10th Class Unit Plans and Year Plan
SCERT Telangana · Mathematics · Class 10
Download PDF
10th Class Unit Plans and Year Plan — SCERT Telangana
10th Class Mathematics Year Plan and Unit Plans — SCERT Telangana
This page provides the complete Year Plan and Unit Plans for Class 10 Mathematics, prepared in alignment with the SCERT Telangana curriculum. The plan has been developed by an experienced team of School Assistant (Mathematics) resource persons — Sri Dr. Kandala Ramaiah (ZPHS Abbapur, Mulugu), Sri Emmadi Ramu (ZPHS Bodangiparthy, Nalgonda), Sri Kasam Santhosh Kumar (ZPSS Areguda, K.B.Asifabad), and Sri Errabelly Ashok (ZPHS Suddpally, Jagtial) — under the advisory guidance of Sri Komanduru Sreedharacharyulu, Faculty at SCERT Hyderabad. Together, these plans cover the entire Class 10 academic year across 143 periods spread over 14 teaching units, giving Mathematics teachers a structured and month-wise road map from June to the start of Public Examinations.
The document is organised into two core sections: a Year Plan that provides a bird's-eye view of the full academic year — month-wise chapter allocation, period distribution, required TLMs, scheduled activities and ICT tool recommendations — and Unit Plans for each of the 14 chapters, providing chapter-level learning outcomes, sub-topic breakdowns with period allocation, concept maps, teaching resources and space for teacher reflections. This plan is also aligned with the five academic standards of Mathematics education: Problem Solving, Reasoning and Proof, Communication, Connection, and Visualisation and Representation.
Year Plan at a Glance — All 14 Units
The Year Plan distributes all 14 chapters across the academic year from June to January, with a dedicated revision period from 11th January until the start of Public Examinations. The table below reflects the exact chapter-wise schedule, period allocation and key activities as specified in the plan document:
Annual Learning Outcomes for Class 10 Mathematics
By the end of the Class 10 academic year, students who follow this teaching plan will be expected to have achieved the following learning outcomes across all 14 units. These outcomes are framed in action-verb format to reflect genuine competency rather than passive knowledge:
Students will generalise properties of numbers and apply the Fundamental Theorem of Arithmetic and Euclid's Division Lemma to solve problems related to HCF and LCM; derive proofs for the irrationality of numbers like √2 and √3 using logical reasoning; identify exponential and logarithmic forms, derive and apply laws of logarithms; classify sets and represent relationships using Venn diagrams; develop algebraic and graphical methods for finding zeroes of polynomials and establish the relationship between zeroes and coefficients; solve pairs of linear equations in two variables using graphical, substitution, and elimination methods; find roots of quadratic equations by factorisation, completing the square, and the quadratic formula, and determine the nature of roots using the discriminant; apply concepts of Arithmetic Progression and Geometric Progression to real-life problems; derive and apply the distance formula, section formula, midpoint formula, centroid formula, and area of triangle formula using coordinate geometry; establish properties of similar triangles using the Basic Proportionality Theorem, area theorem, and Pythagoras Theorem; prove theorems related to tangents drawn from a point to a circle and construct tangents from an external point; determine all trigonometric ratios for acute angles, establish identities, use complementary angle relationships, and apply trigonometry to heights and distances problems; calculate surface areas and volumes of combinations of solids and solve conversion-of-solids problems; calculate mean, median, and mode for grouped data and draw ogive curves; and determine the probability of events using the classical definition and apply it to daily-life problems.
