CBSE Class VIII Mathematics Class Plan

CBSE Class VIII Mathematics (Ganita Prakash) — 160-Day Lesson Plan

A comprehensive, day-to-day instructional plan aligned with the National Curriculum Framework (NCF) covering all 14 chapters across two parts.

Daily 60-Minute Lesson Architecture:

• 00:00 – 00:10 (10 mins) — Retrieval & Concept Warm-up: Rapid oral check, homework review, and 1 slate problem from previous lesson.
• 00:10 – 00:50 (40 mins) — Concept Exploration & Guided Practice: Core theory, blackboard modeling with MathJax/LaTeX notations, and guided student practice.
• 00:50 – 01:00 (10 mins) — Exit Ticket & Formative Check: 2 quick concept-check questions based directly on current class lesson.

Term 1: Part I (Days 1–80)

Chapter 1: A Square and A Cube (14 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 1	Multiplication tables & area of square review.	Discovery of square numbers; visual grid arrays and locker puzzle intro.	"Why does a square number always have an odd number of factors?"
Day 2	Definition of perfect squares.	Properties of perfect squares: Unit digits pattern (\(0, 1, 4, 5, 6, 9\)).	Can \(1057\) be a perfect square? Justify.
Day 3	Unit digit endings of squares.	Patterns in squares: Sum of consecutive odd numbers (\(1+3+5 = 3^2\)).	Express \(49\) as a sum of 7 consecutive odd numbers.
Day 4	Sum of odd numbers pattern.	Numbers between consecutive squares: \(2n\) non-square numbers between \(n^2\) and \((n+1)^2\).	How many non-squares lie between \(12^2\) and \(13^2\)?
Day 5	Non-square count rule.	Finding square roots using Repeated Subtraction & Prime Factorisation.	Find \(\sqrt{144}\) using prime factorisation.
Day 6	Prime factorisation for \(\sqrt{n}\).	Finding smallest number to multiply/divide to obtain a perfect square.	Find smallest \(k\) such that \(180 \times k\) is a square.
Day 7	Factor pairing concept.	Division method for square roots of large numbers: Step-by-step logic.	Find \(\sqrt{529}\) by long division.
Day 8	Long division for integers.	Square roots of decimal numbers using long division.	Compute \(\sqrt{7.29}\) using division.
Day 9	Decimal square roots.	Introduction to Cubes: 3D spatial volumes, prime factorization of cubes.	Is \(216\) a perfect cube? Verify using factors.
Day 10	Perfect cube criteria.	Cube numbers and unit digit patterns (\(1^3 \to 1, 2^3 \to 8, 3^3 \to 7\), etc.).	What is the unit digit of \(23^3\)?
Day 11	Cube digit properties.	Finding cube root through Prime Factorisation method.	Find \(\sqrt[3]{1728}\).
Day 12	Cube root calculations.	Estimation method to find cube roots of large perfect cubes.	Estimate \(\sqrt[3]{13824}\) by grouping digits.
Day 13	Estimation vs Factorisation.	Application word problems on squares and cubes in geometry and physics.	Solve: Minimum plants needed to arrange a square grid.
Day 14	All square/cube properties.	Chapter review, diagnostic speed test, and doubt resolution.	3-minute rapid mental math exit sheet.

