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Maths words, made clear

A primary maths glossary

A child may know how to solve a sum but not yet know the word used in the textbook. Start with the idea, then attach the word to it. This glossary explains common primary maths vocabulary; it is not a list that every child must learn by a particular class.

Current NCERT books are called Joyful Mathematics in Classes 1 and 2 and Maths Mela in Classes 3 to 5. Schools using other books may introduce words at different times. The class in brackets is when most children first meet a word; your child's book may bring it a little earlier or later. Words marked “in many private books”, such as decimals, percentages, lakhs and crores, Roman numerals, HCF and LCM, are included for families who meet them; they are not in the NCERT books for Classes 1 to 5. Where it helps, the Hindi word that many teachers use is given in brackets.

Jump to a letter: A B C D E F G H I K L M N O P Q R S T U V W Z.

A

Abacus (गिनतारा)

A counting aid with beads arranged by place value. On a place-value abacus, 2 beads in the tens column and 4 in the ones column show 24. Many children also go to after-school abacus classes for quick mental sums; they can be fun, but they don't replace understanding place value. (Classes 1 to 3, in many schools.)

Acute angle (न्यून कोण)

An angle smaller than a right angle. The hands of a clock at 1 o'clock make an acute angle. Many private books add that an acute angle is less than 90°. (Classes 4 and 5.)

Addition (जोड़)

Putting quantities together, or increasing a quantity. In 8 + 5 = 13, 13 is the sum. (Class 1, with objects first.) More on addition and subtraction.

am and pm (पूर्वाह्न, अपराह्न)

Labels used with the 12-hour clock. 9 am is in the morning; 9 pm is at night. Some books write a.m. and p.m., or AM and PM. Railway timetables use the 24-hour clock instead: 21:00 is 9 pm. (Classes 3 and 4.)

Angle (कोण)

The amount of turn between two lines that meet at a point. The corner of a page is a right angle; a narrower corner is an acute angle and a wider one is an obtuse angle. (Classes 4 and 5.) More on shapes and geometry.

Anticlockwise

Turning the opposite way to the hands of a clock. Turning from 12 round to 9 anticlockwise is a quarter turn.

Area (क्षेत्रफल)

The amount of surface inside a boundary. A rectangle covered by 3 rows of 4 unit squares has an area of 12 square units. For a rectangle, area = length × breadth. (Class 4 by counting squares; Class 5 with square centimetres.)

Array

Objects arranged in equal rows and columns. 3 rows of 5 buttons make an array of 15 buttons, which shows 3 × 5 = 15 and also 5 × 3 = 15. (Classes 2 and 3.)

Ascending order (आरोही क्रम)

Order from smallest to largest: 7, 12, 19, 25. See also descending order. (Class 2.)

Average

One number that stands for a typical value in a set of data: add the values, then divide by how many there are. Scores of 4, 6 and 8 have an average of 6, because 4 + 6 + 8 = 18 and 18 ÷ 3 = 6. In many private books in Class 5; not in the NCERT books for Classes 1 to 5.

B

Bar graph

A display in which bars represent quantities. If the bar for “mango” reaches 8 on the scale, 8 children chose mango. Read the labels and scale before comparing the bars. (Class 5 in the NCERT book; earlier in some private books.) More on data handling.

Bead string (ginladi)

A string of beads, often 100 beads in groups of 10 in two colours, used for counting on, counting back and seeing tens. The NCERT books call it a ginladi (गिनलड़ी). (Classes 1 to 3.)

Before, after and between

Words for neighbouring numbers. 46 comes immediately before 47, 48 comes immediately after 47, and 47 is between 46 and 48. (Class 1.)

Bill

A list of things bought, their prices and the total. 2 kg rice at ₹60 per kg is ₹120 and 3 notebooks at ₹40 each are ₹120, so the bill comes to ₹240. Indian books love “Make a bill” questions. (Classes 3 to 5.) More on money.

BODMAS

A memory aid for the order of operations: Brackets, Of, Division, Multiplication, Addition, Subtraction. 6 + 4 × 2 = 6 + 8 = 14, not 20, because multiplication comes before addition. In many private books in Class 5; not in the NCERT books for Classes 1 to 5.

Borrowing (उधार)

A word many teachers use for regrouping in subtraction. In 42 − 7, you can't take 7 ones from 2 ones, so borrow 1 ten and change it into 10 ones: 42 becomes 3 tens and 12 ones, without changing its value. Then 12 − 7 = 5 and the answer is 35. The new NCERT books say “regroup” (regrouping). (Class 2.)

Borrowing across a zero

Subtracting when the place you need to borrow from holds 0. In 500 − 278, the 5 hundreds become 4 hundreds and 10 tens, then 9 tens and 10 ones. 10 − 8 = 2, 9 − 7 = 2 and 4 − 2 = 2, so 500 − 278 = 222. Check: 222 + 278 = 500. (Class 3.)