What Each Unit Plan Contains
Every chapter in this Class 10 Mathematics Teaching Plan is structured as a detailed unit plan with the following components:
- Chapter-wise Learning Outcomes — precise, observable outcomes written in action-verb format that every student should achieve by the end of the unit (e.g., applies, justifies, derives, constructs, solves, communicates)
- Prerequisites — the prior knowledge required before beginning the chapter, enabling teachers to check for and address learning gaps before introducing new concepts
- Sub-topic Breakdown with Period Allocation — every chapter is divided into clearly defined sub-topics, each assigned a recommended number of teaching periods including introduction, exercises, and a revision/slip test
- Concept Map — a visual mind-map of the chapter showing how all sub-topics, theorems, and methods connect, helping teachers present the complete picture before diving into individual topics
- Required TLM (Teaching Learning Materials) — specific physical materials listed for each chapter such as logarithm charts, Venn diagram charts, graph papers, models of 3D solids, geometry boxes, trigonometric ratio charts, dice, coins, and decks of cards
- ICT Tools — recommended digital tools for each chapter including GeoGebra, Desmos, DIKSHA App, Khan Academy, IFP (Interactive Flat Panel) LMS App, Robocompass, PhET Simulations, NCTM Illuminations, and Canva — aligned with NEP 2020's emphasis on technology integration
- Teacher's Reflections Space — a dedicated section for teachers to record observations, challenges, and strategies after completing each unit, supporting continuous improvement
- Monthly Activities — chapter-specific co-curricular activities including Quiz competitions, Project and Review work, Venn diagram preparation, graph preparation, and the National Mathematics Day Celebration tied to Mensuration in December
Chapter Highlights — What Students Learn in Each Unit
Real Numbers (15 periods): This foundational chapter opens the Class 10 year by revisiting and deepening students' understanding of the number system. Students learn to apply Euclid's Division Lemma to find the HCF of two numbers and understand the Fundamental Theorem of Arithmetic — that every composite number can be expressed as a unique product of primes. They explore rational numbers and their decimal expansions, distinguishing terminating from non-terminating recurring decimals, and use Theorem 1.3, 1.4, and 1.5 to determine which p/q form numbers produce terminating decimals. A major new concept introduced here is Logarithms — students learn to convert between exponential and logarithmic forms, derive the three laws of logarithms (log of a product, log of a quotient, log of a power), and apply them to solve real-life problems. The concept map for this chapter connects Euclid's Division Lemma, the Fundamental Theorem, rational number decimal expansions, irrational numbers (√2, √3, 5−√3, √2+√3), and logarithm properties into a single coherent visual structure. TLM includes a Chart of Properties of Logarithms and a Chart of Number Systems; ICT tools recommended are GeoGebra, LMS App on IFP, DIKSHA, and Khan Academy.
Sets (11 periods): This chapter introduces students to a new branch of mathematics — Set Theory — which underpins probability, statistics, and modern algebra. Students learn to define different types of sets (empty, singleton, finite, infinite, universal, equal, disjoint) with real-life examples, represent sets in Roster Form and Set Builder Form, and convert between the two representations. Core operations covered are Union, Intersection, and Difference of sets along with Disjoint Sets. Students draw and interpret Venn diagrams to visualise set relationships, determine cardinality of finite sets, and connect set theory concepts to probability and statistics. Prerequisites include familiarity with natural numbers, whole numbers, integers, rational and irrational numbers, even/odd numbers, multiples, and factors. Activities include student preparation of Venn diagrams from given data. The recommended TLM is Charts of Venn Diagrams; ICT tools are IFP, GeoGebra, and DIKSHA App.
Polynomials (11 periods): Building on algebraic foundations from earlier classes, students work with linear, quadratic, and cubic polynomials in depth. They identify degrees and types of polynomials, find the zeroes of a given polynomial, and verify whether given values are zeroes. A key focus is the relationship between zeroes and coefficients — students derive and apply the formulae α + β = −b/a and αβ = c/a for quadratic polynomials, and the corresponding three-root formulae for cubic polynomials. The graphical meaning of zeroes is explored through graphs of linear, quadratic, and cubic polynomials, and the Division Algorithm for polynomials (p(x) = g(x)·q(x) + r(x)) is introduced and applied. The concept map visually connects polynomial types, graphical zeroes, coefficient–zero relationships, and the Division Algorithm. Recommended TLM includes a Chart of polynomials and their degrees, and a Chart of the relationship between zeroes and coefficients. ICT tools are GeoGebra, LMS App on IFP, and DIKSHA App.