Chapter 2: Power Play (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 15	Repeated multiplication basics.	Powers with positive integral exponents; base and index notation.	Express \(2 \times 2 \times 2 \times 3 \times 3\) in exponential form.
Day 16	Positive index notation.	Powers with negative exponents: Meaning of \(a^{-m} = \frac{1}{a^m}\) and reciprocals.	Evaluate \(3^{-2}\) and \((1/2)^{-3}\).
Day 17	Negative exponents rule.	Laws 1 & 2: \(a^m \times a^n = a^{m+n}\) and \(a^m \div a^n = a^{m-n}\).	Simplify: \(2^5 \times 2^{-3} \div 2^4\).
Day 18	Product and quotient laws.	Laws 3 & 4: \((a^m)^n = a^{mn}\) and \(a^m \times b^m = (ab)^m\).	Simplify: \((3^2)^3 \times 2^6\).
Day 19	Power of a power law.	Law 5 & Zero Exponent: \((a/b)^m = a^m/b^m\) and \(a^0 = 1\).	Evaluate: \((5^0 + 4^{-1}) \times 2^2\).
Day 20	All laws of exponents.	Simplifying complex algebraic exponential expressions using multiple laws.	Simplify: \(\frac{25 \times t^{-4}}{5^{-3} \times 10 \times t^{-8}}\).
Day 21	Complex exponential steps.	Powers of 10 and expressing very large numbers in Scientific Standard form.	Express \(150,000,000\text{ km}\) in standard form.
Day 22	Large number standard form.	Expressing very small numbers in Scientific/Standard form.	Write \(0.000007\text{ m}\) in standard form.
Day 23	Small number standard form.	Converting standard scientific form back to usual form.	Convert \(3.52 \times 10^{-5}\) to decimal notation.
Day 24	Standard vs usual form.	Comparison of very large and very small quantities (orders of magnitude).	Compare Sun's diameter (\(1.4 \times 10^9\text{ m}\)) to Earth's (\(1.27 \times 10^7\text{ m}\)).
Day 25	Exponent laws and standard form.	Real-world problem solving (mass of atoms, cell size, planetary distances).	Calculate combined mass of 5 paper sheets + 5 books in scientific notation.
Day 26	Chapter 2 recall.	Chapter Unit Test and rapid exponent puzzle check.	Solve 2 evaluation problems in 5 mins.

Chapter 3: A Story of Numbers (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 27	Natural and whole numbers recap.	Historical number systems (Tally marks, Egyptian, Roman, Babylonian base-60).	What was the key limitation of non-positional systems?
Day 28	Historical counting systems.	The Idea of a Base: Decimal (base-10), Binary (base-2), and other bases.	Represent number 13 in base-2 (binary).
Day 29	Binary vs Decimal base.	Positional Place Value representation and generalized form (\(10a + b\)).	Write \(738\) in generalized expanded form.
Day 30	Generalized number forms.	Rational Numbers on number line: Closure & Commutative properties.	Is subtraction commutative for rational numbers?
Day 31	Commutative property.	Associative and Distributive properties of Rational numbers.	Verify: \(a(b+c) = ab + ac\) for \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\).
Day 32	Associativity & Distributivity.	Additive Identity, Multiplicative Identity, Additive & Multiplicative Inverses.	Write the multiplicative inverse of \(-\frac{13}{19}\).
Day 33	Identities and Inverses.	Finding rational numbers between two rational numbers (Mean method).	Find 3 rational numbers between \(\frac{1}{4}\) and \(\frac{1}{2}\).
Day 34	Rational interpolation.	Word problems involving rational numbers in real-life contexts.	A ribbon of \(\frac{15}{2}\text{ m}\) is cut into 5 equal parts. Find each length.
Day 35	Properties of rationals.	Exploratory number games and structural number patterns.	Find the unknown term in the sequence.
Day 36	Chapter 3 review.	Chapter 3 Unit Diagnostic Assessment.	State closure property under division.

