Further Mathematics Scheme of work for SSS 2. Lagos State Schemes of Work SS2 Further Mathematics for Senior Secondary School
SS2 Scheme of Work Further Mathematics
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| Revision test General review of equations | By the end of the session students should be able to recapitulate Secondary School 1 (SS1) lessons and identify different types of expression and equations. | i. Students solve some revision question, ii. Students solve some equations in preparation for the terms work with teacher’s guidance. | i. Critical thinking and problem solving. ii. Creativity iii. Collaboration and Communication iv. Digital Literacy | 1. Audio Visual Resources -Using past question papers of SS1 examinations. 2. Web Resources www. Examsolution.net/ questions | |
| 2. | I. Finding quadratic equations given and product of roots i.e. x2– sum ( ii. Conditions for quadratic-equations to giveEqual roots (b2= 4ac) Real roots (b2>4ac) and No roots (b2<4ac) important/use It is used to calculate business profit. – In selling and constructing satellites dish. | By the end of the lesson, students should be able to: i. form quadratic equations given sum and products of roots. ii. state the conditions for quadratic equations to have; *equal roots *real roots and no roots | i. Guide students to use algebraic cards of roots: -To form quadratic equations. -To differentiate sum and product. ii. Guide students to find the sum and product of the roots of quadratic equation using: Sum: product | i. Critical Thinking and Problem Solving. Creativity ii. Collaboration and Communication Digital Literacy | 1. Audio Visual Resources -Charts showing: i.Types of equations ii. Quadratic equations with equal roots, real roots and no roots. 2. Web Resources YouTube-Don’t memorize |
| 3 | Quadratic equation continued: i. Conditions for a given line to intersect a curve. II. Tangent to a curve not intersecting the curve. iii. Solution of problems on roots of a quadratic equation and intersection between a street line and a quadratic equation. Important/Use It is used: – to calculate business profit – in setting and to calculate business profit In setting and constructing satellites dish | By the end of the lesson, students should be able to i. draw a quadratic curve with a straight line intersecting the curve ii.. draw a tangent to a curve. solve problems on roots and intersection of the curve and the straight line. | i. Students, as a class, create arbitrary a linear equation and a quadratic one. ii. Guide students to sketch the solution graph of quadratic equation. iii. Students in pair draw a tangent on the curve. iv. Students pair up to solve questions on roots and intersection of curve and straight line using the appropriate formula. | i. Critical Thinking and Problem Solving ii. Creativity iii. Collaboration and Communication. iv. Digital Literacy | 1. Audio Visual Resources. -. Charts showing conditions for line to intersect a curve – Chart showing tangent to a curve, not intersecting the curve. 2. Web Resources. YouTube-Don’t memorize |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 4 | Polynomials: I. Definition of polynomials; II. Addition, subtraction and multiplication and polynomials III. Division of polynomials by another polynomial of lesser degree. IV. Remainder theorem. Important/Use It is used: -frequently by market women. –for finding the displacement of objects. | By the end of the lesson, students should be able to: l. explain polynomials. ii. Perform operation of addition, subtraction, multiplication and division and polynomials apply remainder theorem on polynomials. | i. Students, as a class write out some equationsof different degrees. ii. Students, in pair, evaluate the equations using different simple value. iii. Guide students to use reminder theorem to find values. | i. Critical Thinking and Problem Solving. ii. Creativity iii. Collaboration and Communication. Digital Literacy | 1. Audio Visual Resources -Charts showing polynomials of varying degree -Charts showing long division to get remainder, – Charts on use of remainder theorem to get a remainder. 2. Web Resources. – Khan Academy Polynomial |
| 5 | i. Factorization of polynomials ii. Roots of cubic Important/Use It is used Frequently by market women for finding the displacement of objects. | By the end of the lesson, students should be able to: i. Solve for the factors of polynomials. ii. Find the roots of cubic equations. iii. Use roots of cubic equation to solve problems on cubic equation. | i.Students, as a class, multiply one expression by another. ii. Students pair up to divide polynomial. iii. Guide students to use trial and error to get factors and zero values of polynomials. | Critical Thinking and Problem Solving ii. Digital Literacy iii. Collaboration and Communication | 1. Audio Visual Resources -Charts showing a long division -Charts on cubic function and equations 2. Web Resources, www.en.m.wikipedia. org/polynomials, www.archives.maths .utk.eduf polynomials |