Bundles and sticks

Loose sticks and bundles of 10 sticks, tied with a rubber band, used to show tens and ones. 3 bundles and 4 loose sticks show 34; 10 bundles make 1 hundred. (Classes 1 and 2.) More on counting and place value.

C

Calendar

A chart of the days, weeks and months of a year. April, June, September and November have 30 days; February has 28, or 29 in a leap year; the other months have 31. (Classes 2 and 3.) More on time.

Capacity (धारिता)

How much a container can hold, measured in litres (L) and millilitres (mL). A bucket may hold 10 L; a glass about 200 mL. (Class 3 onwards.) More on measurement.

Carrying, carry over (हासिल)

A word many teachers use for regrouping in addition. 8 ones + 7 ones = 15 ones, which is 1 ten and 5 ones: write 5 in the ones and carry the 1 ten to the tens column. In 347 + 285 = 632, you carry twice. The new NCERT books say “regroup” (regrouping). (Class 2.)

Centimetre

A unit of length, written cm (से.मी. in Hindi books). 100 cm = 1 metre and 1 cm = 10 mm. A new pencil is about 18 cm long. (Classes 2 and 3.)

Centre (केंद्र)

The middle point of a circle. Every point on the circle is the same distance from its centre. (Class 4.)

Change

The money you get back when you pay more than the price. Pay ₹100 for something costing ₹63 and the change is ₹37. Count up to check: ₹63 to ₹70 is ₹7, and ₹70 to ₹100 is ₹30. (Classes 3 and 4.)

Checking an answer

Using the opposite operation to test a result. 532 − 178 = 354 is checked by adding: 354 + 178 = 532. A division is checked with dividend = divisor × quotient + remainder. (Classes 2 to 5.)

Circle (वृत्त)

A round flat shape with no corners, whose edge is always the same distance from the centre. Bangles, a roti and the Ashoka Chakra are circles. (Class 1 to name; Class 4 for centre, radius and diameter.)

Circumference (परिधि)

The distance all the way round a circle: its perimeter. Wrap a thread around a bangle and measure the thread to find the bangle's circumference. In some private books in Class 5.

Clockwise

Turning the same way as the hands of a clock. Turning from 12 round to 3 clockwise is a quarter turn.

Column method

A written calculation with the numbers written one below the other, so that matching place values line up: ones below ones and tens below tens, often under the headings H, T and O. Some books call it the vertical method. (Class 2 onwards.)

Common factor

A number that is a factor of two or more numbers. The common factors of 12 and 18 are 1, 2, 3 and 6. (Class 5.)

Common multiple

A number that is a multiple of two or more numbers. 12, 24 and 36 are common multiples of 4 and 6. (Class 5 in many books.)

Compasses (परकार)

A tool with a point and a pencil, used to draw circles. Open the compasses to 3 cm and you draw a circle of radius 3 cm. (Class 4 onwards.)

Composite number

A whole number greater than 1 that has more than two factors. 9 is composite: its factors are 1, 3 and 9. In many private books in Class 5. In Hindi books, भाज्य संख्या means a composite number, while भाज्य alone can also mean a dividend.

Cone (शंकु)

A solid shape with a circular flat face, a curved surface and one pointed vertex, like an ice-cream cone or a birthday cap. (Class 2 onwards.)

Converting units

Changing a measurement into a different unit without changing its size. 3 m = 300 cm; 2 kg 500 g = 2,500 g; 1 L 250 mL = 1,250 mL. (Classes 3 to 5.)

Counting forwards and backwards

Saying numbers in order going up (17, 18, 19, 20) or down (20, 19, 18, 17). Counting back helps with subtraction. (Class 1.)

Crore (करोड़)

1,00,00,000: one hundred lakh, which is 10 million in the international system. After a number it stays singular: “₹2 crore”. Lakhs and crores are in many private books in Class 5; the NCERT Class 5 book works with five-digit numbers and uses neither lakh nor crore.

Cube (घन)

A solid shape with 6 square faces, all the same size, 12 edges and 8 corners (vertices), like a dice. (Class 2 onwards.)

Cuboid (घनाभ)

A solid shape with 6 rectangular faces, 12 edges and 8 corners, like a brick or a matchbox. A cube is a special cuboid. (Class 2 onwards.)

Cylinder (बेलन)

A solid shape with two circular flat faces and one curved surface, like a pipe or a tin of ghee. It can roll and, standing on a flat face, it can also slide. (Class 2 onwards.)

D

Data handling (आँकड़ों का प्रबंधन)

Data is information collected for a question, such as the number of children choosing each classroom game. Data handling is the Indian textbook name for collecting, sorting and showing data with tally marks, tables, pictographs and bar graphs, then answering questions from them. (Class 1 with pictures and marks; bar graphs in Class 5.)