Chapter 4: Quadrilaterals (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 37	Polygons and basic shapes.	Polygons: Convex and Concave polygons, Regular and Irregular polygons.	Differentiate between convex and concave polygon.
Day 38	Polygon classification.	Angle Sum Property of a Polygon: Interior angle sum \((n - 2) \times 180^\circ\).	Find interior angle sum of a heptagon (\(n=7\)).
Day 39	Interior angle sum formula.	Sum of measures of Exterior Angles of any polygon (\(= 360^\circ\)).	Find measure of each exterior angle of regular nonagon (\(n=9\)).
Day 40	Exterior angle properties.	Quadrilaterals: Exploring Trapezium and Kite (Definitions & properties).	Are adjacent sides equal in a kite? Explain.
Day 41	Trapezium and Kite.	Parallelogram: Properties of opposite sides and opposite angles.	In parallelogram \(ABCD\), \(\angle A = 80^\circ\). Find \(\angle B, \angle C, \angle D\).
Day 42	Parallelogram angles.	Diagonals of a Parallelogram: Bisecting property with algebraic proofs.	If \(OA = x+3\) and \(OC = 7\), find \(x\) for diagonal \(AC\).
Day 43	Diagonal bisection.	Rhombus: Properties, perpendicular diagonals, and relation to parallelogram.	Prove diagonals of rhombus intersect at \(90^\circ\).
Day 44	Rhombus properties.	Rectangle and Square: Diagonals equality and perpendicular properties.	Compare diagonal properties of Rectangle and Square.
Day 45	Special quadrilaterals comparison.	Constructing Quadrilaterals: When 4 sides and 1 diagonal are given.	Outline construction steps for quadrilateral \(ABCD\).
Day 46	Construction with 1 diagonal.	Constructing Quadrilaterals: When 3 sides and 2 diagonals / adjacent angles given.	Construct quadrilateral with 2 adjacent sides and 3 angles.
Day 47	Geometric construction steps.	Practical application problems involving structural properties of quads.	Identify quadrilateral type from 4 given diagonal clues.
Day 48	Quadrilateral hierarchy.	Chapter Unit Test and compass construction precision test.	Draw a kite and state 3 unique properties.

Chapter 5: Number Play (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 49	Generalized number forms (\(10a+b\)).	Number puzzles: "Digits in Disguise" (Cryptarithms / Letters for digits).	Solve for \(A\): \(3A + 25 = B2\).
Day 50	Addition cryptarithms.	Multiplication Cryptarithms: Finding single and multi-digit letter values.	Solve: \(1A \times A = 9A\).
Day 51	Cryptarithm rules.	Divisibility Tests: Mathematical reasons behind tests for 2, 5, and 10.	Prove why divisibility by 5 depends only on units digit.
Day 52	Tests for 2, 5, 10.	Divisibility Tests: Derivation and applications for 3 and 9 (Sum of digits logic).	If \(21y5\) is a multiple of 9, find the digit \(y\).
Day 53	Tests for 3 and 9.	Divisibility Test for 11: Alternating sum of digits proof and application.	Check if \(1331\) and \(90816\) are divisible by 11.
Day 54	Divisibility by 11.	Composite divisibility tests: Divisibility rules for 4, 6, 8, and 12.	Check divisibility of \(7128\) by 4 and 8.
Day 55	Divisibility rules review.	Magic Squares: 3x3 and 4x4 magic square construction and invariant sums.	Complete a 3x3 magic square with numbers 1 to 9.
Day 56	Magic square rules.	Palindromic numbers, Kaprekar's constant (\(6174\)), and exploratory arithmetic.	Run Kaprekar routine on \(3524\) for 2 steps.
Day 57	Pattern exploration.	Complex numerical riddles and logical deduction games.	Find the 3-digit secret number from 3 clues.
Day 58	Chapter 5 puzzle bank.	Chapter Unit Test on cryptarithms and divisibility proofs.	Solve 1 addition cryptarithm \(+\) 1 divisibility check.

