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Maths vocabulary

Words to know

Every maths word used in the lessons, in plain language — with the lesson where it is explained. Using the right word makes your thinking clearer to others (and to yourself).

1080 wordsfrom 22 topics

1080 words

abacus
A frame of rods with sliding beads, one rod per place value, used for calculating; the Japanese version is the soroban.
Four operations · Extend
absolute value | |
The size of a number without its sign.
Example: |−35| = 35
Angles · Extend
abundant number
A number whose proper factors add up to more than itself.
Example: 12 → 16
Prime and composite numbers · Extend
Acceleration
How much the speed changes each second, measured in m/s².
Example: Free fall on Earth: 9.8 m/s².
Gravity · Understand
Accuracy
How close a measured or drawn value is to the true or target value.
Example: A 75° target drawn as 74° is accurate to 1°.
Measuring and constructing angles · Investigate
Acute / right / obtuse triangle
A triangle whose largest angle is less than, equal to, or greater than 90°.
Shape and space · Understand
acute angle
An angle more than 0° and less than 90°.
Example: A slice of pizza.
Angles · DiscoverMeasuring and constructing angles · Discover
addend
Each number that is being added.
Example: In 15 + 9 = 24, the addends are 15 and 9.
Four operations · DiscoverFour operations · Understand
addition
Putting amounts together to find a total. Sign: +.
Example: 15 + 9 = 24
Four operations · Discover
Additive identity
The number 0, because adding 0 leaves any number unchanged.
Example: 25 + 0 = 25
Properties of numbers · DiscoverProperties of numbers · Understand
Additive inverse
The number that adds to a to give 0: the additive inverse of 5 is −5.
Properties of numbers · Go deeperProperties of numbers · Extend
Additive mixing
Adding coloured light. Primaries red, green, blue; mixtures get brighter; all three give white.
Example: Every screen you own.
Light · Understand
Adhik maas
An extra ('leap') lunar month inserted roughly every 32-33 months to keep the Hindu lunisolar calendar aligned with the solar year.
Example: Also called purushottam maas when it falls in certain positions.
Phases of the Moon · Go deeper
adjacent angles
Two angles with a common vertex and a common arm, whose interiors do not overlap.
Example: ∠AOB and ∠BOC
Angles · Understand
Adjacent sides
Two sides of a polygon that share a vertex.
Shape and space · Understand
Aeroelastic flutter
A self-reinforcing feedback loop between wind and a flexible structure's own motion, distinct from simple resonance.
Example: The real cause of the Tacoma Narrows Bridge collapse.
Sound · Go deeper
Age of the tide
The delay of a day or two between a full or new moon and the biggest tides that follow it.
Tides · Understand
Air resistance
The backwards push that air gives to anything moving through it. Also called drag.
Example: A flat sheet of paper feels a lot of it.
Gravity · Discover
Albedo
The fraction of incoming sunlight a surface reflects rather than absorbs.
Example: Earthshine measurements are really a way of measuring Earth's albedo from the Moon's surface.
Phases of the Moon · Investigate
algorithm
A fixed list of steps that always works, such as the column method or long division.
Example: Long division is an algorithm: divide, multiply, subtract, bring down, repeat.
Four operations · UnderstandHCF and LCM · Go deeper
Alidade
The rotating sighting bar on an astrolabe or similar instrument, carrying two holes to line up on a star.
Exploration: reasons and consequences · Understand
Alternate angles
Angles on opposite sides of a line crossing two parallel lines, between them; they are equal.
Shape and space · Go deeper
alternate exterior angles
Angles outside two lines, on opposite sides of a transversal. Equal when the lines are parallel.
Example: Top-left at one crossing and bottom-right at the other.
Angles · Go deeper
alternate interior angles
Angles between two lines, on opposite sides of a transversal. Equal when the lines are parallel.
Example: The Z shape.
Angles · Go deeper
alternating pattern
A pattern whose step changes back and forth between two (or more) values.
Example: +3, −1, +3, −1: 1, 4, 3, 6, 5, …
Number and shape patterns · Understand
Alveoli
The microscopic air sacs at the end of the smallest air tubes, where gases cross into and out of the blood.
Example: About 300 million in a pair of adult lungs.
Body systems and how they connect · Discover
always / sometimes / never
Whether a claim holds for every case, some cases or no cases.
Example: Vertically opposite angles are always equal.
Angles · Investigate
always / sometimes / never true
The three possible verdicts on a statement: true for every case, true for some cases only, or true for no case.
Example: LCM = a × b is sometimes true.
HCF and LCM · InvestigateNumber system · Investigate
Always true
True for every number the statement talks about. Needs a reason that covers every case.
Properties of numbers · Investigate
Ambiguous
Able to be read in more than one reasonable way.
Example: 8 ÷ 2(2 + 2)
Order of operations · Extend
Amplitude
How far the source swings on each vibration. Bigger amplitude means louder.
Example: Hitting a drum harder.
Sound · Discover
anatomical position
The standard pose all direction words are measured from: standing, feet flat, arms down, palms facing forward.
Example: A patient lying in a scanner is still described as if standing in it.
Anatomy of the human body · Understand
anatomy
The study of what the parts of the body are and where they sit.
Example: This whole topic is anatomy.
Anatomy of the human body · Discover
angle
The amount of turn between two rays that start from the same point.
Example: The hands of a clock make an angle.
Angles · DiscoverMeasuring and constructing angles · Discover
angle bisector
A ray that splits an angle into two equal angles.
Example: The bisector of 70° makes two 35° angles.
Angles · InvestigateMeasuring and constructing angles · Understand
angle chasing
Solving a geometry problem by finding one angle after another, with reasons.
Example: Olympiad problems
Angles · Extend
angle of elevation
The angle you look up through, from the horizontal, to see an object above you.
Example: Measured with a clinometer.
Angles · ExtendMeasuring and constructing angles · Extend
Angle of incidence
The angle between the incoming ray and the normal.
Example: Written i.
Light · Understand
Angle of reflection
The angle between the normal and the reflected ray. Always equal to the angle of incidence.
Example: Written r.
Light · Understand
Angle sum
The total of all the interior angles of a polygon: (n − 2) × 180°.
Shape and space · Investigate
angle sum property
The angles of a triangle add up to 180°.
Example: 40° + 60° + 80° = 180°
Angles · Go deeper
angles at a point
Angles that together fill all the space around a point. They add up to 360°.
Example: The slices of a pizza at its centre.
Angles · Understand
Angular momentum
A measure of spinning or orbiting motion that cannot be created or destroyed, only transferred between parts of a system.
Tides · Extend
Angular size
How wide something looks, measured as an angle rather than in kilometres.
Example: The Sun and the Moon are both about 0.5° wide from Earth.
Eclipses · Understand
Annular eclipse
A solar eclipse where the Moon looks too small, leaving a bright ring of Sun.
Example: Also called a ring of fire. Never safe to view unfiltered.
Eclipses · Discover
Anomalistic month
27.555 days: the time for the Moon to return to the same distance from Earth (perigee to perigee).
Eclipses · Go deeper
anonymous
Not identifying any individual person.
Example: Reporting only group totals.
Data handling · Extend
antagonistic pair
Two muscles on opposite sides of a joint, each pulling the opposite way.
Example: Biceps bends the elbow; triceps straightens it.
Anatomy of the human body · Understand
anterior
Towards the front of the body.
Example: Your breastbone is anterior.
Anatomy of the human body · DiscoverAnatomy of the human body · Understand
anticlockwise
Turning in the opposite direction to the hands of a clock.
Example: North to west is an anticlockwise quarter turn.
Angles · Discover
Antisolar point
The point in the sky directly opposite the Sun from your own shadow's position.
Example: A rainbow is always centred on this point, 42° away.
Light · Investigate
Antumbra
The region beyond the tip of an umbra cone, where the blocker looks too small to cover the source.
Example: Standing in the antumbra gives you a ring of fire.
Eclipses · Understand
Apex
The top point of a pyramid or cone.
Shape and space · Understand
Apogee
The Moon's furthest point, about 405,500 km.
Example: Eclipses near apogee are annular.
Eclipses · UnderstandGravity · Investigate
Apparent depth
The shallower depth water seems to have because of refraction: real depth ÷ n.
Example: A 1.2 m pool looks 0.90 m deep.
Light · Understand
Arab
Indian name for 100 crore, 10⁹, equal to one billion.
Number system · Extend
Arcminute (′)
One sixtieth of a degree. Sixty arcminutes make one degree.
Example: The Sun averages 32.0 arcminutes across.
Eclipses · Understand
Area model
Picturing a product as a rectangle and cutting it into smaller rectangles.
Example: 23 × 14 = 200 + 30 + 80 + 12
Properties of numbers · Understand
Arithmetic expression
Numbers combined with operation signs (+, −, ×, ÷) and possibly brackets. It has one value.
Example: 7 + (2 + 8) × 4
Order of operations · Understand
arithmetic mean
The sum of the values divided by how many there are; the full name of the mean.
Data handling · Understand
arithmetic sequence
A sequence where the same number is added (or subtracted) each time.
Example: 20, 17, 14, 11, …
Number and shape patterns · Understand
arm
One of the two rays that form an angle.
Example: Each hand of a clock is an arm.
Angles · DiscoverMeasuring and constructing angles · DiscoverMeasuring and constructing angles · Understand
Arrangement (permutation)
One way of ordering a set of digits or objects.
Example: 258 and 852 are two arrangements of 2, 5, 8
Number system · Investigate
array
Objects arranged in rows and columns, each row the same length.
Example: 6 rows of 8 chairs
Four operations · DiscoverPrime and composite numbers · DiscoverProperties of numbers · Discover
Article 3
The constitutional provision letting Parliament form or reshape a state by a simple-majority law, after seeking (but not needing to follow) the affected state legislature's views.
Example: Telangana was formed in 2014 using Article 3.
How government works in India · Extend
ASA
Two angles and the included side (the side between them): fixes a unique triangle.
Measuring and constructing angles · Extend
ascending order
Arranged from smallest to largest.
Example: 2, 5, 7, 9.
Data handling · UnderstandNumber system · Understand
aspect ratio
The shape of a rectangle as width : height in simplest form.
Example: 1920 × 1080 → 16 : 9
HCF and LCM · Extend
Associative
An operation is associative if grouping does not matter: (a ∘ b) ∘ c = a ∘ (b ∘ c). + and × are; − and ÷ are not.
Example: (2 × 3) × 4 = 2 × (3 × 4)
Order of operations · InvestigateProperties of numbers · Understand
Associative property
When combining three numbers, it does not matter which pair you do first. True for addition and multiplication.
Example: (2 × 7) × 5 = 2 × (7 × 5)
Properties of numbers · Discover
assumed mean
A convenient number subtracted from every value to make a mean easier to find, then added back.
Example: Use 100 for 97, 102, 99, 104, 98.
Data handling · Investigate
Astrolabe
An instrument for measuring the angle of the Sun or a star above the horizon.
Exploration: reasons and consequences · Discover
Astronomical unit (AU)
The average Earth-Sun distance, about 149.6 million km, used as a convenient yardstick for the Solar System.
Eclipses · Extend
Atmosphere
The layer of air that gravity holds around a planet.
Example: The Moon is too small to keep one.
Gravity · Discover
Atmospheric thermal tide
A daily air-pressure wobble driven mainly by the Sun heating the atmosphere, thought to have briefly stalled Earth's day lengthening by cancelling lunar tidal friction.
Tides · Extend
Atmospheric tide
A twice-daily wobble in air pressure, driven mainly by the Sun heating the atmosphere rather than by gravity alone.
Tides · Go deeper
Atrium
One of the two upper collecting chambers of the heart. Plural: atria.
Example: Blood from the body arrives in the right atrium.
Body systems and how they connect · Understand
average
One number chosen to represent a whole set of data; usually the mean, but median and mode are averages too.
Data handling · Discover
axiom (postulate)
A basic statement accepted without proof, used as a starting point.
Example: Corresponding angles on parallel lines are equal.
Angles · Go deeper
axis
One of the two reference lines of a graph: one for categories or values along the bottom, one for numbers up the side.
Data handling · Understand
Axis of symmetry
Another name for a line of symmetry.
Shape and space · Understand
back bearing
The bearing for the return journey, differing by 180°.
Example: The back bearing of 063° is 243°.
Angles · Extend
Back-projection
Working backwards from a later, better-known figure using an assumed rate of change, to estimate an earlier, unknown one.
Exploration: reasons and consequences · Go deeper
Baily's beads
Points of sunlight shining through valleys on the Moon's ragged edge.
Example: They appear in the last seconds before totality.
Eclipses · Discover
balance point
The point where the values' deviations cancel out; the mean.
Data handling · Go deeper
Balanced forces
Two equal forces acting in opposite directions, leaving the motion unchanged.
Example: Sitting on a chair: gravity down, chair up.
Gravity · Discover
bar graph
A chart of bars of equal width whose heights (or lengths) show the numbers.
Data handling · Discover
bar model
A drawing of quantities as strips, used to see the structure of a word problem.
Example: Half the bar is the book; the other half is ₹40 + ₹60
Four operations · Go deeper
Barycentre
The common centre of mass that two orbiting bodies actually circle around.
Example: The Earth–Moon barycentre sits inside the Earth, off-centre.
Gravity · Go deeper
Base
The number each place is worth times the place to its right. Our system uses base ten.
Number system · Go deeperNumber system · ExtendPrime and composite numbers · Extend
base line
The protractor's zero line through the centre point; one arm lies along it.
Measuring and constructing angles · Understand
basic structure
Features of the Constitution so fundamental that Parliament's amending power cannot be used to remove them, established in the 1973 Kesavananda Bharati case.
Example: Judicial review has been treated as part of the basic structure.
How government works in India · Go deeper
batting average
In cricket, total runs divided by the number of times the batter was out.
Example: 6,996 ÷ 70 ≈ 99.94.
Data handling · Go deeper
Beam
A bundle of rays travelling together.
Example: A headlight beam in fog.
Light · Discover
bearing
A direction given as an angle measured clockwise from north, written with three figures.
Example: East is 090°.
Angles · Extend
Benchmark angle
A well-known angle used as a reference when estimating: 30°, 45°, 60°, 90°, 180°, 360°.
Example: A book corner is a 90° benchmark.
Measuring and constructing angles · Investigate
Bézout’s identity
The HCF of a and b can be written as ax + by for some whole numbers x and y.
Example: 18 = 4 × 252 − 5 × 198
HCF and LCM · Go deeper
Bile
A greenish fluid made by the liver and stored in the gall bladder. It contains no enzyme; it breaks fat into droplets.
Example: Squirted into the small intestine when fat arrives.
Body systems and how they connect · Understand
Billion
One thousand million, 1,000,000,000. Equal to one hundred crore.
Number system · Discover
bimodal
Having two modes: two values tie for the highest frequency.
Example: 3, 3, 5, 7, 7 → modes 3 and 7.
Data handling · Understand
binary
The base-two place-value system with only the digits 0 and 1; each place is worth twice the place to its right. Computers use it.
Example: 37 = 100101 in binary
Four operations · ExtendNumber system · ExtendNumber and shape patterns · Extend
Binary operation
A rule that combines two numbers to give one number.
Example: +, ×, max, average
Properties of numbers · Go deeper
Bit
A single binary digit, 0 or 1.
Number system · Extend
Black drop effect
An optical smearing of a transiting planet's silhouette against the Sun's edge, which limited historic timing precision.
Eclipses · Extend
Blood-brain barrier
An unusually tight capillary wall around the brain, far stricter than an ordinary capillary about what it lets through.
Example: Protects the brain, but also makes it harder for medicines to reach it.
Body systems and how they connect · Go deeper
BODMAS
A longer memory word: Brackets, Of, Division, Multiplication, Addition, Subtraction.
Order of operations · Discover
body-based unit
A unit of length defined by a part of the human body.
Example: The cubit, the hasta, the foot and the hand span are all body-based units.
Anatomy of the human body · Extend
Bone conduction
Sound reaching the inner ear through the skull's bones rather than through the air and ear canal.
Example: Why your recorded voice sounds different from how you hear yourself.
Sound · Extend
Bone marrow
Soft tissue inside the hollow shaft of a long bone, where red cells, white cells and platelets are made.
Example: Found in the femur, pelvis, spine and other long bones.
Body systems and how they connect · Go deeper
borrow
In subtraction, taking 1 from the next column on the left to make 10 more in the current column. Also called regrouping or exchanging.
Example: In 52 − 17, borrow a ten: 12 − 7 = 5.
Four operations · Understand
Bound
A value that a quantity is guaranteed not to go beyond.
Example: The error is at most 300.
Number system · Go deeper
Braces
Curly brackets { }.
Order of operations · Understand
Bracketing
A way of placing brackets in an expression to fix the order.
Example: (2 + 3) × (4 − 1)
Order of operations · Investigate
Brackets
Pairs of symbols such as ( ) that group part of an expression. Whatever is inside is worked out first.
Example: (2 + 3) × 4 = 20
Order of operations · Discover
Brahmi numerals
Ancient Indian numerals (from about the 3rd century BCE), ancestors of our digit shapes, used without place value.
Number system · Go deeper
Capillary
The narrowest blood vessel, with a wall one cell thick — where everything actually crosses.
Example: No cell of yours is far from one.
Body systems and how they connect · Discover
cardinal directions
The four main compass directions: north, east, south and west, 90° apart.
Example: N, E, S, W
Angles · Understand
Carmichael number
A composite number that passes Fermat’s shortcut primality check for every base co-prime to it.
Example: 561
Prime and composite numbers · Extend
carry
In addition or multiplication, the extra ten (or hundred…) moved into the next column on the left.
Example: 7 + 8 = 15: write 5, carry 1 ten.
Four operations · Understand
Carrying capacity
How many people a given area of farmland could support, used by archaeologists to estimate past populations.
Exploration: reasons and consequences · Go deeper
cartilage
Smooth, rubbery connective tissue that caps bone ends, cushions joints and shapes the nose and outer ear.
Example: A baby skeleton starts out mostly cartilage.
Anatomy of the human body · Understand
casting out nines
Checking a calculation by doing the same operation on the digit sums and comparing with the answer's digit sum.
Example: 5 × 8 = 40 → 4 matches 9,022 → 4
Four operations · Go deeper
Catalan numbers
1, 2, 5, 14, 42, 132, … The number of ways to fully bracket 2, 3, 4, 5, 6, 7, … numbers.
Order of operations · Investigate
categorical data
Data that sorts things into named groups (categories), such as colour or language. It can be counted but not added.
Example: Blood groups A, B, AB, O.
Data handling · Understand
Caustic
A bright line or curve formed where many light rays bunch together at a minimum or maximum deviation.
Example: The rainbow, and the bright curve inside a sunlit coffee cup.
Light · Go deeper
cavity
A space inside the body that holds organs.
Example: The chest cavity holds the heart and lungs.
Anatomy of the human body · DiscoverAnatomy of the human body · Understand
Cell
The smallest living unit of the body. You have roughly 30 trillion of them.
Example: A red blood cell, a muscle cell, a nerve cell.
Body systems and how they connect · DiscoverAnatomy of the human body · Discover
census
An official count of every member of a population, such as the Census of India.
Data handling · Extend
central angle
The angle at the centre between two neighbouring corners of a regular polygon: 360° ÷ n.
Example: 72° for a pentagon.
Measuring and constructing angles · ExtendData handling · Extend
centre point (protractor)
The point at the centre of the protractor's semicircle, placed on the vertex when measuring.
Measuring and constructing angles · Understand
centred hexagonal number
A dot in the middle surrounded by hexagonal rings of 6, 12, 18, … dots.
Example: 1, 7, 19, 37
Number and shape patterns · Extend
Centripetal acceleration
The acceleration needed to keep an object moving on a circular path, always pointing towards the centre.
Example: For an orbit, gravity supplies it.
Gravity · Go deeper
Chart datum
The fixed zero level at a port from which all tide heights are measured, close to the lowest expected tide.
Tides · Understand
Chemical digestion
Cutting long food molecules into short ones, so they can be absorbed.
Example: Starch → glucose; protein → amino acids.
Body systems and how they connect · Understand
Chinese Remainder Theorem
For pairwise co-prime divisors, any set of remainders has exactly one solution below their LCM.
Example: Sunzi: 23
HCF and LCM · Extend
Chord
A straight segment joining two points on a circle.
Example: PQ in the copy-angle construction.
Measuring and constructing angles · Go deeperShape and space · Understand
Chronometer
An accurate, sturdy clock built to keep a reference time at sea despite motion and temperature change.
