Ch 1Patterns in Mathematics
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Key terms for this chapter
Ch 1
Number Sequence
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Definition
An ordered list of numbers that follows a fixed rule. Example: 1, 3, 6, 10, 15.
Ch 1
Triangular Numbers
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Definition
Numbers arranged as a triangle: 1, 3, 6, 10, 15... Each equals the sum of counting numbers up to that point.
Ch 1
Square Numbers
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Definition
Numbers arranged as a square: 1, 4, 9, 16, 25... Each equals n×n.
Ch 1
Cube Numbers
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Numbers arranged as a cube: 1, 8, 27, 64, 125... Each equals n×n×n.
Ch 1
Virahanka Numbers
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Definition
Each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13... Also called Fibonacci numbers.
Ch 1
Powers of 2
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Definition
The sequence 1, 2, 4, 8, 16, 32... where each term doubles the previous one.
Ch 1
Number Theory
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Definition
The branch of Mathematics that studies patterns in whole numbers.
Ch 1
Shape Sequence
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Definition
A pattern made of shapes changing in a regular way. Example: triangle, square, pentagon, hexagon...
Ch 1
Geometry
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Definition
The branch of Mathematics that studies patterns in shapes — in 1D, 2D, or 3D.
Ch 1
Koch Snowflake
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Definition
A shape sequence where each line segment is replaced by a speed-bump shape, repeated again and again.
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Chapter Practice
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Q1 Triangular Numbers
Which of the following is a triangular number?
Q2 Square Numbers
What comes next in the square numbers: 1, 4, 9, 16, ___?
Q3 Number Theory
The branch of Mathematics that studies patterns in whole numbers is called:
Q4 Virahanka Numbers
In the Virahanka sequence 1, 1, 2, 3, 5, 8, 13, ___, what is the next number?
Q5 Cube Numbers
What is the 3rd cube number?
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Ch 2Lines and Angles
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Ch 2
Ray
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Definition
A part of a line that starts at a point and goes on endlessly in one direction.
Ch 2
Angle
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Definition
The amount of rotation between two rays that share a common endpoint (vertex). Measured in degrees.
Ch 2
Vertex
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Definition
The common endpoint where two rays of an angle meet.
Ch 2
Right Angle
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An angle that is exactly 90° — half of a straight angle. Looks like the letter L.
Ch 2
Straight Angle
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Definition
An angle that is exactly 180° — formed by a half turn. Looks like a straight line.
Ch 2
Acute Angle
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Definition
An angle greater than 0° but less than 90°.
Ch 2
Obtuse Angle
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Definition
An angle greater than 90° but less than 180°.
Ch 2
Reflex Angle
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Definition
An angle greater than 180° but less than 360°.
Ch 2
Perpendicular Lines
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Definition
Two lines that meet at exactly 90° (a right angle).
Ch 2
Protractor
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Definition
A tool used to measure angles in degrees.
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Chapter Practice
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Q1 Types of Angles
An angle that is exactly 90° is called a:
Q2 Perpendicular Lines
Two lines that meet at a right angle are called:
Q3 Types of Angles
An obtuse angle is:
Q4 Straight Angle
A straight angle measures:
Q5 Measuring Angles
What tool is used to measure angles?
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Ch 3Number Play
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Ch 3
Palindrome
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A number that reads the same forwards and backwards. Example: 121, 1331, 12321.
Ch 3
Collatz Conjecture
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Definition
Start with any number: if even divide by 2; if odd multiply by 3 and add 1. You always reach 1.
Ch 3
Computational Thinking
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Definition
Thinking about and forming step-by-step procedures to use numbers to solve puzzles and play games.
Ch 3
Magic Square
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Definition
A square grid of numbers where the sum of every row, column, and diagonal is the same.
Ch 3
Digit Sum
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Definition
The sum of all digits of a number. Example: digit sum of 135 = 1+3+5 = 9.
Ch 3
Number Pattern
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Definition
A sequence of numbers arranged according to a rule that can be predicted and extended.
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Chapter Practice
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Q1 Palindromes
Which of these numbers is a palindrome?
Q2 Collatz Conjecture
In the Collatz game, if your number is 6 (even), what do you do?
Q3 Digit Sum
What is the digit sum of 135?
Q4 Collatz Conjecture
In the Collatz game, if your number is 7 (odd), what is the next number?
Q5 Computational Thinking
What does computational thinking mean?
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Ch 4Data Handling and Presentation
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Ch 4
Data
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Any collection of facts, numbers, measures or observations that convey information about things.
Ch 4
Frequency
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The number of times a particular value or observation occurs in a data set.
Ch 4
Tally Marks
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Definition
A method of counting using vertical marks, with every 5th mark crossing the previous four.
Ch 4
Frequency Distribution Table
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Definition
A table listing all values/categories and their corresponding frequencies.
Ch 4
Pictograph
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Definition
A way to represent data using pictures or symbols, where each picture represents a fixed number.
Ch 4
Bar Graph
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Definition
A diagram representing data using equally-spaced bars of equal width — the length shows frequency.
Ch 4
Scale
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Definition
In a bar graph, the rule deciding how many units one unit length represents.
Ch 4
Ascending Order
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Definition
Arranging data from the smallest value to the largest value.
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Chapter Practice
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Q1 What is Data
What is data?
Q2 Frequency
The number of times a value occurs in a data set is called its:
Q3 Pictograph
In a pictograph, each picture represents 5 students. If there are 4 pictures for Science, how many students chose Science?
Q4 Bar Graph
In a bar graph, what does the height of each bar represent?