Chapter 6: We Distribute, Yet Things Multiply (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 59	Terms, factors, and coefficients.	Algebraic Expressions: Monomials, Binomials, Polynomials, and Like/Unlike terms.	Classify: \(4xy, 2x+3y, x^2+y+1\).
Day 60	Classification of polynomials.	Multiplication of Monomial by Monomial: Geometric area representation.	Multiply: \((3x^2y) \times (-5xy^3)\).
Day 61	Monomial multiplication.	Multiplication of Monomial by Binomial: Distributive Property (\(a(b+c) = ab+ac\)).	Multiply: \(2x(3x + 5y)\).
Day 62	Monomial by Binomial.	Multiplication of Monomial by Trinomial and multi-term expansion.	Expand: \(-3a(2a^2 - 4a + 7)\).
Day 63	Distributive expansions.	Multiplication of Binomial by Binomial: Grid method & FOIL method.	Expand: \((2x + 3)(3x - 4)\).
Day 64	Binomial multiplication.	Multiplication of Binomial by Trinomial with simplification of like terms.	Multiply: \((a + b)(a^2 - ab + b^2)\).
Day 65	Binomial by trinomial.	Standard Identity 1: \((a + b)^2 = a^2 + 2ab + b^2\) (Geometric & algebraic proof).	Expand: \((3x + 2y)^2\).
Day 66	Identity 1 application.	Standard Identity 2: \((a - b)^2 = a^2 - 2ab + b^2\) (Visual proof and evaluation).	Expand: \((4p - 3q)^2\) and evaluate \(99^2\).
Day 67	Identity 2 application.	Standard Identity 3: \((a + b)(a - b) = a^2 - b^2\).	Evaluate \(51^2 - 49^2\) and expand \((2x-5)(2x+5)\).
Day 68	Identity 3 application.	Standard Identity 4: \((x + a)(x + b) = x^2 + (a + b)x + ab\).	Evaluate \(103 \times 104\) using Identity 4.
Day 69	All 4 identities.	"Mind the Mistake, Mend the Mistake": Analyzing algebraic common errors.	Spot the error: \((2x)^2 = 2x^2\).
Day 70	Error correction & practice.	Chapter Unit Test on algebraic multiplication and identities.	Solve 3 expansions using identities.

Chapter 7: Proportional Reasoning – 1 (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 71	Ratio and proportion basics.	Concept of Direct Proportion: Constant ratio \(x/y = k\) with real-life tables.	If 5 pens cost ₹25, find cost of 12 pens using ratio.
Day 72	Direct proportion formula.	Solving word problems on Direct Proportion (Speed-distance, unitary scaling).	A train moves at \(75\text{ km/h}\). How far does it go in 20 minutes?
Day 73	Direct proportion word problems.	Concept of Inverse Proportion: Constant product \(x \times y = k\).	If 10 men build a wall in 6 days, how long do 15 men take?
Day 74	Inverse proportion formula.	Solving word problems on Inverse Proportion (Speed-time, work-time).	Speed changes from \(40\text{ km/h}\) to \(60\text{ km/h}\). Find new travel time.
Day 75	Direct vs Inverse identification.	Discriminating between Direct and Inverse Proportions in mixed scenarios.	Is "Number of workers and time taken" direct or inverse?
Day 76	Proportional reasoning models.	Proportions in Maps and Scale Drawings: Scale factor calculations.	Map scale is \(1\text{ cm} : 50\text{ km}\). Real distance for \(4.5\text{ cm}\)?
Day 77	Scale factors.	Compound Proportions: Multi-variable unit scaling problems.	6 pumps fill a tank in 8 hours. Time for 8 pumps?
Day 78	Complex proportion problems.	Graphic representation of direct and inverse variations.	What shape is the graph of an inverse proportion?
Day 79	Part I full review.	Term 1 Mock Exam Revision: Core concepts across Chapters 1–7.	Rapid 5-concept formula sprint.
Day 80	Mock Exam Analysis.	Mid-Term / Half-Yearly Assessment and Part I diagnostic wrap-up.	Term 1 self-assessment reflection.