Exploration: reasons and consequences · UnderstandExploration: reasons and consequences · Go deeper
chunking
Dividing by subtracting convenient multiples of the divisor (chunks) and adding up how many were taken.
Example: 8,736 ÷ 24: take 7,200, then 1,440, then 96
Four operations · Go deeper
Circle
A round closed curve whose every point is the same distance from the centre.
Shape and space · Discover
Circular reasoning
An argument that assumes what it is trying to prove.
Example: "They are parallel because they never meet"
Lines, rays and line segments · Go deeper
Circumcentre
The point where the perpendicular bisectors of a triangle's sides meet; equally far from all three corners.
Example: Where the three folds meet
Lines, rays and line segments · Investigate
Circumference
The distance around a circle; about 3.14 times the diameter.
Shape and space · Understand
citizen
A full member of a country, with rights the state must protect and duties the country expects.
Example: Indian citizens aged 18 or more may vote.
How government works in India · Discover
civil service
Officials recruited on merit who carry out government work and remain in post across a change of government.
Example: An IAS officer runs district administration whichever party is in power.
How government works in India · Understand
class interval
A range of values used as one group in grouped data, such as 20–30.
Data handling · Go deeper
class width
The difference between the upper and lower limits of a class interval.
Example: 30 − 20 = 10.
Data handling · Go deeper
clinometer
An instrument for measuring angles of slope or elevation.
Measuring and constructing angles · Extend
clockwise
Turning in the same direction as the hands of a clock.
Example: North to east is a clockwise quarter turn.
Angles · Discover
Closed (under an operation)
A set is closed under an operation if combining any two of its members always gives a member of the same set.
Example: Whole numbers are closed under +; not under −.
Properties of numbers · Understand
Closed curve
A curve that ends where it began, fencing in a region.
Example: The letter O.
Shape and space · Discover
Closed–open resonance
The quarter-wavelength resonance of a basin closed at one end (like a bay) and open at the other — the same physics as a closed organ pipe.
Tides · Go deeper
Closure
A family of numbers is closed under an operation if the answer is always in the same family.
Example: Whole number + whole number = whole number.
Properties of numbers · Discover
CMYK
The four-ink printing system: cyan, magenta, yellow and a separate true black (K).
Light · Go deeper
co-interior angles
Angles between two lines, on the same side of a transversal. They add to 180° when the lines are parallel. Also called interior angles on the same side.
Example: The C or U shape.
Angles · Go deeperShape and space · Go deeper
co-prime (relatively prime)
Two numbers whose only common factor is 1, so their HCF is 1.
Example: 8 and 15 are co-prime.
HCF and LCM · Understand
co-prime numbers
Two numbers whose only common factor is 1. Also called relatively prime.
Example: 8 and 15
Prime and composite numbers · Discover
coalition
Two or more parties combining their seats to reach a majority together.
Example: Four parties combined reached 278 seats, past the 272 needed.
How government works in India · Investigate
Cochlea
The pea-sized liquid-filled coil in your inner ear where movement becomes nerve signals.
Example: Contains about 16,000 hair cells.
Sound · DiscoverSound · Understand
coefficient
The number that multiplies a variable.
Example: In 5n + 1, the coefficient of n is 5.
Number and shape patterns · Go deeper
Cold trap
A permanently shadowed, extremely cold region where volatile substances such as water ice can survive for very long periods without evaporating.
Example: The floors of some lunar polar craters act as cold traps.
Phases of the Moon · Extend
collagen
The tough, rope-like protein in tendons, ligaments, cartilage, skin and bone. The most abundant protein in the body.
Example: It is what makes a tendon strong without being brittle.
Anatomy of the human body · Understand
Collapsing compass
Euclid's imagined compass that snaps shut when lifted, so it cannot carry a distance.
Example: Euclid proved it can still copy lengths (Elements I.2).
Measuring and constructing angles · Go deeper
Collatz conjecture
The unproved claim that “halve if even, 3n + 1 if odd” always reaches 1.
Example: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Number and shape patterns · Extend
collegium
The Chief Justice of India and the four senior-most Supreme Court judges, who together recommend judicial appointments and transfers.
Example: The collegium took its current five-member form after the 1998 Third Judges Case.
How government works in India · Go deeper
Collinear points
Points that lie on one straight line.
Example: Three beads on a tight thread
Lines, rays and line segments · Understand
Columbian exchange
The two-way movement of crops, animals and diseases between the Americas and the rest of the world after 1492.
Exploration: reasons and consequences · Discover
combination (nCr)
A way of counting how many groups of a given size can be chosen from a larger set, when order does not matter.
Example: 5 choose 2 gives 10 possible two-party pairings.
How government works in India · Extend
common difference
The fixed amount added each time in an arithmetic sequence.
Example: 5, 8, 11, 14 has common difference 3.
Number and shape patterns · Understand
common division (ladder)
The LCM method that divides all the numbers together by primes, row by row.
Example: LCM(12, 18, 30) = 180
HCF and LCM · Understand
common factor
A number that is a factor of two or more numbers at once.
Example: 3 is a common factor of 12 and 18.
HCF and LCM · DiscoverPrime and composite numbers · UnderstandProperties of numbers · Understand
common multiple
A number that is a multiple of two or more numbers at once.
Example: 24 is a common multiple of 6 and 8.
HCF and LCM · DiscoverPrime and composite numbers · Understand
common ratio
The fixed number you multiply by each time in a geometric sequence.
Example: 2, 6, 18, 54 has common ratio 3.
Number and shape patterns · Understand
commutative
An operation where order does not change the answer: true for + and ×, false for − and ÷.
Example: 6 × 15 = 15 × 6
Four operations · InvestigateProperties of numbers · Understand
Commutative property
Swapping the order of two numbers does not change the answer. True for addition and multiplication.
Example: 4 × 6 = 6 × 4
Properties of numbers · Discover
comparative anatomy
The scientific study of similarities and differences between the body plans of different species.
Example: Comparing a giraffe’s neck bones with a human’s is comparative anatomy.
Anatomy of the human body · Extend
compass
A tool with a sharp point and a pencil leg, used to draw circles and arcs.
Measuring and constructing angles · DiscoverExploration: reasons and consequences · Discover
compatible numbers
Numbers chosen because they work neatly together, making an estimate easy.
Example: 4,872 ÷ 6 ≈ 4,800 ÷ 6 = 800
Four operations · Investigate
compensation
Changing numbers to make a calculation easier, then adjusting (or choosing a change that needs no adjustment).
Example: 58 + 37 = 60 + 35
Four operations · InvestigateProperties of numbers · UnderstandProperties of numbers · Investigate
complement
The angle that makes a given angle up to 90°: 90° − x.
Example: The complement of 20° is 70°.
Angles · Understand
complementary angles
Two angles that add up to 90°.
Example: 30° and 60°
Angles · DiscoverAngles · Understand
complete angle
An angle of exactly 360°, one full turn.
Example: A wheel turning round once.
Angles · Discover
composite number
A whole number greater than 1 with more than two factors.
Example: 4, 6, 8, 9, 10, 12, …
HCF and LCM · UnderstandPrime and composite numbers · Discover
Compression
A region of a sound wave where the particles are crowded and the pressure is above normal.
Example: The bunched coils on a slinky.
Sound · Understand
Compression (digital audio)
Storing an almost-identical-sounding file in far less space, usually by discarding sound details hearing barely notices.
Example: Why two files at the same sampling rate can differ greatly in size.
Sound · Extend
Comptroller and Auditor General (CAG)
The independent office that audits government spending and reports its findings to the legislature.
Example: The CAG's report goes to Parliament's Public Accounts Committee.
How government works in India · Go deeper
Concatenation
Joining pieces of text end to end. Associative but not commutative.
Example: "rain" + "bow" = "rainbow"
Properties of numbers · Extend
Concave mirror
A mirror curving inward like the inside of a spoon; can give either a magnified virtual image or a real, inverted image.
Example: A torch or headlight reflector.
Light · Investigate
Concave polygon
A polygon with at least one interior angle greater than 180°, so it has a dent.
Example: The outline of a star.
Shape and space · Understand
Concurrent lines
Three or more lines passing through one point.
Example: Spokes of a wheel, extended
Lines, rays and line segments · Understand
Concurrent List
The list of subjects on which both Parliament and state legislatures may make law.
Example: Education and forests are Concurrent List subjects.
How government works in India · Understand
Congruent
Exactly the same shape and size: one figure fits on the other after sliding, turning or flipping.
Example: Triangles OPT and OQT in the bisector construction.
Measuring and constructing angles · Go deeperMeasuring and constructing angles · Extend
conjecture
A statement you think is true because of the examples you have tried, but have not yet proved.
Example: “The corners of a triangle always make 180°.”
Angles · InvestigateHCF and LCM · InvestigateLines, rays and line segments · InvestigateOrder of operations · Investigate
connective tissue
Tissue with scattered cells and a lot of material between them; that material decides what it is.
Example: Bone, cartilage, tendon, fat and blood.
Anatomy of the human body · Understand
consecutive
Following one after another without gaps.
Example: 17, 18, 19 are consecutive numbers.
Number and shape patterns · Investigate
consecutive numbers
Whole numbers that follow one another with a gap of 1.
Example: 35 and 36
HCF and LCM · InvestigateProperties of numbers · Investigate
consistent
Having a small spread: values stay close together.
Example: Arjun: 40 to 50 runs every time.
Data handling · Investigate
constant
A number on its own in an expression, not multiplied by a variable.
Example: In 5n + 1, the constant is 1.
Number and shape patterns · Go deeper
Constant width
Having the same width measured in every direction, like a circle or a Reuleaux triangle.
Shape and space · Go deeper
constitution
A country's highest rule book, which all other laws and all offices must obey.
Example: India's Constitution came into force on 26 January 1950.
How government works in India · Discover
construct
To draw a shape exactly using only a ruler (for straight lines) and a compass.
Measuring and constructing angles · DiscoverMeasuring and constructing angles · Understand
Constructible angle
An angle that can be drawn exactly using only an unmarked straightedge and a compass.
Example: 60°, 45°, 75° are constructible; 20° is not.
Measuring and constructing angles · InvestigateMeasuring and constructing angles · Extend
Continental shelf
The shallow sea floor around a continent. Wide shelves slow tides down and make them bigger.
Tides · Understand
continued division
The long division method for HCF: divide, then divide the divisor by the remainder, again and again, until the remainder is 0.
Example: HCF(252, 198) = 18
HCF and LCM · Understand
continuous data
Numerical data from measuring, which can take any value in a range.
Example: Time to run 100 m: 15.73 s.
Data handling · Understand
Control (in an experiment)
The sample or condition left unchanged, so you can tell what "no effect" looks like.
Example: Cup B, with no saliva added, in the amylase test.
Body systems and how they connect · Investigate
Control test
An observation designed so that two rival explanations predict different, checkable outcomes.
Example: A half-lit Moon at 90 degrees elongation is a control test that rules out the shadow explanation.
Phases of the Moon · Investigate
Controlled comparison
Testing a claim by comparing cases that differ in only the one thing being tested, keeping everything else the same.
Example: Comparing eclipse-day food with non-eclipse-day food, all else equal.
Eclipses · Go deeper
controlled variable
Something you deliberately keep the same, so it cannot explain a difference in your result.
Example: Using the same size and type of paper for both columns controls for the material.
Anatomy of the human body · Investigate
Convention
A rule people agree to follow so that everyone understands things the same way.
Example: Driving on the left in India is a convention.
Order of operations · Discover
converse
The statement you get by swapping the “if” and “then” parts. It may or may not be true.
Example: If corresponding angles are equal, the lines are parallel.
Angles · Go deeper
Convex mirror
A mirror curving outward; always gives a virtual, upright, diminished image.
Example: A car's side mirror.
Light · Investigate
Convex polygon
A polygon with no dents: every diagonal lies inside it.
Shape and space · Understand
cooperative federalism
The Union and States solving a shared problem together through joint institutions, rather than each acting entirely alone.
Example: The GST Council is a cooperative-federalism body.
How government works in India · Go deeper
Corona
The Sun's faint, pearly outer atmosphere, visible only during totality.
Example: About as bright as a full moon, and a million times fainter than the Sun's disc.
Eclipses · Discover
Coronagraph
An instrument with a small built-in disc that blocks a star's or the Sun's bright disc, revealing its faint surroundings.
Example: India's Aditya-L1 carries a coronagraph to watch the Sun's corona every day.
Eclipses · Extend
corresponding angles
Angles in the same position at each crossing of a transversal. Equal when the lines are parallel.
Example: The F shape.
Angles · Go deeper
Council of Ministers
The Prime Minister and other ministers, collectively responsible to the Lok Sabha.
Example: It must resign together if it loses a no-confidence vote.
How government works in India · Understand
counter-example
A single example showing that a claim is not always true.
Example: 9 × 1 = 9 disproves 'multiplying always makes bigger'.
Four operations · InvestigateFour operations · Go deeper
counterexample
One example that shows a claim is not always true.
Example: 50° + 60° = 110° breaks “acute + acute is acute”.
Angles · InvestigateData handling · InvestigateExploration: reasons and consequences · InvestigateHCF and LCM · Investigate
Counting two ways
Proving two expressions equal by counting the same collection in two different orders.
Example: Rows × columns = columns × rows
Properties of numbers · Go deeper
Crescent
Less than half the disc lit: a curved sliver. From Latin for 'growing'.
Example: The thin Moon seen just after sunset a day or two after new moon.
Phases of the Moon · Discover
Critical angle
The angle of incidence inside a denser material above which no light can refract out; total internal reflection takes over.
Example: Water: 48.8°. Diamond: 24.4°.
Light · Investigate
Crore
One hundred lakh, 1,00,00,000. Equal to ten million.
Number system · Discover
cryptarithm
A puzzle in which digits in a calculation are hidden or replaced by letters or boxes, and you must work out what they are.
Example: □7 × □3 = 2,491 → 47 × 53
Four operations · Extend
cryptography
The science of keeping messages secret and secure.
Prime and composite numbers · Extend
cube number
A number that is a whole number times itself three times; the small cubes in a big cube.
Example: 27 = 3 × 3 × 3
Number and shape patterns · Understand
cumulative frequency
A running total of frequencies, adding each row to those before it.
Example: 4, 16, 25, 29, 30.
Data handling · Understand
Curve
A path that bends. In geometry, a line is always straight; a bending path is a curve.
Example: The outline of a bangle
Lines, rays and line segments · DiscoverShape and space · Discover
Customs ledger
An official record of goods and duty paid, kept for tax purposes rather than to impress anyone.
Exploration: reasons and consequences · Go deeper
cycle
A part of a pattern that repeats exactly, such as the last digits of powers.
Example: 7, 9, 3, 1
Number and shape patterns · Extend
cycle / period
The length of time (or count) after which something repeats.
Example: A 4-year Olympic cycle
HCF and LCM · Extend
Cyclic number
A number whose multiples by 1, 2, … are rotations of its digits.
Example: 142857
Properties of numbers · Extend
Damping
Anything that removes energy from a vibration, such as friction or air resistance.
Example: Why a struck bell eventually falls silent.
Sound · Go deeper
Danjon scale
A 0-to-4 scale for how dark and what colour a totally eclipsed Moon looks.
Example: 0 is almost invisible; 4 is bright copper-orange.
Eclipses · Understand
Dark matter
Unseen mass, inferred from its gravitational effect on galaxies, whose nature is not yet known.
Example: Explains why galaxies spin faster than their visible mass predicts.
Gravity · Extend
data
Facts, numbers or measurements collected to answer a question.
Example: The heights of all children in Class 5.
Data handling · Discover
Decibel (dB)
The unit of loudness. Every extra 10 dB means about twice as loud to your ears.
Example: 85 dB for a long time damages hearing.
Sound · DiscoverSound · Understand
Decibel combination
Combining two sound levels by adding their energies, not their decibel numbers directly.
Example: Two 70 dB sources together read about 73 dB, not 140 dB.
Sound · InvestigateSound · Go deeper
Deciding digit
When rounding, the digit one place to the right of the rounding place. 0–4 round down, 5–9 round up.
Number system · Understand
Declination (magnetic)
The angle between true north and magnetic north at a given place, which changes slowly over decades.
Exploration: reasons and consequences · Understand
Declination (of the Sun)
The Sun's yearly drift north and south of the equator, from about +23.4° to −23.4°.
Exploration: reasons and consequences · Understand
decomposition
The borrowing method of subtraction, in which the top number is repacked into different places.
Example: 5,003 = 4,000 + 900 + 90 + 13
Four operations · Go deeper
deficient number
A number whose proper factors add up to less than itself. All primes are deficient.
Example: 8 → 7
Prime and composite numbers · Extend
Degenerate case
A squashed or collapsed version of a figure.
Example: A segment of length 0
Lines, rays and line segments · Go deeper
Degenerate triangle
Three points in a straight line: a “triangle” that has collapsed flat.
Example: Sticks 3, 3 and 6 cm.
Shape and space · Investigate
degree (°)
The unit for measuring angles. A full turn is 360 degrees.
Example: A right angle is 90°.
Angles · DiscoverMeasuring and constructing angles · Discover
delimitation
The process of drawing and redrawing constituency boundaries and reserved seats.
Example: The current boundaries date from the 2008 delimitation order.
How government works in India · Understand
democracy
A system in which the people choose their government and can replace it at the next election.
Example: India holds a Lok Sabha election about every five years.
How government works in India · Discover
Density
How much mass is packed into a given volume. More density, on its own, means slower sound.
Example: Helium is light, so sound is fast in it.
Sound · Understand
Descending order
Arranged from greatest to smallest.
Example: 300, 45, 12
Number system · Understand
deviation
How far a value is from the mean, with a sign: positive above, negative below.
Example: 7 − 5 = +2.
Data handling · Go deeper
diagonal
A line segment joining two corners of a polygon that are not next to each other.
Example: A diagonal splits a quadrilateral into two triangles.
Angles · Go deeperLines, rays and line segments · Go deeperShape and space · Understand
Dialysis
A machine that filters waste and excess fluid from the blood outside the body, standing in for failed kidneys.
Example: Copies the kidney's thin-membrane, diffusion-driven hand-over.
Body systems and how they connect · Extend
Diameter
A straight line across a circle through its centre; twice the radius.
Shape and space · Discover
Diamond ring
The last single bead of sunlight blazing on the ring of corona.
Eclipses · Discover
Diaphragm
The sheet of muscle under the lungs that flattens to pull air in.
Example: A hiccup is this muscle twitching suddenly.
Body systems and how they connect · DiscoverSound · Investigate
difference
The answer to a subtraction: what is left, or the gap between two numbers.
Example: The difference between 138 and 129 is 9.
Four operations · DiscoverFour operations · UnderstandNumber and shape patterns · DiscoverNumber and shape patterns · Understand
Differential heating
Land and water warming and cooling at different rates under the same sunlight; the underlying cause of the monsoon.
Exploration: reasons and consequences · Go deeper
Diffraction
Waves spreading slightly around obstacles or through narrow gaps — evidence for light's wave nature.
Example: A CD's rainbow, or light spreading through a narrow slit.
Light · Extend
Diffuse reflection
Reflection from a rough surface: rays scatter in all directions, so you get a glow, not a picture.
Example: Paper, wall paint, a cinema screen.
Light · Understand
Diffusion
The spreading of a substance from where it is crowded to where it is scarce, by random movement alone. It costs no energy and is hopeless over distance.
Example: Oxygen crossing an alveolus wall.
Body systems and how they connect · Understand
Diffusion time ∝ distance²
A rule of physics: diffusion time rises with the square of the distance, not in simple proportion to it.
Example: Doubling a gap does not double the crossing time — it quadruples it.
Body systems and how they connect · Go deeper
Digit
One of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.
Example: 472 has three digits: 4, 7 and 2.
Number system · Discover
Digit sum
The sum of a number’s digits.
Example: The digit sum of 3,999 is 30.
Number system · ExtendPrime and composite numbers · UnderstandProperties of numbers · Go deeper
digit sum (digital root)
Add a number's digits repeatedly until one digit is left (9 counts as 0); it equals the remainder on division by 9.
Example: 9,022 → 13 → 4
Four operations · Go deeper
Dioptre (D)
Unit of lens or mirror power, equal to 1 divided by the focal length in metres.
Example: A −0.5 D lens corrects a far point of 2 m.
Light · Go deeper
Discovery
Finding something genuinely unknown to anyone. Use it carefully about places, which usually had people in them already.