Pair of Linear Equations in Two Variables (10 periods): This chapter extends students' earlier work on linear equations to systems of two equations in two unknowns. Students form linear equations from real-life situations, represent them graphically, and interpret the graph — recognising whether lines intersect (unique solution), are parallel (no solution), or coincide (infinite solutions). The relationship between the coefficients a₁, b₁, c₁ and a₂, b₂, c₂ and the nature of the system (consistent or inconsistent) is established as a key analytical tool. Two algebraic methods — Substitution and Elimination — are practised in detail, and equations reducible to a pair of linear equations are covered. Real-life problems from diverse contexts (ages, speeds, coins, fractions) are solved using these methods. The recommended TLM is a Chart of the relationship between coefficients and the nature of the system; ICT tools include GeoGebra, Desmos, LMS App on IFP, and Khan Academy.
Quadratic Equations (8 periods): Students study quadratic equations in the standard form ax² + bx + c = 0 and learn three methods of solving them: Factorisation, Completing the Square, and the Quadratic Formula. They verify whether given values are roots, form a quadratic equation when two roots are known, and determine the nature of roots using the discriminant D = b² − 4ac — understanding that D > 0 gives two distinct real roots, D = 0 gives two equal real roots, and D < 0 means no real roots exist. Graphical representations connecting the parabola to roots are also explored. Daily-life application problems involving area, speed, and time are solved, providing context for the algebraic methods. Recommended TLM includes a Chart of Quadratic Equations and a Chart of the Nature of Roots; ICT tools are GeoGebra, LMS App on IFP, DIKSHA App, and Khan Academy.
Progressions (10 periods): This chapter introduces two types of mathematical sequences — Arithmetic Progressions (A.P.) and Geometric Progressions (G.P.). For A.P., students define the general form a, a+d, a+2d, a+3d,…, identify the first term and common difference, determine whether a given sequence is an A.P., find the nth term using tₙ = a + (n−1)d, calculate the sum of n terms using Sₙ = n/2[2a + (n−1)d], and apply these to real-life problems including the sum of first n natural numbers. For G.P., students define the general form a, ar, ar², ar³,…, identify the common ratio, and find the nth term using aₙ = arⁿ⁻¹. Visualisation on number lines and grid paper is emphasised throughout. The concept map integrates finite and infinite A.P., parameters of A.P. and G.P., and the sum formula into a single visual structure. ICT tools recommended are GeoGebra, LMS App on IFP, and DIKSHA App.
Coordinate Geometry (10 periods): Students apply coordinate geometry to derive and use several important formulae on the Cartesian plane. The chapter covers: the Distance Formula for finding the distance between any two points; the Section Formula for finding the coordinates of a point dividing a line segment in a given ratio; the Midpoint Formula as a special case of the section formula; trisection points and the centroid of a triangle; the Area of a Triangle formula using vertex coordinates; collinearity of three points (area = 0); and the Slope of a Line. Students verify whether given coordinates form specific quadrilaterals (square, rectangle, rhombus, parallelogram), and connect coordinate geometry to algebraic geometry and real-life contexts such as maps and land area measurement. TLM includes charts of formulae and graph paper; ICT tools are GeoGebra, Desmos, and IFP LMS App.
Similar Triangles (16 periods): The largest chapter in the Class 10 plan, Similar Triangles is taught over 16 periods and covers a wide range of geometric theorems and constructions. Students begin with similar figures and similar polygons, then move to the Basic Proportionality Theorem (Thales Theorem) and its converse — the foundation for all further results. The three criteria for similarity — AA (Angle-Angle), SSS (Side-Side-Side), and SAS (Side-Angle-Side) — are established with their associated theorems (8.3, 8.4, 8.5). Students solve problems on Areas of Similar Triangles (Theorem 8.6) and prove the Pythagoras Theorem (Boudhayan Theorem) using similarity (Theorem 8.7, 8.8, 8.9). Construction of similar triangles with a given scale factor is included, along with theoretical statements: negation of a statement, converse of a statement, and proof by contradiction. The concept map integrates all eight theorems plus constructions into one visual framework. TLM includes a Chart of Criteria for Similarity of Triangles and a Chart of the Pythagoras Theorem; ICT tools are GeoGebra, LMS App on IFP, and DIKSHA App.