| 6 | Polynomials continued: Sum of roots of cubic equation: Sum of products of two roots: ax3+ bx2± cx + d = 0Importance/Use It isused: -frequently by market women. -for finding the displacement of objects. | By the end of the lesson, students should be able to: i.use roots of cubic equation to solve problems on: ii. Sum of cubic roots iii. Product of cubic sum of products of true roots | i. Students, as a class form some arbitrary roots with variable x and find product of the roots of polynomials. ii. Guide students to find the sum of cubic equation using: | i. Critical Thinking and Problem Solving. ii. Creativity iii. Collaboration and Communication | 1. Audio Visual Resources – Charts showing sum of cubic roots of cubic equation ii. Products of cubic iii. Roots of cubic equation iv. Sum of products of two roots and three roots of a cubic equation 2. Web Resources, www.en,m,Wikipedia.org /polynomials- www.archives.maths.utk .edu/polynomials |
| 7 | Review of first half term’s work, periodic test and mid-term break. | By the end of the lesson, students should be able to: i. solve questions on topics taught in first half term ii. Solve correctly the test questions. | i. Students, as a class, solve some revision questions ii. Students, as a class, solve test questions independently. ii. Students with parents, visit subject and class teacher for academic and moral progress record | i. Critical Thinking and Problem Solving Digital Literacy | 1. Audio Visual Resources -Prepared test question papers 2. Web Resources www.aquinnasmaths.com/multiple/ choice/question |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 8 | Logical reasoning: i. Fundamental issues in intelligent system ii. Fundamental definitions; iii. Introduction to propositional and predicate logical resolution iv. Modeling the world; v. Introduction to theorem proving. Important/Uses – ‘it Widens the reasoning and thinking of students -it is used lawyers and judges to reach a conclusion | By the end of the lesson, students should be able to: i. reproduce basic issues and intelligent System ii. give basic definitions of intelligent system iii. state and interpret propositional end predicate logical resolution iv. explain modeling of the world explain proving of theorem | i, Students, as a class, make some arbitrary reasonable statements, simple ones ii. Students in pairs make – related statements to explain simple statements in logic. iii. Students, in pairs, classify the statements under true and false statements. iv, Students, as a class, differentiate between negation and false statement, v. Students, as a classexplain the meaning of antecedents and . consequences vi. Students, as a class watch a short video on application of logical statements | i. Critical Thinking and Problem Solving. ii. Creativity iii. Collaboration and communication iv. Digital Literacy v. Leadership and Personal Development | 1. Audio Visual Resources: – Small groups on critical issues in intelligence system – Charts on key points on modeling the world – Charts to note some points in proving the theorem. 2. Web Resources www.skillsyouneed.com/logic -YouTube-tecmaths www.geeksforgeeks.org/logic table |
| i | Trigonometric function: i. Trigonometric iifunctions of angles: sine, cosine, tangent, cosec, secant, cotangent ii. Range and domain of specified trigonometry; iii. Graph of trigonometric ratios with emphasis on amplitude and periodicity. iv.Relationship between graphs of trigonometric ratios. Important/Uses it is used: -in satellite system -to describe sound wave and light wave. | By the end of the lesson, students should be able to: i. State the size, important trigonometric functions of angles of any magnitude. ii. Identify range and dimension of trigonometric ratio draw graphs of trigonometric functions. | Students, in pair, state the six trigonometric ratios, Sin 0+ Cos 0 1 Sin0/Cos @ Tan 0 Students show the ratios in a sketch of right- angled triangle with general dimensions.iii. Guide students to show the relationship between graph of trigonometric function. e.g. sinx and sin 2x; graphs of y a sin (bx) + c; y acos (bx) + c y atan (bx) + C | i. Critical Thinking and Problem solving. ii, Creativity iii: Digital Literacy iv. Leadership and Personal Development | 1. Audio Visual Resources -Charts showing relationship between the sizes of trigonometric ratios e.g. sin x = tan x etc cos xii. Chart showing sketches of the six trigonometric ratios 2. Web Resources. www.briliant.org/inverse/ratio www.mathsisfun.com.trigonometric/ function -Khan academy- Trigonometric Function (video) |