Decimal (दशमलव)

A way of writing numbers using tenths, hundredths and smaller place-value parts. In 2.5, the 5 represents 5 tenths. In many private books in Class 4 or 5, often through money and centimetres; the NCERT books for Classes 1 to 5 don't teach decimals. More on decimals and percentages.

Decimal point

The dot that separates whole units from parts. ₹25.50 means 25 rupees and 50 paise; 2.5 is read “two point five”. Money with paise appears from Class 3; decimals as such are in many private books in Classes 4 and 5.

Degree (°)

The unit for measuring angles. A right angle is 90°, a straight angle is 180° and a full turn is 360°. In many private books in Class 5, with a protractor; the NCERT books for Classes 1 to 5 name angles but don't measure them in degrees.

Denominator (हर)

The bottom number in a fraction. In ¾, the denominator 4 tells us that the whole is divided into 4 equal parts. (Class 5 in the NCERT book; Class 3 or 4 in many private books.)

Descending order (अवरोही क्रम)

Order from largest to smallest: 25, 19, 12, 7. (Class 2.)

Diameter (व्यास)

A straight line across a circle through its centre, from one side to the other. The diameter is twice the radius: a circle of radius 3 cm has a diameter of 6 cm. (Class 4.)

Difference (अंतर)

The result of subtraction. The difference between 18 and 11 is 7.

Digit (अंक)

One of the ten symbols 0–9 used to write numbers. 405 has 3 digits; its middle digit is 0. In Hindi, अंक also means marks in a test.

Dividend (भाज्य)

The quantity being divided. In 24 ÷ 6 = 4, the dividend is 24. (Classes 4 and 5.)

Divisibility rules

Quick checks for whether a number divides exactly. A number divides by 2 if its last digit is even, by 5 if it ends in 0 or 5, and by 10 if it ends in 0. 135 divides by 5 but not by 2 or 10. In many private books in Classes 4 and 5.

Division (भाग)

Sharing into equal groups, or finding how many equal-sized groups fit. 24 counters shared among 6 children give 4 each; 24 counters put into groups of 6 make 4 groups. The ÷ sign comes in Class 3 in the NCERT book. More on multiplication and division.

Division facts (विभाजन तथ्य)

Divisions that come straight from a table. 4 × 6 = 24 gives two division facts: 24 ÷ 4 = 6 and 24 ÷ 6 = 4. (Class 3.)

Divisor (भाजक)

The number we divide by. In 24 ÷ 6 = 4, the divisor is 6. In long division the divisor is written on the left of the bracket. (Classes 4 and 5.)

Doubling

Adding a number to itself, or multiplying it by 2. Double 7 is 14. Knowing doubles helps with near doubles: 7 + 8 is double 7 plus 1, which is 15. (Classes 1 and 2.)

E

Edge (किनारा)

A line where two faces of a solid shape meet. A cube has 12 edges. (Class 3 onwards.)

Equal groups

Groups with the same number in each. 4 groups of 3 laddoos make 12 laddoos: 3 + 3 + 3 + 3 = 12, or 4 × 3 = 12. (Class 2.)

Equal sharing

Sharing so that everyone gets the same amount. 12 laddoos shared equally among 3 children give 4 each: 12 ÷ 3 = 4. (Classes 2 and 3.)

Equals sign (=)

The sign meaning “is equal to”: both sides have the same value. In 7 + 8 = 15 and in 15 = 10 + 5, each side is worth 15. (Class 1.)

Equivalent fractions (तुल्य भिन्न, समतुल्य भिन्न)

Fractions with the same value: ½, ²⁄₄ and ³⁄₆ cover the same amount of the same-sized whole. (Classes 4 and 5.) More on fractions.

Estimate (अनुमान)

A sensible approximate answer. Before calculating 198 + 203 exactly, use 200 + 200 to estimate 400; the exact answer is 401. (Class 3 onwards.)

Even number (सम संख्या)

A whole number that can be paired with no item left over. Even numbers end in 0, 2, 4, 6 or 8, such as 14 and 230. See also odd number. (Class 2.)

Expanded form (विस्तारित रूप)

Writing a number as the sum of its place-value parts: 345 = 300 + 40 + 5 and 4,205 = 4,000 + 200 + 5. (Class 2 onwards.)

F

Face (फलक)

A flat or curved surface of a solid shape. A cube has 6 flat faces; a cylinder has 2 flat faces and 1 curved surface. (Class 3 onwards.)

Face value

The digit itself, whatever its position. The face value of 7 in 572 is 7, while its place value is 70. In many private books from Class 3; the NCERT books don't use the term.

Factor (गुणनखंड)

A whole number that divides another exactly. 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. (Class 5 in the NCERT book; Class 4 in many private books.)

