Where Mindful Learning Begins
Where Mindful Learning Begins
The Class 9 Maths Lab Practical carries 5 of the 20 Internal Assessment marks, and the NCERT lab manual's activities were written before Ganita Manjari. This guide matches every manual activity to its Ganita Manjari chapter, gives ready-to-run substitutes where the manual has no match, and — for teachers setting the theory paper too — explains the conventions behind our 80-mark mock paper, downloadable from our syllabus page.
Last updated: 3 October 2026
| Point | What CBSE and NCERT say |
|---|---|
| Marks | 5 of the 20 Internal Assessment marks. The other parts are Pen Paper Test and Multiple Assessment (10) and Portfolio (5). |
| Source of activities | The syllabus says the lab activities are to be done from the prescribed books. |
| Prescribed lab books | Guidelines for Mathematics Laboratory in Schools, Class IX (CBSE) and Laboratory Manual - Mathematics, Secondary Stage (NCERT). |
| The NCERT manual | 34 activities in its Class IX section. Each is written under six headings: Objective, Material Required, Method of Construction, Demonstration, Observation and Application. |
| Mark breakdown | CBSE gives no breakdown for the 5 marks, so each school decides how to award them. |
Source: CBSE Academic, Mathematics Class IX (2026-27) - see Internal Assessment on our syllabus page - and the NCERT Laboratory Manual.
The syllabus still names the existing NCERT lab manual, which was published before Ganita Manjari. Some manual activities line up neatly with new chapters, some line up only partly, and four chapters have nothing in the manual. Activity numbers can differ between reprints, so we list activities by title.
Seven chapters have a direct match, three have a partial match, and four have none. The mapping is ours, made by comparing each activity's topic with the chapter's content and the syllabus's key concepts.
| Textbook chapter | NCERT lab manual activities | Match | Suggestion |
|---|---|---|---|
| Ganita Manjari - Part I - Chapters 1-8 | |||
| Ch 1 — Orienting Yourself: The Use of Coordinates | Finding the abscissa and ordinate of plotted points (the manual's coordinate activities). | Direct match | Add a floor-plan activity: distance, midpoint and collinearity on a grid (plan below). |
| Ch 2 — Introduction to Linear Polynomials | No matching activity in the manual. | No match | Slope and y-intercept on graph paper, and the growing tile pattern (plan below). |
| Ch 3 — The World of Numbers | Construct a square-root spiral; represent some irrational numbers on the number line. | Direct match | The spiral uses threads, nails and plywood; a cheaper version uses paper strips and a compass. |
| Ch 4 — Exploring Algebraic Identities | Eight identity verifications: (a+b)^2, (a-b)^2, a^2-b^2, (a+b+c)^2, (a+b)^3, (a-b)^3, a^3+b^3, a^3-b^3. | Direct match | Squares-and-rectangles identities use paper cut-outs; the cube identities use cuboid models. Add algebra tiles from the chapter (plan below). |
| Ch 5 — I'm Up and Down, and Round and Round | Angle subtended by an arc at the centre; angles in the same segment; opposite angles of a cyclic quadrilateral. | Direct match | Optional extension: find a triangle's circumcentre by paper folding (acute, right and obtuse cases). |
| Ch 6 — Measuring Space: Perimeter and Area | Formula for the area of a trapezium; parallelograms and triangles on the same base between the same parallels; ratio of the areas of a parallelogram and a triangle. | Direct match | For the area of a circle, use the manual's suggested model of a circle sliced into sectors. |
| Ch 7 — The Mathematics of Maybe: Introduction to Probability | Probability of the unit's digit of telephone numbers; probability of each outcome of a die. | Direct match | Optional: toss a coin and roll a die 60 times and compare empirical and theoretical probability. |
| Ch 8 — Predicting What Comes Next: Sequences and Progressions | No matching activity in the manual. | No match | Tower of Hanoi and a paper-folding fractal, both named or implied in the syllabus (plan below). |
| Ganita Manjari - Part II - Chapters 9-14 | |||