| 10 | Graph of inverse ratio: I. Solution of simple equations involving six trigonometric identities. e.g. sin2x cos2x = sec2x = 1 ÷ tan 2x. Important/Uses It is used: -in satellite system -to describe sound wave ad light wave. | By the end of the lesson, students should be able to: – find inverse trigonometric ratios. i. find solution of trigonometric ratios prove simple trigonometric identities, | i. Students, as a class, state – the six trigonometric ratios. ii. Students show the ratios in a stretch of right- angled triangle with general dimensions. | i. Critical Thinking and Problem Solving. Creativity ii. Digital Literacy | 1. Audio Visual Resources -Charts showing sketches of inverse of sinx, cosx and tanx 2. Web Resources. -www.brilliant.org/inverse/ratio -www.mathsisfun.com/inverse/ratio www.vasily/tutors.com/inverse/ratio -YouTube Khan academy-(video) |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 11 | Revision of the terms work | By the end of the lesson, students should be able to recapitulate the topics they have learnt in the term | Students solve some past questions with teachers guidance | 1. Critical Thinking and Problem Solving. ii. Creativity iii Digital Literacy | Audio Visual Resources -Past question papers -Selected likely Examinations questions from recommended textbooks. 2. Web Resources -wwwexamsolution.net objective/questions |
| 12 | Examination | By the end of the lesson, students should be able to attempt the examination questions correctly | Students attempt examination questions correctly | i. Critical Thinking . and Problem Solving ii. Creativity iii Digital literacy | Audio Visual Resources -Examination questions and answer sheets. |
Further Mathematics Scheme of work for SSS 2. Lagos State Schemes of Work SS2 Further Mathematics for Senior Secondary School
Further Mathematics Scheme of Work SSS 2 Second Term
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 1 | Resumption test Comic section i. Definition and parts of a circle | By the end of the Lesson, students should be able to: i. Solve correctly the test questions ii. State circle and its properties iii. Mention and identify parts of a circle | i. Student solve resumption test questions correctly. ii. Students draw a circle in a Cartesian plane etc. | i. Critical Thinking and Problem Solving ii. Creativity iii. Digital Literacy vi. Leadership and Personal Development | 1. Audio Visual Resources -Chart depicting circle as a section of a cone. 2. Web Resources www.mathplanet.com www.emathzone.com Khan academy-(video) |
| 2 | Equation of a circle given centre and radius ii. General evaluation of a circle iii. Finding center and radius of d given circle iv. Finding equation of a circle given the endpoints of the diameter. Important/Uses ‘It is used in: construction of beam on buildings. -construction of bicycle wheels. | By the end of the Lesson, students should be able to: i. Explain why a circle can be regarded as part of conic section. ii. Find equation of a circle given radius and center. iii. Find equation of a circle given the end paints of the Diameter: | Students locate center, radius of each circle and list other properties of circle. ii. Guide students to join joints that form the locus through the center point, with teacher’s guidance etc. iii. Students, as a class apply, the formula for equation of a circle | i. Critical Thinking and Problem Solving ii. Creativity iii. Digital Literacy vi. Leadership and Personal Development | 1. Audio Visual Resources -Use of concrete materials to show parts of a circle, e.g. -Modeled Plywood -Use of cardboard to depict a circle as section of a cone. 2. Web Resources. -www.dummies.com/edu cation/of/circle -www.khanacaclemy.org education/f/circle |
| 3 | i. Equation of a circle passing through 3 points; ii. Equation of a tangent… to a circle Length of a tangent to a Circle.important/Uses It is used in: -. construction of beam on buildings. – construction on bicycle wheels. | By the end of the Lesson, students should be able to: i. Explain why a circle can be regarded as part of conic section. ii. Find equation of a circle given radius and center. iii. Find equation of a circle given the end paints of the Diameter: | i. Students locate any three points on the circle and name them. ii Students draw a straight line touching a point on the circumference with teacher’s guidance. | i. Critical Thinking and Problem Solving ii. Creativity iii. Digital Literacy vi. Leadership and Personal Development | 1. Audio Visual Resources -Chart showing a tangent to a circleand length of tangent -Project work: use cardboard, beads, gum and broom sticks to construct a circle with a tangent to it. 2. Web Resources. -www.durnmies,çom/eguat ion/of/circle – -www. khanacademy.org/ equation/of/circle |