Fill in the blanks (रिक्त स्थान भरिए)

A classic exercise heading: write the missing number or word. In 7 + ___ = 15 the blank is 8. Some books use a box instead: 7 + □ = 15.

Flat shapes (2D shapes)

Shapes drawn on paper, with length and breadth but no thickness: circle, triangle, square, rectangle, pentagon, hexagon. See also solid shapes. (Class 1 onwards.)

Fraction (भिन्न)

A number that can represent equal parts of a whole or a quantity. ¾, read “three-fourths” (or three quarters), means 3 of 4 equal parts, not 3 unequal pieces out of any 4 pieces. In Hindi, ¾ is read तीन बटे चार or तीन-चौथाई. (Class 3 onwards.)

Fraction of a collection

A fraction of a group of objects. ½ of 12 laddoos is 6 laddoos; ¼ of 12 laddoos is 3, because 12 shared into 4 equal groups gives 3 in each. (Class 3.)

G

Gram

A small unit of weight, written g (ग्रा. in Hindi books). 1,000 g = 1 kg, so half a kilo is 500 g. In markets you may hear “paav” for 250 g. (Classes 3 and 4.)

Greater than and less than

Comparison words. 9 > 6 reads “9 is greater than 6”; 6 < 9 reads “6 is less than 9” (many books say “smaller than”). The symbols come in Class 3 in the NCERT book; some private books bring them in earlier.

Greatest and smallest number

A favourite question: make the greatest and smallest numbers from given digits. With 3, 0, 7 and 5, the greatest is 7,530 and the smallest is 3,057, because a number does not start with 0. (Classes 3 to 5.)

H

Half (आधा)

One of 2 equal parts, written ½. Half a roti is one of two equal pieces; half of 10 is 5. (Class 3, and earlier in everyday talk.)

Half past

30 minutes after the hour. Half past 3 is 3:30; in Hindi, साढ़े तीन. Half past 1 is डेढ़ बजे and half past 2 is ढाई बजे. (Classes 2 and 3.) More on time.

HCF (म.स.)

Highest common factor: the greatest factor shared by two numbers. The HCF of 12 and 18 is 6. In many private books in Class 5; not in the NCERT books for Classes 1 to 5.

Hexagon (षट्भुज)

A flat shape with 6 straight sides and 6 corners. Each cell of a honeycomb is a hexagon. (Class 3 onwards.)

Horizontal line

A line going straight across, like the edge of a table top or the horizon. See also vertical line. (Class 3.)

Hundreds (सैकड़ा)

The third place from the right in a whole number. 1 hundred = 10 tens = 100 ones. In 572, the 5 stands for 5 hundreds, which is 500. (Class 2 onwards.)

Hundredth (शतांश)

One of 100 equal parts, written 0.01 or ¹⁄₁₀₀. 1 paisa is a hundredth of a rupee, so 25 paise = ₹0.25. In many private books in Classes 4 and 5.

I

Improper fraction

A fraction whose numerator is equal to or greater than its denominator, such as ⁷⁄₄. ⁷⁄₄ = 1¾, because 4 quarters make 1 whole and 3 quarters are left. In many private books in Classes 4 and 5.

Indian place value chart

A chart that groups places into periods: ones (ones, tens, hundreds), thousands (thousands, ten thousands), lakhs and crores. Commas follow the periods: 3,45,672 is 3 lakh, 45 thousand and 672. The NCERT books call this the Indian place value system and go up to ten thousands by Class 5; lakhs and crores are in many private books. More on counting and place value.

International place value system

The system that groups digits in threes: thousands, millions, billions. 345,672 is three hundred forty-five thousand six hundred seventy-two; in the Indian system it is written 3,45,672. 10 lakh = 1 million and 1 crore = 10 million. In many private books in Classes 4 and 5, beside the Indian system.

K

Key

The line on a pictograph or graph that says what each picture stands for. If the key says one picture = 5 children, 4 pictures stand for 20 children. (Class 3 onwards.)

Kilogram

A unit of weight, written kg (कि.ग्रा. in Hindi books). 1 kg = 1,000 grams (g). Rice, atta and vegetables are sold by the kg. (Classes 2 and 3.)

Kilometre

A unit for long distances, written km. 1 km = 1,000 m. Distances between towns are measured in km. (Classes 3 and 4.)

L

Lakh (लाख)

1,00,000: one hundred thousand. Indian grouping puts the last 3 digits together, then groups digits in pairs: 3,45,672 reads “three lakh forty-five thousand six hundred seventy-two”. Write “lakh”, not “lac”. In many private books in Class 5; the NCERT books for Classes 1 to 5 stop at ten thousands.

LCM (ल.स.)