Exploration: reasons and consequences · Discover
discrete data
Numerical data that can only take separate values, usually whole numbers from counting.
Example: Number of siblings.
Data handling · Understand
Dispersion
The splitting of white light into colours, because each colour bends by a different amount.
Example: A prism, and every raindrop in a rainbow.
Light · DiscoverLight · UnderstandLight · Investigate
Distance between parallel lines
The length of a segment perpendicular to both lines; it is the same everywhere.
Example: The gap between notebook lines
Lines, rays and line segments · Understand
Distributive
Multiplication distributes over addition: a × (b + c) = a × b + a × c. It also distributes over subtraction.
Example: 4 × 27 = 4 × 20 + 4 × 7
Properties of numbers · Understand
distributive property
Multiplying a sum equals multiplying each part and adding: a × (b + c) = a × b + a × c.
Example: 347 × 26 = 347 × 20 + 347 × 6
Four operations · Go deeperOrder of operations · UnderstandOrder of operations · Go deeperProperties of numbers · Discover
Diurnal tide
Just one high water and one low water each lunar day, as on the Gulf of Mexico.
Tides · Investigate
dividend
The number being divided.
Example: In 36 ÷ 6, the dividend is 36.
Four operations · DiscoverFour operations · Understand
dividend, divisor, quotient, remainder
In 38 ÷ 5 = 7 remainder 3: 38 is the dividend, 5 the divisor, 7 the quotient, 3 the remainder.
Example: 38 = 5 × 7 + 3
HCF and LCM · Understand
divides exactly
Goes into a number with no remainder. Also said as "is divisible by".
Example: 15 is divisible by 3, because 15 ÷ 3 = 5.
Prime and composite numbers · Discover
divisibility rule
A shortcut test for whether a number is divisible by a small number, using its digits.
Example: Digit sum for 3 and 9
Prime and composite numbers · Understand
divisible
A number is divisible by another if it can be divided by it with no remainder.
Example: 36 is divisible by 9.
HCF and LCM · Discover
divisible by
Can be divided by a number with remainder 0.
Example: 42 is divisible by 7.
Prime and composite numbers · Understand
division
Sharing a total equally, or finding how many equal groups fit in it. Sign: ÷.
Example: 36 ÷ 6 = 6
Four operations · Discover
division algorithm
For whole a and d bigger than 0, there is exactly one q and r with a = d × q + r and r less than d.
Example: 400 = 23 × 17 + 9
Four operations · Go deeper
Diwani
The right to collect land revenue over a region, granted to the East India Company for Bengal in 1765.
Exploration: reasons and consequences · Understand
DMAS
A memory word for the order of operations: Division, Multiplication, Addition, Subtraction. D and M share a rank; A and S share a rank.
Order of operations · Discover
Doppler effect
The change in frequency an observer hears because of relative motion between a source and the observer.
Example: A siren sounding higher as it approaches, lower as it recedes.
Sound · Extend
double bar graph
A bar graph with pairs of bars for comparing two data sets, with a legend.
Data handling · Go deeper
Double rounding
Rounding a number in two stages (for example to tens, then to hundreds), which can give a different answer from rounding once.
Example: 2,449 → 2,450 → 2,500, but 2,449 → 2,400 directly
Number system · Investigate
doubling and halving
Multiplying by repeatedly halving one number and doubling the other; the basis of Egyptian and Russian peasant multiplication.
Example: 37 × 24 = 24 + 96 + 768 = 888
Four operations · ExtendProperties of numbers · Investigate
Draconic month
27.212 days: the time for the Moon to return to the same node.
Eclipses · Go deeperPhases of the Moon · Go deeper
Drag
Air resistance: the backwards push of air on a moving object. It grows roughly with speed squared.
Example: What slows a flat sheet of paper.
Gravity · Understand
Dual solid
The solid made by joining the face-centres of another; faces and vertices swap.
Example: Cube and octahedron.
Shape and space · Extend
Dynamic theory
Laplace's theory treating tides as real waves sloshing through ocean basins of real shape and depth, which is why every port needs its own table.
Tides · Go deeper
Eardrum
The thin, tight skin at the end of the ear canal that the arriving sound pushes.
Example: About the size of a small fingernail.
Sound · Discover
Earth tide
The twice-daily flexing of the solid ground itself, by tens of centimetres, detected by precise instruments rather than felt directly.
Tides · Go deeper
Earthshine
Faint light on the Moon's night side, bounced off Earth. Seen best near a thin crescent.
Example: "The old Moon in the new Moon's arms."
Phases of the Moon · DiscoverPhases of the Moon · Understand
Ebb tide
The hours when the water is going out and the level is falling.
Tides · Discover
Echo
A sound heard again after it has bounced off a surface and returned.
Example: A clap in an empty hall.
Sound · Discover
Echolocation
Using self-made sound and its returning echo to sense surroundings.
Example: Bats in the dark, dolphins in murky water.
Sound · Investigate
Eclipse
One body moving into another's shadow, or blocking our view of it.
Example: A solar eclipse and a lunar eclipse are the only two we see well from Earth.
Eclipses · Discover
Eclipse season
A window of about a month, twice a year, when eclipses are possible.
Eclipses · DiscoverEclipses · Understand
Eclipse year
346.6 days — the time for the Sun to return to the same node. 18.6 days shorter than a normal year.
Eclipses · Understand
Ecliptic
The plane of Earth's orbit around the Sun, and the line the Sun appears to trace across our sky.
Eclipses · Understand
Edge
A line where two faces of a solid meet.
Example: A cube has 12 edges.
Shape and space · Discover
election
The process by which people choose their representatives.
Example: The Election Commission runs India's elections.
How government works in India · Discover
Electrocardiograph (ECG)
A machine that records the heart's own electrical signal from sensors on the skin.
Example: Invented in working form by Einthoven in 1903.
Body systems and how they connect · Extend
Electromagnetic spectrum
The full family of waves that includes radio, microwave, infrared, visible light, ultraviolet, X-rays and gamma rays, all travelling at the speed of light.
Light · Extend
ellipsis
The three dots … that mean “and so on”.
Example: 1, 2, 3, …
Number and shape patterns · Understand
Elongation
The angle at Earth between the direction of the Sun and the direction of the Moon. It sets the phase completely.
Example: Elongation 90° means a quarter moon, half the disc lit.
Phases of the Moon · Understand
emirp
A prime that becomes a different prime when its digits are reversed.
Example: 13 and 31
Prime and composite numbers · Extend
Encounter
A meeting between groups who did not know each other before.
Example: 1498 at Calicut was an encounter, not a discovery.
Exploration: reasons and consequences · Discover
End point
A point where a segment or ray stops.
Example: A and B are the end points of segment AB
Lines, rays and line segments · Discover
Envelope
A curve touched by every line in a family of lines.
Example: String-art parabola
Lines, rays and line segments · Extend
Enzyme
A chemical that speeds up the breaking-down (or building-up) of other chemicals without being used up itself.
Example: Amylase in your saliva, which cuts starch into sugar.
Body systems and how they connect · Discover
epistolary jurisdiction
A court treating a letter or petition from a concerned third party as the start of a case, used to widen access to public interest litigation.
Example: Courts used this from the late 1970s to help undertrial prisoners.
How government works in India · Go deeper
epithelial tissue
Sheets of tightly packed cells that cover and line surfaces.
Example: The lining of your mouth and gut.
Anatomy of the human body · Understand
equal additions
A subtraction method that adds the same amount to both numbers, column by column, so the difference is unchanged.
Example: 13 − 7 in the ones, then add 1 ten to the bottom
Four operations · Go deeper
equal groups
Groups that all have the same number of things. Multiplication counts them quickly.
Example: 5 boxes of 12 laddoos
Four operations · Discover
equally likely
Having the same chance of happening, like each face of a fair die.
Data handling · Extend
equilateral triangle
A triangle with all three sides equal; each of its angles is 60°.
Measuring and constructing angles · UnderstandMeasuring and constructing angles · Go deeperShape and space · Understand
Equilibrium theory
Newton's original tide theory, treating the ocean as if it always sat in instant balance with the Moon and Sun. Right about the cause, wrong about the details.
Tides · Go deeper
Equivalence principle
The observation, later built into general relativity, that gravitational mass and inertial mass are always equal.
Example: Tested to better than one part in 10¹⁴.
Gravity · Go deeper
equivalent expressions
Expressions that give the same value for every value of the variable.
Example: 4 + 3(n − 1) and 3n + 1
Number and shape patterns · Go deeper
Eradicated (a disease)
Wiped out completely, everywhere, with no cases left anywhere in the world.
Example: Smallpox, declared eradicated by the WHO in 1980.
Body systems and how they connect · Extend
Escape velocity
The speed an object needs to leave a planet's gravity for good; about 11.2 km/s for Earth.
Exploration: reasons and consequences · ExtendGravity · Understand
Establishment of the port
The steady delay between the Moon passing overhead and high water at a particular port.
Tides · Understand
estimate
A sensible guess made before measuring, using what you already know.
Example: “It looks a bit less than a right angle, about 80°.”
Measuring and constructing angles · DiscoverMeasuring and constructing angles · InvestigateExploration: reasons and consequences · DiscoverFour operations · Discover
Estimation error
The difference between an estimate and the exact value, sometimes given as a percentage of the exact value.
Number system · Investigate
Estuary
The wide mouth of a river where it meets the sea and the water is part fresh, part salt, and full of tide.
Tides · Discover
Euclid’s algorithm
Replace (a, b) by (b, remainder of a ÷ b) until the remainder is 0; the last divisor is the HCF.
Example: (252, 198) → (198, 54) → (54, 36) → (36, 18) → 18
HCF and LCM · Go deeper
Euclid's Elements
A Greek geometry textbook from about 300 BCE that builds geometry from a few assumptions using constructions and proofs.
Measuring and constructing angles · Go deeper
Euclid’s lemma
If a prime divides a product, it divides at least one of the numbers multiplied.
Example: 7 divides 42 × 5, and 7 divides 42.
Prime and composite numbers · Go deeper
Euclidean geometry
The geometry of a flat plane, built on Euclid's five postulates.
Example: Triangle angles add to 180°
Lines, rays and line segments · Go deeper
Euler characteristic
The number F + V − E; it is 2 for polyhedra without holes and 0 for a solid with one hole.
Shape and space · Go deeper
Euler’s formula
For any (simple) polyhedron, faces + vertices − edges = 2.
Shape and space · Investigate
Euler’s totient φ(n)
How many numbers from 1 to n are co-prime with n.
Example: φ(10) = 4: 1, 3, 7, 9
Prime and composite numbers · Go deeper
Evaluate
Find the value of an expression.
Example: Evaluating 6 + 8 ÷ 2 gives 10.
Order of operations · Understand
even number
A whole number that can be split into pairs with none left over; it ends in 0, 2, 4, 6 or 8.
Example: 14, 30, 256
Number and shape patterns · DiscoverPrime and composite numbers · DiscoverProperties of numbers · Discover
Event horizon
The boundary around a black hole beyond which nothing, not even light, can escape.
Example: Marked by the Schwarzschild radius.
Gravity · Extend
Evidence category
A label such as supports, contradicts, not relevant or uncertain, used to judge how a piece of evidence relates to a claim.
Exploration: reasons and consequences · Investigate
exact division
A division with remainder 0: the divisor is a factor of the dividend.
Example: 63 ÷ 9 = 7 exactly.
Four operations · Understand
Exclusion zone
An area outsiders are legally kept out of.
Example: India enforces a 5 km exclusion zone around North Sentinel Island.
Exploration: reasons and consequences · Extend
Excretion
Getting rid of waste that was made inside your body.
Example: Urine, and the carbon dioxide in every breath out.
Body systems and how they connect · Discover
executive
The organ that carries out the laws and runs the country day to day.
Example: Ministers and the civil service.
How government works in India · Discover
Exeligmos
Three Saros cycles, about 54 years and 34 days, which returns an eclipse to nearly the same longitude.
Eclipses · Go deeper
Exoplanet
A planet orbiting a star other than the Sun.
Example: Most known exoplanets were found by the transit method.
Eclipses · Extend
Expand
Remove brackets by multiplying out with the distributive law.
Example: 3(x + 2) = 3x + 6
Properties of numbers · Go deeper
expanded form
A number written as the sum of its place values.
Example: 2,47,368 = 2,00,000 + 40,000 + 7,000 + 300 + 60 + 8
Four operations · Go deeperNumber system · DiscoverNumber system · Understand
Exploration
Travelling somewhere to find out what is there.
Example: Cook's first voyage explored the south Pacific.
Exploration: reasons and consequences · Discover
Exponent
The small raised number that says how many times the base is multiplied by itself.
Example: In 10⁷ the exponent is 7.
Number system · Go deeper
exponential growth
Growth by the same multiplying factor each step.
Example: Doubling: 1, 2, 4, 8, 16
Number and shape patterns · Go deeper
expression
A calculation written with numbers and operation signs, without an equals sign.
Example: 4500 + 45 × 60
Four operations · InvestigateOrder of operations · DiscoverNumber and shape patterns · Go deeper
Expression tree
A diagram of an expression with the last operation at the top and each operation branching to what it combines.
Order of operations · Go deeper
Extended source
A light source with real width, so different edges of it are blocked at different places, giving a soft penumbra.
Example: The Sun is a large extended source, half a degree wide.
Eclipses · Investigate
Exterior angle
The angle between one side of a polygon and the extension of the next side.
Shape and space · Go deeper
exterior angle of a triangle
The angle between one side of a triangle and the extension of the next side.
Example: Extending BC to D gives exterior angle ∠ACD.
Angles · Extend
exterior angle property
An exterior angle of a triangle equals the sum of the two interior opposite angles.
Example: ∠ACD = ∠A + ∠B
Angles · Extend
exterior of an angle
All of the flat surface outside the two arms.
Example: The rest of the pizza, outside the slice.
Angles · Discover
Face
A flat surface of a solid.
Example: A dice has 6 faces.
Shape and space · Discover
Face value
The value of the digit itself, wherever it is.
Example: In 472 the face value of 4 is 4.
Number system · Discover
fact family
A set of related facts made from the same three numbers.
Example: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 8 = 7, 56 ÷ 7 = 8
Four operations · Discover
factor
Either number in a multiplication. Multiplicand and multiplier are both factors.
Example: In 24 × 6 = 144, 24 and 6 are factors of 144.
Four operations · UnderstandHCF and LCM · DiscoverPrime and composite numbers · Discover
factor pair
Two numbers that multiply to give the number.
Example: 3 and 8 are a factor pair of 24.
Prime and composite numbers · DiscoverProperties of numbers · Investigate
factor tree
A branching diagram that splits a number into factor pairs until every branch ends in a prime.
Example: 36 → 6 × 6 → 2 × 3 × 2 × 3
HCF and LCM · UnderstandPrime and composite numbers · Understand
Factorial
n! is the product of the whole numbers from 1 to n.
Example: 4! = 4 × 3 × 2 × 1 = 24
Order of operations · ExtendPrime and composite numbers · Extend
Factorise
Write a sum as a product by taking out a common factor.
Example: 6x + 9 = 3(2x + 3)
Properties of numbers · Go deeper
Fair test
Changing exactly one thing at a time while keeping everything else the same.
Example: Same rice, same amount of iodine — the only difference is saliva or not.
Body systems and how they connect · InvestigateGravity · Investigate
Far side
The hemisphere of the Moon permanently turned away from Earth. Not the same as the dark side.
Example: First photographed by Luna 3 in October 1959.
Phases of the Moon · UnderstandPhases of the Moon · Extend
Fermat prime
A prime of the form 2 raised to a power of 2, plus 1. Known ones: 3, 5, 17, 257, 65,537.
Measuring and constructing angles · Extend
Fermi estimate
A rough calculation built from round numbers, aimed at getting close to the right size of answer quickly.
Exploration: reasons and consequences · ExtendNumber system · Extend
Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, … where each term is the sum of the two before it.
Example: 13 + 21 = 34
Number and shape patterns · Understand
figurate number
A number that can be arranged as dots in a regular shape.
Example: Pentagonal numbers 1, 5, 12, 22
Number and shape patterns · Extend
finite / infinite
A finite sequence stops; an infinite sequence goes on for ever.
Example: Days of a month are finite; odd numbers are infinite.
Number and shape patterns · Understand
First quarter
Exactly half the disc lit and growing, a quarter of the way through the cycle.
Example: Rises around noon, sets around midnight.
Phases of the Moon · Discover
first-past-the-post
An election method where the candidate with the most votes in a constituency wins it, with no requirement to reach half.
Example: India's Lok Sabha and state assembly elections use first-past-the-post.
How government works in India · Understand
Floating-point number
The rounded way computers store decimals, which can make addition non-associative.
Properties of numbers · Extend
Flood tide
The hours when the water is coming in and the level is rising.
Tides · Discover
Focal length
The distance from a mirror or lens to the point where parallel rays meet (or seem to meet).
Example: A concave shaving mirror often has f ≈ 25 cm.
Light · Investigate
Force
A push or a pull on an object. Measured in newtons (N).
Example: The chair pushes up on you; gravity pulls down.
Gravity · Discover
Forced vibration
Vibration driven continuously by an outside push at a frequency the pusher chooses.
Example: A washing machine's frame, driven by the motor.
Sound · Go deeper
formula
An equation that tells you how to calculate one quantity from others.
Example: Tₙ = 4n + 3
Number and shape patterns · Go deeper
Four fours
A puzzle: make numbers using exactly four 4s and chosen operations.
Example: (44 − 4) ÷ 4 = 10
Order of operations · Extend
Free fall
Falling with only gravity acting, and nothing else in the way.
Example: On the Moon, every drop is a free fall.
Gravity · DiscoverGravity · Understand
Free vibration
How an object vibrates once disturbed and then left alone, at its own natural frequency.
Example: A plucked string ringing after release.
Sound · Go deeper
frequency
The number of times a value appears in the data.
Example: Samosa has a frequency of 9.
Data handling · DiscoverSound · Discover
frequency table
A table listing each value (or category) with its frequency.
Data handling · Discover
front-end estimation
Estimating using only the leading digits of each number.
Example: 4,872 + 3,195 ≈ 4,000 + 3,000
Four operations · Investigate
fulcrum
The fixed point a lever turns about.
Example: The elbow joint is the fulcrum when the biceps bends the arm.
Anatomy of the human body · Go deeper
Full moon
The phase when Earth is between the Sun and the Moon and we see a full lit disc.
Example: The only phase at which a lunar eclipse can happen.
Eclipses · DiscoverPhases of the Moon · Discover
full turn
Turning all the way round to face the same way again: 360°. Also called a complete turn or revolution.
Example: A fan blade going round once.
Angles · Discover
Fully bracketed
Every operation has its own pair of brackets, so no rule is needed to read it.
Example: ((2 + 3) × 4) − 1
Order of operations · Investigate
Fundamental
The lowest, usually loudest, frequency a vibrating source produces; what your ear reports as pitch.
Example: A sitar string's main note.
Sound · Go deeper
Fundamental Theorem of Arithmetic
Every whole number greater than 1 has exactly one prime factorisation, apart from order.
Example: 360 = 2³ × 3² × 5 and no other way.
HCF and LCM · Go deeperPrime and composite numbers · Go deeper
g
The strength of gravity at a place: how many newtons pull on each kilogram. On Earth, about 9.8 N/kg.
Example: On Mars g is 3.72; on Jupiter, 24.79.
Gravity · DiscoverGravity · UnderstandGravity · Go deeper
gambler's fallacy
The mistaken belief that past random results change future chances, such as "tails is due".
Data handling · Extend
GCD / GCF
Greatest Common Divisor / Greatest Common Factor: other names for the HCF.
Example: GCD(8, 12) = 4.
HCF and LCM · Discover
gelosia method
Another name for lattice multiplication, from the Italian word for a criss-cross window screen.
Four operations · Extend
General associativity
For an associative operation, every way of bracketing a long list gives the same result.
Properties of numbers · Go deeper
General position
Lines with no two parallel and no three through one point.
Example: 4 such lines make 6 crossings
Lines, rays and line segments · Investigate
General relativity
Einstein's 1915 theory in which gravity is the bending of space and time, predicting that light itself is deflected near a massive body.
Eclipses · Go deeper
Generalisation
A broad statement meant to cover every case of something, often signalled by words like 'always' or 'every'.
Example: "Every voyage was funded by a king" is a generalisation.
