Math's Olympiad Grade IV

Number Sense & Place Value

Numbers up to 1,00,000 (1 lakh) or 999,999 depending on the board. Reading, writing, comparing, and ordering large numbers. Place value up to the lakhs/hundred-thousands place. Expanded form, standard form, and word form. Rounding to the nearest 10, 100, and 1,000. Roman numerals up to 500 (or 1,000 in some syllabi). Successor and predecessor of numbers. Prime and composite numbers (introductory). Factors and multiples — finding factors of numbers up to 100.

Addition & Subtraction

Addition and subtraction of 5- and 6-digit numbers. Estimating sums and differences by rounding. Word problems involving multiple operations. Properties — commutative, associative, identity. Missing number problems in complex expressions.

Multiplication & Division

Multiplication of 3-digit numbers by 2-digit numbers. Long division with remainders. Divisibility rules for 2, 3, 4, 5, 6, 9, and 10. Relationship between multiplication and division. Multiples and LCM (Least Common Multiple) — introductory. HCF (Highest Common Factor) — introductory. Word problems involving multiplication and division in real-life contexts.

Fractions & Decimals

This is a major expansion at Grade 4. Like and unlike fractions. Comparing and ordering fractions. Equivalent fractions and simplification. Addition and subtraction of like fractions. Mixed numbers and improper fractions — conversion and operations. Introduction to decimals — tenths and hundredths. Comparing and ordering decimals. Addition and subtraction of decimals. Relationship between fractions and decimals (e.g., ½ = 0.5).

Factors, Multiples & Number Theory

Finding all factors of a number. Prime factorisation (factor trees). LCM and HCF of two numbers. Even/odd properties. Identifying prime numbers up to 100. Divisibility tests. Simple problems using LCM and HCF in real-life contexts.

Patterns & Algebra Readiness

Number sequences using multiple operations. Input-output function tables with two-step rules. Finding the rule and extending patterns. Introduction to variables — simple equations like 3n + 2 = 14. Number puzzles and magic squares. Properties of operations applied to solve unknowns.

Geometry

Properties of triangles — equilateral, isosceles, scalene; acute, obtuse, right-angled. Properties of quadrilaterals — square, rectangle, rhombus, parallelogram, trapezium. Measuring angles with a protractor. Types of angles — acute, obtuse, right, straight, reflex. Lines — parallel, perpendicular, transversal. Circles — centre, radius, diameter, circumference (conceptual). Symmetry — lines of symmetry, reflective symmetry. Introduction to tessellations and tiling patterns.

Perimeter & Area

Perimeter of triangles, rectangles, squares, and irregular shapes. Area of squares and rectangles using length × breadth. Area of irregular shapes by counting unit squares. Relationship between perimeter and area. Word problems involving fencing, flooring, tiling, etc.

Measurement

Conversion between units of length (km, m, cm, mm). Conversion between units of weight (kg, g). Conversion between units of capacity (L, mL). Elapsed time problems — hours, minutes, seconds. 24-hour clock and AM/PM conversion. Temperature — reading thermometers, comparing temperatures. Money — profit and loss (basic), bills and invoices.

Data Handling & Statistics

Constructing and interpreting bar graphs and pictographs. Double bar graphs (reading level). Introduction to line graphs. Mean (average) of a data set. Mode and range. Organising data in tables. Simple probability — expressing as a fraction (e.g., probability of getting heads = ½).

Logical Reasoning

This section is the most olympiad-specific and requires the most preparation. Key topics include:

• Venn diagrams with two and three overlapping sets
• Number puzzles — magic squares, cross-number puzzles
• Direction and distance problems (N/S/E/W navigation)
• Coding-decoding of numbers
• Age problems — "If A is 3 years older than B and their sum is 19…"
• Arrangement problems — seating, ranking, ordering
• Analogy-based reasoning — number and shape analogies
• Calendar problems — day of the week, date calculations
• Clock problems — angle between hands, time elapsed
• Series completion — number and alphabet series

Key Differences from Grade 3