| 4 | Probability: 1. Classical, sequential and axiomatic approaches to probability i. Sample space and event space. ii Mutually exclusive, independent and conditional event iii. Conditional probability Probability tree. Importance/Use. -lt helps in widens the knowledge of students in calculation. lt is used for risk management. management | By the end of the lesson, Students will be able to: i. Identify the classical, frequential and axiomatic approaches to probability ii. State some terms in probability e.g. random experiment, sample space, event space, etc iii. Solve probability problems use probability tree to solve probability problem | i. Students, as a class pick beads of different colours from a bowl. ii. Students, in pair, play a game of ludo in small groups. iii. Students record results of game and solve probability questions using the sample games | i. Critical Thinking and Problem Solving ii. Creativity iii. Digital Literacy vi. Leadership and Personal Development iv. Collaboration & communication | 1. Audio Visual Resources. -Use of concrete materials like ludo dice, coins, pack of cards. – Charts showing problem on probability trees. 2. Web Resources -www.dummies.com/ probability -www.khanacademy.org /probability |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 5 | Permutation: I. Permutation arrangement ii. Cyclic permutation iii. Arrangement of identical objects. lv. Arrangements with repetition. Important/Uses It is used: – in phone number; the last four digits re permutated to form new numbers. -for car pate number, the numbers is permutated uniquely for each car. | By the end of the lesson, students should be able to: i. Explain the term permutation ii. . Solve problems on cyclic permutation iii. Solve problems on permutation with identical objects | Students fill the hole of ‘ayo’ game with different colours of seeds i. Students choose according to conditions and arrange. ii. Students arrange cards of a playing card pack etc. | i. Critical Thinking and Problem Solving ii. Creativity iii. Leadership and Personal Development iv. Digital Literacy | 1. Audio Visual Resources -Charts showing different permutations and arrangement of objects (identical and non- identical) -Use of bead with different colours four different arrangements. 2. Web Resources. -www.mathzone.com/ permutation, -www.mathsisfun.com/ permutation YouTube Wikipedia |
| 6 | Combination: I. introduction to combination on selection and choice II: Conditional arrangements and selection Ill. Probability involving arrangement and selection. Important/Use -It is used1 in game of lottery | By the end of the lesson, students should be able to: i. Explain the meaning of combination ii. Solve probability problems involving selection and choice using combination analysis. iii. Demonstrate the use of combination in daily life situation. | i. From playing cards, students select without restraints and record. ii. From ‘ayo’ game ask students pick any number etc. Guide students to demonstrate the use of combination | i. Critical Thinking and Problem Solving ii. Creativity iii. Leadership and Personal Development iv. Digital Literacy | 1. Audio Visual Resources. -Chart showing the definition of combination. -Charts showing combination of: i. Direct combination ii. Conditional combination 2. Web Resources. -www.mathzone.combination -.mathsifun.com/ combination -YouTube-Wikipedia |
| 7 | I. Review of first half term’s work II. Periodic test and Mid-term break | By the end of the lesson, students should be able to: Recapitulate second half terms work learnt solve correctly the test questions. | i. Students, as a class, solve some revision questions in grounds. ii. Student attempts correctly the midterm test questions. iii. Students with parents, see teachers for moral and academic progress of their wards. | i. Critical thinking and Problem Solving ii. Creativity. iv. Digital Literacy | 1. Audio Visual Resources. -Prepared test question papers 2. Web Resources. a.mathdone.com/ questions www.mathsisfun.com/guestions -YouTube-Wikipedia |