Lowest common multiple: the smallest positive multiple shared by two numbers. The LCM of 4 and 6 is 12. In many private books in Class 5; not in the NCERT books for Classes 1 to 5.

Leap year

A year with 366 days, when February has 29 days instead of 28. It usually comes every 4 years; 2028 is a leap year. (Class 3.)

Length (लंबाई)

How long something is, measured in mm, cm, m or km. Class 1 compares lengths directly or with handspans; centimetres and metres come in Class 2. (Classes 1 to 5.)

Like fractions (सजातीय भिन्न)

Fractions with the same denominator, such as ²⁄₇ and ⁵⁄₇. Like fractions are added by adding the numerators: ²⁄₇ + ³⁄₇ = ⁵⁄₇. See also unlike fractions. In many private books in Classes 4 and 5.

Litre

A unit of capacity, written L (ली. in Hindi books). 1 litre = 1,000 millilitres (mL), so two 500 mL milk packets make 1 L. (Classes 2 and 3.)

Long division

A written method for dividing larger numbers: divide, multiply, subtract, bring down. In the traditional Indian layout the divisor goes on the left and the quotient on the right: 4 ) 857 ( 214, with remainder 1. Check: 4 × 214 + 1 = 857. Some books write the quotient above the dividend instead; the steps are the same. (Classes 4 and 5.) How maths is taught now.

Long multiplication

Multiplying by a two-digit (or larger) number in columns. For 234 × 23, work out 234 × 3 = 702, then 234 × 20 = 4,680 (with a 0, or a cross, in the ones place of the second row), and add: 702 + 4,680 = 5,382. (Classes 4 and 5.)

M

Magic square

A grid of numbers in which every row, column and diagonal adds up to the same total. In this square of 1 to 9, each line adds up to 15: 8, 1, 6 / 3, 5, 7 / 4, 9, 2. Many Indian books use magic squares as puzzles. (Classes 3 to 5.)

Mental maths (मानसिक गणित)

Calculating by thinking about number relationships; some teachers say “oral maths”. It need not mean answering instantly or keeping every step unspoken. Mental maths strategies.

Metre

A unit of length, written m. 1 m = 100 cm, and 1,000 m = 1 km. Cloth is sold by the metre. (Classes 2 and 3.)

Millilitre

A small unit of capacity, written mL (मि.ली. in Hindi books; the NCERT books print “ml”). 1,000 mL = 1 L. A teaspoon holds about 5 mL. (Class 3 onwards.)

Millimetre

A small unit of length, written mm: the smallest marks on a scale. 10 mm = 1 cm. (Class 4.)

Mixed number, mixed fraction (मिश्रित भिन्न)

A whole number and a fraction written together, such as 1½, read “one and a half”, or 2¾, read “two and three-fourths”. Use a drawing before introducing the notation. In many private books in Classes 4 and 5.

Multiple (गुणज)

A number obtained by multiplying a given number by a whole number. 5, 10, 15 and 20 are positive multiples of 5. (Class 4.)

Multiplicand and multiplier (गुण्य, गुणक)

In 234 × 23 = 5,382, the multiplicand is 234 (the number being multiplied), the multiplier is 23 and the product is 5,382. (Classes 4 and 5, in many books.)

Multiplication (गुणा)

Working with equal groups. 4 groups of 6 contain 24 altogether: 4 × 6 = 24. (Class 2 as repeated addition.) More on multiplication and division.

Multiplying by 10 and 100

Each digit moves one place to the left for × 10 and two places for × 100, with zeros filling the empty places: 36 × 10 = 360 and 36 × 100 = 3,600. (Class 3.)

N

Negative numbers

Numbers less than zero, such as −3. Together with 0 and the counting numbers they make the integers, a Class 6 and later topic. Children may meet them earlier on a thermometer, where −2 °C is 2 degrees below zero.

Net

A flat shape that folds up to make a solid shape. Six squares joined in the right pattern fold into a cube. (Classes 4 and 5.)

Non-standard units

Everyday things used to measure before rulers: handspans (बालिश्त), footsteps, pencils. A table might be 6 handspans long. Different hands give different answers, which is why we need cm and m. (Class 1.)

Number chart

A chart of the numbers 1 to 100 in rows of 10. Moving down one row adds 10: below 23 is 33. (Classes 1 and 2.)

Number line (संख्या रेखा)

A line marked with numbers in order. For 8 + 5, start at 8 and jump 5 steps forward to 13; for 13 − 5, jump back to 8. (Class 1 onwards.)

Number name

A number written in words. 4,058 is “four thousand fifty-eight”. NCERT books leave out “and”; many people say “and”, and both are fine. (Class 1 onwards.)

Number pairs (pairs that make 10)

Pairs of numbers that add up to a whole, often 10: 7 and 3, 6 and 4. Some books call them addition facts or number bonds. The pair 7 + 3 = 10 also gives 10 − 7 = 3. (Class 1.) Pairs that make 10 and 20.