Term 2: Part II (Days 81–160)

Chapter 8: Fractions in Disguise (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 81	Percentage basics (\(x\% = x/100\)).	Understanding Percentages as "Fractions in Disguise": Rapid conversions.	Convert \(\frac{3}{8}\) to percentage and \(35\%\) to fraction.
Day 82	Fraction to percentage.	Finding percentage increase and decrease in real-world quantities.	Price increases from ₹500 to ₹575. Find % increase.
Day 83	Percentage change formula.	Discounts and Marked Price: Calculating Discount \(\%\) and Net Selling Price.	Item MP \(=\) ₹800, Discount \(= 15\%\). Find SP.
Day 84	Discount calculations.	Profit and Loss review: Cost Price, Selling Price, Profit \(\%\) and Loss \(\%\).	CP \(=\) ₹450, SP \(=\) ₹540. Calculate Profit \(\%\).
Day 85	Profit/Loss formulas.	Value Added Tax (VAT) and Goods and Services Tax (GST) estimation.	Bill amount is ₹1200 with 18% GST. Find total price.
Day 86	Sales tax / GST.	Simple Interest vs Compound Interest: Concept of interest compounding annually.	How does Compound Interest differ from Simple Interest?
Day 87	CI concept.	Compound Interest Formula derivation: \(A = P(1 + \frac{R}{100})^n\) and \(CI = A - P\).	Calculate CI on ₹10,000 at 10% p.a. for 2 years.
Day 88	CI annual calculation.	Compounded Half-Yearly: Rate halving (\(R/2\)) and time doubling (\(2n\)) formula.	Find amount on ₹8000 at 10% compounded half-yearly for 1 year.
Day 89	Half-yearly compounding.	Real-world applications of CI: Population growth and depreciation of assets.	Machine value ₹50,000 depreciates at 10% per year. Value after 2 years?
Day 90	Chapter 8 formulas.	Chapter Unit Test on commercial arithmetic.	Solve 1 GST \(+\) 1 CI calculation problem.

Chapter 9: The Baudhayana–Pythagoras Theorem (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 91	Right-angled triangles recap.	Baudhayana Sulba Sutras and history of the theorem in Indian and Greek maths.	State the Baudhayana-Pythagoras theorem statement.
Day 92	Theorem statement.	Visual and Geometric Dissection Proof of \(a^2 + b^2 = c^2\).	Explain the geometric square dissection proof.
Day 93	Dissection proof.	Finding hypotenuse and leg lengths in right triangles.	In \(\triangle ABC\) right-angled at \(B\), \(AB=6, BC=8\). Find \(AC\).
Day 94	Hypotenuse calculation.	Pythagorean Triplets: Definition and generating triplets using \((2m, m^2-1, m^2+1)\).	Write a Pythagorean triplet whose smallest member is 8.
Day 95	Triplet generation formula.	Converse of Baudhayana-Pythagoras Theorem: Checking if a triangle is right-angled.	Check if sides \(9\text{ cm}, 12\text{ cm}, 15\text{ cm}\) form a right triangle.
Day 96	Converse theorem.	Real-life applications: Ladder against a wall, broken tree problem.	A \(13\text{ m}\) ladder reaches a \(12\text{ m}\) window. Find distance of foot from wall.
Day 97	Ladder/tree problems.	Distance between two points on a grid using right-triangle properties.	Find diagonal distance of rectangle \(8\text{ cm} \times 6\text{ cm}\).
Day 98	Grid distance.	Advanced problems involving multi-step geometric figures and heights.	Find perimeter of rhombus whose diagonals are \(16\text{ cm}\) and \(12\text{ cm}\).
Day 99	Rhombus/triplet applications.	Indian mathematical history context & Sulba Sutra cord constructions.	Mention Baudhayana's approximation for \(\sqrt{2}\).
Day 100	Chapter 9 review.	Chapter Unit Test on Baudhayana-Pythagoras Theorem.	Solve 2 application word problems.