| 8 | Binomial expansion (a+.b)* where n is either positive or negative integer or fractional power; Finding terms and expansion of binomial expression and application Important/Use It is used: -by economist to count probabilities, -for National economics prediction. | By the end of the lesson, students should be able to: i. Write out a binomial expansion for (a + b) ii. Find the nth term of a given binomial expression iii. Apply the binomial expansion to evaluation of powers of numbers. | i. Students, as a class expand some brackets. ii. Students collect like terms. iii. Guide students collect coefficient by power. Guide students to apply the binomial expansion rule e.g. (1.03)x1 | i. Critical Thinking and Problem Solving. ii. Creativity iii. Leadership and Personal Development iv. Digital Literacy | 1. Audio Visual Resources. -Charts showing expansion using binomial theorem -Chart showing the nth term of a binomial expansion. 2. Web Resources. www.mathzone.com/binomial/ expansion vww.mathsisfun.com/binomial/ expansion -YouTube-Wikipedie.org |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 9. | i. Work, power and energy ii. Impulse and momentum. Importance/Use it s used in: -lifting aweight. -electricity | By the end of the lesson, students should be able to: i. Explain the concept of work, power and energy ii. Solve problems on work, power and energy solve problems on impulse and momentum | I. Guide students to use string, weight and a plane surface for various movement and activities. ii. Students, as a class, solve questions on work, power and energy. | i. Critical Thinking and Problem Solving ii. Creativity iii D gal Literacy | 1. Audio Visual Resources -An inclined plane with an object on it 2. Web Resources. www.geeksforgeeks.org/work energy/ www.khanacademy.org/ work/power |
| 10. | Projectiles I. Trajectory of projectiles ii. Greatest height reached iii. Time of flight iv. Range v. Projection along inclined plane. Important/Use it is used:-during baseball. -by players during football, especially the goal keeper. | By the end of the lesson, students should be able to problems an projectiles. | i. Guide students use string, weight and surface (imaginary) for reading the projectiles, in small groups. | i. Critical Thinking and Problem Solving ii. Creativity iii. Digital Literacy | Audio Visual Resources. -Chart showing projectiles of a particle 2. Web Resources. www.geeksforgeeks. org/projectile www.khanacademy.org/ projectile |
| 11 | Introduction to operations research: I. Inventorymodel Concept of inventory II, Definition of terms in inventory definition terms in inventory holding 1st, demand operating list etc Ill. Computation of optimal quantity to make decision. | By the end of the lesson, students should be able to: Explain the concept of inventory ii. Explain important terms in inventory compute the optimum quantity in an inventory model | Students as a class brainstorm on meaning of inventory | i. Critical Thinking and Problem Solving. ii. Leadership and. Personal Development. iii. Creativity. lv. Digital Literacy | 1 Audio Visual Resources. -Charts depicting items on inventory -Graph of EOQ mgdel -Chart showing the EOQ formula, – r 2. Web Resources – sforeeks.or giopeiation/research, -ww.khanacademy.org/ratio research |
| 12 | Revision of the term’s work | By the end of the lesson, students should be able to reproduce the topics they have been taught in the term | Students solve revision questions with teacher’s guidance. | i. Critical Thinking and Problem Solving ii. Creativity iii Digital Literacy | 1. Audio Visual Resources. -Past tests and examination question papers. 2. Web Resources. . www.geeksforgeeks.org/ questions www.khanacademy.org /questions. |
| 13 | Examination | By the end of the lesson, students should be able to write the examination | Students solve examination questions correctly. | i. Critical Thinking and Problem Solving ii. Creativity iii Digital Literacy |
Further Mathematics Scheme of Work SSS 2 Third Term
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 1 | Welcome test and review of second terms work, and introduction to Dynamics | By the end of the lesson, students should be able to: i. Solve the test questions correctly. ii. Recapitulate what they have learnt in the previous term iii. solve binomial expansion problem using Pascal triangle | i. Students solve resumption test questions. ii. Students use a weight, a string and a surface for movement. iii. Students solve practical problem in the class introducing Dynamics. | i. Critical Thinking and Problem Solving. ii. Creativity iii. Digital Literacy iv. Leadership and Personal Development | 1. Audio Visual Resources Chas showing Pascals triangle -A wooden triangular shape with graded ruled faces in rectangular array of plane shapes. 2. Web Resources -www,math,utk.edu/questions -www.examseducation.net/ questions |
