If this scheme pleases you, click here to download.
| 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
Compound 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
Calculators, compound interest tables |
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 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 | 4 |
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 | 5 |
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 | 6 |
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
|
|
| 2 | 7 |
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 | 1 |
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 | 2 |
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 | 3 |
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 | 4 |
Circles: Chords and Tangents
|
Equal chords
Intersecting 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 | 5 |
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
|
|
| 3 | 6 |
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
|
|
| 3 | 7 |
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 | 1 |
Circles: Chords and Tangents
|
Properties of tangents to a circle from an external point
|
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 | 2 |
Circles: Chords and Tangents
|
Tangent properties
|
By the end of the
lesson, the learner
should be able to:
Solve comprehensive tangent problems Apply all tangent concepts Integrate tangent knowledge systematically |
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 139-147
|
|
| 4 | 3 |
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 | 4 |
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
|
|
| 4 | 5 |
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
|
|
| 4 | 6 |
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
|
|
| 4 | 7 |
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 | 1 |
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 | 2 |
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
|
|
| 5 | 3 |
Circles: Chords and Tangents
|
Centroid
Orthocenter |
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
|
|
| 5 | 4 |
Circles: Chords and Tangents
|
Circle and triangle relationships
|
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
|
KLB Mathematics Book Three Pg 164-167
|
|
| 5 | 5 |
Matrices
|
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:
Define matrices and identify matrix applications Recognize matrices in everyday contexts Understand tabular data representation Appreciate the importance of matrices |
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 |
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 168-169
|
|
| 5 | 6 |
Matrices
|
Addition of matrices
Subtraction of matrices Combined addition and subtraction |
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 |
KLB Mathematics Book Three Pg 170-171
|
|
| 5 | 7 |
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 | 1 |
Matrices
|
Matrix multiplication (2×2 matrices)
Matrix multiplication (larger 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
Chalk and blackboard, large sheets of paper for working, exercise books |
KLB Mathematics Book Three Pg 176-179
|
|
| 6 | 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
|
|
| 6 | 3 |
Matrices
|
Real-world matrix multiplication applications
|
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
|
KLB Mathematics Book Three Pg 176-179
|
|
| 6 | 4 |
Matrices
|
Identity matrix
Determinant of 2×2 matrices |
By the end of the
lesson, the learner
should be able to:
Define and identify identity matrices Understand identity matrix properties Apply identity matrices in multiplication Recognize the multiplicative identity role |
Q/A on identity concepts using number 1 analogy
Discussions on multiplicative identity using examples Solving identity problems using pattern recognition Demonstrations using multiplication by 1 concept Explaining diagonal properties using visual patterns |
Chalk and blackboard, exercise books, pattern cards made from paper
Chalk and blackboard, exercise books, crossed sticks for demonstration |
KLB Mathematics Book Three Pg 182-183
|
|
| 6-7 |
Games |
|||||||
| 7 | 2 |
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 | 3 |
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 | 4 |
Matrices
|
Introduction to solving simultaneous equations
Solving 2×2 simultaneous equations using matrices |
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
Chalk and blackboard, exercise books, previous elimination method examples |
KLB Mathematics Book Three Pg 188-189
|
|
| 7 | 5 |
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
|
|
| 7 | 6 |
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
|
|
| 7 | 7 |
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
|
|
| 8 | 1 |
Matrices
Formulae and Variations |
Matrix equation solving
Introduction to formulae |
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
Chalk and blackboard, measuring tape or string, exercise books |
KLB Mathematics Book Three Pg 183-190
|
|
| 8 | 2 |
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
|
|
| 8 | 3 |
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
|
|
| 8 | 4 |
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
|
|
| 8 | 5 |
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