Exploration: reasons and consequences · Investigate
generalise
To state a rule that works for every case, often using n.
Example: “n squares need 3 × n + 1 sticks.”
Number and shape patterns · Investigate
Geodesic dome
A dome built from many flat triangles that together approximate a sphere.
Shape and space · Extend
geometric sequence
A sequence where each term is the one before multiplied by the same number.
Example: 1, 10, 100, 1,000, …
Number and shape patterns · Understand
geometry box
A small case holding a ruler, protractor, compass, divider, set squares and pencil.
Measuring and constructing angles · Discover
Geostationary orbit
A circular orbit 35,786 km above the equator, where one lap takes exactly one day.
Example: Where communication satellites sit.
Gravity · Understand
Gibbous
More than half lit but not yet full. From Latin for 'humped'.
Example: The fat lopsided Moon a few nights before full.
Phases of the Moon · Discover
Gimbal
A pivoted mounting that keeps an instrument level even as the object carrying it rolls and pitches.
Example: H4 was gimbal-mounted so a ship's rolling would not disturb its mechanism.
Exploration: reasons and consequences · Go deeper
gnomon
An L-shaped piece that turns one square (or rectangle) into the next larger one.
Example: Adding 5 tiles turns a 2 × 2 square into 3 × 3.
Number and shape patterns · Investigate
Goldbach’s conjecture
The unproved claim that every even number above 2 is the sum of two primes.
Example: 28 = 5 + 23
Prime and composite numbers · Extend
golden ratio
The number (1 + √5) ÷ 2 ≈ 1.618, approached by ratios of neighbouring Fibonacci numbers.
Example: 89 ÷ 55 ≈ 1.618
Number and shape patterns · Go deeper
goniometer
An instrument for measuring angles, especially joint angles in the body.
Example: Used by physiotherapists.
Angles · Extend
Googol
The number 10¹⁰⁰, a 1 followed by 100 zeros.
Number system · Extend
government
The set of people and offices a group uses to make its rules, carry them out and settle disputes about them.
Example: India's government has three organs and three levels.
How government works in India · Discover
gram sabha
The meeting of every adult voter registered in a village.
Example: The gram panchayat must present its accounts to the gram sabha.
How government works in India · Understand
Gravimeter
A precise instrument that detects tiny local changes in g, used to study what lies underground.
Example: Can find dense ore or hidden cavities.
Gravity · Go deeper
Gravitational wave
A ripple of curving spacetime, travelling at the speed of light, from a violently accelerating mass.
Example: First detected by LIGO in 2015.
Gravity · Extend
Gravity
The attraction between any two objects that have mass.
Example: The Earth and an apple pull on each other.
Gravity · Discover
Great circle
A circle on a sphere whose centre is the sphere's centre; the sphere's version of a line.
Example: The equator
Lines, rays and line segments · Go deeper
Greater than (>) / less than (<)
Symbols comparing two numbers; the open side faces the bigger number.
Example: 8 > 3 and 3 < 8
Number system · Understand
greedy strategy
Solving a problem by always taking the best available option at each step; sometimes provably optimal, as in the coalition-size puzzle.
Example: Taking the largest parties first gives the fewest parties needed for a majority.
How government works in India · Extend
grid (area) model
A table or rectangle that splits both factors by place value; each cell is a partial product.
Example: 300 × 20 = 6,000 is one cell of 347 × 26
Four operations · Go deeper
grouping
Division where you know the size of each group and want how many groups.
Example: 40 bangles in sets of 8
Four operations · Discover
growing pattern
A pattern in which each step gets bigger by a rule.
Example: Matchstick squares: 4, 7, 10, 13 sticks.
Number and shape patterns · Discover
GST
Goods and Services Tax, added to prices in India as a percentage.
Example: ₹500 at 18% → ₹590
Order of operations · Extend
Haemoglobin
The iron-containing red pigment in red blood cells that grabs oxygen where there is plenty and releases it where there is little.
Example: It is what makes blood red.
Body systems and how they connect · Understand
half turn
Turning to face the opposite way: 180°.
Example: An about-turn in a parade.
Angles · Discover
Hand-over
A place where two systems touch closely enough for something to cross between them.
Example: The alveolus wall, the villus wall, a capillary.
Body systems and how they connect · Discover
Harmonic (overtone)
An extra frequency present alongside the fundamental, at a whole-number multiple of it.
Example: 440 Hz and 660 Hz above a 220 Hz fundamental.
Sound · Go deeper
Harmonic analysis
The mathematics that splits a measured tide into simple, steady waves (constituents) tied to the Moon and Sun, which can then be projected forward to predict future tides.
Tides · Investigate
HCF
Highest Common Factor: the greatest number that divides all the given numbers exactly.
Example: HCF(12, 18) = 6.
HCF and LCM · Discover
Hertz (Hz)
The unit of frequency. 1 Hz is one vibration per second; 1,000 Hz is 1 kilohertz (kHz).
Example: Human hearing runs from 20 Hz to 20,000 Hz.
Sound · Discover
Hexomino
A shape made of six equal squares joined edge to edge. There are 35 of them; 11 fold into a cube.
Shape and space · Investigate
High tide (high water)
The moment when the sea is at its highest and stops rising.
Tides · Discover
highest common factor (HCF)
The largest number that is a factor of all the given numbers. Also called the greatest common divisor.
Example: HCF of 12 and 18 is 6.
Prime and composite numbers · Understand
Highlands
The pale, heavily cratered older regions of the Moon, standing above the maria.
Example: Brighter because the rock is more reflective.
Phases of the Moon · Understand
highly composite number
A number with more factors than any smaller number. Studied by Ramanujan.
Example: 12, 24, 36, 48, 60
Prime and composite numbers · Investigate
Hindsight bias
The tendency to remember a past prediction as more accurate than it really was, once the outcome is known.
Example: Writing predictions down before observing is the standard defence against it.
Phases of the Moon · Investigate
Hindu–Arabic numerals
The ten digits 0–9 and their place-value system, developed in India and spread by Arabic-writing scholars.
Number system · Go deeper
histogram
A bar graph for grouped continuous data, with bars touching because the intervals join up.
Data handling · Go deeper
Hohmann transfer
The lowest-fuel route between two circular orbits: one burn onto a connecting ellipse, one burn to circularise.
Example: Used by Mangalyaan to reach Mars.
Gravity · Go deeper
Homeostasis
Holding the conditions inside the body steady while the outside changes.
Example: Core temperature near 37 °C whatever the weather.
Body systems and how they connect · Understand
Horizon line
The line at the viewer's eye level in a perspective drawing.
Example: Where sea meets sky
Lines, rays and line segments · Extend
Horizontal
Level, like still water.
Example: The horizon at sea
Lines, rays and line segments · Understand
Hormone
A chemical message carried slowly in the blood to the whole body, rather than fast along a nerve.
Example: Insulin, which tells cells to take sugar out of the blood.
Body systems and how they connect · DiscoverBody systems and how they connect · Understand
hundred square
A 10 by 10 grid of the numbers 1 to 100, used to spot number patterns.
Example: Down a column adds 10.
Number and shape patterns · Discover
hunting tooth
An extra gear tooth that makes the two tooth counts co-prime, so every tooth meets every other.
Example: 12 and 17 teeth
HCF and LCM · Extend
Hybrid eclipse
A rare eclipse that is total along the middle of its track and annular at the ends, because Earth is round.
Eclipses · UnderstandEclipses · Go deeper
Hyperopia
Long-sightedness: the near point is farther than the usual 25 cm; corrected with a converging lens.
Light · Go deeper
hypotenuse
The longest side of a right triangle, opposite the right angle.
Measuring and constructing angles · ExtendShape and space · Go deeper
hypothesis
A testable guess about how something works, made before you collect evidence.
Example: "A hollow tube will resist bending better than a solid rod of the same mass" is a hypothesis.
Anatomy of the human body · Investigate
Hypothetical
A constructed 'what if' scenario, built from real numbers or facts, used to see the shape of a comparison rather than to claim it happened.
Exploration: reasons and consequences · Investigate
Identity element
A number that leaves every number unchanged under an operation, on either side.
Example: 0 for +, 1 for ×
Properties of numbers · Understand
Image
What you see when light appears to come from somewhere it did not actually come from.
Example: Your reflection, seemingly behind the glass.
Light · Discover
Immediate execution
How basic calculators work: each step is finished as soon as the next key is pressed, ignoring the order of operations.
Example: 2 + 3 × 4 → 20 on a basic calculator
Order of operations · Understand
Immunity
A body's ability to resist a disease it has met before. The peoples of the Americas had none to smallpox or measles.
Exploration: reasons and consequences · Discover
Implied multiplication
Multiplication shown by writing things side by side, with no × sign.
Example: 2(2 + 2), 3x
Order of operations · Extend
Incandescence
Giving out light because you are hot.
Example: A flame, a filament bulb, the Sun.
Light · Understand
inclusion–exclusion
Count "a or b" as count(a) + count(b) − count(both).
Example: 250 + 166 − 83 = 333
HCF and LCM · Extend
Indeterminate
Used for 0 ÷ 0: many values would fit, so none can be chosen.
Properties of numbers · Understand
index form
Prime factorisation written with powers (indices) for repeated primes.
Example: 60 = 2² × 3 × 5
HCF and LCM · UnderstandPrime and composite numbers · Understand
Indian system
Place-value naming with periods ones (3 places), thousands, lakhs, crores (2 places each).
Example: 1,23,45,678
Number system · Understand
Indices / exponents
Powers, like the 2 in 5² = 25. Done after brackets and before × and ÷.
Order of operations · Understand
Indigenous
Belonging to a place from long before outsiders arrived.
Exploration: reasons and consequences · Discover
Inertia
An object’s resistance to any change in its motion. It depends on mass, not on gravity.
Example: A trolley is just as hard to shove on the Moon.
Gravity · Understand
inferior
Towards the feet.
Example: The bladder is inferior to the intestines.
Anatomy of the human body · Understand
Inferior conjunction
The moment an inner planet (Mercury or Venus) passes between Earth and the Sun.
Example: A transit can only happen at inferior conjunction, near one of the planet's nodes.
Eclipses · Extend
infinitely many
More than any number you can name; the list never ends.
Prime and composite numbers · Go deeper
Infix notation
Writing the operation between its two numbers, as in 2 + 3.
Order of operations · Extend
Infrasound
Sound below 20 Hz: too low for humans to hear.
Example: Elephant calls, earthquakes.
Sound · DiscoverSound · Understand
Integers
The whole numbers together with their negatives: … −2, −1, 0, 1, 2, …
Example: Temperature −5 °C
Properties of numbers · Extend
intercardinal directions
The directions half-way between the cardinal ones, 45° from each: NE, SE, SW, NW.
Example: North-east
Angles · Understand
Interference
Two overlapping waves reinforcing (brighter) or cancelling (darker) depending on their alignment.
Example: Young's double-slit banding pattern.
Light · Extend
Interior / exterior / boundary
The inside, the outside and the curve itself, for a simple closed curve.
Shape and space · Understand
interior angle
An angle inside a polygon at a corner; for a regular n-gon it is (n − 2) × 180° ÷ n.
Measuring and constructing angles · Extend
interior of an angle
The region between the two arms of an angle.
Example: The cheesy part of a pizza slice.
Angles · Discover
interior opposite angles
For an exterior angle of a triangle, the two inside angles at the other corners.
Example: For ∠ACD, they are ∠A and ∠B.
Angles · Extend
International system
Place-value naming with periods of three places: ones, thousands, millions, billions.
Example: 12,345,678
Number system · Understand
interpreting a remainder
Deciding from the story whether to round up, round down, give the leftover, or split it.
Example: 250 students, 45 per bus → 6 buses
Four operations · Investigate
interquartile range (IQR)
Upper quartile − lower quartile: the spread of the middle half of the data.
Data handling · Go deeper
intersecting lines
Lines that cross at one point.
Example: The two lines of an X.
Angles · UnderstandLines, rays and line segments · Discover
Intertidal zone
The strip of shore that is covered at high tide and bare at low tide.
Tides · Discover
Invariant
A quantity that never changes during a process, used to prove some outcomes impossible.
Example: The parity of upside-down cups.
Properties of numbers · Go deeperProperties of numbers · Extend
inverse operation
An operation that undoes another. Subtraction undoes addition; division undoes multiplication.
Example: 72 − 30 = 42 is undone by 42 + 30 = 72.
Four operations · UnderstandFour operations · InvestigateProperties of numbers · Understand
inverse operations
Operations that undo each other: + and −, × and ÷.
Example: 15 − 6 = 9 undoes 9 + 6 = 15.
Four operations · Discover
inverse proportion
When one quantity doubles and the other halves, so their product stays the same.
Example: 6 workers × 10 days = 15 workers × 4 days
Four operations · Go deeper
Inverse-square law
A rule in which a quantity falls off as one over the distance squared.
Example: Twice as far, a quarter of the pull.
Gravity · Understand
invertebrate
An animal with no internal backbone or skeleton.
Example: An octopus is an invertebrate.
Anatomy of the human body · Extend
investigation
A careful exploration of a question: collect cases, spot a rule, test it and explain it.
Example: How many sticks for 100 squares?
Number and shape patterns · Investigate
Isometric drawing
A drawing of a solid on a triangular grid where all three directions are drawn to the same scale.
Shape and space · Extend
Isosceles triangle
A triangle with two equal sides.
Example: A slipped compass turns the equilateral triangle into an isosceles one.
Measuring and constructing angles · InvestigateMeasuring and constructing angles · Go deeperShape and space · Understand
Jaali
A carved stone lattice screen in Indian architecture, often built on tiling patterns.
Shape and space · Extend
joint sitting
A meeting of both Houses of Parliament together to resolve a deadlock over an ordinary bill.
Example: Used three times so far, most recently in 2002.
How government works in India · Understand
judicial review
The power of courts to strike down a law or executive action that conflicts with the Constitution.
Example: The Supreme Court used judicial review to strike down laws that violated fundamental rights.
How government works in India · Understand
judiciary
The organ of independent courts that settles disputes and decides what the law means.
Example: The Supreme Court is at the top of it.
How government works in India · Discover
Juxtaposition
Placing symbols next to each other. In maths it usually means multiplication.
Order of operations · Extend
Jya
The Indian tradition of sine tables that historically influenced the mathematical idea of the sine function.
Eclipses · Go deeper
Kamal
A wooden card on a knotted cord, used by Indian Ocean sailors to measure a star's height above the horizon.
Exploration: reasons and consequences · Discover
Kaprekar's constant
The number 6174, which every four-digit number (not all digits the same) reaches by repeatedly subtracting its digits arranged smallest-first from largest-first.
Example: 3524 → 3087 → 8352 → 6174
Four operations · Extend
Kaprekar’s constant
6,174: the number every 4-digit number (digits not all equal) reaches by repeatedly subtracting its smallest arrangement from its largest.
Example: 7,641 − 1,467 = 6,174
Number system · Investigate
key
The note on a pictograph telling how many one symbol stands for.
Example: ● = 10 mangoes.
Data handling · Discover
Khahara
The traditional Sanskrit name for a quantity divided by zero, commonly attributed to Bhaskara II (c. 1150 CE), who described it as an infinite quantity.
Properties of numbers · Go deeper
Kharab
Indian name for 100 arab, 10¹¹, equal to 100 billion.
Number system · Extend
Kilo, centi, milli
Metric prefixes meaning 1,000, one hundredth and one thousandth.
Example: 1 km = 1,000 m
Number system · Understand
Kite
A four-sided shape with two pairs of equal adjacent sides; one diagonal is the perpendicular bisector of the other.
Example: APBQ when different radii are used above and below AB.
Measuring and constructing angles · Go deeperShape and space · Understand
kolam
A traditional South Indian floor design drawn with rice flour around a grid of dots, often built from repeating units.
Example: A doorstep border of repeated loops.
Number and shape patterns · Discover
kuttaka
Aryabhata’s "pulveriser" method (499 CE) for solving equations like ax − by = c by repeated division.
Example: Used for astronomical cycle problems
HCF and LCM · Go deeper
Lacteal
A tiny lymphatic vessel inside a villus that absorbs digested fat, instead of the fat going straight into a blood capillary.
Example: The one thing at the villi that does not head straight to the liver.
Body systems and how they connect · Go deeper
Lagrange point
A location in space where the gravity of two large bodies balances so a spacecraft can hold a stable position with little fuel.
Example: L1, about 1% of the way from Earth to the Sun, gives an unobstructed view of the Sun.
Eclipses · ExtendGravity · Extend
Lakh
One hundred thousand, 1,00,000. Ten lakh make one million.
Number system · Discover
Landmark method
Timing an event (such as moonrise) against a fixed reference point on the horizon, such as a rooftop or tree, to get precise, repeatable measurements.
Example: Used to measure the daily lag in Investigation 4.
Phases of the Moon · Investigate
Laplace resonance
A repeating pattern in which each of several orbiting moons takes exactly twice as long to orbit as the one just inside it, as with Io, Europa and Ganymede.
Tides · Extend
Last quarter
Exactly half lit and shrinking, three quarters of the way through the cycle. Also called third quarter.
Example: Rises around midnight, sets around noon.
Phases of the Moon · Discover
Lateen sail
A triangular sail on a slanted yard, able to hold a much sharper angle to the wind than a square sail.
Exploration: reasons and consequences · Understand
lateral
Away from the midline, towards one side.
Example: Your ears are lateral.
Anatomy of the human body · Understand
Lateral inversion
The left-right swap a plane mirror gives an image.
Example: AMBULANCE painted backwards on a van.
Light · DiscoverLight · Understand
Latitude
How far north or south of the equator you are, in degrees. Measurable from the Sun or the Pole Star.
Example: Kozhikode is about 11 degrees north.
Exploration: reasons and consequences · DiscoverLines, rays and line segments · Extend
lattice multiplication
A written method that fills a grid with digit products, split by diagonals into tens and ones, then adds along the diagonals.
Example: 473 × 58 = 27,434 in a 3 × 2 lattice
Four operations · Extend
law
A rule made by a legislature that a whole country or state must follow, and that will be enforced.
Example: A road safety law applies to everyone driving on that road.
How government works in India · Discover
Law of reflection
Angle of incidence = angle of reflection, and both rays and the normal lie in one plane.
Example: The whole behaviour of every mirror.
Light · Understand
LCM
Lowest (or Least) Common Multiple: the smallest number that is a multiple of all the given numbers.
Example: LCM(4, 6) = 12.
HCF and LCM · Discover
leading digit
The first (left-most) non-zero digit of a number; it tells you most about the number's size.
Example: In 4,872 the leading digit is 4 (thousands).
Four operations · Investigate
Left to right
The rule for partners: when two operations of the same rank are next to each other, do the one on the left first.
Example: 10 − 3 + 2 = 7 + 2 = 9
Order of operations · Discover
Left-associative
Repeated operations of the same level group from the left: a − b − c = (a − b) − c.
Order of operations · Go deeper
Left-to-right rule
Operations of equal precedence are done in the order they appear, reading from the left.
Example: 8 ÷ 4 × 2 = 4
Order of operations · Understand
legend
The key on a graph that says what each colour or bar style stands for.
Data handling · Go deeper
legislature
The organ of government that makes laws.
Example: Parliament is India's Union legislature.
How government works in India · Discover
lemma
A smaller result used as a stepping stone to prove a theorem.
Example: Euclid’s lemma
Prime and composite numbers · Go deeper
lever
A rigid bar turning about a fixed point, used to move a load with an effort.
Example: Every limb bone moved by a muscle is a lever.
Anatomy of the human body · Go deeper
Libration
A small, real wobble in the Moon's orientation as seen from Earth, letting slightly more than half its surface become visible over time.
Example: Longitude libration reaches about 7.9 degrees each way.
Phases of the Moon · Extend
ligament
A band of tough tissue tying bone to bone across a joint.
Example: Ligaments inside the knee stop it sliding too far.
Anatomy of the human body · Understand
Light
A form of energy that travels, carries pictures of the world to your eyes, and needs no material to travel through.
Example: Sunlight crosses empty space to reach us.
Light · Discover
Light curve
A graph of a star's brightness over time.
Example: A transiting exoplanet shows up as a small, repeating dip in the light curve.
Eclipses · Extend
Light-year
The distance light travels in one year, used to measure vast astronomical distances.
Example: Proxima Centauri is 4.25 light-years away.
Light · ExtendNumber system · Extend
Like terms
Terms with the same letter part, which can be collected by the distributive law.
Example: 5x and 3x
Properties of numbers · Go deeper
Line
A straight path with no end points that goes on forever in both directions.