Numerator (अंश)

The top number in a fraction. In ¾, the numerator 3 counts the equal parts being considered. (Class 5 in the NCERT book; Class 3 or 4 in many private books.)

O

Obtuse angle (अधिक कोण)

An angle bigger than a right angle but smaller than a straight angle. The hands of a clock at 4 o'clock make an obtuse angle. Many private books add that it is between 90° and 180°. (Classes 4 and 5.)

O'clock

An exact hour, when the long hand points to 12. At 3 o'clock the short hand points to 3 and the long hand to 12. (Classes 1 and 2.)

Odd number (विषम संख्या)

A whole number that leaves one item unpaired. Odd numbers end in 1, 3, 5, 7 or 9, such as 15 and 233. See also even number. (Class 2.)

One-fourth, quarter (एक-चौथाई)

One of 4 equal parts, written ¼. Indian books say “one-fourth” and “quarter”; both are correct. ¼ of 20 is 5. Three-fourths, ¾, is 3 of the 4 parts. (Class 3.)

Ones (इकाई)

The first place on the right in a whole number. In 572, the 2 stands for 2 ones. Older books call this place “units”. (Class 1 onwards.)

Ordinal numbers

Numbers that give a position: first (1st), second (2nd), third (3rd), fourth (4th) and so on. In a queue of 10, the 10th child is last. (Class 1.)

P

Paise

Parts of a rupee: ₹1 = 100 paise. ₹25.50 means 25 rupees and 50 paise. The NCERT books show paise from Class 2; in daily life you rarely see paise coins now. More on money.

Partial quotients

A way into long division used in the NCERT books for Classes 4 and 5: take away convenient multiples of the divisor and add up the parts of the quotient. For 857 ÷ 4: 4 ) 857 ( 200 + 10 + 4. 857 − 800 = 57, 57 − 40 = 17 and 17 − 16 = 1, so the quotient is 214 and the remainder 1.

Pattern (पैटर्न)

Something that repeats or grows by a rule. In 2, 4, 6, 8, … the rule is “add 2”, so the next number is 10. Rangoli and kolam designs are full of shape patterns. (Class 1 onwards.) More on patterns.

Pentagon (पंचभुज)

A flat shape with 5 straight sides and 5 corners. (Class 3 onwards.)

Percentage (प्रतिशत)

A way of expressing an amount out of 100. 25% means 25 out of 100 and equals ¼; 50% of ₹200 is ₹100. In many private books in Class 5; the NCERT books for Classes 1 to 5 don't teach percentages.

Perimeter (परिमाप)

The distance around a boundary. A rectangle with sides 6 cm and 4 cm has perimeter 6 + 4 + 6 + 4 = 20 cm. (Classes 4 and 5.) More on measurement.

Pictograph

A display using pictures to represent quantities. If one picture stands for 2 children, 3 pictures represent 6 children. Always read the key first. (Classes 1 to 4.)

Place value (स्थानीय मान)

The value a digit has because of its position. In 572, 5 means 500, 7 means 70 and 2 means 2. (Class 1 with tens and ones, then larger numbers each year.) More on counting and place value.

Place value chart (स्थानीय मान सारणी)

A table with a column for each place, such as TTh, Th, H, T and O, used to write a number digit by digit. 45,018 has 4 in the TTh column, 5 in Th, 0 in H, 1 in T and 8 in O. Hindi books write सै. द. इ. for hundreds, tens and ones and द.ह. for ten thousands, and older English books write U (units) for ones. (Class 2 onwards with H, T and O.)

Pre-number concepts

Ideas that come before counting: big and small, tall and short, more and less, inside and outside, before and after, sorting and matching. Many Class 1 books open with them.

Predecessor

The whole number immediately before a number; many books say “the number before”. The predecessor of 40 is 39 and the predecessor of 1,000 is 999. The word itself is in many private books from Class 2.

Prime number (अभाज्य संख्या)

A whole number greater than 1 with exactly two factors, 1 and itself. 2, 3, 5, 7, 11 and 13 are prime. 1 is not a prime number. (Class 5.)

Product (गुणनफल)

The result of multiplication. The product of 6 and 8 is 48.

Proper fraction (उचित भिन्न)

A fraction whose numerator is smaller than its denominator, such as ¾ or ²⁄₅. It is less than 1 whole. In many private books in Classes 4 and 5.

Protractor (चाँदा)

A half-circle tool, marked from 0° to 180°, for measuring and drawing angles. In many private books in Class 5; the NCERT books for Classes 1 to 5 don't use one.

Q

Quarter past and quarter to

15 minutes after or before the hour. Quarter past 3 is 3:15 (सवा तीन); quarter to 4 is 3:45 (पौने चार). (Classes 2 and 3.)