Tangents and Secants to a Circle (9 periods): This chapter develops students' understanding of the relationship between straight lines and circles. Students distinguish between a line that does not intersect a circle, a secant that cuts at two points, and a tangent that touches at exactly one point. They prove that a tangent is perpendicular to the radius at the point of contact (Theorem 9.1), verify that the two tangents drawn from an external point to a circle are equal in length (Theorem 9.2), and construct tangents to a circle — both from a point on the circle and from an external point. The chapter also covers finding the area of a segment of a circle using the formula: Area of segment = Area of sector − Area of triangle. Real-life applications include tangent concepts in wheels, pulleys, and clocks. TLM includes charts of tangents and secants and a geometry box; ICT tools are GeoGebra and Robocompass.
Mensuration (10 periods): Students extend their knowledge of surface areas and volumes from earlier classes to solve problems involving combinations and conversions of solids. The chapter reviews and applies formulae for the lateral surface area (LSA), curved surface area (CSA), total surface area (TSA), and volume of cube, cuboid, cylinder, cone, sphere, hemisphere, right prism, and pyramid. The core focus is on two new types of problems: combinations of solids (for example, a cone mounted on a cylinder, or a hemisphere embedded in a cuboid) and conversion of solids from one shape to another (for example, a metallic sphere melted and recast into cylinders). Unit conversion between cm², m², cm³, m³, and litres is practised throughout. The chapter culminates in the National Mathematics Day Celebration activity. TLM includes models of 3D shapes and a chart of formulae; ICT tools are GeoGebra, IFP Maths Tools, NCTM Illuminations, PhET Simulations, Canva, and Quizzes.
Trigonometry (11 periods): Building on students' knowledge of right-angled triangles and Pythagoras Theorem, this chapter develops all six trigonometric ratios — sine, cosine, tangent, cosecant, secant, and cotangent — for an acute angle in a right-angled triangle. Students find the exact values of trigonometric ratios for standard angles 0°, 30°, 45°, 60°, and 90° using equilateral and isosceles right-angled triangle proofs, and represent them in tabular form. Complementary angle relationships — such as sin(90°−A) = cos A, tan(90°−A) = cot A, and their counterparts — are derived and applied. Three fundamental trigonometric identities are derived and verified: sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, and cosec²θ − cot²θ = 1. Students also learn to express one trigonometric ratio in terms of others. The concept map integrates all six ratios, the standard angle table, complementary angle results, and all three identities into a single visual framework. The primary ICT tool recommended is GeoGebra.
Applications of Trigonometry (6 periods): This chapter applies the trigonometric ratios from the previous chapter to real-world situations involving heights and distances. Students learn to identify the horizontal line, the line of sight, the angle of elevation, and the angle of depression from a diagram, and convert word problems into geometrical right-triangle models. Problems are classified into two types: situations involving a single triangle (finding the height of a tower, the length of a shadow, the distance to a ship) and situations involving two triangles (finding the width of a river from two observations, determining the height of an object from two angles). Students must select the correct trigonometric ratio based on which sides and angle are known. TLM includes a chart showing horizontal line, line of sight, angle of elevation, and angle of depression; ICT tools are GeoGebra and IFP LMS App.