Example: Line AB, or line l
Lines, rays and line segments · Discover
Line of nodes
The straight line joining the two nodes. Eclipses need it to point roughly at the Sun.
Example: It rotates backwards once every 18.6 years.
Eclipses · Understand
Line of symmetry
A line that splits a shape into two halves that are mirror images of each other.
Shape and space · Discover
Line segment
The straight path between two points. It has two end points and a length.
Example: Segment AB, 6 cm long
Lines, rays and line segments · DiscoverShape and space · Understand
linear pair
Two adjacent angles whose outer arms form a straight line. They are supplementary.
Example: A lane meeting a straight road makes a linear pair.
Angles · Understand
linear sequence
A sequence with a constant first difference; its nth term has the form dn + c.
Example: 5, 8, 11, 14
Number and shape patterns · Go deeper
Lit fraction
The share of the Moon's visible disc that is sunlit, from 0 at new moon to 1 at full moon.
Example: At 45° elongation the lit fraction is about 0.15.
Phases of the Moon · Understand
Local noon
The moment the Sun reaches its highest point in the sky at a given place; fixes local time.
Exploration: reasons and consequences · Understand
Locus
The set of all points that satisfy a rule.
Example: The locus of points equidistant from A and B is the perpendicular bisector of AB.
Measuring and constructing angles · Go deeper
Longitude
How far east or west you are, in degrees. Much harder to measure: it needs an accurate clock.
Exploration: reasons and consequences · Discover
Longitude (meridian)
Lines running north–south on the globe, all meeting at the poles.
Example: 82°30′ E, India's standard meridian
Lines, rays and line segments · Extend
Longitudinal wave
A wave in which the particles move back and forth along the direction the wave travels. All sound is longitudinal.
Example: A slinky pushed along its length.
Sound · Understand
Loudness
How strong a sound seems to a listener, measured in decibels (dB).
Example: A whisper is 30 dB, traffic is 80 dB.
Sound · Discover
Low tide (low water)
The moment when the sea is at its lowest and stops falling.
Tides · Discover
lower limit / upper limit
The smallest and largest boundaries of a class interval; usually the lower is included and the upper excluded.
Data handling · Go deeper
lowest common multiple (LCM)
The smallest number that is a multiple of all the given numbers.
Example: LCM of 4 and 6 is 12.
Prime and composite numbers · Understand
Lucas numbers
The Fibonacci rule started from 2 and 1.
Example: 2, 1, 3, 4, 7, 11, 18
Number and shape patterns · Go deeper
Lucas–Lehmer test
A fast test for whether a Mersenne number is prime.
Prime and composite numbers · Extend
Luminescence
Giving out light without being hot.
Example: A firefly, an LED, glowing plankton.
Light · Understand
Luminous
Making its own light.
Example: The Sun, a flame, an LED, a firefly.
Light · Discover
Lunar day (tidal day)
The time Earth takes to turn back round to face the Moon: 24 h 50 min, 50 minutes longer than a clock day.
Tides · DiscoverTides · Understand
Lunar eclipse
Earth's shadow falling on the Moon, so the Moon darkens and reddens. Always at full moon.
Eclipses · DiscoverPhases of the Moon · Understand
Lunar month
One full round of the phases, about 29.5 days. Also called a synodic month.
Example: New moon to the next new moon.
Phases of the Moon · Discover
Lunisolar calendar
A calendar that keeps lunar months but periodically inserts an extra month to stay aligned with the solar year.
Example: The Hindu calendar and the Hebrew calendar are both lunisolar.
Phases of the Moon · Extend
Lymph node
A checkpoint along the lymphatic system where white blood cells inspect fluid for germs.
Example: Swells when it is busy fighting an infection nearby.
Body systems and how they connect · Go deeper
Lymphatic system
A one-way network of vessels that collects leaked plasma from body tissues, filters it through lymph nodes, and returns it to the blood.
Example: No pump of its own — muscle squeeze and one-way valves move it, like veins.
Body systems and how they connect · Go deeper
magic constant
The total of each line in a magic square; n(n² + 1) ÷ 2 for the numbers 1 to n².
Example: 34 for a 4 × 4 square
Number and shape patterns · Extend
magic square
A square grid of numbers in which every row, column and diagonal adds to the same total, the magic sum.
Example: 1 to 9 in a 3 × 3 grid: magic sum 15
Four operations · ExtendNumber and shape patterns · Extend
Magnetic north
The direction a compass needle actually points: towards Earth's wandering magnetic pole.
Exploration: reasons and consequences · Understand
majority
More than half of the votes cast, or of the total membership, depending on the rule being used.
Example: The Lok Sabha's majority is 272 of 543.
How government works in India · Understand
Map projection
A method of flattening the round Earth onto a flat map; every projection distorts something.
Example: The Mercator map
Lines, rays and line segments · Extend
margin of error
How far a real value might reasonably be from an estimate.
Example: A femur-based height estimate is usually stated with a margin of error of several centimetres, not as one exact number.
Anatomy of the human body · Investigate
Maria
The large dark smooth plains on the Moon, made of ancient hardened lava. Latin for 'seas'.
Example: The rabbit and the man in the Moon are patterns of maria.
Phases of the Moon · Understand
marrow
The soft tissue inside bones. Red marrow makes blood cells; yellow marrow stores fat.
Example: Red marrow is busiest in the breastbone, ribs, pelvis and the ends of long bones.
Anatomy of the human body · Understand
Mass
The amount of matter in an object, measured in kilograms (kg). It never changes when you travel.
Example: A 40 kg child is 40 kg on the Moon too.
Gravity · DiscoverGravity · Understand
mean
The fair share: add all the values and divide by how many there are.
Example: 3, 7, 4, 6, 5 → 25 ÷ 5 = 5.
Data handling · DiscoverHow government works in India · Investigate
Mean, median, mode, range
Four different summaries of a set of measurements: the average, the middle value, the most common value, and the spread from lowest to highest.
Example: A pulse data set with mean 77.3 bpm and range 20 bpm.
Body systems and how they connect · Investigate
measure of an angle
The size of an angle in degrees: the amount of rotation from one arm to the other.
Example: The measure of a right angle is 90°.
Angles · Understand
measurement error
The small difference between a measured value and the true value.
Example: Measuring 181° for a triangle's angle sum.
Angles · Investigate
mechanical advantage
How much a lever multiplies force (or, in exchange, gives up in speed and range).
Example: A wheelbarrow has a mechanical advantage greater than one; a fishing-rod-like third-class lever has one less than one.
Anatomy of the human body · Go deeper
Mechanical digestion
Making food pieces smaller without changing what they are.
Example: Chewing; the stomach churning; bile breaking fat into droplets.
Body systems and how they connect · Understand
medial
Towards the midline of the body.
Example: Your big toe is on the medial side of your foot.
Anatomy of the human body · Understand
median
The middle value once the data is put in order.
Example: 126, 128, 131, 132, 135, 138, 140 → 132.
Data handling · DiscoverHow government works in India · Investigate
Medium
The material a sound travels through: a gas, a liquid or a solid.
Example: Air, water, wood, steel.
Sound · DiscoverSound · Understand
Mersenne prime
A prime of the form 2ᵖ − 1.
Example: 7, 31, 127, 8,191
Prime and composite numbers · Extend
Meru Prastara
The triangle of numbers (Pascal’s triangle) described in Halāyudha’s commentary on Pingala; each number is the sum of the two above.
Example: Row 4: 1 4 6 4 1
Number and shape patterns · Go deeper
Metonic cycle
19 years, almost exactly 235 lunar months: the basis of many lunisolar calendars.
Example: 19 × 365.24 ≈ 235 × 29.53 days
HCF and LCM · Extend
Metric prefix
A word in front of a unit that multiplies it by a power of ten, such as kilo (10³) or milli (one thousandth).
Number system · Go deeper
Microgravity
The near-weightless condition of an orbiting spacecraft, where gravity's pull is not felt because the craft is continuously falling around the Earth.
Example: Astronauts on the ISS float because they, and the station, are in constant freefall.
Body systems and how they connect · ExtendGravity · DiscoverGravity · Understand
midpoint
The point that divides a line segment into two equal parts.
Measuring and constructing angles · UnderstandLines, rays and line segments · Understand
midpoint (class mark)
The middle of a class interval, (lower + upper) ÷ 2, used to estimate the mean of grouped data.
Example: (20 + 30) ÷ 2 = 25.
Data handling · Go deeper
Million
One thousand thousand, 1,000,000. Equal to ten lakh.
Number system · Discover
min / max
The smaller / larger of two numbers.
Example: min(3, 5) = 3, max(3, 5) = 5
HCF and LCM · Go deeper
minuend
In a subtraction, the number you start with and take away from.
Example: In 90 − 35 = 55, the minuend is 90.
Four operations · Understand
minute of arc (′)
One sixtieth of a degree.
Example: 28° 36′
Angles · Understand
misleading graph
A graph that gives a false impression, even from true numbers.
Data handling · Extend
mitre joint
A corner joint made by cutting two pieces at equal angles.
Example: Two 45° cuts make a 90° corner.
Angles · ExtendMeasuring and constructing angles · Extend
Mixed tide
Two highs and two lows each day, like a semidiurnal tide, but noticeably unequal in height.
Tides · Investigate
Mnemonic
A memory aid such as a word made of first letters.
Example: DMAS, BODMAS, BIDMAS, PEMDAS
Order of operations · Understand
modal class
The class interval with the highest frequency.
Data handling · Go deeper
mode
The value that appears most often.
Example: Shoe sizes 4, 5, 5, 6, 5 → mode 5.
Data handling · Discover
modular (clock) arithmetic
Arithmetic where only the remainder after dividing by a fixed number matters.
Example: 50 hours after 9 o’clock is 11 o’clock.
Number and shape patterns · Extend
Modular arithmetic
Arithmetic in which numbers wrap round after reaching a fixed number, as on a clock.
Example: 9 + 5 = 2 (mod 12)
Properties of numbers · Extend
money bill
A bill dealing only with taxation, borrowing or spending from the government's main account; the Rajya Sabha can only recommend changes to it.
Example: The annual Finance Bill is a money bill.
How government works in India · Understand
Monopoly
A situation where only one trader is allowed to buy or sell something, letting it set prices far from a competitive level.
Exploration: reasons and consequences · Understand
Monsoon
A wind that reverses direction between summer and winter, and the rains it brings. The Indian Ocean's sailing timetable.
Exploration: reasons and consequences · Discover
Mortality rate
The share of a population that died over a given period, used as the key assumption in back-projecting past populations.
Exploration: reasons and consequences · Go deeper
MRI
Magnetic resonance imaging: a strong magnet and radio waves produce detailed images of soft tissue, with no radiation.
Example: First achieved as a whole-body scan in 1977.
Body systems and how they connect · Extend
Multi-messenger astronomy
Studying one cosmic event using more than one kind of signal, such as light and gravitational waves together.
Example: Born from the 2017 neutron-star merger detection.
Gravity · Extend
multiple
A number you get by multiplying a given number by 1, 2, 3, …
Example: Multiples of 7: 7, 14, 21, 28, …
HCF and LCM · DiscoverNumber and shape patterns · DiscoverPrime and composite numbers · DiscoverProperties of numbers · Investigate
multiplicand
The number being multiplied (the size of each group).
Example: In 24 × 6, the multiplicand is 24 if we read it as 6 groups of 24.
Four operations · Understand
multiplication
Adding equal groups quickly; also 'times as many'. Sign: ×.
Example: 4 × 30 = 120 eggs in 4 trays
Four operations · Discover
Multiplicative identity
The number 1, because multiplying by 1 leaves any number unchanged.
Example: 25 × 1 = 25
Properties of numbers · DiscoverProperties of numbers · Understand
Multiplicative inverse (reciprocal)
The number that multiplies a to give 1: the reciprocal of 5 is ⅕. Zero has none.
Properties of numbers · Go deeper
multiplier
The number you multiply by (how many groups).
Example: In 24 × 6, the multiplier is 6.
Four operations · Understand
municipality
An elected body that governs a town or city.
Example: A municipal corporation runs a large city's water and rubbish collection.
How government works in India · Discover
Mutual tidal locking
The end state where both bodies in a pair always show each other the same face, as Pluto and Charon already do.
Tides · Extend
Myopia
Short-sightedness: the far point is closer than infinity; corrected with a diverging lens.
Light · Go deeper
Naked-eye astronomy
Observing the sky using only the unaided eye, no telescope or binoculars required.
Example: Every investigation in this layer can be done naked-eye.
Phases of the Moon · Investigate
Napier's bones
A set of rods, one per digit, each carrying that digit's times table in diagonal-split squares; published by John Napier in 1617.
Four operations · Extend
Natural frequency
The rate an object vibrates at when disturbed and left alone.
Example: A swing's natural frequency depends on the length of its chains.
Sound · Investigate
Natural numbers
The counting numbers 1, 2, 3, 4, … They go on for ever.
Example: You count 1, 2, 3 goats; you never count "zero goats".
Properties of numbers · DiscoverProperties of numbers · Understand
Neap tide
The smallest tides of the fortnight, at the quarter moons, when the Sun and Moon pull at right angles.
Tides · DiscoverTides · Understand
Near side
The hemisphere permanently facing Earth, dominated by dark maria.
Example: Every crater you can see from the ground is on the near side.
Phases of the Moon · Understand
Necessary / sufficient
A necessary condition must hold; a sufficient one guarantees the result. Euler’s formula is necessary but not sufficient for a polyhedron.
Shape and space · Go deeper
necessary condition
Something that must be true, but is not enough on its own.
Example: Ending in 1, 3, 7 or 9 is necessary for a prime above 5.
Prime and composite numbers · Investigate
Negative feedback
A control loop in which the response always pushes in the opposite direction to the change.
Example: Too hot → sweat; blood sugar too high → insulin.
Body systems and how they connect · Understand
neither prime nor composite
The number 1, which has only one factor.
Prime and composite numbers · Discover
Nephron
One of the roughly two million microscopic filter-and-reclaim units in your kidneys.
Example: Filter almost everything, then take back what is worth keeping.
Body systems and how they connect · Understand
Nested brackets
Brackets inside other brackets. Work from the innermost outwards.
Example: [50 − {12 + (18 − 6) ÷ 4}]
Order of operations · Understand
Net
A flat pattern that can be folded to make a solid.
Example: A cross of 6 squares folds into a cube.
Shape and space · Discover
Neuron
A nerve cell, built to send an electrical signal a long way, fast.
Example: Some run from the base of the spine to the toe.
Body systems and how they connect · Understand
Neusis
A construction that slides a marked ruler into place; not allowed by Euclid's rules.
Example: Archimedes' method for trisecting any angle.
Measuring and constructing angles · Go deeperMeasuring and constructing angles · Extend
Neutron star
The extremely dense, city-sized crushed core left behind by a massive exploding star.
Example: About 2.7 times larger than its own Schwarzschild radius.
Gravity · Extend
Never true
False for every number. Needs a reason that covers every case.
Properties of numbers · Investigate
New moon
The phase when the Moon is between Earth and the Sun and its lit side faces away.
Example: The only phase at which a solar eclipse can happen.
Eclipses · DiscoverPhases of the Moon · Discover
Newton (N)
The unit of force, named after Isaac Newton. One newton is roughly the pull on a small apple.
Example: Your weight is your mass in kg times 9.8.
Gravity · DiscoverGravity · Understand
nikhilam
A shortcut for numbers near a base such as 100: subtract a shortfall for the left part and multiply the shortfalls for the right part.
Example: 97 × 96 = 93 | 12 = 9,312
Four operations · Extend
no mode
The situation when every value appears the same number of times (for example, each once), so none is most common.
Data handling · Understand
No-go zone
The range of angles closest to the wind that no sail can make any ship sail directly into.
Exploration: reasons and consequences · Understand
Node
One of the two places where the Moon's tilted orbit crosses Earth's orbital plane.
Example: Eclipses can only happen near a node. Indian astronomy calls them Rahu and Ketu.
Eclipses · DiscoverEclipses · UnderstandPhases of the Moon · Go deeper
Node regression
The slow backward slide of the Moon's nodes around the ecliptic, completing one circuit in about 18.61 years.
Eclipses · Go deeper
Noise
Sound with no repeating pattern and no definite pitch; usually unwanted.
Example: A horn in traffic.
Sound · Discover
Non-collinear points
Points that do not all lie on one line.
Example: The corners of a triangle
Lines, rays and line segments · Understand
non-Euclidean geometry
Geometry on curved surfaces, where the parallel postulate fails and triangle angle sums are not 180°.
Example: A triangle on a globe with three 90° angles.
Angles · Go deeperLines, rays and line segments · Go deeper
Non-luminous
Making no light of its own; visible only by reflecting light from elsewhere.
Example: The Moon, this page, a rangoli.
Light · Discover
Normal
A line drawn at right angles to a surface at the point where a ray meets it. All optical angles are measured from it.
Example: A ray "at 30° to the mirror" is at 60° to the normal.
Light · Understand
nth term
The term in position n; also a formula that gives any term from its position.
Example: For 3, 6, 9, …, the nth term is 3 × n.
Number and shape patterns · Understand
Number line
A straight line with numbers marked at equal steps; bigger numbers lie further right.
Example: Adding 3 is a jump of 3 steps to the right.
Properties of numbers · Discover
Numeral
A symbol or group of symbols that stands for a number, such as 47, XLVII or the word forty-seven.
Number system · Understand
numerical data
Data made of numbers that count or measure something, so adding and averaging make sense.
Example: Heights in cm.
Data handling · Understand
Nyquist-Shannon theorem
The rule that a sampling rate must exceed twice the highest frequency to be captured faithfully.
Example: 40,000 Hz minimum for 20,000 Hz hearing.
Sound · Extend
observation
Collecting data by watching and counting; also, one single value in a data set.
Example: Counting vehicles at a signal.
Data handling · Discover
obtuse angle
An angle more than 90° and less than 180°.
Example: A reclining chair.
Angles · DiscoverMeasuring and constructing angles · Discover
Occultation
A nearer body passing in front of a more distant one and hiding or dimming it — the general case an eclipse or transit belongs to.
Example: The Moon occulting a star has a sharp edge, since it has no atmosphere to blur it.
Eclipses · Extend
Octave
A doubling of frequency, heard as the same note higher up.
Example: 110, 220, 440 and 880 Hz.
Sound · Understand
odd number
A whole number that leaves one over when split into pairs; it ends in 1, 3, 5, 7 or 9.
Example: 7, 21, 1,001
Number and shape patterns · DiscoverPrime and composite numbers · DiscoverProperties of numbers · Discover
Of
Means multiply, as in ½ of 10 = 5. In BODMAS it is done before ordinary × and ÷.
Order of operations · Understand
offset (head start)
How far apart two cycles start.
Example: FIFA World Cup is offset 2 years from the Olympics.
HCF and LCM · Extend
Opaque
Letting no light through at all.
Example: Wood, metal, cardboard, your hand.
Light · Discover
Open curve
A curve with two loose ends that do not meet.
Example: The letter C or S.
Shape and space · Discover
Operation
Something you do to numbers to get a new number. The four basic operations are addition, subtraction, multiplication and division.
Example: +, −, × and ÷ are operation signs.
Order of operations · Discover
Operator precedence
The order-of-operations table built into a programming language.
Order of operations · Extend
Opposing pair
Two muscles arranged so one bends a joint and the other straightens it, because a muscle can only pull.
Example: Biceps and triceps.
Body systems and how they connect · Investigate
Opposite rays
Two rays with the same end point pointing in opposite directions; together they form a line.
Example: Ray QP and ray QR, with Q between P and R
Lines, rays and line segments · Understand
Optical illusion
A picture that tricks the eye into a wrong judgement.
Example: Müller-Lyer arrows
Lines, rays and line segments · Investigate
Orbit
The curved path of one object round another, caused by falling sideways fast enough to keep missing.
Example: The Moon orbits the Earth in 27.3 days.
Gravity · DiscoverGravity · Understand
Orbital resonance
A simple whole-number ratio between two or more orbital periods, such as the Galilean moons' 1:2:4, which keeps orbits from settling into neat circles.
Tides · Extend
Orbital speed
The sideways speed needed for a circular orbit. Higher orbits need slower speeds.
Example: 7.91 km/s at the surface; 3.07 at geostationary.
Gravity · Understand
Order of operations
The agreed order for working out an expression: brackets, then × and ÷ from left to right, then + and − from left to right.