Quarter turn (चौथाई घुमाव)

A turn through a right angle. Four quarter turns make a full turn, back to where you started. (Classes 4 and 5.)

Quotient (भागफल)

The result of division. In 35 ÷ 5 = 7, the quotient is 7. For 857 ÷ 4, many books write the answer as Q = 214, R = 1. (Classes 4 and 5.)

R

Radius (त्रिज्या)

A straight line from the centre of a circle to its edge. The plural is radii. A circle with radius 4 cm has diameter 8 cm. (Class 4.)

Rate

A price or amount for one unit, such as “₹40 per kg”. At ₹40 per kg, 3 kg of tomatoes cost 3 × ₹40 = ₹120. (Classes 4 and 5.)

Reasoning

Explaining why an answer or method makes sense, using words, objects, drawings or a counterexample. Reasoning and problem-solving.

Rectangle (आयत)

A flat shape with 4 straight sides and 4 right angles; opposite sides are equal. A page of a copy is a rectangle. (Class 1 onwards.)

Regrouping (पुनः समूहीकरण)

The word the new NCERT books use for carrying and borrowing: changing between place-value units without changing the quantity, because 1 hundred = 10 tens and 1 ten = 10 ones. 15 ones can be regrouped as 1 ten and 5 ones. See carrying and borrowing.

Remainder (शेषफल)

What is left after making equal whole-number groups. 17 ÷ 5 gives 3 groups with remainder 2, since 3 × 5 + 2 = 17. The remainder is always smaller than the divisor. (Classes 3 to 5.)

Repeated addition

Adding the same number again and again, the first way into multiplication. 3 + 3 + 3 + 3 = 12 is the same as 4 × 3 = 12. (Class 2.)

Right angle (समकोण)

A square corner, like the corner of a book or a tile. The hands of a clock at 3 o'clock make a right angle. Many private books add that it measures 90°. (Classes 4 and 5.)

Roman numerals

A number-writing system using letters: I = 1, V = 5, X = 10, L = 50, C = 100. IV is 4 (one before five), IX is 9 and XIV is 14. In many private books in Classes 3 to 5; they are not in the NCERT books for Classes 1 to 5, and they aren't needed to understand place value.

Rounding off (पूर्णांकन)

Replacing a number with a nearby chosen place-value amount. 47 rounded off to the nearest ten is 50; 342 to the nearest hundred is 300; 1,682 to the nearest thousand is 2,000. A 5 rounds up: 35 becomes 40. (Classes 3 to 5, in many books.)

Rupee (₹)

India's money. The sign ₹ goes before the number: ₹50. Coins in use are ₹1, ₹2, ₹5, ₹10 and ₹20; notes are ₹10, ₹20, ₹50, ₹100, ₹200 and ₹500. Older books and shops may write Rs. (Class 1 onwards.) More on money.

S

Scale

Two meanings. A scale is a ruler, often 15 cm or 30 cm long (स्केल, पटरी). The scale of a graph says what each step stands for, such as each square = 2 children.

Side (भुजा)

One of the straight lines that make up a flat shape. A triangle has 3 sides and a square has 4. (Class 2 onwards.)

Simplest form

A fraction written with the smallest possible numbers, also called lowest terms. ⁶⁄₈ in simplest form is ¾, dividing the numerator and denominator by 2. In many private books in Class 5.

Skip counting

Counting in equal jumps: in 2s (2, 4, 6, 8), in 5s (5, 10, 15, 20) or in 10s (10, 20, 30). It prepares children for tables. (Classes 1 and 2.)

Solid shapes (3D shapes)

Shapes with length, breadth and height that you can hold: cube, cuboid, cylinder, cone and sphere. Class 1 sorts things that roll and things that slide; names come later. (Class 1 onwards.)

Sphere (गोला)

A perfectly round solid shape with one curved surface and no edges or corners, like a ball or a laddoo. (Class 2 onwards.)

Square (वर्ग)

A flat shape with 4 equal sides and 4 right angles. A carrom board is a square. (Class 1 onwards.)

Square centimetre

A unit of area: a square 1 cm long and 1 cm wide, written sq cm or cm² (वर्ग से.मी. in Hindi books). A rectangle 6 cm long and 4 cm wide has an area of 6 × 4 = 24 sq cm. (Class 5.)

Square number

The result of multiplying a whole number by itself. 1, 4, 9, 16 and 25 are square numbers; 16 = 4 × 4, and 16 dots make a 4 by 4 square. In some books in Class 5, as a number pattern.

Straight angle (सरल कोण)

A half turn, making a straight line: two right angles, or 180°. In many private books in Class 5.

Subtraction (घटाना)

Taking away, or finding the difference between two numbers. 15 − 6 = 9: from 15 mangoes, 6 are eaten and 9 are left. (Class 1 with objects first.) More on addition and subtraction.