| Ch 9 — Propositions and their Converses | Triangle and angle activities: vertically opposite angles; angle sum of a triangle; exterior angle; congruence criteria; longer side and greater angle. | Partial match | These serve the syllabus's Lines and Angles and Triangles topics. Add a counterexample hunt and the SSA case (plan below). |
| Ch 10 — How Quantities Combine: Understanding Data | Draw histograms for classes of equal and varying widths. | Partial match | The chapter is about weighted mean and stacked bar charts, so add a weighted-mean and stacked-bar activity (plan below). |
| Ch 11 — The World of Algorithms | No matching activity in the manual. | No match | Unplugged algorithm activities: Euclid's subtraction with paper strips and tracing tables (plan below). |
| Ch 12 — Quadrilaterals | Sum of the angles of a quadrilateral is 360 degrees. | Partial match | The chapter's main themes are new: midpoint triangle, Varignon parallelogram, centroid and tiling (plan below). |
| Ch 13 — Two Variables, One Line | No matching activity in the manual. | No match | Graphical solution of a pair of linear equations (plan below). |
| Ch 14 — Math of Space: Surface Area and Volume | Form a cube and a cuboid and find their surface areas; form a cone from a sector; curved surface area of a cylinder; volume relationship of a cone with a cylinder and a sphere; surface area of a sphere. | Direct match | The chapter has matching hands-on tasks of its own: the cone-and-cylinder salt experiment and the string-on-a-ball activity (plan below). |
Direct means the manual has activities that fit the chapter's main ideas. Partial means the manual has an activity on part of the chapter, but the chapter's main themes are new. No match means nothing in the manual fits, so use the plans below. Chapters 10 and 12 changed most: the manual's histogram and area-theorem activities belong to older statistics and area topics.
Each plan follows the manual's format and uses cheap materials. Several reuse tasks the textbook chapter itself describes, such as algebra tiles in Chapter 4 and the salt experiment in Chapter 14.
Objective
To locate objects with coordinates and use the distance and midpoint formulas.
Materials
Graph paper, ruler, coloured pencils.
Steps
What to record
A table of objects with their coordinates, and the calculated and measured distances side by side.
Objective
To see how a and b in y = ax + b change a line, and to read the slope as rise over run.
Materials
Graph paper, ruler, coloured pencils; square tiles or coins for the pattern task.
Steps
What to record
A table with a, b, the measured slope and the measured y-intercept for every line drawn.
Objective
To factorise a quadratic by arranging tiles into a rectangle.
Materials
Card or paper cut into one big square (side x), seven strips (x by 1) and twelve unit squares (1 by 1).
Steps
What to record
The tile layout, the two side lengths, and the product multiplied out to confirm x^2 + 7x + 12.
Objective
To find the rule behind a sequence by playing a puzzle, and to meet a geometric progression in a fractal.
Materials
Three pegs (or three marked spots) and four or five discs or coins of different sizes; plain paper, ruler, pencil.
Steps
What to record
Two tables: discs against minimum moves, and step against number of unshaded triangles.
Objective
To test converses with models and to see why some 'if... then...' statements fail.
Materials
Straws or strips, paper, ruler, protractor, compass, scissors.
Steps
What to record
Each statement, its converse, and whether the converse is true or false, with the counterexample where it is false.
Objective
To see why averaging averages fails unless the groups are equal in size, and to compare groups with stacked bar charts.
Materials
Class data (for example, marks or travel mode by section), counters, graph paper, coloured pencils.
Steps
What to record
The two averages side by side, and both charts with a one-line reading for each.
Objective
To follow and trace step-by-step procedures, and to count steps.
Materials
Paper strips marked in centimetres, ruler, scissors; tracing tables on paper.
Steps
What to record
Each algorithm as numbered steps, with its tracing table and the number of steps it took.
Objective
To discover results about midpoints, parallelograms and medians by paper cutting and measurement.