Order of operations · Discover
Order of rotational symmetry
How many times a shape fits onto itself during one full turn.
Shape and space · Go deeperShape and space · Extend
Organ
A structure made of several tissues, with a job of its own.
Example: The heart, the stomach, a kidney.
Body systems and how they connect · DiscoverAnatomy of the human body · Discover
organ pair
Two of the same organ, one on each side.
Example: Lungs, kidneys, eyes, ears.
Anatomy of the human body · Discover
Organ system
A group of organs sharing one big job.
Example: The digestive system: mouth, stomach, intestines, liver, pancreas.
Body systems and how they connect · DiscoverAnatomy of the human body · Discover
origami construction
Making exact shapes and angles by folding paper; it can trisect angles.
Measuring and constructing angles · Extend
Orthographic drawing
A set of flat views (plan and elevations) of a solid, lined up with each other.
Shape and space · Extend
Ossicles
The three small bones of the middle ear: malleus, incus and stapes.
Example: The stapes is the body's smallest bone.
Sound · Understand
outcome
One possible result of an experiment, such as a 4 on a die.
Data handling · Extend
outlier
A value much larger or smaller than the rest of the data.
Example: ₹400 among amounts of ₹40–₹90.
Data handling · Investigate
P wave
A fast, longitudinal earthquake wave, like sound, travelling through the solid Earth.
Example: About 6 km/s in the upper crust.
Sound · Extend
Pacemaker (artificial)
A device that generates electrical pulses to keep a heart beating on a steady rhythm.
Example: Stands in for the heart's own built-in electrical signal.
Body systems and how they connect · Extend
pairwise co-prime
A group of numbers in which every pair has HCF 1.
Example: 3, 4, 5 are pairwise co-prime; 6, 10, 15 are not.
HCF and LCM · Investigate
Palindrome
A number that reads the same forwards and backwards.
Example: 12,321
Number system · Extend
palindromic prime
A prime that reads the same forwards and backwards.
Example: 131
Prime and composite numbers · Extend
panchayat
An elected council that governs a village or a group of villages.
Example: A gram panchayat decides local repairs and water supply.
How government works in India · Discover
pandiagonal
A magic square whose broken (wrap-around) diagonals also add to the magic constant.
Example: The Khajuraho square
Number and shape patterns · Extend
Parallax
The reading error caused by looking at a scale from the side instead of straight down.
Measuring and constructing angles · Go deeperEclipses · Go deeperExploration: reasons and consequences · Extend
parallax error
A reading error caused by looking at a scale from an angle instead of straight on.
Measuring and constructing angles · UnderstandLines, rays and line segments · Understand
Parallel lines
Lines on the same plane that never meet and stay the same distance apart.
Example: Railway rails
Lines, rays and line segments · Discover
parallel lines (∥)
Lines in the same plane that never meet.
Example: The rails of a straight railway track.
Angles · Go deeper
Parallelogram
A quadrilateral with both pairs of opposite sides parallel.
Shape and space · Understand
Paraphrase
A retelling of an account in different words, keeping its general meaning. Not the same as a direct quotation.
Exploration: reasons and consequences · Investigate
Parentheses
Round brackets ( ). Also called small brackets.
Order of operations · Understand
Parity
Whether a whole number is even or odd.
Example: 17 has odd parity.
Properties of numbers · Understand
Parliament
India's Union legislature: the Lok Sabha, the Rajya Sabha and the President together.
Example: A bill must pass both Houses.
How government works in India · Discover
parliamentary system
A system where the head of government is chosen by, and answerable to, the legislature's confidence.
Example: India and the UK both use parliamentary systems.
How government works in India · Extend
Partial eclipse
Only part of the Sun or Moon is covered.
Example: A crescent Sun projected onto paper is the safe way to see one.
Eclipses · Discover
partial product
In long multiplication, the product of the multiplicand with one digit of the multiplier, shifted to that digit's place.
Example: In 46 × 23, the partial products are 46 × 3 = 138 and 46 × 20 = 920.
Four operations · UnderstandFour operations · Go deeper
Path of totality
The narrow track on Earth's surface where a total solar eclipse's umbra actually lands.
Example: About 160 km wide and roughly 0.31% of Earth's whole surface.
Eclipses · Investigate
pattern
An arrangement of shapes, colours, sounds or numbers that repeats or changes in a regular way.
Example: green, gold, green, gold, …
Number and shape patterns · Discover
peak bone mass
The greatest density a person’s bones reach in a lifetime, typically in the twenties.
Example: Weight-bearing activity in childhood and the teenage years contributes to a higher peak.
Anatomy of the human body · Go deeper
pentagram
A five-pointed star drawn with five straight lines.
Example: Its tip angles add to 180°.
Angles · Extend
Penumbra
The grey outer part of a shadow, where part of the light source is still visible.
Example: Stand in the Moon's penumbra and you see a partial eclipse.
Eclipses · DiscoverLight · Understand
percentage point
The plain arithmetic difference between two percentages.
Example: A rise from 40% to 50% turnout is 10 percentage points.
How government works in India · Investigate
perfect cube
A whole number multiplied by itself three times.
Example: 1,728 = 12³
Prime and composite numbers · Go deeper
perfect number
A number equal to the sum of its proper factors.
Example: 6 = 1 + 2 + 3
Prime and composite numbers · ExtendProperties of numbers · Extend
perfect square
A number that is a whole number multiplied by itself. All powers in its factorisation are even.
Example: 3,600 = 2⁴ × 3² × 5²
Prime and composite numbers · Go deeper
Perigee
The Moon's closest point to Earth, about 363,300 km.
Example: Eclipses near perigee are total and long.
Eclipses · UnderstandGravity · Investigate
Perigee / apogee
The closest and farthest points of an orbit around the Earth.
Example: Speed is highest at perigee, lowest at apogee.
Gravity · Go deeper
Perihelion / aphelion
The closest and farthest points of an orbit around the Sun — the same idea as perigee/apogee, for a different centre.
Example: A comet moves fastest at perihelion.
Gravity · Go deeper
Perihelion precession
The slow rotation, over time, of an orbit’s closest point to the Sun.
Example: Mercury’s leftover 43″/century, explained by general relativity.
Gravity · Extend
Perimeter
The total length of the boundary of a closed figure.
Shape and space · Understand
Period
A group of places separated by a comma: ones, thousands, lakhs, crores (Indian) or ones, thousands, millions, billions (International).
Number system · DiscoverNumber system · Understand
Period (of a pendulum)
The time for one complete swing, out and back.
Example: A 1 m pendulum on Earth: about 2.01 s.
Gravity · Investigate
periodical cicada
An insect that emerges in huge numbers every 13 or 17 years.
Prime and composite numbers · Extend
Peristalsis
The wave of muscle squeezing that pushes food along the gut. It works even if you are upside down.
Example: Why an astronaut can swallow in orbit.
Body systems and how they connect · Discover
Permanently shadowed crater
A polar crater deep enough that its floor never receives direct sunlight, because of the Moon's very small axial tilt.
Example: These cold traps are the leading candidate sites for lunar water ice.
Phases of the Moon · Extend
perpendicular
Meeting at a right angle (90°).
Example: The sides of a page are perpendicular.
Measuring and constructing angles · Understand
perpendicular (⊥)
Meeting at a right angle.
Example: The sides of a square are perpendicular.
Angles · Understand
perpendicular bisector
The line that passes through the midpoint of a segment at 90° to it.
Measuring and constructing angles · UnderstandLines, rays and line segments · UnderstandShape and space · Go deeper
Perpendicular lines
Lines that meet at a right angle (90°).
Example: The strokes of a plus sign
Lines, rays and line segments · Discover
personal data
Information that can identify a person, such as name, address, phone number or ID number.
Data handling · Extend
Perspective
A way of drawing that makes a flat picture look deep, by making distant things smaller.
Example: Railway tracks meeting at the horizon
Lines, rays and line segments · Extend
Phase
How much of the Moon's sunlit half is facing Earth right now. Not a shape the Moon takes, but a view we get.
Example: "Tonight's phase is waxing gibbous."
Phases of the Moon · Discover
Phase lag
The delay between a rhythmic push and a system's peak response, seen in a pushed swing and in an ocean basin driven by the Moon and Sun alike.
Tides · Go deeper
Photoelectric effect
Light knocking electrons out of a metal, only above a minimum frequency — evidence for light's particle nature.
Example: Explained by Einstein in 1905.
Light · Extend
Photon
A discrete packet of light energy, with energy E = h × f.
Example: A green laser emits billions of billions of photons every second.
Light · Extend
Photoplethysmography
Estimating pulse by shining light into the skin and measuring how the reflected light dims slightly with each heartbeat.
Example: How most wrist-worn fitness bands measure heart rate.
Body systems and how they connect · Extend
Pi (π)
The ratio circumference ÷ diameter, the same for every circle: about 3.14159.
Shape and space · Investigate
pictograph
A chart that uses repeated symbols to show numbers; a key says what one symbol stands for.
Data handling · Discover
pie chart
A circle divided into sectors whose angles show each part as a fraction of a whole.
Data handling · Extend
Pinhole camera
A dark box where light rays through a small hole form an upside-down image.
Example: Viewing a window on tracing paper
Lines, rays and line segments · Extend
Pitch
How high or low a sound seems. Higher frequency means higher pitch.
Example: A mosquito is high, a dhol is low.
Sound · Discover
Place
A position in a number, such as ones, tens or hundreds. Each place is worth ten times the place to its right.
Example: In 472, the 4 is in the hundreds place.
Number system · Discover
Place value
What a digit is worth because of its place: the digit times the value of the place.
Example: In 472 the place value of 4 is 400.
Number system · Discover
Place-value system
A way of writing numbers in which a digit's value depends on its position. Ours is a base-ten place-value system.
Number system · Understand
Placeholder
A zero that keeps other digits in their correct places.
Example: The 0 in 408.
Number system · Discover
Plan / elevation
An architect’s top view / front or side view of a building.
Shape and space · Understand
Plane
A perfectly flat surface that goes on forever in every direction.
Example: A table top is a small piece of a plane
Lines, rays and line segments · Discover
Plasma
The straw-coloured liquid part of blood, about 55% of it, mostly water.
Example: Glucose, urea, hormones and most carbon dioxide travel dissolved here.
Body systems and how they connect · Understand
Platonic solid
A convex polyhedron whose faces are identical regular polygons, with the same number meeting at every vertex. There are exactly five.
Shape and space · Extend
Playfair's axiom
Through a point not on a line there is exactly one parallel to it.
Example: The modern parallel postulate
Lines, rays and line segments · Go deeper
pocket veto
Effectively killing a bill by taking no action on it at all, rather than formally rejecting it.
Example: India's Constitution sets no explicit deadline for a first decision, making this a genuine grey area.
How government works in India · Go deeper
Point
An exact position. It has no size. Named with a capital letter.
Example: Point A
Lines, rays and line segments · Discover
Point of concurrence
The common point of concurrent lines.
Example: The hub of the wheel
Lines, rays and line segments · Understand
Point of intersection
The single point where two lines cross.
Example: The screw of a pair of scissors
Lines, rays and line segments · Discover
Point source
A light source small enough that its rays fan out from one spot, giving shadows with sharp edges.
Example: A bare, tiny bulb or a distant torch behaves like one.
Eclipses · Investigate
Polygon
A simple closed figure made only of straight line segments.
Example: Triangle, square, hexagon.
Shape and space · Discover
Polyhedron
A solid whose faces are all flat polygons.
Example: Cube, prism, pyramid.
Shape and space · Understand
polyrhythm
Two or more different beat cycles played at the same time.
Example: 3 against 2 repeats every 6 pulses.
HCF and LCM · Extend
Portolan chart
An early navigational chart built from compass bearings and rough distances logged between ports.
Exploration: reasons and consequences · Understand
position (term number)
Where a term sits in the sequence: 1st, 2nd, 3rd, …; often called n.
Example: In 3, 6, 9, 12 the term 12 is in position 4.
Number and shape patterns · Understand
position-to-term rule
A rule that gets a term directly from its position.
Example: “Multiply the position by 5, then subtract 2.”
Number and shape patterns · Understand
posterior
Towards the back of the body.
Example: Your spine is posterior.
Anatomy of the human body · DiscoverAnatomy of the human body · Understand
Postulate (axiom)
A starting statement accepted without proof.
Example: Two points fix exactly one line
Lines, rays and line segments · Go deeper
power / index
A number multiplied by itself; the index says how many times.
Example: 2⁵ = 32
Number and shape patterns · Go deeper
power / index / exponent
The small raised number saying how many times a factor is repeated.
Example: In 2³ the index is 3: 2 × 2 × 2.
HCF and LCM · UnderstandOrder of operations · Go deeper
power of 2
A number made by multiplying 2 by itself some number of times.
Example: 2, 4, 8, 16, 32, 64
Number and shape patterns · Investigate
Power of ten
A number made by multiplying 10 by itself; written 10ⁿ, where n is the exponent.
Example: 10⁴ = 10,000
Number system · Go deeper
Preamble
The opening sentence of the Constitution, which states who the power belongs to and what kind of country it is building.
Example: It begins 'WE, THE PEOPLE OF INDIA'.
How government works in India · Discover
Precedence
How strongly an operation binds, i.e. which level it belongs to. × and ÷ have higher precedence than + and −.
Order of operations · Understand
Predecessor
The number just before a number: subtract 1.
Example: The predecessor of 1,000 is 999.
Number system · DiscoverProperties of numbers · Discover
prediction
What you expect to observe if your hypothesis is correct.
Example: If the hypothesis about tubes is right, the paper tube should hold more books.
Anatomy of the human body · InvestigateNumber system · Investigate
Prefix (Polish) notation
Writing the operation before its numbers, as in + 2 3.
Order of operations · Extend
presidential system
A system where the head of government is elected separately from the legislature and is not simply removable by losing its confidence.
Example: The USA uses a presidential system.
How government works in India · Extend
primality test
A method for deciding whether a number is prime.
Example: Trial division; AKS
Prime and composite numbers · Go deeper
primary data
Data you collect yourself for your own question.
Data handling · Understand
Primary source
Evidence made at the time by someone involved: a log, a letter, a customs record, an object.
Exploration: reasons and consequences · Investigate
prime desert
A long run of consecutive composite numbers.
Example: 90 to 96
Prime and composite numbers · Investigate
prime factor
A factor of a number that is itself prime.
Example: The prime factors of 12 are 2 and 3.
HCF and LCM · Understand
prime factorisation
Writing a number as a product of primes only.
Example: 60 = 2 × 2 × 3 × 5
HCF and LCM · UnderstandPrime and composite numbers · Understand
prime gap
The difference between a prime and the next prime.
Example: The gap after 89 is 8.
Prime and composite numbers · Investigate
prime number
A whole number greater than 1 with exactly two factors: 1 and itself.
Example: 2, 3, 5, 7, 11, 13, …
HCF and LCM · UnderstandPrime and composite numbers · Discover
prime triplet
Here: three primes each 2 apart. The only example is 3, 5, 7.
Prime and composite numbers · Understand
Principle of permanence
The idea that new kinds of numbers should keep the old properties where possible.
Properties of numbers · Extend
Prism
A block of glass, usually triangular, that splits white light into its colours.
Example: A prism in a sunbeam paints a spectrum.
Light · DiscoverShape and space · Understand
probability
A number from 0 (impossible) to 1 (certain) measuring how likely something is.
Example: P(heads) = ½.
Data handling · Extend
product
The answer to a multiplication.
Example: The product of 6 and 8 is 48.
Four operations · DiscoverFour operations · Understand
Projection
Forming an image of a light source without looking at it directly, by letting its light fall on a screen.
Example: A pinhole, a colander, and gaps between leaves all work by projection.
Eclipses · Investigate
Projective geometry
Geometry with extra points at infinity, in which any two lines meet.
Example: Used in cameras and computer graphics
Lines, rays and line segments · Extend
proof
A chain of statements, each justified by a definition, axiom, given fact or earlier result, that shows something must be true.
Example: The proof that vertically opposite angles are equal.
Angles · Go deeperHCF and LCM · Go deeperNumber and shape patterns · Go deeperPrime and composite numbers · Investigate
Proof by contradiction
Assume the opposite of what you want, and show it leads to something impossible.
Example: Assuming two lines share two points
Lines, rays and line segments · Go deeperPrime and composite numbers · Go deeperProperties of numbers · Go deeper
proper factor
A factor of a number other than the number itself.
Example: Proper factors of 10: 1, 2, 5.
Prime and composite numbers · Understand
Property
A rule that is true for every number of a certain kind, not just for one example.
Example: For any two numbers, a + b = b + a.
Properties of numbers · Discover
proportional
Two quantities are proportional if doubling (tripling…) one doubles (triples…) the other.
Example: Cost of rice and its weight
Four operations · Go deeper
prosody (chandaḥśāstra)
The study of the rhythm and metre of poetry; Indian prosody led to early discoveries about patterns.
Example: Short and long syllables
Number and shape patterns · Go deeper
protractor
A half-circle (or full-circle) tool marked in degrees, used to measure and draw angles.
Measuring and constructing angles · Discover
prove
To give a reason that shows a statement must be true in every case.
Example: The L-shape picture proves 1 + 3 + … + (2n − 1) = n².
Number and shape patterns · Investigate
public interest litigation (PIL)
A case brought on behalf of people who cannot easily reach a court themselves, allowed since the late 1970s.
Example: PILs have been used to help undertrial prisoners and bonded labourers.
How government works in India · Understand
public-key cryptography
A system where anyone can lock a message with a public key but only the owner of a secret key can unlock it.
Example: RSA
Prime and composite numbers · Extend
Pulmonary circuit
The short loop: heart → lungs → heart.
Example: Where blood picks up oxygen.
Body systems and how they connect · Understand
Pyramid
A polyhedron with a polygon base and triangular faces meeting at one apex.
Shape and space · Understand
Q value
A number describing how sharply and strongly a resonator responds; the Bay of Fundy–Gulf of Maine system has a Q of roughly 5.
Example: A high-Q system rings on for a long time once excited; a low-Q one damps out quickly.
Tides · Go deeper
quadratic sequence
A sequence with a constant second difference; its nth term has n² in it.
Example: 2, 5, 10, 17 (n² + 1)
Number and shape patterns · Go deeper
quadrilateral
A polygon with four sides; its angles add to 360°.
Example: A kite, a trapezium.
Angles · Go deeperShape and space · Discover
quarter turn
One quarter of a full turn: 90°.
Example: Turning from facing north to facing east.
Angles · Discover
quartiles
The values that cut ordered data into four equal parts; the lower and upper quartiles are the medians of the two halves.
Data handling · Go deeper
Quasicrystal
A structure that is ordered but never exactly repeats, and can have 5-fold symmetry.
Shape and space · Extend
questionnaire
A written set of questions for people to answer, often with boxes to tick.
Data handling · Discover
quotient
The answer to a division (how many in each share, or how many groups).
Example: In 36 ÷ 6 = 6, the quotient is 6.
Four operations · DiscoverFour operations · UnderstandOrder of operations · Extend
radian
The angle at the centre of a circle made by an arc as long as the radius. 1 radian ≈ 57.3°.
Example: 180° = π radians
Angles · Extend
radius
The distance from the centre of a circle to its edge; for a compass, the gap between the point and the pencil.
Measuring and constructing angles · UnderstandShape and space · Discover
range
The difference between the largest and smallest values; it measures spread.
Example: 140 − 126 = 14 cm.
Data handling · DiscoverHow government works in India · Investigate
Range (statistics)
The difference between the highest and lowest value in a dataset; a quick measure of how spread out it is.
Example: The 1492 population estimates have a range of over 100 million.
Exploration: reasons and consequences · Investigate
Rarefaction
A region where the particles are spread out and the pressure is below normal.
Example: The stretched coils between the bunches.
Sound · Understand
rate
A quantity per one unit of something else, found by dividing.
Example: 4,500 kg per hectare
Four operations · Go deeper
Ratify
For a country to formally approve and agree to be bound by a treaty it has signed.
Exploration: reasons and consequences · Extend
ratio
A term divided by the term before it.
Example: In 3, 12, 48, the ratio is 4.
Number and shape patterns · Understand
Rational numbers
Numbers that can be written as a fraction p/q of integers with q ≠ 0.
Example: ¾, −2, 7/3
Properties of numbers · Extend
raw data
Data exactly as collected, before it is sorted or counted.
Data handling · Discover
ray
A straight path that starts at a point and goes on forever in one direction.