| 2 | Dynamic: I. Newton’s law of motion II. Motion along inclined plane Ill. Motion of connected practices. Important/Uses It is used in: -lifting a weight. -electricity | By the end of the lesson, students should be able to: i. State Newton’s law ii. Explain clearly each of motion. iii. Apply Newton’s laws to practical problems. | i. Guide students to measure and state values of Problem Solving movement and ii. Guide students to state iii. Digital Literacy the laws of motion. iv. Students, as a class, explain the application of laws of motion. | i. Critical Thinking and Problem Solving. ii. Creativity iii. Digital Literacy iv. Leadership and Personal Development | 1. Audio Visual Resources A ball to demonstrate first law of motion -An heavy block to demonstrate third law of motion An inclines object with a weight on it -Light pulley with two blocks connected by string. 2. Web Resources. www.rnathzone.com/d ynamics, w.mathsisfun.com/d cs YouTubeWikipedia.org!dynami.org/differentiation |
| 3 | I. Differentiation II. Limits of a function Ill. Differentiation from the first principle. important/Use It is used in: -lifting a weight. -electricity | By the end of the lesson, students should be able to: i. Find the limit of a function at a given point. ii. Differentiate from the first principle, iii. Differentiate polynomial of the form. iv. y = ax3+ bx2+cx +d, where a, b, c and d are constants. | i. Guide students to make a rectangle array of numbers using real numbers. ii. Guide students to apply law of first principle to solve questions. iii. Guide students to use differentiation method to v and solve polynomials. | i. Critical Thinking and problem solving ii. Creativity iii. Digital Literacy iv. Leadership Personal Development . | 1. Audio Visual’ Resources. -Charts showing differentiation from first principle. – Charts showing derivatives of polynomials 2. Web Resources -www.mathzone.com/ differentiation www.mathsisfun.com /differentiation YouTube Wikipedia |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 4 | Differentiation of transcendental such as I. y = sinax II. y = cobax Ill. y = cosxax IV. y = logax V. y = eax Important/Use lt is used b business women/men to calculate profit and lobs using graph. | By the end of the lesson, students should be able to differentiate special functions such as sinax, cosax, eax an logax problems on differentiation of functions of the form; F(x) = Q(x). P(x) F(x) P( x) = y(x) | i. Students solve problem on limit of a given function ii Students apply some principle to differentiate some trigonometric functions | I. Critical Thinking and Problem Solving ii Creativity iii. Digital Literacy iv. Collaboration and Communication v. Leadership and Personal Development | 1. Audio Visual Resources. -Charts showing derivative of functions such as cosax, sinax, eax,etc 2. Web Resources -YouTube-tecmath www.easy/math/learning/weekly.com/differentiation, www.splashlearning.com/differential dy du dv dx = |
| 5 | Trigonometric functions | problems on differentiation of functions of the form; F(x) Q(x)P(x) F(x = y(x) p(x) | i. Guide students to apply me principle to differentiate some trigonometric functions ii. Students identity and differentiate between types of expressions: | i. Critical Thinking and Problem Solving | www.math.utk/edu/differentiation www.mathplanet.com/differentiation |
| 6 | Application of differentiation to: I. Rate of range II. Maximum and minimum problem Ill, Equation of motion and gradients impulse It is used: -by business women/men to calculate profit and loss using graph. – to determine the minimum and maximum value of particular function. | By the end of the lesson, students should be able to: i. Apply differentiate to practical problems in optimization in economics, motion, science and rate change. ii. Use formula to solve question on equation of motion and gradient. | i. Guide students to draw rectangular plane, shape of any arbitrary dimension on a cardboard then make some increase or decrease in sides. ii. Guide students to use formula to solve question on equation of motion and gradient. | i. Critical thinking and Problem Solving: ii. Creativity iii. Digital Literacy iv. Collaboration and Communication | 1. Audio Visual Resources. -Charts showing gradients equation of motion and rate of change -Model solid materials like set square for rate of change. 2. Web Resources. www.skillyouneed.com/differentiation/and/its/application www.mathsisfunom/differentiation/and/its/application |