|
|
| 8 | 6 |
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
|
|
| 8 | 7 |
Sequences and Series
|
Introduction to sequences and finding terms
General term of sequences and applications |
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
Chalk and blackboard, numbered cards made from paper, exercise books |
KLB Mathematics Book Three Pg 207-208
|
|
| 9 | 1 |
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
|
|
| 9 | 2 |
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
|
|
| 9 | 3 |
Sequences and Series
|
Geometric sequences and nth term
Geometric sequence applications |
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
Chalk and blackboard, population/growth data examples, exercise books |
KLB Mathematics Book Three Pg 211-213
|
|
| 9 | 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
|
|
| 9 | 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
|
|
| 9 | 6 |
Sequences and Series
|
Mixed problems and advanced applications
Sequences in nature and technology |
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
Chalk and blackboard, natural and technology examples, exercise books |
KLB Mathematics Book Three Pg 207-219
|
|
| 9-10 |
Midterm break |
|||||||
| 10 | 4 |
Binomial Expansion
|
Binomial expansions up to power four
|
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
|
KLB Mathematics Book Three Pg 256
|
|
| 10 | 5 |
Binomial Expansion
|
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 Handle increasingly complex coefficient patterns Apply systematic expansion techniques efficiently Verify expansions using substitution methods |
Q/A on power expansion using multiplication techniques
Discussions on coefficient identification using pattern analysis Solving expansion problems using systematic approaches Demonstrations using geometric representations Explaining verification methods using numerical substitution |
Chalk and blackboard, squared paper for geometric models, exercise books
|
KLB Mathematics Book Three Pg 256
|
|
| 10 | 6 |
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
|
|
| 10 | 7 |
Binomial Expansion
|
Pascal's triangle applications
Pascal's triangle (continued) |
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
Chalk and blackboard, advanced triangle patterns, exercise books |
KLB Mathematics Book Three Pg 257-258
|
|
| 11 | 1 |
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
|
|
| 11 | 2 |
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
|
|
| 11 | 3 |
Binomial Expansion
Probability |
Applications to numerical cases (continued)
Introduction |
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
Chalk and blackboard, coins, dice made from cardboard, exercise books |
KLB Mathematics Book Three Pg 259-260
|
|
| 11 | 4 |
Probability
|
Experimental Probability
|
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability Conduct probability experiments systematically Record and analyze experimental data Compare experimental results with expectations |
Q/A on frequency counting using repeated experiments
Discussions on trial repetition and result recording Solving experimental probability problems using data collection Demonstrations using coin toss and dice roll experiments Explaining frequency ratio calculations using practical examples |
Chalk and blackboard, coins, cardboard dice, tally charts, exercise books
|
KLB Mathematics Book Three Pg 262-264
|
|
| 11 | 5 |
Probability
|
Experimental Probability applications
|
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability Apply experimental methods to various scenarios Handle large sample experiments Analyze experimental probability patterns |
Q/A on advanced experimental techniques using extended trials
Discussions on sample size effects using comparative data Solving complex experimental problems using systematic methods Demonstrations using extended experimental procedures Explaining pattern analysis using accumulated data |
Chalk and blackboard, extended experimental materials, data recording sheets, exercise books
|
KLB Mathematics Book Three Pg 262-264
|
|
| 11 | 6 |
Probability
|
Range of Probability Measure
Probability Space |
By the end of the
lesson, the learner
should be able to:
Calculate the range of probability measure Express probabilities on scale from 0 to 1 Convert between fractions, decimals, and percentages Interpret probability values correctly |
Q/A on probability scale using number line representations
Discussions on probability conversion between forms Solving probability scale problems using systematic methods Demonstrations using probability line and scale examples Explaining scale interpretation using practical scenarios |
Chalk and blackboard, number line drawings, probability scale charts, exercise books
Chalk and blackboard, playing cards (locally made), spinners from cardboard, exercise books |
KLB Mathematics Book Three Pg 265-266
|
|
| 11 | 7 |
Probability
|
Theoretical Probability
|
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Apply mathematical reasoning to find probabilities Use equally likely outcome assumptions Calculate theoretical probabilities systematically |
Q/A on theoretical calculation using mathematical principles