Example: A beam of light from a torch.
Angles · DiscoverLight · DiscoverLines, rays and line segments · Discover
Ray tracing
A computer graphics method that follows rays of light to colour each pixel.
Example: Realistic reflections in games
Lines, rays and line segments · Extend
Rayleigh scattering
Scattering of light by particles much smaller than its wavelength, with intensity proportional to 1 ÷ wavelength⁴.
Example: Explains the blue sky and red sunsets.
Light · Go deeper
Real image
An image made where light rays actually meet, which can be caught on a screen.
Example: The picture inside a pinhole camera.
Light · Understand
Reciprocal
The number that multiplies to give 1. Dividing by a number is multiplying by its reciprocal.
Example: The reciprocal of 4 is ¼.
Order of operations · Go deeperProperties of numbers · Investigate
Rectangle
A quadrilateral with four right angles.
Shape and space · Understand
rectangular number
A number of dots that makes an n by (n + 1) rectangle; twice a triangular number.
Example: 2, 6, 12, 20, 30
Number and shape patterns · Investigate
Redshift / blueshift
Light's Doppler effect: shifted towards red when a source recedes, towards blue when it approaches.
Example: Evidence that most distant galaxies are moving away from Earth.
Sound · Extend
Reflection
Light bouncing off a surface instead of passing into it.
Example: Your face in a mirror.
Light · Discover
Reflex
An automatic response decided in the spinal cord, before the brain is involved.
Example: The knee jerk; pulling your hand off something hot.
Body systems and how they connect · Discover
reflex angle
An angle more than 180° and less than 360°.
Example: The body of Pac-Man.
Angles · DiscoverMeasuring and constructing angles · DiscoverMeasuring and constructing angles · Understand
Refraction
The bending of light as it passes into a denser or thinner material, such as air.
Example: Refraction is what curls sunlight into Earth's shadow.
Eclipses · UnderstandLight · DiscoverLight · Understand
Refractive index
The speed of light in vacuum divided by its speed in the material. Bigger means slower and more bending.
Example: Water 1.33, glass 1.5, diamond 2.42.
Light · Understand
regeneration
The regrowth of lost or damaged body parts.
Example: A starfish regrowing a lost arm; a human liver regrowing much of its own lost tissue.
Anatomy of the human body · Extend
regrouping
Exchanging 10 of one place for 1 of the next place up (carrying), or 1 for 10 of the place below (borrowing).
Example: 12 ones are regrouped as 1 ten and 2 ones.
Four operations · UnderstandFour operations · Go deeper
regular polygon
A shape with all sides equal and all angles equal.
Example: A square; an equilateral triangle.
Angles · InvestigateMeasuring and constructing angles · ExtendShape and space · Discover
Regular reflection
Reflection from a smooth surface: parallel rays stay parallel, so you get an image.
Example: Mirror, still water, polished steel.
Light · Understand
relative frequency
How often something happened in an experiment divided by the number of trials; an estimate of probability.
Example: 103 heads in 200 tosses → 0.515.
Data handling · Extend
relatively prime
Another name for co-prime: having HCF 1.
Example: 9 and 20
Prime and composite numbers · Understand
Reliable
Giving nearly the same answer each time it is repeated.
Example: Divider readings in the trial
Lines, rays and line segments · Investigate
remainder
What is left over when a number cannot be divided exactly. It is always smaller than the divisor.
Example: 23 ÷ 5 = 4 remainder 3
Four operations · DiscoverFour operations · UnderstandHCF and LCM · DiscoverHCF and LCM · Investigate
remainder class
All the numbers that leave the same remainder when divided by a given number.
Example: Remainder 1 on dividing by 3: 1, 4, 7, 10, …
Prime and composite numbers · Investigate
Repeated addition
Multiplication as adding equal groups: 3 × 4 = 4 + 4 + 4.
Order of operations · Go deeper
repeating pattern
A pattern in which the same group of items comes round again and again.
Example: clap, clap, stamp, clap, clap, stamp
Number and shape patterns · Discover
repeating unit
The smallest group of items that repeats in a repeating pattern (sometimes called the core).
Example: In red, red, blue, red, red, blue, the unit is red, red, blue.
Number and shape patterns · Discover
republic
A country whose head of state is elected rather than born into the job.
Example: India's head of state is the President.
How government works in India · Discover
repunit
A number made only of the digit 1.
Example: 1,111
Prime and composite numbers · Investigate
required run rate
Runs still needed divided by overs remaining.
Example: 78 runs in 8 overs = 9.75
Four operations · Extend
resistant (robust)
Hardly affected by outliers. The median is resistant.
Data handling · Investigate
Resolution (of an echo system)
The smallest detail a sonar or ultrasound system can distinguish, tied to its wavelength.
Example: A higher frequency gives finer resolution.
Sound · Go deeper
Resonance
A large vibration built up by repeated small pushes at (or near) an object's natural frequency.
Example: A pushed swing climbing higher and higher.
Sound · InvestigateTides · UnderstandTides · Investigate
Retroreflector
A mirror device that reflects light straight back the way it came, regardless of the incoming angle.
Example: Apollo astronauts left retroreflector arrays that are still used for laser ranging today.
Phases of the Moon · Go deeperTides · Extend
Reverberation
The lingering, blurred tail of sound in a room caused by many overlapping reflections.
Example: A clap in an empty hall.
Sound · Investigate
Reverberation time (RT60)
How many seconds sound takes to fade by 60 decibels after the source stops.
Example: A bare classroom: about 0.8 s.
Sound · Investigate
Reverse Polish Notation (RPN)
Postfix notation: operations come after their two numbers. Needs no brackets.
Example: 2 3 4 × + means 2 + 3 × 4
Order of operations · Go deeper
Rhombus
A four-sided shape with four equal sides; its diagonals bisect each other at right angles.
Example: APBQ when the same radius is used above and below AB.
Measuring and constructing angles · Go deeperShape and space · Understand
RHS
Right angle, hypotenuse and one other side: fixes a unique right triangle.
Measuring and constructing angles · Extend
right angle
An angle of exactly 90°, a square corner. Marked with a small square.
Example: The corner of a page.
Angles · DiscoverMeasuring and constructing angles · DiscoverLines, rays and line segments · Discover
Roman numerals
An ancient number system using letters (I, V, X, L, C, D, M) without place value or zero, which makes written calculation hard.
Example: CXXIII + XLVIII = CLXXI
Four operations · ExtendNumber system · Discover
rotational symmetry
Looking the same after a turn of less than a full turn; the order is how many times in one full turn.
Example: An 8-petal rangoli has order 8.
Number and shape patterns · ExtendShape and space · Investigate
round
Replace a number by a nearby friendly number, such as the nearest ten.
Example: 47 rounds to 50; 42 rounds to 40.
Four operations · Discover
Round half to even
A rounding convention in which exact halves round to the even neighbour.
Example: 45 → 40, 55 → 60
Number system · Go deeper
Rounding
Replacing a number with a nearby simpler number, such as the nearest ten or hundred.
Example: 47 rounds to 50.
Number system · Discover
Rounding band
The set of all numbers that round to the same value.
Example: 450 to 549 round to 500
Number system · Investigate
Royal charter
A legal grant from a state giving a company exclusive trading rights, and often the power to fortify, arm and make treaties.
Exploration: reasons and consequences · Understand
RSA
A public-key method (1977) whose security rests on how hard it is to factorise the product of two huge primes.
Prime and composite numbers · Extend
rule
The instruction that tells you how a pattern continues.
Example: “Start at 3 and add 3 each time.”
Number and shape patterns · Discover
rule of three (trairāśika)
The ancient Indian method: from three known quantities in proportion, find the fourth.
Example: 36 × 70 ÷ 45 = 56
Four operations · Go deeper
Rule of twelfths
A sailor's estimate: in six hours the tide rises 1, 2, 3, 3, 2 and 1 twelfths of its range.
Tides · Understand
run rate
In cricket, runs scored divided by overs bowled.
Example: 94 runs in 12 overs ≈ 7.83
Four operations · Extend
running total
The total so far as you add terms one by one.
Example: Running totals of 1, 3, 5, 7 are 1, 4, 9, 16.
Number and shape patterns · Investigate
Rutter
Written sailing directions: bearings, distances, landmarks, hazards and timing notes for a route.
Exploration: reasons and consequences · Understand
S wave
A slower, transverse earthquake wave, more like a shaken rope.
Example: About 3.5 km/s in the upper crust.
Sound · Extend
Sabin
The unit of sound absorption, roughly one square metre of open window, named after Wallace Sabine.
Example: One theatre cushion absorbs about 0.7 sabins.
Sound · Go deeper
sample
A part of a population chosen to represent the whole in a survey.
Data handling · Extend
sample size
How many people, objects or measurements a test is based on.
Example: A class of fifteen pupils is a small sample; a real forensic study uses thousands of skeletons.
Anatomy of the human body · Investigate
Sampling
Measuring an audio signal's height at many evenly spaced instants and storing each as a number.
Example: CD audio samples 44,100 times a second.
Sound · Extend
Sampling rate
How many samples are taken every second, in hertz.
Example: 44,100 Hz for CD-quality audio.
Sound · Extend
Saros
A period of about 6,585.32 days (≈18 years 11⅓ days) after which similar eclipses recur.
Example: Named from a Babylonian-era word, though the astronomical use of the term is more recent.
Eclipses · Go deeperPhases of the Moon · Go deeper
SAS
Two sides and the included angle (the angle between them): fixes a unique triangle.
Measuring and constructing angles · Extend
SAS rule
If two sides and the angle between them match, the triangles are congruent.
Example: Used in the kite proof of the perpendicular bisector.
Measuring and constructing angles · Go deeper
scale
How much one unit on a graph (such as one square) stands for.
Example: 1 square = 10 mangoes.
Data handling · Discover
scale (a pair)
Multiply both numbers by the same whole number.
Example: Scaling 4 and 6 by 10 gives 40 and 60.
HCF and LCM · Investigate
Scale model
A model where every real distance and size is shrunk by the same factor.
Example: A 2 cm Moon-ball needs a 7.3 cm Earth-ball 221 cm away to stay to scale.
Eclipses · Investigate
Scalene triangle
A triangle with no two sides equal.
Shape and space · Understand
Screen
Any surface a shadow or an image falls on — a wall, the floor, a sheet of cloth.
Example: The cloth in a shadow-puppet show.
Light · Discover
seat share
The percentage of a legislature's seats a party has won.
Example: Party A's seat share was 100.0% despite a lower vote share.
How government works in India · Investigate
second difference
The difference between neighbouring first differences.
Example: For 1, 4, 9, 16 it is always 2.
Number and shape patterns · Go deeper
secondary data
Data collected by someone else that you reuse.
Example: IMD rainfall records.
Data handling · Understand
sector
A slice of a circle between two radii; one part in a pie chart.
Data handling · ExtendShape and space · Understand
Semi-regular tiling
A tiling by two or more kinds of regular polygon with the same arrangement at every vertex. There are 8.
Shape and space · Extend
Semidiurnal tide
A tide with two highs and two lows a day of similar size — the pattern on almost all of India's coast.
Tides · UnderstandTides · Investigate
sensitive
Strongly affected by extreme values. The mean and the range are sensitive.
Data handling · Investigate
sequence
A list of numbers or things in a definite order, usually following a rule.
Example: 1, 4, 9, 16, …
Number and shape patterns · DiscoverNumber and shape patterns · Understand
sesamoid bone
A small, rounded bone embedded inside a tendon.
Example: The kneecap is the largest sesamoid bone in the body.
Anatomy of the human body · Go deeper
Set point
The value a control system is currently trying to hold — usually fixed, but reset upward on purpose during a fever.
Example: Body temperature's normal set point is about 37 °C.
Body systems and how they connect · Investigate
set square
A triangle-shaped tool with fixed angles: 45°–45°–90° or 30°–60°–90°.
Measuring and constructing angles · Discover
Set-square combination
An angle made by placing set-square corners side by side (adding) or overlapping (subtracting).
Example: 30° + 45° = 75°.
Measuring and constructing angles · Investigate
sexagesimal
Counting in base 60, as the Babylonians did.
Example: 60 minutes in a degree.
Angles · Go deeper
Shadow
The dark patch on a screen where an opaque object stopped the light from reaching.
Example: Your shadow on the ground at noon.
Light · Discover
sharing
Division where you know the number of groups and want the size of each share.
Example: 18 chocolates among 3 children
Four operations · Discover
short division
Long division written compactly, carrying each remainder to the next digit mentally.
Example: 9,875 ÷ 7 = 1,410 r 5
Four operations · Go deeper
Short scale / long scale
Two meanings of billion: 10⁹ (short scale, modern English) or 10¹² (long scale, older British and many European languages).
Number system · Extend
shrinking pattern
A pattern in which each step gets smaller by a rule.
Example: 50, 45, 40, 35, …
Number and shape patterns · Discover
Shunya
Sanskrit for empty or void, the Indian name for zero.
Number system · Go deeper
Side
One of the straight line segments that make up a polygon.
Shape and space · Discover
Sidereal month
One orbit measured against the distant stars: 27.32 days. Shorter than the synodic month.
Example: Also the Moon's rotation period, which is why we see one face.
Phases of the Moon · UnderstandPhases of the Moon · Go deeper
Sieve of Eratosthenes
A way to find all primes up to a number by crossing out the multiples of each prime in turn.
Prime and composite numbers · Discover
Signal delay
How long a radio or light signal takes to travel a distance; also called light-time.
Example: Voyager 1's one-way signal delay is about 23 hours.
Exploration: reasons and consequences · Extend
Simple closed curve
A curve that ends where it starts and never crosses itself.
Shape and space · Understand
Simplify
Work an expression out step by step until only one number is left.
Example: 6 + 8 ÷ 2 simplifies to 10.
Order of operations · DiscoverOrder of operations · Understand
Singularity
The point predicted at a black hole’s centre where general relativity’s equations give an infinite result.
Example: Considered a sign the theory is incomplete there, not a literal infinity.
Gravity · Extend
Skew lines
Lines in space that never meet and are not parallel, because they do not lie in one plane.
Example: A wall-ceiling edge and a floor edge on another wall
Lines, rays and line segments · UnderstandLines, rays and line segments · Extend
skewed
Lopsided: a few very large (or very small) values stretch the data to one side, pulling the mean away from the median.
Example: Monthly rainfall in Mumbai.
Data handling · Investigate
skip counting
Counting forwards or backwards in equal steps other than 1.
Example: Counting in 5s: 5, 10, 15, 20
Number and shape patterns · Discover
Slack water
The short, quiet pause at the top and the bottom of a tide, when the water hardly flows.
Tides · Discover
Solar eclipse
The Moon's shadow falling on Earth, so the Sun is hidden. Always at new moon.
Eclipses · Discover
Solar parallax
The Sun's own tiny parallax, about 8.78 arcseconds — historically one of astronomy's hardest numbers to measure.
Eclipses · Go deeper
Solar retinopathy
Damage to the retina caused by looking at the Sun. Painless, and often permanent.
Eclipses · Understand
Sometimes true
True for some numbers and false for others. Show one example of each.
Properties of numbers · Investigate
Sonar
SOund Navigation And Ranging: finding distance underwater by timing an echo.
Example: A fishing boat's depth sounder.
Sound · Investigate
Sonic boom
The single strong crack heard when a source moves faster than sound, breaking the ordinary Doppler picture.
Example: The sound of a supersonic aircraft passing overhead.
Sound · Extend
Source
The thing that is vibrating and making the sound.
Example: The skin of a tabla.
Sound · Discover
Sovereignty
A country's authority to govern a place and make its own laws there.
Exploration: reasons and consequences · Extend
Spacetime
The combination of three dimensions of space and one of time into a single four-dimensional fabric.
Example: Mass curves spacetime; objects follow the curve.
Gravity · Extend
special majority
A vote requiring both two-thirds of members present and voting, and more than half of the total membership.
Example: Most Constitution amendments need a special majority.
How government works in India · Go deeper
Spectrum
The band of colours that white light separates into.
Example: Red, orange, yellow, green, blue, indigo, violet.
Light · DiscoverLight · Understand
Speed of light
About 300,000 kilometres every second in empty space — the fastest anything can go.
Example: Sunlight takes 8 minutes 20 seconds to reach us.
Light · Discover
spread
How far apart the values of a data set are; the range is one measure of spread.
Data handling · Understand
Spring tide
The biggest tides of the fortnight, at new moon and full moon, when the Sun and Moon pull in line.
Example: Nothing to do with the season.
Tides · DiscoverTides · Understand
Square
A quadrilateral with four equal sides and four right angles.
Shape and space · Understand
Square brackets
Box brackets [ ], often used outside round and curly brackets.
Example: [20 − (3 + 5)] ÷ 4 = 3
Order of operations · Understand
square number
The number of dots in a square array; a number multiplied by itself.
Example: 5 × 5 = 25
Number and shape patterns · DiscoverNumber and shape patterns · UnderstandProperties of numbers · Investigate
square root
The number that, multiplied by itself, gives the original number. Written √.
Example: √49 = 7
Prime and composite numbers · Understand
SSS
Three sides known: fixes a unique triangle (if the triangle inequality holds).
Example: 5 cm, 6 cm, 7 cm
Measuring and constructing angles · Extend
SSS rule
If all three sides of one triangle equal the three sides of another, the triangles are congruent.
Example: Used to prove the angle bisector and the copy-angle constructions.
Measuring and constructing angles · Go deeper
Stack
A pile where you can only add or take from the top. Used to evaluate RPN.
Order of operations · Go deeper
Standard form
A number written in the usual way with digits (and commas), such as 7,04,396.
Number system · Understand
Statio Shiv Shakti
The name given to Chandrayaan-3's Vikram lander touchdown site near the lunar south pole.
Example: Named after the 2023 landing that made India the first country to land so close to the pole.
Phases of the Moon · Extend
statistics
The science of collecting, organising, summarising and interpreting data; the word comes from "state".
Data handling · Go deeper
Steady-state resonance
The balance point where energy added by resonance each cycle equals energy lost to damping.
Example: A pushed swing settling at a maximum height.
Sound · Go deeper
Sternpost rudder
A steering blade hinged on the ship's centreline at the stern, replacing a side-mounted steering oar.
Exploration: reasons and consequences · Understand
Stethoscope
A simple instrument that channels chest sounds to a listener's ear, invented by Laennec in 1816.
Example: Still built on the same basic idea over two centuries later.
Body systems and how they connect · Extend
Stiffness
How strongly a material resists being squashed and how fast it springs back. More stiffness means faster sound.
Example: Steel is very stiff.
Sound · Understand
Storm surge
A rise in sea level caused by a cyclone's low pressure and onshore wind, added on top of whatever the ordinary tide is doing.
Example: The 1999 Odisha Super Cyclone's surge was about 6–7 m.
Tides · Investigate
straight angle
An angle of exactly 180°: the arms make a straight line.
Example: Clock hands at 6:00.
Angles · DiscoverMeasuring and constructing angles · Discover
straightedge
A ruler used only to draw straight lines, not to measure.
Measuring and constructing angles · UnderstandMeasuring and constructing angles · Go deeper
Sub-lunar point
The spot on Earth directly under the Moon at a given moment; the near bulge is centred there.
Tides · Understand
Submersible
A small underwater vehicle, crewed or uncrewed, built to withstand deep-sea pressure.
Example: Matsya6000 is a crewed Indian submersible.
Exploration: reasons and consequences · Extend
subtraction
Taking one amount away from another, or finding how far apart two amounts are. Sign: −.
Example: 24 − 9 = 15
Four operations · Discover
Subtractive mixing
Removing colours with pigments or filters. Primaries cyan, magenta, yellow; mixtures get darker.
Example: Paints, inks, printer cartridges.
Light · Understand
subtrahend
In a subtraction, the number being taken away.
Example: In 90 − 35 = 55, the subtrahend is 35.
Four operations · Understand
Successor
The number just after a number: add 1.
Example: The successor of 999 is 1,000.
Number system · DiscoverProperties of numbers · Discover
Sulba Sutras
Ancient Indian texts on geometry for altar building using cords and pegs.
Example: Fixing an east–west line
Lines, rays and line segments · Go deeper
sum
The answer to an addition; the total.
Example: The sum of 15 and 9 is 24.
Four operations · DiscoverFour operations · Understand
superior
Towards the head.
Example: The lungs are superior to the diaphragm.
Anatomy of the human body · Understand
supplement
The angle that makes a given angle up to 180°: 180° − x.
Example: The supplement of 20° is 160°.