Probability (6 periods): This chapter introduces the theoretical (classical) approach to probability. Students define key terms — experiment, outcome, event, sample space, equally likely outcomes — and calculate the probability of simple events using the formula P(E) = (Number of outcomes favourable to E) / (Number of all possible outcomes). Mutually exclusive events, complementary events (P(Ē) = 1 − P(E)), impossible events (P = 0), and certain events (P = 1) are all covered with examples from coins, dice, and decks of cards. Students connect probability with set theory (sample space as universal set, event as subset) and with statistics (frequency interpretation). Quiz activities are scheduled for this unit. TLM includes charts of types of events, dice, coins, and a deck of cards; ICT tools are GeoGebra and IFP LMS App.
Statistics (12 periods): The final major chapter covers descriptive statistics for grouped data. Students calculate the Mean of grouped data using three methods: the Direct Method (x̄ = Σfᵢxᵢ / Σfᵢ), the Deviation Method (x̄ = a + Σfᵢdᵢ / Σfᵢ), and the Step Deviation Method (x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h). The Mode of grouped data is found using the formula z = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h, and the Median is located using M = l + [(n/2 − cf)/f] × h. Two periods are devoted to Ogive Curves — both the less-than and greater-than cumulative frequency curves — and students learn to obtain the Median value graphically from the intersection of the two ogives. Project and Review activities are linked to this chapter. TLM includes charts of formulae and Ogive curves; ICT tools are GeoGebra and IFP LMS App.
ICT Tools and Resources Recommended for Class 10 Maths Teachers
The Class 10 teaching plan recommends a carefully selected set of digital tools integrated across all 14 chapters. GeoGebra is the most widely recommended tool, used across virtually every chapter for dynamic exploration of graphs, geometric constructions, coordinate geometry, trigonometric ratios, and probability simulations. Desmos is recommended specifically for Coordinate Geometry and Linear Equations, enabling students to plot and explore equations interactively. The DIKSHA App provides curriculum-aligned content videos and activities mapped to the SCERT Telangana syllabus. Khan Academy is recommended for chapters on Real Numbers, Sets, Polynomials, Quadratic Equations, and Similar Triangles, offering practice exercises and mastery-based progression. Robocompass is specifically recommended for Tangents and Secants — enabling digital compass-and-straightedge constructions. NCTM Illuminations and PhET Simulations are recommended for Mensuration, providing interactive 3D visualisations. The IFP (Interactive Flat Panel) LMS App is recommended across nearly all chapters for whole-class demonstrations. Canva and Quizzes are included for Mensuration activities. These resources align with the NEP 2020 emphasis on ICT and AI integration in school education and are all available at no cost to schools and teachers.
How to Use This Teaching Plan
Mathematics teachers in Telangana government and aided schools can use this plan at the start of the academic year to map their complete teaching schedule from June to the Public Examination period. The Year Plan provides a month-by-month overview with period counts, activity allocations, and TLM requirements for each chapter. The Unit Plans provide a sub-topic level road map with period-by-period guidance including introduction, exercise periods, and a revision/slip test at the end of each unit. Teachers should review the prerequisite section of each chapter before beginning a new unit to assess prior knowledge gaps — particularly important in Class 10, where chapters like Trigonometry depend heavily on Pythagoras Theorem mastery and Coordinate Geometry builds directly on Class 9 work. The Concept Map provided for each chapter should be introduced to students at the beginning of the unit so they understand the full scope before individual topics are taught. The plan builds in a structured revision period from 11th January onwards specifically for Public Examination preparation, ensuring that revision is a planned activity rather than a rushed afterthought. As the resource group emphasises, this plan is intended as a model — teachers may adapt period allocations and activities to suit their specific classroom context, student needs, and school calendar.
Download the PDF
The complete 10th Class Mathematics Unit Plans and Year Plan — prepared by the SCERT Telangana resource group — is available as a free PDF download from EduBadi. The PDF is printer-friendly and contains the full Year Plan table, all 14 chapter-wise unit plans with sub-topic schedules and period allocations, concept maps for every chapter, TLM lists, ICT tool recommendations, a Model Teaching Diary format, a list of useful ICT web resources, and teacher reflection pages. Click the Download PDF button above to save it to your device.