Chapter 10: Proportional Reasoning – 2 (10 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 101	Direct & inverse proportion (Part I).	Time and Work: Concept of 1 day's work (\(\text{Work Rate} = 1/n\)).	If \(A\) finishes work in 6 days, what fraction does \(A\) do in 1 day?
Day 102	Work rate concept.	Combined Work Problems: Working together (\(A + B\)) efficiency.	\(A\) takes 4 days, \(B\) takes 6 days. How long working together?
Day 103	Combined work formula.	Pipes and Cisterns: Inlets and outlets (Filling vs Emptying rates).	Pipe \(P\) fills in 3 hrs, \(Q\) empties in 6 hrs. Net rate?
Day 104	Pipes and cisterns.	Time, Speed, and Distance: Average speed and relative speed concepts.	Convert \(72\text{ km/h}\) to \(\text{m/s}\) (Multiply by \(\frac{5}{18}\)).
Day 105	Speed conversions.	Problems on Trains: Crossing stationary pole vs crossing long platform.	Train \(150\text{ m}\) long crosses pole at \(54\text{ km/h}\). Find time taken.
Day 106	Train crossing problems.	Upstream and Downstream motion in rivers: Effective speed modeling.	Boat speed \(10\text{ km/h}\), stream \(2\text{ km/h}\). Find upstream & downstream speeds.
Day 107	River speed equations.	Mixture and Alligation: Ratio of mixtures when two components are blended.	In 40 L milk-water mix, ratio is \(3:1\). How much water is present?
Day 108	Mixture problems.	Unitary method vs Algebraic Proportion comparative modeling.	Solve 1 speed problem using both methods.
Day 109	Proportional strategies.	Challenging multi-step aptitude problems.	Solve combined work problem with leaving workers.
Day 110	Chapter 10 review.	Chapter Unit Test on Time-Work & Speed-Distance.	Solve 1 work \(+\) 1 train problem.

Chapter 11: Exploring Some Geometric Themes (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 111	2D vs 3D shapes.	Visualising Solid Shapes: Polyhedra vs Non-polyhedra, Faces, Edges, Vertices (\(F, E, V\)).	Count \(F, E, V\) for a triangular prism.
Day 112	\(F, E, V\) definitions.	Euler's Formula for Polyhedra: \(F + V - E = 2\) verification on pyramids and prisms.	If a polyhedron has 6 faces and 8 vertices, find edges using Euler's formula.
Day 113	Euler's formula.	Mapping Space: Reading and interpreting maps, scale references, and symbols.	Identify landmarks and scale from given classroom map.
Day 114	Map reading basics.	Drawing 3D shapes on 2D surfaces: Isometric and Oblique sketches.	Draw an oblique sketch of a \(2 \times 2 \times 2\) cube.
Day 115	Isometric sketching.	Different views of 3D shapes: Front view, Top view, Side view.	Draw top, front, side view of a step-block structure.
Day 116	3-view projections.	Symmetry in Geometry: Rotational symmetry, order and angle of rotation.	What is the order of rotational symmetry of an equilateral triangle?
Day 117	Rotational symmetry.	Line Symmetry vs Rotational Symmetry in standard geometric figures.	Tabulate lines of symmetry and rotational order for Square, Rectangle, Circle.
Day 118	Symmetry classification.	Tessellations: Tiling the plane with regular and semi-regular polygons.	Why can regular pentagons not tile a flat floor?
Day 119	Tessellation rules.	Cross-sections and shadows of 3D objects.	What cross-section is obtained when cutting a cylinder horizontally?
Day 120	Cross-sections & shadows.	Mathematical art: Rangoli, Kolam and geometric tiling patterns.	Identify symmetrical axes in a given Kolam pattern.
Day 121	Chapter 11 themes.	Hands-on 3D origami/net verification.	Fold a net to construct a regular octahedron.
Day 122	Solid geometry review.	Chapter Unit Test on Solid Geometry & Symmetry.	Verify Euler's formula on 2 polyhedra.