Angles · Understand
supplementary angles
Two angles that add up to 180°.
Example: 120° and 60°
Angles · DiscoverAngles · Understand
survey
Collecting data by asking people questions.
Example: Asking each classmate their favourite snack.
Data handling · Discover
suspensive veto
Returning a bill once for reconsideration rather than rejecting it outright; if passed again, assent must follow.
Example: This is the ordinary bill's built-in safety valve.
How government works in India · Go deeper
symmetric
Balanced on both sides of the middle, so the mean and median are close.
Example: Heights in one class.
Data handling · Investigate
symmetry
Having matching halves. The outside of a human is roughly symmetric; the inside is not.
Example: Two ears, two eyes — but only one heart.
Anatomy of the human body · Discover
Sympathetic string
An unplayed string that vibrates by resonance when a nearby string or note matches its tuning.
Example: The tarab strings under a sitar's neck.
Sound · Investigate
Synapse
The tiny gap where one neuron passes its signal to the next, or to a muscle, using a chemical.
Example: One-way, which is what stops signals running backwards.
Body systems and how they connect · Understand
Synchronous lateral excitation
A feedback loop where a crowd's footsteps unconsciously synchronise with a bridge's sway, amplifying it.
Example: London's Millennium Bridge in 2000.
Sound · Go deeper
Synchronous rotation
Spinning exactly once per orbit, so the same face always points at the partner body.
Example: The Moon spins once every 27.32 days and orbits in 27.32 days.
Phases of the Moon · UnderstandTides · Extend
Synodic month
New moon to new moon: 29.53 days. The cycle of the phases.
Example: 29 days, 12 hours, 44 minutes.
Phases of the Moon · UnderstandPhases of the Moon · Go deeper
synodic period
How often two orbiting bodies line up again as seen from the Sun (or Earth).
Example: Jupiter–Saturn: about 19.9 years
HCF and LCM · Extend
Systemic circuit
The long loop: heart → the whole body → heart.
Example: Where blood delivers everything.
Body systems and how they connect · Understand
Syzygy
Three bodies roughly in a straight line. Every eclipse is a syzygy.
Eclipses · Understand
Tacking
Sailing a zig-zag of angled legs to make progress towards a destination that lies upwind.
Exploration: reasons and consequences · Understand
tala
A repeating cycle of beats in Indian classical music.
Example: Teentaal has 16 beats.
Number and shape patterns · Extend
tala / sam
A rhythmic cycle in Indian classical music, and its first beat.
Example: Teentaal has 16 beats.
HCF and LCM · Extend
tally mark
A short stroke drawn for each item counted; every fifth stroke crosses the previous four to make a group of 5.
Example: 卌 || means 7.
Data handling · Discover
Tangram
A puzzle of 7 pieces cut from a square, used to make pictures.
Shape and space · Discover
Target puzzle
A puzzle where numbers must be combined with operations to reach an exact value.
Example: Make 24 from 7, 5, 8, 6.
Order of operations · Investigate
tendon
A cord of tough tissue tying muscle to bone, so the pull reaches the skeleton.
Example: The Achilles tendon at the back of the ankle.
Anatomy of the human body · Understand
Term
A part of an expression separated from the rest by a + or − that is not inside brackets.
Example: In 5 × 6 − 3 the terms are 5 × 6 and 3.
Order of operations · UnderstandNumber and shape patterns · DiscoverNumber and shape patterns · Understand
term-to-term rule
A rule that gets each term from the one before it.
Example: “Add 5 each time.”
Number and shape patterns · Understand
Terminal velocity
The steady speed reached when air resistance grows to equal weight, so the falling stops speeding up.
Example: A skydiver: about 200 km/h; a raindrop: about 23 km/h.
Gravity · DiscoverGravity · Understand
Terminator
The line on the Moon between its day side and its night side, where the Sun is rising or setting.
Example: The curved edge of the bright part.
Phases of the Moon · DiscoverPhases of the Moon · Understand
tessellation
A pattern of shapes covering a flat surface with no gaps or overlaps.
Example: Hexagons in a honeycomb
Number and shape patterns · Extend
Tessellation (tiling)
A pattern of shapes covering a surface with no gaps and no overlaps.
Shape and space · Investigate
tetrahedral number
The number of balls in a triangular pyramid; a running total of triangular numbers.
Example: 1, 4, 10, 20, 35
Number and shape patterns · Go deeper
Tetrahedron / octahedron / dodecahedron / icosahedron
Platonic solids with 4, 8, 12 and 20 faces.
Shape and space · Extend
the two scales
The two rows of numbers on a protractor, running in opposite directions with their 0s at opposite ends; readings at one point add to 180. Which row is the inner one varies between protractors.
Example: 40 on one scale, 140 on the other.
Measuring and constructing angles · Understand
theorem
A statement that has been proved.
Example: The angle sum of a triangle is 180°.
Angles · Go deeperLines, rays and line segments · Go deeperPrime and composite numbers · Go deeperShape and space · Go deeper
Threshold
A value below which changing something makes no difference, and above which it starts to matter.
Example: The 1.475° separation limit is a threshold for the Moon's tilt.
Eclipses · Investigate
Tidal barrage
A dam across a bay or estuary with turbines, generating electricity from the rise and fall of the tide.
Tides · Investigate
Tidal bore
A wave of the incoming tide that travels up a river against the current.
Tides · DiscoverTides · Investigate
Tidal bulge
A slight elongation of a body caused by the stronger gravitational pull on its near side than its far side.
Example: Earth's tidal bulge, dragged ahead by its fast spin, is what is currently pushing the Moon away.
Phases of the Moon · Go deeperTides · DiscoverTides · Understand
Tidal constituent
One of the simple, steady waves (such as M2, S2, K1 or O1) that add up to make a real, measured tide.
Tides · Go deeper
Tidal force
The part of the Moon's or Sun's pull that is left over after subtracting the average pull on Earth. It is what stretches the ocean.
Tides · Understand
Tidal form factor
F = (K1 + O1) ÷ (M2 + S2): a single number that classifies a tide as semidiurnal, mixed or diurnal.
Tides · Go deeper
Tidal heating
Heat generated inside a moon or planet by repeated tidal flexing, powering Io's volcanoes and warming the oceans under Europa's and Enceladus's ice.
Tides · Extend
Tidal locking
The process by which a body’s spin slows until it matches its orbital period.
Example: Why the Moon always shows the same face to Earth.
Gravity · ExtendPhases of the Moon · Understand
Tidal range
The height difference between high water and low water.
Example: High 5.9 m, low 0.4 m, so the range is 5.5 m.
Tides · Discover
Tidal rhythmite
A layered sedimentary rock formation that preserves a daily and monthly record of ancient tides, used to infer past day length.
Example: Ediacaran-period rhythmites suggest a roughly 21.9-hour day about 620 million years ago.
Phases of the Moon · ExtendTides · Extend
Tidal stream
The sideways flow of water that produces the rise and fall. Often the dangerous part of a tide.
Tides · Understand
Tidal volume
The amount of air moved in one ordinary resting breath, about 500 mL.
Example: About the volume of a small water bottle.
Body systems and how they connect · Understand
Tide
The regular rise and fall of the sea, usually twice a day, caused mainly by the Moon's gravity.
Example: “The tide is coming in” means the water is rising.
Tides · Discover
Tide table
A list of the times and heights of high and low water for a port, printed a year or more in advance.
Tides · DiscoverTides · Understand
tihai
A rhythmic phrase played three times to land exactly on the first beat of a tala cycle.
Example: Three phrases of 5 beats in Teentaal
Number and shape patterns · Extend
tiling (tessellation)
Covering a flat surface with shapes, with no gaps and no overlaps.
Example: Square floor tiles.
Angles · Investigate
Timbre
The character or colour of a sound, created by the relative loudness of its harmonics.
Example: Why a sitar and a bansuri differ at the same pitch.
Sound · Go deeper
Time period (T)
The time one complete vibration takes, in seconds. T = 1 ÷ f.
Example: 440 Hz means T = 0.0023 s.
Sound · Understand
Tissue
A group of similar cells doing one job together.
Example: Muscle tissue, nerve tissue, bone tissue.
Body systems and how they connect · DiscoverAnatomy of the human body · Discover
tolerance
How far from the exact value a drawing may be and still count as accurate, such as ± 1°.
Measuring and constructing angles · UnderstandMeasuring and constructing angles · InvestigateMeasuring and constructing angles · Go deeper
Topology
The study of properties that do not change when a shape is stretched or bent without tearing.
Shape and space · Go deeper
Torsion balance
A sensitive instrument that measures a tiny twisting force, used by Cavendish to weigh the Earth and by later scientists to test the equivalence principle.
Example: A beam on a fine wire, twisted by a very small force.
Gravity · Go deeper
Total internal reflection
When light hitting a boundary from the denser side, at an angle greater than the critical angle, reflects completely instead of refracting out.
Example: Why light stays trapped inside an optical fibre.
Light · Investigate
total station
A surveying instrument that measures angles and distances very precisely.
Measuring and constructing angles · Extend
Totality
The part of a total eclipse when the disc is completely covered.
Example: Up to 7 min 32 s for the Sun; up to about 1 h 40 min for the Moon.
Eclipses · Discover
Trading company
A company given a charter by its government to trade in a region, sometimes with its own ships, forts and soldiers.
Exploration: reasons and consequences · Discover
Transit
A smaller body crossing in front of a larger, more distant one, without covering it completely.
Example: Mercury and Venus transit the Sun; Phobos transits it from Mars.
Eclipses · Extend
Translucent
Letting some light through but scrambling it, so you see brightness but no detail.
Example: Tracing paper, frosted glass, mist.
Light · Discover
Transparent
Letting almost all the light through, so you see a clear picture through it.
Example: Window glass, clean water.
Light · Discover
transversal
A line that crosses two or more other lines.
Example: A sleeper across the rails.
Angles · Go deeperLines, rays and line segments · Understand
Transverse wave
A wave in which the particles move across the direction of travel.
Example: A flicked rope; ripples; light.
Sound · Understand
Trapezium
A quadrilateral with a pair of parallel sides.
Shape and space · Understand
Treaty
A formal, legally binding agreement between countries.
Example: The Antarctic Treaty has been in force since 1961.
Exploration: reasons and consequences · Extend
trial division
Testing whether a number is prime by dividing it by primes up to its square root.
Prime and composite numbers · Understand
Triangle
A polygon with 3 sides.
Shape and space · Discover
triangle inequality
In any triangle, the sum of any two sides is greater than the third side.
Example: 3, 4, 8 cm cannot make a triangle.
Measuring and constructing angles · ExtendShape and space · Investigate
triangular number
The number of dots in a triangle with rows of 1, 2, 3, … dots.
Example: 1, 3, 6, 10, 15
Number and shape patterns · DiscoverNumber and shape patterns · Understand
Triangular numbers
1, 3, 6, 10, 15…: the numbers of dots in growing triangles, and of segments on a line.
Example: 10 = 1 + 2 + 3 + 4
Lines, rays and line segments · Investigate
Triangulation
Locating an event by combining distance circles from at least three separate measuring stations.
Example: How seismologists pinpoint an earthquake's epicentre.
Sound · Extend
Trillion
In the short scale used today, a million million, 10¹². Equal to 1 lakh crore.
Number system · Extend
Trisect
To split into three equal parts. Trisecting a general angle is impossible with ruler and compass alone.
Example: Trisecting 60° would give 20°.
Measuring and constructing angles · InvestigateMeasuring and constructing angles · Go deeperMeasuring and constructing angles · Extend
True north
The direction of the geographic North Pole, the point Earth spins around.
Exploration: reasons and consequences · Understand
truncated (broken) axis
A value axis that does not start at zero; it can exaggerate differences between bars.
Data handling · Extend
Truncated icosahedron
The football shape: 12 pentagons and 20 hexagons, 90 edges, 60 vertices.
Shape and space · Extend
turning angle
The angle you turn through at a corner when walking around a shape.
Example: 90° at each corner of a square.
Angles · Investigate
twin prime conjecture
The unproved idea that there are infinitely many twin prime pairs.
Prime and composite numbers · Understand
twin primes
Two prime numbers that differ by 2.
Example: 11 and 13; 41 and 43
Prime and composite numbers · Discover
Ultrasound
Imaging using echoes of very high-pitched sound, with no radiation.
Example: Can show a beating heart valve moving live.
Body systems and how they connect · ExtendSound · DiscoverSound · Understand
Ultrasound (medical)
Sound above hearing, used with timed echoes to build a picture inside the body.
Example: A scan before a baby is born.
Sound · Investigate
Umbra
The fully dark middle of a shadow, where the light source is completely hidden.
Example: Stand in the Moon's umbra and you see totality.
Eclipses · DiscoverLight · Understand
Unary minus
A minus sign that makes a number negative rather than subtracting.
Example: −3 + 5 = 2
Order of operations · Go deeper
Uncontacted people
A community that has deliberately avoided sustained contact with the outside world.
Example: The Sentinelese of North Sentinel Island.
Exploration: reasons and consequences · Extend
undefined
Having no meaningful answer. Division by zero is undefined.
Example: 12 ÷ 0 is undefined
Four operations · Go deeperOrder of operations · Go deeperProperties of numbers · DiscoverProperties of numbers · Understand
Undefined term
A starting idea that is described but not defined, because defining it would need other words. Point, line and plane are the three undefined terms of school geometry.
Example: A point is described as a position with no size
Lines, rays and line segments · Understand
Unique
There is exactly one. The additive identity is unique.
Properties of numbers · Go deeper
Uniqueness
The fact that each whole number has exactly one standard way of being written with digits.
Number system · Go deeper
unit
A number that divides every number. Among counting numbers, only 1.
Prime and composite numbers · Go deeper
unitary method
Solving a proportional problem by first finding the value for one unit.
Example: 12 cost ₹540 → 1 costs ₹45
Four operations · Go deeper
unitary state
A country where regional power is delegated by the central government rather than fixed by the constitution itself.
Example: The UK is a unitary state with devolved administrations.
How government works in India · Extend
Upper / lower estimate
Estimates that are guaranteed to be at least / at most the exact answer.
Number system · Go deeper
Urea
The waste made by the liver from used-up protein, handed to the blood for the kidneys to remove.
Example: The main solid waste dissolved in urine.
Body systems and how they connect · Understand
Vacuum
A space with no matter in it at all. Sound cannot travel through one.
Example: Between the planets.
Sound · Discover
Value
The single number an expression works out to.
Example: The value of 2 + 3 × 4 is 14.
Order of operations · Discover
Vanishing point
The point in a perspective drawing where parallel lines running away from the viewer appear to meet.
Example: Where the rails meet on the horizon
Lines, rays and line segments · Extend
variable
Anything in a test that can change or be changed.
Example: The shape of the paper column, the number of books, and who is stacking them are all variables.
Anatomy of the human body · InvestigateNumber and shape patterns · Go deeper
Venn diagram
Overlapping circles showing what two groups share; here, shared prime factors go in the overlap.
Example: HCF = product of the overlap
HCF and LCM · Understand
Ventricle
One of the two lower pumping chambers. The left one has a far thicker wall.
Example: The left ventricle supplies the whole body.
Body systems and how they connect · Understand
vertebrate
An animal built around an internal backbone.
Example: Humans, giraffes, birds and snakes are all vertebrates.
Anatomy of the human body · Extend
vertex
The common starting point of the two arms of an angle; the corner point. Plural: vertices.
Example: The screw of a pair of scissors.
Angles · DiscoverMeasuring and constructing angles · DiscoverMeasuring and constructing angles · Understand
Vertex (plural: vertices)
A corner: where two sides of a polygon, or several edges of a solid, meet.
Shape and space · Discover
Vertex configuration
The list of polygons round a vertex of a tiling, such as 4.8.8.
Shape and space · Extend
Vertical
Straight up and down, like a plumb line.
Example: A flag pole
Lines, rays and line segments · Understand
vertically and crosswise
A one-line method for multiplying two-digit numbers: ones × ones, then the cross products for the tens, then tens × tens.
Example: 47 × 36 = 1,692
Four operations · Extend
vertically opposite angles
The pairs of opposite angles formed when two lines intersect. They are equal.
Example: Scissor blades and handles.
Angles · Understand
Vibration
A fast back-and-forth movement about a resting position. Every sound begins with one.
Example: Fingers on your throat while you hum.
Sound · Discover
Villi
Millions of tiny finger-shaped folds in the small intestine wall that make its surface enormous. Singular: villus.
Example: Each one is about a millimetre tall and holds a loop of capillary.
Body systems and how they connect · Discover
Vinculum
A bar over a Roman numeral that multiplies its value by 1,000.
Number system · UnderstandNumber system · Go deeperOrder of operations · Go deeper
Virtual image
An image the light only appears to come from; it cannot be caught on a screen.
Example: Your reflection behind a mirror.
Light · Understand
Vis-viva equation
The formula v = √(G M (2/r − 1/a)) giving speed anywhere on an elliptical orbit, not just at perigee or apogee.
Example: Used to compare speed at two points of the same ellipse.
Gravity · Go deeper
vote
The choice one person makes in an election; each adult citizen gets exactly one.
Example: Your vote counts the same as everybody else's.
How government works in India · Discover
vote share
The percentage of all votes cast that went to a party.
Example: Party A's vote share was 40.0% in the identical-seats example.
How government works in India · Investigate
Waning
Getting smaller, night after night.
Example: Full moon to new moon is the waning half.
Phases of the Moon · DiscoverPhases of the Moon · Understand
wasted vote
A vote that did not change the result: every vote for a losing candidate, and a winner's votes beyond what they needed.
Example: Landslide wins waste far more votes than narrow ones.
How government works in India · Investigate
Wave equation
v = f × λ: speed equals frequency times wavelength, for every wave.
Example: 343 = 440 × 0.78.
Sound · Understand
Wave–particle duality
The genuinely quantum fact that light (and matter) shows wave behaviour in some experiments and particle behaviour in others, with no contradiction.
Light · Extend
Wavelength (λ)
The distance from one compression to the next, in metres.
Example: 440 Hz in air has λ = 0.78 m.
Sound · Understand
Waxing
Getting bigger, night after night. From an old word meaning to grow.
Example: New moon to full moon is the waxing half.
Phases of the Moon · DiscoverPhases of the Moon · Understand
Weight
The force of gravity on an object, measured in newtons (N). It changes from world to world.
Example: 40 kg weighs 392 N on Earth, 64.8 N on the Moon.
Gravity · DiscoverGravity · Understand
Weighted average
An average where each value is multiplied by how often it occurs before dividing.
Properties of numbers · Extend
weighted mean
A mean in which some values or groups count more than others, according to their weights (such as group sizes).
Example: Combined mean of two sections.
Data handling · Go deeper
Whole numbers
Zero together with all the natural numbers: 0, 1, 2, 3, …
Example: 0 is a whole number but not a natural number.
Properties of numbers · DiscoverProperties of numbers · Understand
Wolff’s law
Bone adds material along lines of load and removes it where load is absent.
Example: A tennis player’s playing arm has measurably denser bone than their other arm.
Anatomy of the human body · Go deeper
X-ray
A kind of ray, discovered by Röntgen in 1895, that passes through soft tissue more easily than through bone.
Example: Used to image broken bones quickly.
Body systems and how they connect · Extend
zero angle
An angle of 0°: the arms lie on top of each other.
Example: Clock hands at 12:00.
Angles · Discover
Zero property of multiplication
Any number multiplied by 0 gives 0.
Example: 4,321 × 0 = 0
Properties of numbers · Understand
∎ (end of proof)
A symbol marking that a proof is complete.
Example: Every common multiple is a multiple of the LCM. ∎
HCF and LCM · Go deeper
∠ (angle sign)
The symbol for angle. ∠ABC is the angle with vertex B and arms through A and C.
Example: ∠ABC = 40°
Angles · Understand
24 game
A puzzle: combine four given numbers with + − × ÷ to make 24.
Example: 8 ÷ (3 − 8 ÷ 3) = 24
Order of operations · Extend
2D shape
A flat shape with length and breadth but no thickness, such as a square or a circle.
Example: The outline of a train ticket is a 2D rectangle.
Shape and space · Discover
3D shape (solid)
A shape that takes up space, with length, breadth and height.
Example: A brick, a ball and a cone are 3D shapes.
Shape and space · Discover
6k ± 1
Numbers one less or one more than a multiple of 6. Every prime above 3 has this form.
Example: 29 = 6 × 5 − 1
Prime and composite numbers · Investigate