Math's Olympiad Grade V

---

Number Sense & Large Numbers

Numbers up to 10,00,00,000 (10 crore) or 100,000,000 (100 million) in the international system. Reading, writing, and comparing numbers in both Indian and International place value systems. Conversion between the two systems. Rounding to the nearest 10, 100, 1,000, and 10,000. Estimation in real-life problems. Roman numerals up to 1,000 (M). Predecessor, successor, and the concept of infinity.

Number Theory

This becomes a major olympiad topic at Grade 5. Prime and composite numbers up to 200. Prime factorisation using factor trees and division method. HCF (Highest Common Factor) — by listing factors and by prime factorisation. LCM (Least Common Multiple) — by listing multiples and prime factorisation. Relationship between HCF and LCM: HCF × LCM = Product of two numbers. Divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Perfect numbers, twin primes, and co-prime numbers (introductory in advanced olympiads).

Operations on Large Numbers

Addition and subtraction of numbers up to 8 digits. Multiplication of 4-digit numbers by 3-digit numbers. Long division with 2-digit divisors. BODMAS / PEMDAS rule — order of operations with brackets. Word problems involving all four operations with large numbers.

Fractions

This is a cornerstone topic at Grade 5 olympiads. Types of fractions — proper, improper, mixed, like, unlike, equivalent. Comparison and ordering of unlike fractions (using LCM). Addition and subtraction of unlike fractions and mixed numbers. Multiplication of fractions — fraction × fraction, fraction × whole number. Division of fractions — fraction ÷ whole number, whole number ÷ fraction. Simplification of complex fractions. Multi-step word problems involving fractions.

Decimals

Place value up to thousandths. Reading, writing, comparing, and ordering decimals. Conversion — fractions to decimals and vice versa. Addition, subtraction, multiplication, and division of decimals. Multiplying and dividing decimals by 10, 100, 1,000. Rounding decimals to the nearest whole number, tenth, and hundredth. Real-life word problems (money, measurement, science data).

Percentage

Introduction to percentage as "per hundred." Conversion — percentage to fraction, fraction to percentage, percentage to decimal, decimal to percentage. Finding percentage of a quantity. Finding what percentage one number is of another. Simple problems on percentage increase and decrease. Real-life applications — discounts, tax (basic), scores.

Ratio & Proportion

Concept of ratio — part to part and part to whole. Simplifying ratios. Equivalent ratios. Proportion — definition and verification (cross multiplication). Direct proportion problems. Unitary method — finding unit value and scaling. Word problems on ratio and proportion in real contexts (recipes, maps, scale drawings).

Integers

Introduction to negative numbers and integers. Number line with positive and negative numbers. Ordering integers. Addition and subtraction of integers using the number line. Real-life contexts — temperature below zero, floors below ground, sea level.

Algebra (Pre-Algebra)

Use of variables and expressions. Writing algebraic expressions from word statements. Evaluating expressions by substitution. Simple one-step and two-step equations. Identifying patterns and writing rules using variables. Introduction to inequalities (basic). Input-output tables with algebraic rules.

Geometry

Classification of triangles by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). Properties of quadrilaterals — square, rectangle, rhombus, parallelogram, trapezium, kite. Sum of angles in a triangle = 180°; in a quadrilateral = 360°. Constructing angles and bisecting angles (compass and ruler). Types of angles — acute, obtuse, right, straight, reflex, complete. Vertically opposite angles and linear pairs. Introduction to 3D shapes — cube, cuboid, cylinder, cone, sphere, prism, pyramid. Faces, edges, and vertices of 3D shapes. Euler's formula: F + V − E = 2 (in advanced olympiads).

Perimeter, Area & Volume

Perimeter of all polygons including irregular shapes. Area of square, rectangle, triangle, and parallelogram. Area of compound (composite) shapes. Introduction to volume — volume of cube and cuboid (l × b × h). Surface area of cube and cuboid (introductory). Conversion of units — cm² to m², cm³ to m³. Real-life problems — tiling, fencing, painting, packing.

Measurement & Conversions

Length — mm, cm, m, km (conversion and real-life problems). Weight — mg, g, kg (conversion). Capacity — mL, L, kL. Time — 12-hour and 24-hour formats, time zones (basic), elapsed time. Temperature — Celsius and Fahrenheit (reading; conversion formula in advanced olympiads). Metric system prefixes — milli, centi, deci, deca, hecto, kilo.

Data Handling & Statistics

Collecting and organising raw data. Frequency tables and grouped data. Bar graphs, double bar graphs, pie charts (reading and interpreting). Line graphs — plotting and interpreting. Mean, median, mode, and range of a data set. Choosing the appropriate measure of central tendency. Basic probability — expressing as a fraction, decimal, and percentage. Experimental vs. theoretical probability (introductory).

Logical Reasoning

The highest-weightage section in most olympiads. Topics at Grade 5 include:

• Series completion — number series, alphabet series, mixed series
• Coding-decoding — number and letter codes
• Venn diagrams — two and three overlapping sets with complex conditions
• Direction & distance — multi-turn navigation, shortest path
• Clock problems — angle between hands, time calculation, fast/slow clocks
• Calendar problems — finding day of week, date arithmetic
• Age problems — present, past, future age relationships
• Ranking & arrangement — linear and circular
• Blood relations — family tree reasoning
• Mathematical puzzles — magic squares, cross-number grids, balance puzzles
• Analogies — number, shape, and mixed analogies
• Matrix reasoning — find the missing figure in a 3×3 grid
• Mirror & water images — reflections of shapes and numbers

---

Key Differences from Grade 4

---

Topic-Wise Weightage (Approximate, across major olympiads)