Chapter 12: Tales by Dots and Lines (Data & Graphs) (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 123	Bar graphs and pictographs recap.	Frequency Distribution: Grouped data, Class Intervals, Upper/Lower limits.	Find class mark and class size for interval \(20-30\).
Day 124	Class intervals.	Histograms: Construction and interpretation with equal class intervals.	When is a jagged line (kink \(\sim\)) used on the axis?
Day 125	Histogram plotting.	Circle Graphs (Pie Charts): Concept of central angle \(\theta = \frac{\text{Value}}{\text{Total}} \times 360^\circ\).	Find central angle for an expenditure of 25% on food.
Day 126	Central angle formula.	Constructing Pie Charts with compass and protractor from frequency tables.	Draw pie chart sectors for given 3-category data.
Day 127	Pie chart construction.	Interpreting information from published Pie Charts.	Answer 3 inference questions from given student time-pie chart.
Day 128	Pie chart interpretation.	Introduction to Line Graphs & Linear Graphs: Continuous data over time.	Plot temperature vs time on a line graph.
Day 129	Line graph plotting.	Reading Cartesian coordinates \((x, y)\) on coordinate plane graphs.	Name the coordinates of the origin and plot \((3, 5)\).
Day 130	Coordinate reading.	Application of Linear Graphs: Distance-Time graphs and Cost-Quantity relationships.	Find speed from the slope of a distance-time graph.
Day 131	Graph applications.	Introduction to Probability: Random experiment, Outcomes, and Events (\(P(E) = \frac{n(E)}{n(S)}\)).	Find probability of rolling a prime number on a fair die.
Day 132	Basic probability.	Probability with Coins, Dice, and Cards (Equally likely outcomes).	Find probability of getting at least one head when tossing 2 coins.
Day 133	Probability events.	Misleading graphs and critical data analysis.	Identify how changing scale distorts graph perception.
Day 134	Chapter 12 review.	Chapter Unit Test on Data, Graphs & Probability.	Construct 1 pie chart \(+\) 1 probability calculation.

Chapter 13: Algebra Play (14 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 135	Algebraic terms and factors.	Factorisation concept: Factoring by Highest Common Factor (HCF) method.	Factorise: \(12a^2b + 15ab^2\).
Day 136	Common factor method.	Factorisation by Grouping terms (\(ax + bx + ay + by\)).	Factorise: \(6xy - 4y + 6 - 9x\).
Day 137	Grouping method.	Factorisation using Identities: \(a^2 \pm 2ab + b^2 = (a \pm b)^2\).	Factorise: \(49x^2 + 70xy + 25y^2\).
Day 138	Identity factorisation (\(\pm\)).	Factorisation using Difference of Two Squares: \(a^2 - b^2 = (a+b)(a-b)\).	Factorise: \(49p^2 - 36\) and \(x^4 - y^4\).
Day 139	Difference of squares.	Factorisation of form \((x^2 + (a+b)x + ab)\) by Splitting the Middle Term.	Factorise: \(y^2 - 7y + 12\).
Day 140	Middle term splitting.	Factoring quadratics with leading coefficients: \(ax^2 + bx + c\).	Factorise: \(2x^2 + 7x + 3\).
Day 141	Advanced quadratic factorisation.	Division of Algebraic Expressions: Monomial by Monomial.	Divide: \(28x^4 \div 56x\).
Day 142	Monomial division.	Division of Polynomial by Monomial: Term-by-term method.	Divide: \((5x^2 - 6x) \div 3x\).
Day 143	Polynomial by monomial.	Division of Polynomial by Polynomial using common factor cancellation.	Divide: \((x^2 + 7x + 10) \div (x + 2)\).
Day 144	Long division / Factor cancellation.	Solving Linear Equations in One Variable (Variable on one side).	Solve: \(2x - 3 = 7\).
Day 145	1-sided linear equations.	Solving Linear Equations with Variables on both sides (Transposition method).	Solve: \(5x + 9 = 5 + 3x\).
Day 146	Transposition steps.	Reducing Equations to Simpler Form & Cross-multiplication method.	Solve: \(\frac{x+1}{2x+3} = \frac{3}{8}\).
Day 147	Cross-multiplication.	Word problems based on Linear Equations (Ages, numbers, perimeters).	"Sum of two numbers is 95; one exceeds other by 15." Find them.
Day 148	Linear equation word problems.	Chapter Unit Test on Factorisation and Linear Equations.	Factorise 1 quadratic \(+\) 1 solve linear equation.

