning |
Chalk and blackboard, mixed problem collections, exercise books
|
KLB Mathematics Book Three Pg 207-219
|
|
| 11 | 7 |
Sequences and Series
|
Sequences in nature and technology
|
By the end of the
lesson, the learner
should be able to:
Identify mathematical patterns in natural phenomena Analyze sequences in biological and technological contexts Apply sequence concepts to environmental problems Appreciate mathematics in the natural and modern world |
Q/A on natural and technological patterns using examples
Discussions on biological sequences and digital applications Solving nature and technology-based problems Demonstrations using natural pattern examples Explaining mathematical beauty using real phenomena |
Chalk and blackboard, natural and technology examples, exercise books
|
KLB Mathematics Book Three Pg 207-219
|
|
| 12 | 1 |
Binomial Expansion
|
Binomial expansions up to power four
Binomial expansions up to power four (continued) |
By the end of the
lesson, the learner
should be able to:
Expand binomial function up to power four Apply systematic multiplication methods Recognize coefficient patterns in expansions Use multiplication to expand binomial expressions |
Q/A on algebraic multiplication using familiar expressions
Discussions on systematic expansion using step-by-step methods Solving basic binomial multiplication problems Demonstrations using area models and rectangular arrangements Explaining pattern recognition using organized layouts |
Chalk and blackboard, rectangular cutouts from paper, exercise books
Chalk and blackboard, squared paper for geometric models, exercise books |
KLB Mathematics Book Three Pg 256
|
|
| 12 | 2 |
Binomial Expansion
|
Pascal's triangle
|
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Construct Pascal's triangle systematically Apply triangle coefficients for binomial expansions Recognize number patterns in the triangle |
Q/A on triangle construction using addition patterns
Discussions on coefficient relationships using triangle analysis Solving triangle construction and application problems Demonstrations using visual triangle building Explaining pattern connections using systematic observation |
Chalk and blackboard, triangular patterns drawn/cut from paper, exercise books
|
KLB Mathematics Book Three Pg 256-257
|
|
| 12 | 3 |
Binomial Expansion
|
Pascal's triangle applications
|
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply Pascal's triangle to binomial expansions efficiently Use triangle coefficients for various powers Solve expansion problems using triangle methods |
Q/A on triangle application using coefficient identification
Discussions on efficient expansion using triangle methods Solving expansion problems using Pascal's triangle Demonstrations using triangle-guided calculations Explaining efficiency benefits using comparative methods |
Chalk and blackboard, Pascal's triangle reference charts, exercise books
|
KLB Mathematics Book Three Pg 257-258
|
|
| 12 | 4 |
Binomial Expansion
|
Pascal's triangle (continued)
|
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply triangle to complex expansion problems Handle higher powers using Pascal's triangle Integrate triangle concepts with algebraic expansion |
Q/A on advanced triangle applications using complex examples
Discussions on higher power expansion using triangle methods Solving challenging problems using Pascal's triangle Demonstrations using detailed triangle constructions Explaining integration using comprehensive examples |
Chalk and blackboard, advanced triangle patterns, exercise books
|
KLB Mathematics Book Three Pg 258-259
|
|
| 12 | 5 |
Binomial Expansion
|
Pascal's triangle advanced
|
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply general binomial theorem concepts Understand combination notation in expansions Use general term formula applications |
Q/A on general formula understanding using pattern analysis
Discussions on combination notation using counting principles Solving general term problems using formula application Demonstrations using systematic formula usage Explaining general principles using algebraic reasoning |
Chalk and blackboard, combination calculation aids, exercise books
|
KLB Mathematics Book Three Pg 258-259
|
|
| 12 | 6 |
Binomial Expansion
|
Applications to numerical cases
|
By the end of the
lesson, the learner
should be able to:
Use binomial expansion to solve numerical problems Apply expansions for numerical approximations Calculate values using binomial methods Understand practical applications of expansions |
Q/A on numerical applications using approximation techniques
Discussions on calculation shortcuts using expansion methods Solving numerical problems using binomial approaches Demonstrations using practical calculation scenarios Explaining approximation benefits using real examples |
Chalk and blackboard, simple calculation aids, exercise books
|
KLB Mathematics Book Three Pg 259-260
|
|
| 12 | 7 |
Binomial Expansion
|
Applications to numerical cases (continued)
|
By the end of the
lesson, the learner
should be able to:
Use binomial expansion to solve numerical problems Apply binomial methods to complex calculations Handle decimal approximations using expansions Solve practical numerical problems |
Q/A on advanced numerical applications using complex scenarios
Discussions on decimal approximation using expansion techniques Solving challenging numerical problems using systematic methods Demonstrations using detailed calculation procedures Explaining practical relevance using real-world examples |
Chalk and blackboard, advanced calculation examples, exercise books
|
KLB Mathematics Book Three Pg 259-260
|
|
| 13 |
ENDTERM EXAMS |
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| 14 |
MARKING, REVISION AND CLOSING |
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