| 7 | I Review of first half term’s work II. Periodic1 test and Mid-term break | By the end of the lesson students should be able to: i. Explain third half term’s work learnt solve correctly the test questions | . i. Students solve revision questions in groups:ii. Students solve mid-term test correctly. iii. Students with parent meet teachers for progress report | i. Critical Thinking and Problem Solving. ii. Digital Literacy Collaboration and Communication | 1. Audio Visual Resources -Evaluation and test items, past questions papers 2. Web Resources Easymathslearning.weably.com/questions. |
| 8 | I. Higher derivatives II. Differentiation of implicit functions. Important/Use It is used: -by business women/men to calculate Profit and using graph. -to determine the minimum and maximum value of particular | By the end of the lesson, students should be able to: i. Solve problems on higher derivatives differentiate implicit functions. | i. Guide students to show the differences between two qualities or dimensions using cardboard shapes. | i. Critical Thinking and Problem Solving. ii. Digital Literacy | 1. Audio Visual Resources – Question papers – Writing materials |
| WKS | TOPICS | LEARNING OBJECTIVES | LEARNING ACTIVITIES | EMBEDDED CORE SKILLS | LEARNING RESOURCES |
| 9 | Mechanics i. Vectors in three dimensions ii. Scalar products of vectors in 3D dimension. Important/Use -Fluid mechanics is used in industrial engineers. | By the end of the lesson students should be able to: i. identify a vectoring 3-dimensions. ii. find dot or scalar product of vectors. iii. solve problems involving application of dot product | i. Students, in pair, sketch triangular shapes and rectangular shapes of 3- dimensions. ii. Students, as a class, questions on dot/scalar vector. iii. Guide students to apply dot product on questions. | i. Critical Thinking and Problem Solving. ii. Creativity iii. Digital Literacy | 1. Audio Visual Resources. -Corners of the classroom and its floor Charts showing examples of 3 dimensional vectors. -List of some applications of dot or spalar and cross products 2. Web Resources. www.skillsyouneed.com www.wikipedia.org |
| 10 | i. Vector or cross product of 3 dimensional vector. ii. Application of cross product. Important/Use It is used by engineers and scientist to derive results. | By the end of the lesson students should be able to: i. Find a cross product of two vectors ii. Solve simple problems on application of cross or sector product | I. Guide students to measure dimensions of triangles and rectangles draw, noting the beginning of the measuring points. ii. Guide students to solve questions on vector cross product. | i.Critical Thinking and Problem Solving. ii.. Creativity: iii. Digital Literacy vi. Leadership and Personal Development | 1. Audio Visual Resources -List of application of dot add cross product 2. Web Resources -www.skillsyouneed.com/vector www.wikipedia.org/vector |
| 11 | i. Operations research ii. Concert of replacement iii. Individual replacement of sudden failure items iv. Replacement of item that wear out gradually. Important/Use –It is used to formulate real word problem and develop mathematical models from it. | By the end of the lesson students should be able to: i. Explain the concept of operations and replacement items. ii. types of replacement solve problems on replacement of items. | Students state individually on a sheet of paper, their favourite subject, easy subjects, scores over, time and challenging subjects. Students state their solutions steps to improve on good scores and solve the difficult areas | i. Critical Thinking and Problem Solving ii Digital Literacy iii. Digital Literacy question iv Collaboration and Communication v. Leadership and Personal Development | 1. Audio Visual Resources. -Practical test items on replacement of items in a production line, e.g. battery cells. 2. Web Resources –www.skillsyouneed.com/ operation/research -www.wikipedia.org/operation/ research. |
| 12 | Review of the term’s work | By the end of the lesson students should be able to solve questions on the terms topics. | Students revise in groups the lessons so far by solving problems from past examination and test. | i. Critical Thinking and Problem Solving ii Digital Literacy iii. Collaboration and Communication v. Leadership and Personal Development | 1. Audio Visual Resources Evaluation and test items, past question papers. 2.Web Resources Easymathematics.weebly.com/questions |
| 13 | Examination | By the end of the lesson, students should be able to: solve the examination questions correctly. | Students attempt examination questions correctly | i. Critical Thinking and Problem Solving ii Digital Literacy | 1. Audio Visual Resources. -Question papers -Writing materials |