Chapter 14: Area & Mensuration (12 Days)

Day	10 Min (Previous Class Recap)	40 Min (Teaching & Guided Practice)	10 Min (Current Class Exit Check)
Day 149	Area of rectangle, triangle, square.	Area of a Trapezium: Derivation (\(\text{Area} = \frac{1}{2}(a+b)h\)) and problems.	Find area of trapezium with parallel sides \(10\text{ cm}, 12\text{ cm}\), height \(5\text{ cm}\).
Day 150	Trapezium area formula.	Area of a General Quadrilateral (Splitting into 2 triangles using diagonal and heights).	Formula: \(\frac{1}{2}d(h_1 + h_2)\). Calculate area for \(d=10, h_1=3, h_2=5\).
Day 151	General quadrilateral area.	Area of Special Quadrilaterals: Rhombus (\(\text{Area} = \frac{1}{2} d_1 d_2\)).	Diagonals of rhombus are \(7.5\text{ cm}\) and \(12\text{ cm}\). Find area.
Day 152	Rhombus area formula.	Area of regular and irregular Polygons by dividing into triangles and trapeziums.	Compute field book polygon area by adding sub-regions.
Day 153	Polygon area division.	Surface Area of Cube and Cuboid (Lateral & Total Surface Area).	Find TSA and LSA of cuboid \(10\text{ cm} \times 8\text{ cm} \times 6\text{ cm}\).
Day 154	Cube/cuboid surface area.	Surface Area of Right Circular Cylinder: \(\text{CSA} = 2\pi rh\), \(\text{TSA} = 2\pi r(r+h)\).	Find CSA of cylinder with \(r = 7\text{ cm}, h = 10\text{ cm}\).
Day 155	Cylinder surface area.	Volume of Cube and Cuboid (\(V = l \times b \times h\) and \(V = a^3\)).	Find volume of cube of side \(8\text{ cm}\).
Day 156	Cube/cuboid volume.	Volume of a Cylinder: \(V = \pi r^2 h\) and capacity in litres.	Find capacity in litres of cylindrical tank \(r=1.4\text{ m}, h=2\text{ m}\).
Day 157	Cylinder volume & litres.	Ratio comparison of Surface Area and Volume when dimensions are doubled/halved.	If edge of cube is tripled, by what factor does volume increase?
Day 158	Dimension change effects.	Comprehensive mensuration word problems (painting walls, digging wells).	Cost of plastering cylindrical tank inner surface.
Day 159	Full Mensuration review.	Full Syllabus Rapid Formula Blitz & Mock Assessment.	Rapid 10-formula recall test.
Day 160	Final exam readiness.	Final Examination Strategy, Presentation Tips, and Step-Marking Guidelines.	Closing review and feedback check.

Classroom Delivery Guidelines for Ganita Prakash

• Inquiry & Indian Mathematics: Introduce historical and exploratory elements (such as Baudhayana's Sulba Sutra cord geometry, Kaprekar's constant \(6174\), and the locker problem) during the first 10 minutes of new units.
• Board Architecture (Left-to-Right):
  • Left (15%): Key terms, active identities, and formulas.
  • Center (65%): Conceptual derivations, diagram constructions, and worked examples.
  • Right (20%): Starter recap problem, current exit check, and assigned homework.