Q5 Tally Marks
Tally marks are used to:
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Ch 5Prime Time
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Ch 5
Factor
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A number that divides another number exactly with no remainder. Example: 4 is a factor of 12.
Ch 5
Prime Number
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Definition
A number greater than 1 with exactly two factors: 1 and itself. Example: 2, 3, 5, 7, 11.
Ch 5
Composite Number
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A number greater than 1 with more than two factors. Example: 4, 6, 8, 9.
Ch 5
Prime Factorisation
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Definition
Writing a number as a product of only prime numbers. Example: 84 = 2×2×3×7.
Ch 5
Co-prime Numbers
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Definition
Two numbers that share no common factor other than 1. Example: 4 and 9.
Ch 5
Sieve of Eratosthenes
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Definition
A method to find all prime numbers up to a given number by crossing out multiples of each prime.
Ch 5
Divisibility
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Definition
A number is divisible by another if it divides it exactly leaving remainder 0.
Ch 5
Twin Primes
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A pair of prime numbers with a difference of 2. Example: (3,5), (11,13), (17,19).
Ch 5
Prime Factor
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A factor of a number that is also a prime. Example: prime factors of 56 are 2 and 7.
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Chapter Practice
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Q1 Prime Numbers
Which of the following is a prime number?
Q2 Prime and Composite
The number 1 is:
Q3 Prime Factorisation
What is the prime factorisation of 36?
Q4 Co-prime Numbers
Are 4 and 9 co-prime?
Q5 Sieve of Eratosthenes
The Sieve of Eratosthenes is a method to find all:
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Ch 6Perimeter and Area
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Ch 6
Perimeter
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The total length of the boundary of a closed figure — the sum of all its sides.
Ch 6
Area
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The measure of the region enclosed by a closed figure. Measured in square units.
Ch 6
Perimeter of Rectangle
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Definition
Twice the sum of length and breadth: P = 2 × (length + breadth).
Ch 6
Perimeter of Square
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Definition
Four times the side length: P = 4 × side.
Ch 6
Area of Rectangle
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Definition
Length multiplied by breadth: A = length × breadth.
Ch 6
Area of Square
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Definition
Side multiplied by itself: A = side × side.
Ch 6
Area of Triangle
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Half the area of the rectangle that encloses it: A = ½ × base × height.
Ch 6
Square Unit
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The unit used to measure area. Example: cm², m². A square with side 1 cm has area 1 cm².
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Chapter Practice
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Q1 Perimeter of Rectangle
What is the perimeter of a rectangle with length 8 cm and breadth 5 cm?
Q2 Perimeter of Square
A square has a perimeter of 20 cm. What is the length of each side?
Q3 Area of Rectangle
What is the area of a rectangle with length 6 cm and width 4 cm?
Q4 Units of Area
Area is measured in:
Q5 Perimeter vs Area
Can two figures have the same perimeter but different areas?
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Ch 7Fractions
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Ch 7
Fraction
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Definition
A number representing equal parts of a whole. Written as numerator/denominator.
Ch 7
Numerator
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The top number of a fraction — tells how many equal parts are being considered.
Ch 7
Denominator
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The bottom number of a fraction — tells the total number of equal parts the whole is divided into.
Ch 7
Fractional Unit
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The basic piece when a whole is divided equally. When divided into 4 parts, each part is 1/4.
Ch 7
Equivalent Fractions
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Definition
Fractions that represent the same value. Example: 1/2 = 2/4 = 3/6.
Ch 7
Proper Fraction
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Definition
A fraction where the numerator is smaller than the denominator. Example: 3/4.
Ch 7
Improper Fraction
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Definition
A fraction where the numerator is greater than or equal to the denominator. Example: 7/4.
Ch 7
Mixed Number
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Definition
A number with a whole number and a proper fraction. Example: 3¼.
Ch 7
Fraction Wall
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Definition
A visual diagram showing equivalent fractions — rows from 1/2 down to 1/10.
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Chapter Practice
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Q1 Numerator and Denominator
In the fraction 3/7, what is the numerator?
Q2 Equivalent Fractions
Which fraction is equivalent to 1/2?
Q3 Fractional Unit
A roti is divided into 4 equal parts. What fraction does each part represent?
Q4 Improper Fractions
Which of these is an improper fraction?
Q5 Understanding Fractions
Reading 3/4 as "3 times 1/4" helps understand that:
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Ch 8Playing with Constructions
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Ch 9Symmetry
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Ch 9
Line of Symmetry
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Definition
An imaginary line that divides a figure into two equal mirror-image halves.
Ch 9
Reflection Symmetry
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Definition
One half of a figure is the mirror image of the other half across a line.
Ch 9
Rotational Symmetry
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Definition
A figure looks the same after being rotated by less than 360° around its centre.
Ch 9
Angle of Symmetry
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Definition
The smallest angle by which a figure can be rotated to look exactly the same.
Ch 9
Regular Polygon
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Definition
A shape with all sides equal and all angles equal. Example: equilateral triangle, square, regular hexagon.
Ch 9
Ashoka Chakra Symmetry
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Definition
The Ashoka Chakra has 24 lines of symmetry and 24 angles of rotational symmetry (every 15°).
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Chapter Practice
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Q1 Line of Symmetry
A line of symmetry divides a figure into:
Q2 Lines of Symmetry
How many lines of symmetry does an equilateral triangle have?
Q3 Rotational Symmetry
A figure has rotational symmetry if it looks the same after rotating by:
Q4 Lines of Symmetry
How many lines of symmetry does a square have?
Q5 Ashoka Chakra
How many lines of symmetry does the Ashoka Chakra have?
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Ch 10The Other Side of Zero
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