Successor

The whole number immediately after a number; many books say “the number after”. The successor of 99 is 100 and the successor of 4,999 is 5,000. The word itself is in many private books from Class 2.

Sum (योगफल)

The result of addition. In 12 + 8 = 20, the sum is 20. In everyday classroom speech, “sums” can also mean calculation exercises generally.

Symmetry (सममिति)

A line of symmetry divides a shape into matching halves that coincide when folded along that line. The capital letter A has one line of symmetry and a square has four. A rangoli pattern may have symmetry, but not every pattern does. (Class 3 onwards.)

T

Tables (पहाड़े)

Multiplication facts, such as the table of 4. Children recite “two ones are two, two twos are four”; in Hindi, दो एकम दो, दो दूनी चार. Most schools expect tables up to 10 by the end of Class 3, and many families go on to 20. Connect recitation to equal groups and arrays. Tables practice.

Tally marks (मिलान चिह्न)

Marks used to count observations. Each fifth mark crosses the previous four, making groups of 5 quicker to read: 3 crossed groups and 2 more marks show 17. (Classes 2 and 3.)

Tangram

A square puzzle cut into 7 pieces (5 triangles, a square and a parallelogram) that can be rearranged into many pictures. (Classes 2 and 3.)

Ten thousands (दस हजार)

The fifth place from the right, written TTh. 10 thousands = 10,000. In 45,018, the 4 stands for 4 ten thousands, which is 40,000. (Class 5 in the NCERT book; Class 4 in many private books.)

Tens (दहाई)

The second place from the right. 1 ten = 10 ones. In 34, the 3 stands for 3 tens, which is 30. (Class 1.)

Tenth (दशांश)

One of 10 equal parts, written 0.1 or ¹⁄₁₀. 1 mm is a tenth of a centimetre, so 3 mm = 0.3 cm. In many private books in Classes 4 and 5.

Thousands (हजार)

The fourth place from the right, written Th. 1 thousand = 10 hundreds = 1,000. In 4,205, the 4 stands for 4,000. (Classes 3 and 4.)

Triangle (त्रिभुज)

A flat shape with 3 straight sides and 3 corners. (Class 1 onwards.)

24-hour clock

A way of telling the time that counts the hours from 00 to 23, so am and pm aren't needed. 14:30 is 2:30 pm and 21:00 is 9 pm. Indian Railways timetables use it. (Classes 4 and 5.) More on time.

U

Unit

A chosen measure or counting amount. A length answer needs a unit, such as 8 cm; “8” alone does not tell us the length. Older books also say “units” for ones.

Unitary method

Finding the value of one item before finding the value of several. If 3 identical notebooks cost ₹60, one costs ₹20 and 5 cost ₹100. Use only when the same price per item applies. (Classes 4 and 5, in many books.)

Unlike fractions (विजातीय भिन्न)

Fractions with different denominators, such as ½ and ¼. To add them, first make the denominators the same: ½ + ¼ = ²⁄₄ + ¼ = ¾. In many private books in Class 5.

V

Vedic maths

A popular set of mental-calculation shortcuts, taught in some after-school classes and books. For 23 × 11, write 2, then 2 + 3 = 5, then 3: 253. The tricks work because of place value and are most useful once children understand why. They are optional, never needed for school.

Vertex, corner (शीर्ष, कोना)

A point where sides or edges meet. The plural is vertices. A triangle has 3 vertices and a cube has 8. Younger children's books say “corner”. (Class 2 onwards.)

Vertical line

A line going straight up and down, like a flagpole. See also horizontal line. (Class 3.)

Volume (आयतन)

The amount of space a solid takes up. A box built from 3 rows of 2 cubes, 2 layers high, has a volume of 3 × 2 × 2 = 12 cubes. In some books in Class 5, by counting cubes.

W

Weight (भार, वज़न)

How heavy something is, measured in grams and kilograms. Indian primary books say weight; a few books say mass. A bag of atta might weigh 5 kg. (Class 1 by comparing; Class 2 onwards in kg and g.)

Word problems (इबारती सवाल)

Maths questions told as a short story. “Meera has 24 bangles and gives 9 to Zoya. How many are left?” 24 − 9 = 15 bangles. Read the question twice and decide what is being asked before calculating. (Class 1 onwards.) Reasoning and problem-solving.

Z

Zero

A number representing no quantity, and a placeholder in numbers such as 405. 405 has no tens; it is not the same number as 45. Adding 0 changes nothing (7 + 0 = 7), and multiplying by 0 gives 0 (7 × 0 = 0). Zero and the place-value way of writing numbers have a long history in India.

For examples with more space to practise, visit mental maths strategies, counting and place value or reasoning and problem-solving.