Materials
Card or thick paper, scissors, ruler, set square, pencil, a pin.
Steps
What to record
A sketch of each result and a table of the measured lengths and their ratios.
Objective
To connect the picture of two lines with the number of solutions.
Materials
Graph paper, ruler, coloured pencils.
Steps
What to record
A table of the three pairs with the graph type, the number of solutions and the three ratios.
Objective
To check that a cone holds one-third of a cylinder with the same base and height, and to verify the sphere's surface area.
Materials
Card for a cone and a cylinder of equal radius and height, fine dry salt or sand; a rubber ball, a nail, string, glue, compass and paper.
Steps
What to record
The number of cones needed, and the number of circles filled, with a sentence linking each to a formula.
These plans are suggestions by Boundless Maths, not CBSE or NCERT activities. Schools may swap in any activity from the prescribed books.
CBSE does not prescribe how many activities to do. If you want a balanced set, this one touches every unit of the syllabus and mixes manual activities with our plans, weighted toward the units that carry more marks in the theory paper.
| Syllabus unit | Unit marks (CBSE) | Textbook chapter | Proposed chapter marks | Suggested activity |
|---|---|---|---|---|
| I - Number System | 7 | Ch 3 — The World of Numbers | 7 | Construct a square-root spiral |
| II - Algebra | 20 | Ch 4 — Exploring Algebraic Identities | 6 | Verify (a + b)^2 = a^2 + 2ab + b^2 with paper cut-outs |
| II - Algebra | 20 | Ch 8 — Predicting What Comes Next: Sequences and Progressions | 4 | Tower of Hanoi and the moves table |
| III - Coordinate Geometry | 4 | Ch 1 — Orienting Yourself: The Use of Coordinates | 4 | Floor plan on a grid |
| IV - Geometry | 25 | Ch 5 — I'm Up and Down, and Round and Round | 10 | Angle at the centre is double the angle at the circumference |
| IV - Geometry | 25 | Ch 12 — Quadrilaterals | 10 | Midpoint triangle and Varignon parallelogram |
| V - Mensuration | 14 | Ch 6 — Measuring Space: Perimeter and Area | 7 | Area of a trapezium, or of a circle by slicing into sectors |
| V - Mensuration | 14 | Ch 14 — Math of Space: Surface Area and Volume | 7 | Form a cone from a sector, or the cone-and-cylinder experiment |
| VI - Statistics and Probability | 10 | Ch 7 — The Mathematics of Maybe: Introduction to Probability | 5 | Probability of each outcome of a die |
| VI - Statistics and Probability | 10 | Ch 10 — How Quantities Combine: Understanding Data | 5 | Weighted mean and stacked bars |
Unit marks are official. Proposed chapter marks are our adjustable proposal - see the weightage table on the syllabus page. The activity set is a suggestion; swap any activity to match what your class has covered.
| Heading in the lab record | What the student writes |
|---|---|
| Objective | One line: what is to be verified or found. |
| Material Required | The list of items used. |
| Method of Construction | Numbered steps, with a neat figure. |
| Demonstration | The reasoning that links the model to the result. |
| Observation | Measured values in a table, and the result they give. |
| Application | Where the result is used. |
The six headings are those used in the NCERT lab manual.
Performing the activity: 2 marks. Lab record: 2 marks. Viva voce: 1 mark. CBSE's syllabus gives only the total of 5, so use whatever split your school follows.