Discussions on equally likely assumptions and calculations Solving theoretical problems using systematic approaches Demonstrations using fair dice and unbiased coin examples Explaining mathematical probability using logical reasoning |
Chalk and blackboard, fair dice and coins, probability calculation aids, exercise books
|
KLB Mathematics Book Three Pg 266-268
|
|
| 12 | 1 |
Probability
|
Theoretical Probability advanced
|
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Apply theoretical probability to complex problems Handle multiple outcome scenarios Solve advanced theoretical problems |
Q/A on advanced theoretical applications using complex scenarios
Discussions on multiple outcome analysis using systematic methods Solving challenging theoretical problems using organized approaches Demonstrations using complex probability setups Explaining advanced theoretical concepts using detailed reasoning |
Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books
|
KLB Mathematics Book Three Pg 268-270
|
|
| 12 | 2 |
Probability
|
Theoretical Probability applications
Combined Events |
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Apply theoretical concepts to real situations Solve practical probability problems Interpret results in meaningful contexts |
Q/A on practical probability using local examples
Discussions on real-world applications using community scenarios Solving application problems using theoretical methods Demonstrations using local games and practical situations Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, local game examples, practical scenario materials, exercise books
Chalk and blackboard, playing cards, multiple dice, Venn diagram drawings, exercise books |
KLB Mathematics Book Three Pg 268-270
|
|
| 12 | 3 |
Probability
|
Combined Events OR probability
|
By the end of the
lesson, the learner
should be able to:
Find the probability of a combined events Apply addition rule for OR events Calculate "A or B" probabilities Handle mutually exclusive events |
Q/A on addition rule application using systematic methods
Discussions on mutually exclusive identification and calculation Solving OR probability problems using organized approaches Demonstrations using card selection and event combination Explaining addition rule logic using Venn diagrams |
Chalk and blackboard, Venn diagram materials, card examples, exercise books
|
KLB Mathematics Book Three Pg 272-274
|
|
| 12 | 4 |
Probability
|
Independent Events
|
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Apply multiplication rule for independent events Calculate "A and B" probabilities Understand independence concepts |
Q/A on multiplication rule using independent event examples
Discussions on independence identification and verification Solving AND probability problems using systematic calculation Demonstrations using multiple coin tosses and dice combinations Explaining multiplication rule using logical reasoning |
Chalk and blackboard, multiple coins and dice, independence demonstration materials, exercise books
|
KLB Mathematics Book Three Pg 274-275
|
|
| 12 | 5 |
Probability
|
Independent Events advanced
Independent Events applications |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Distinguish between independent and dependent events Apply conditional probability concepts Handle complex independence scenarios |
Q/A on independence verification using mathematical methods
Discussions on dependence concepts using card drawing examples Solving dependent and independent event problems using systematic approaches Demonstrations using replacement and non-replacement scenarios Explaining conditional probability using practical examples |
Chalk and blackboard, playing cards for replacement scenarios, multiple experimental setups, exercise books
Chalk and blackboard, complex experimental materials, advanced calculation aids, exercise books |
KLB Mathematics Book Three Pg 276-278
|
|
| 12 | 6 |
Probability
|
Tree Diagrams
|
By the end of the
lesson, the learner
should be able to:
Draw tree diagrams to show the probability space Construct tree diagrams systematically Represent sequential events using trees Apply tree diagram methods |
Q/A on tree construction using step-by-step methods
Discussions on sequential event representation Solving basic tree diagram problems using systematic drawing Demonstrations using branching examples and visual organization Explaining tree structure using logical branching principles |
Chalk and blackboard, tree diagram templates, branching materials, exercise books
|
KLB Mathematics Book Three Pg 282
|
|
| 12 | 7 |
Probability
|
Tree Diagrams advanced
|
By the end of the
lesson, the learner
should be able to:
Use tree diagrams to find probability Apply trees to multi-stage problems Handle complex sequential events Calculate final probabilities using trees |
Q/A on complex tree application using multi-stage examples
Discussions on replacement scenario handling Solving complex tree problems using systematic calculation Demonstrations using detailed tree constructions Explaining systematic probability calculation using tree methods |
Chalk and blackboard, complex tree examples, detailed calculation aids, exercise books
|
KLB Mathematics Book Three Pg 283-285
|
|
Your Name Comes Here