CBSE fixes the unit-wise marks and the thinking-level split; everything else about the paper's shape is convention. These are the conventions our mock paper follows, with each one marked official or ours.
| Element | What we follow | Source |
|---|---|---|
| Unit-wise marks | Number System 7, Algebra 20, Coordinate Geometry 4, Geometry 25, Mensuration 14, Statistics and Probability 10. | CBSE (official) |
| Chapter-wise marks | The proposed weightage on our syllabus page, splitting each unit's marks across its chapters. | Boundless Maths (adjustable) |
| Thinking levels | 43 marks Remembering and Understanding, 19 marks Applying, 18 marks Analysing, Evaluating and Creating. | CBSE (official) |
| Five-section layout | Section A (MCQ + Assertion-Reason, 1 mark), B (very short, 2 marks), C (short, 3 marks), D (long, 5 marks), E (case-based, 4 marks). | Common CBSE-style convention |
| Chapter order | Questions are ordered so that no two neighbouring questions come from the same chapter. | Follows CBSE's own sample papers |
| Internal choice | Two questions each in Sections B, C and D, and part (iii) of each Section E case study, carry an OR alternative from the same chapter, same marks, same thinking level. | Follows CBSE's Class X 2025-26 sample paper |
| Chapter 11 | The World of Algorithms carries no marks, as it has no place in CBSE's course structure. | Boundless Maths (follows CBSE's structure) |
Source: CBSE Academic, Mathematics Class IX (2026-27) course structure and paper design, and CBSE's Class X Maths Standard sample paper for 2025-26 (the official sample paper we could check for a five-section, internal-choice layout).
Want the full tables — chapter-by-chapter, unit-by-unit, question-by-question? Download our Blueprint & Paper-Construction Notes.
| Principle | What it means |
|---|---|
| Step marking | Marks are shown against the specific step that earns them, not only at the end of a question, so method is rewarded as well as the final answer. |
| Alternative methods | Any mathematically valid method that reaches the correct answer earns full marks, even if it differs from the model answer shown. |
| Internal choice | A student attempts only one of the two alternatives offered; mark only the one attempted, at the same marks as the question. |
| Model answers | Our marking scheme writes out each answer the way a student is expected to present it - full reasoning shown, with the mark for each step placed against it. |
| Mark breakdown within a question | Where CBSE gives no official breakdown (as for the Lab Practical's 5 marks), we suggest one and say clearly that it is ours, not CBSE's. |
This is the same proposed weightage as on our syllabus page, shown here for convenience while setting a paper. It is adjustable - see the editable version on the syllabus page.
| Chapter | Marks | ||
|---|---|---|---|
| Unit I - Number System | 7 | ||
| Ch 3 — The World of Numbers | 7 | ||
| Unit II - Algebra | 20 | ||
| Ch 2 — Introduction to Linear Polynomials | 4 | ||
| Ch 4 — Exploring Algebraic Identities | 6 | ||
| Ch 8 — Predicting What Comes Next: Sequences and Progressions | 4 | ||
| Ch 13 — Two Variables, One Line | 6 | ||
| Unit III - Coordinate Geometry | 4 | ||
| Ch 1 — Orienting Yourself: The Use of Coordinates | 4 | ||
| Unit IV - Geometry | 25 | ||
| Ch 5 — I'm Up and Down, and Round and Round | 10 | ||
| Ch 9 — Propositions and their Converses | 5 | ||
| Ch 12 — Quadrilaterals | 10 | ||
| Unit V - Mensuration | 14 | ||
| Ch 6 — Measuring Space: Perimeter and Area | 7 | ||
| Ch 14 — Math of Space: Surface Area and Volume | 7 | ||
| Unit VI - Statistics and Probability | 10 | ||
| Ch 7 — The Mathematics of Maybe: Introduction to Probability | 5 | ||
| Ch 10 — How Quantities Combine: Understanding Data | 5 | ||
| Not in CBSE's course structure | 0 | ||
| Ch 11 — The World of Algorithms | 0 | ||
| Total | 80 | ||
An 80-mark, 3-hour mock paper built to the conventions above, with 38 questions across five sections, 9 carrying internal choice, and three companion documents: the paper itself, a marking scheme of solutions only, and the full blueprint behind it.
80 marks · 3 hours · 38 questions · 9 with internal choice
The methodology behind the mock paper, for building your own
The kit manual is a separate NCERT document with activities that use the Secondary Mathematics kit. The CBSE Guidelines for Mathematics Laboratory in Schools, Class IX is also prescribed; check your school's copy.
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